Tissue optics : light scattering methods and instruments for medical diagnosis

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Library of Congress Cataloging-in-Publication Data

Tuchin, V. V. (Valerii Viktorovich), author.Tissue optics : light scattering methods and instruments for medical diagnosis / Valery Tuchin. –Third edition.

pages cmIncludes bibliographical references and index.ISBN 978-1-62841-516-21. Tissues–Optical properties. 2. Light–Scattering. 3. Diagnostic imaging. 4. Imaging systems in

medicine. I. Title.QH642.T83 2014616.07′54–dc23

2014039083

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Printed in the United States of America.First printing


To My GrandkidsDasha, Zhenya, Stepa, Serafim, and Ksusha


Contents

Nomenclature xiiiAcronyms xxxiiiPreface to the First Edition xliPreface to the Second Edition xlvPreface to the Third Edition xlix

PART I: INTRODUCTION TO TISSUE OPTICS 1

1 Optical Properties of Tissues with Strong (Multiple) Scattering 3

1.1 Propagation of Continuous Wave Light in Tissues 31.1.1 Basic principles and major scatterers and absorbers 31.1.2 Theoretical description 111.1.3 Monte Carlo simulation techniques 18

1.2 Short Pulse Propagation in Tissues 251.2.1 Basic principles and theoretical background 251.2.2 Techniques for time-resolved spectroscopy and imaging 281.2.3 Coherent backscattering 30

1.3 Diffuse Photon-Density Waves 311.3.1 Basic principles and theoretical background 311.3.2 Principles of FD spectroscopy and imaging of tissues 34

1.4 Spatially Modulated Light Propagation in Tissues 371.4.1 Introduction 371.4.2 Theory and measurement of diffuse light spatial

frequency spectrum 391.4.3 Spatially modulated spectroscopy and imaging of tissues 47

1.5 Conclusion 53

2 Propagation of Polarized Light in Tissues 55

2.1 Introduction 552.2 Tissue Structure and Anisotropy 562.3 Light Scattering by a Particle 602.4 Description and Detection of Polarized Light 61

vii


viii Contents

2.5 Light Interaction with a Random Single-Scattering Media 642.6 Vector Radiative Transfer Equation 682.7 Monte Carlo Simulation 712.8 Strongly Scattering Tissues and Phantoms 80

3 Discrete Particle Models of Tissue 89

3.1 Introduction 893.2 Refractive-Index Variations of Tissue 903.3 Particle Size Distributions 913.4 Spatial Ordering of Particles 933.5 Scattering by Densely Packed Particle Systems 943.6 Optical Properties of Eye Tissues 100

3.6.1 Optical models 1003.6.2 Spectral characteristics 1183.6.3 Polarization properties 130

4 Optothermal, Optoacoustic, and Acousto-Optic Interactions of Lightwith Tissues 137

4.1 Basic Principles and Classification 1374.2 OA/PA Gas Cell Technique 1414.3 Modulated (Phase) OA/PA Technique 1424.4 Pulsed OA/PA 1444.5 Grounds of OA/PA Tomography and Microscopy 1464.6 Optothermal Radiometry 1554.7 Optothermal Spectroscopy and Imaging 1614.8 Acousto-Optical Interactions 1744.9 Thermal Effects 1804.10 Sonoluminescence 1824.11 Prospective Applications and Measuring Techniques 184

4.11.1 Vascular imaging 1844.11.2 Glucose monitoring 1844.11.3 Quantification of total hemoglobin and blood oxygenation 1864.11.4 Temperature measurement and monitoring of

temperature effects 1874.11.5 In vivo cytometry and imaging of sentinel lymph nodes 1934.11.6 OA/PA sensors and systems 197

4.12 Conclusion 202

5 Fluorescence and Inelastic Light Scattering 205

5.1 Fluorescence 2055.2 Multiphoton Fluorescence 2175.3 Vibrational and Raman Spectroscopies 225

6 Tissue Phantoms 231

6.1 Introduction 231


Contents ix

6.2 Concepts of Phantom Construction 2326.3 Examples of Designed Tissue Phantoms 2356.4 Examples of Whole Organ Models 2426.5 Summary 242

7 Methods and Algorithms for Measurement of the Optical Parametersof Tissues 245

7.1 Basic Principles 2457.2 Integrating Sphere Technique 2957.3 Multiflux Models 2967.4 Inverse Adding-Doubling Method 2987.5 Inverse Monte Carlo Method 3017.6 Spatially Resolved Techniques 3047.7 Optical Coherence Tomography 3097.8 Direct Measurement of the Scattering Phase Function 3117.9 Estimates of the Optical Properties of Tissues 3127.10 Determination of Optical Properties of Blood 3167.11 Measurements of Tissue Penetration Depth and Light Dosimetry 3247.12 Refractive Index Measurements 327

8 Coherent Effects at the Interaction of Laser Radiation with Tissuesand Cell Flows 359

8.1 Formation of Speckle Structures 3598.2 Interference of Speckle Fields 3678.3 Propagation of Spatially Modulated Laser Beams in a Scattering

Medium 3688.4 Dynamic Light Scattering 371

8.4.1 Quasi-elastic light scattering 3718.4.2 Dynamic speckles 3728.4.3 Full-field speckle technique: LASCA 3758.4.4 Diffusion wave spectroscopy 379

8.5 Confocal Microscopy 3838.6 Optical Coherence Tomography 3878.7 Digital Holographic and Interferential Microscopy 3948.8 Second Harmonic Generation and Nonlinear Raman Scattering 4048.9 Terahertz Spectroscopy and Imaging 409

9 Controlling Optical Properties of Tissues 419

9.1 Fundamentals of Controlling Optical Properties of Tissue and BriefReview 419

9.2 Tissue Optical Immersion by Exogenous Chemical Agents 4259.2.1 Principles of optical immersion technique 4259.2.2 Water transport 4309.2.3 Tissue swelling and hydration 431

9.3 Optical Clearing of Fibrous Tissues 433


x Contents

9.3.1 Spectral properties of immersed sclera 4339.3.2 Scleral in vitro frequency-domain measurements 4489.3.3 Scleral in vivo measurements 4509.3.4 OCT monitoring of OCA and drug delivery in eye sclera

and cornea 4539.3.5 Dura mater immersion and agent diffusion rate 457

9.4 Skin 4599.4.1 Introduction 4599.4.2 In vitro spectral measurements 4619.4.3 In vivo spectral reflectance measurements 4689.4.4 In vivo frequency-domain measurements 4739.4.5 OCT imaging 4759.4.6 OCA delivery, skin permeation, and reservoir function 480

9.5 Optical Clearing of Digestive Tract Tissue 4889.5.1 Spectral measurements 4889.5.2 OCT imaging 489

9.6 Optical Clearing of Other Tissues 4919.6.1 Muscle 4919.6.2 Breast and lung 4969.6.3 Cranial bone 4989.6.4 Tooth dentin 502

9.7 Other Prospective Optical Techniques 5069.7.1 Polarization measurements 5069.7.2 Confocal microscopy 5099.7.3 Fluorescence detection 5139.7.4 Two-photon scanning fluorescence microscopy 5159.7.5 Second harmonic generation 5189.7.6 Vibrational, Raman, and CARS spectroscopy 5219.7.7 Tissue clearing in the terahertz range 522

9.8 Imaging of Cells and Cell Flows 5239.8.1 Blood flow imaging 5239.8.2 Optical clearing of blood 5279.8.3 Cell studies 5439.8.4 “Self-clearing” or metabolic clearing effects 548

9.9 Applications of the Tissue Immersion Technique 5499.9.1 Glucose sensing 5499.9.2 Characterization of atherosclerotic vascular tissues 5589.9.3 Optical imaging of lymph nodes 5599.9.4 Precision femtosecond laser surgery 5609.9.5 Skin tattoo imaging and laser removal 563

9.10 Other Techniques for Controlling Tissue Optical Properties 5739.10.1 Tissue compression and stretching 5739.10.2 Temperature effects and tissue coagulation 5849.10.3 Tissue whitening 588

9.11 Conclusion 589


Contents xi

PART II LIGHT-SCATTERING METHODS AND INSTRUMENTS FORMEDICAL DIAGNOSIS 591

10 Continuous Wave Spectrophotometry and Imaging 593

10.1 Techniques and Instruments for in vivo Spectroscopy and Imagingof Tissues 593

10.2 Example of the Spectroscopic System 59710.3 Example of the Imaging System 59810.4 Light Scattering Spectroscopy 599

COLOR PLATE SECTION

11 Time-Resolved and Spatially Modulated Spectroscopy andTomography of Tissues 605

11.1 Time-Domain Techniques and Instruments 60511.2 Frequency-Domain Techniques and Instruments 61111.3 Phased-Array Technique 61711.4 In vivo Measurements, Detection Limits, and Examples of Clinical

Study 62111.5 Spatially Modulated Method 628

12 Polarization-Sensitive Techniques 635

12.1 Polarization Imaging 63512.1.1 Transillumination polarization technique 63512.1.2 Backscattering polarization imaging 636

12.2 Polarized Reflectance Spectroscopy of Tissues 64212.2.1 In-depth polarization spectroscopy 64212.2.2 Superficial epithelial layer polarization spectroscopy 646

12.3 Polarization Microscopy 64712.4 Digital Photoelasticity Measurements 65412.5 Fluorescence Polarization Measurements 65512.6 Conclusion 660

13 Coherence-Domain Methods and Instruments 661

13.1 Photon-Correlation Spectroscopy of Transparent Tissuesand Cell Flows 66113.1.1 Introduction 66113.1.2 Cataract diagnostics 66213.1.3 Blood and lymph flow monitoring in microvessels 665

13.2 Diffusion-Wave Spectroscopy and Interferometry: Measurement ofBlood Microcirculation 670

13.3 Blood Flow Imaging 67513.4 Interferometric and Speckle-Interferometric Methods

for the Measurement of Biovibrations 68613.5 Optical Speckle Topography and Tomography of Tissues 690


xii Contents

13.6 Methods of Coherent Microscopy 70013.7 Interferential Retinometry and Blood Sedimentation Study 706

14 Optical Coherence Tomography and Heterodyne Imaging 711

14.1 Optical Coherence Tomography 71114.1.1 Introduction 71114.1.2 Time-domain OCT 71114.1.3 Two-wavelength fiber OCT 71314.1.4 Ultrahigh-resolution fiber OCT 71414.1.5 Frequency-domain OCT 71514.1.6 Doppler OCT and blood flow measurements 71814.1.7 Polarization sensitive OCT 72114.1.8 Phase-sensitive OCT 72314.1.9 Optical coherence elastography 72314.1.10 Full-field OCT 72614.1.11 Optical coherence microscopy 72814.1.12 Endoscopic OCT 73114.1.13 Speckle OCT 73414.1.14 OCT quantitative parametric imaging of attenuation 73714.1.15 Combined OCT systems 738

14.2 Optical Heterodyne Imaging 74014.3 Summary 746

Conclusion 749

References 755

Index 917


Nomenclature

2l separation between two point light sources formed inthe nodal plane

2Ra diameter of circular apertureA = log(1/Rd) apparent absorbancea numerical coefficient, depending on the form of the

diffusion equationa radius of a scatterer (particle), nm or μmA signal amplitude in the frequency-domain measuring

techniqueA acoustic amplitudeA = 〈i〉2 square of the mean value of the photocurrent (base-

line of the autocorrelation function)A ∼= π [λexc/(2NA)]2 illuminated areaa′ largest dimension of a nonspherical particle, nm

or μmA0 initial amplitude due to the instrumental responseAac ac component of the amplitude of the photon-density

waveAdc dc component of the amplitude of the photon-density

waveam more probable scatterer radius, μman and bn Mie coefficientsA(r) describes the optical absorption properties of the

tissue at rasph radius of spherical particleaT thermal diffusivity of the medium, m2/sBd detection bandwidthbs accounts for additional irradiation of upper layers of

a tissue due to backscattering (photon recyclingeffect)

c velocity of light in the medium, cm/sc0 velocity of light in vacuum, cm/s

xiii


xiv Nomenclature

C1 and C2 concentrations of molecules in two spaces separatedby a membrane

Ca(x, t) concentration of the agentCa0 initial concentration of the agentcab concentration of absorber in μmol, mmol, or molcb blood specific heat, J/kgKCHb hemoglobin concentrationCf(x, t) fluid concentrationcP specific heat capacity for a constant pressure, J/kgKcs relative concentration of the scattering centersCS average concentration of dissolved matter in two

interacting solutionscV specific heat capacity for a constant volume, J/kgKCα

n Gegenbauer polynomials〈C〉 average blood concentration〈C〉V rms blood flux or perfusionD = zλ/πL2

ϕ wave parameterD photon diffusion coefficient, cm2/sDA diattenuation (linear dichroism)Da agent diffusion coefficient, cm2/sDB coefficient of Brownian diffusion, cm2/sDf fluid coefficient of diffusion, cm2/sDmedia (λ) age-related optical density of transparent media

of the eyed sample (tissue layer or slab) thickness, cmD−1 inverse of the measurement matrixD|| dimension of incident light beam along the area

where the total radiant energy fluence rate ismaximal (determined from the 1/e2 level), cm

D⊥ dimension of incident light beam across the areawhere the total radiant energy fluence rate ismaximal (determined from the 1/e2 level), cm

d�′ unit solid angle about a chosen direction, srdav average size of a speckle in the far-field zoneDf fractal (volumetric) dimensionDI, DI(�ξ) structure function of the fluctuation intensity com-

ponentdp length of the space where the exciting and the probe

laser beams are overlapped, cmds mean distance between the centers of gravity of the

particlesDT coefficient of translation diffusionDTf coefficient of translation diffusion for fast process


Nomenclature xv

DTs coefficient of translation diffusion for slow processDV diameter of a microvesseldn/dλ material dispersion, 1/nmdn/dT medium (tissue) refractive index temperature

gradient, 1/◦CDPF differential path length factor accounting for the

increase in photon migration paths attributable toscattering

dS thermoelastic deformation, cmE incident pulse energy, JE electron chargeE0 incident laser pulse energy at the sample surface

(J/cm2)E0j scattering amplitude of an isolated particle, V/mEref(ω) incident THz pulse amplitudeEsample(ω) transmitted THz pulse amplitudeE||i electric field component of the incident light paral-

lel to the scattering plane, V/mE⊥i electric field component of the incident light per-

pendicular to the scattering plane, V/mE||s electric field component of the scattered light paral-

lel to the scattering plane, V/mE⊥s electric field component of the scattered light per-

pendicular to the scattering plane, V/mEs scattered electric field vector, V/mEs amplitude of a scattered wave, V/mET absorbed pulse energy, JE(0) subsurface irradiance, J/cm2

F(Hct) packing function of RBCF(r) radiant flux density or irradiance, W/cm2

f (t, t′) describes the temporal deformation of a δ-shapedpulse following its single scattering

f 1,2 volume fractions of tissue componentsf a frequency of acoustic oscillations, Hzf c volume fraction of the collagen in tissuef cp volume fraction of the fluid in the tissue contained

inside the cellsf cyl surface fraction of the cylinders’ facesf D Doppler frequencyf Ds Doppler frequency shiftf f volume fraction of the fibers in the tissuef ge oscillator strength of transition between the ground

and excited states


xvi Nomenclature

Fint(θ) interference term taking into account the spatialcorrelation of particles

f n = gn nth order moment of the phase functionf nc volume fraction of the nuclei in the tissue contained

inside the cellsf or volume fraction of the organelles in the tissue con-

tained inside the cellsf p pulse repetition ratef r fixed reference (lock-in) frequencyf RBCi volume fraction of RBCsf s volume fraction of scatterersf T focal length of the thermal lens, cmFv total volume fraction of the particlesfx = (kx/2π), f y = (ky/2π) spatial frequenciesfσ material fringe valueF(λ) packing factor of the particlesFP(ω) reflection of pulses in a parallel plate: Fabry–Perot

modesG domain where radiative transport is examinedG( f ) power spectrum with a Gaussian shapeg scattering anisotropy factor [mean cosine of the

scattering angle θ, <cos(θ)>]g1(τ) first-order autocorrelation function (normalized

autocorrelation function of the optical field)g2(�ξ) normalized autocorrelation function of intensity

fluctuationsG1(τ) autocorrelation function of the scalar electric field,

E(t), of the scattered lightG2(τ) autocorrelation function of intensity fluctuationsG2(�ξ) autocorrelation function of the fluctuation intensity

componentg2 normalized autocorrelation function of the fluctua-

tion intensity componentg(r) radial distribution function of scattering centers

(local-to-average density ratio for scattering cen-ters)

G(r) binary density–density correlation functiongd scattering anisotropy factor of dermisge scattering anisotropy factor of epidermisGs attenuation factor accounting for scattering and

geometry of the tissueGV gradient of the flow rateHct blood hematocritH tissue hydration


Nomenclature xvii

H(x, y, t) = (λ/2π�n)φ(x, y, t) dynamic profile of the geometric thickness ofthe cell

h Planck’s constanth apparent energy transfer coefficienth(x, y, t) =

∫[n(x, y, z, t) – n0]dz two-dimensional distribution of optical path dif-

ferenceH(r, t) heating function, defined as the thermal energy

per time and volume deposited by the lightsource in the close proportion to the opticalabsorption coefficient of interest

Hb hemoglobinHbO2 oxyhemoglobinHbR deoxyhemoglobinhν photon energyh(x, y) spatial variations in the thickness of the RPSI(θ)/I(0) ≡ p(θ) normalized scattering indicatrix, 1/srI(θ) scattering indicatrix (angular dependence of the

scattered light intensity), W/cm2sri = (–1)1/2 imaginary numberIac, Idc ac and dc components of diffusely reflected

intensityIAS, IS intensity of the anti-Stokes and Stokes Raman

lines for a given vibration stateIF fluorescence intensityIi irradiance or intensity of the incident light beam,

W/cm2

〈I〉 mean value of the intensity fluctuations<i2(z)> rms of photodetector heterodyning signal of the

OCT system, obtained from probing depth zI refers to the irradiance or intensity of the light,

W/cm2

I(r, s) radiance (or the specific intensity) of averagepower flux density at point r in given direc-tion s, W/cm2 sr

I(r, s, t) time-dependent radiance (or specific intensity),W/cm2 sr

I(0) intensity at the center of the beamI(d) intensity of light transmitted by a sample of

thickness d measured by using a distant pho-todetector with a small aperture (online orcollimated transmittance), W/cm2

I, Q, U, and V Stokes parameters


xviii Nomenclature

IH, IV, I+45◦ , I−45◦ , IR,and IL

light intensities measured with a horizontal linearpolarizer, a vertical linear polarizer, a +45 deg lin-ear polarizer, a –45 deg linear polarizer, a rightcircular analyzer, and a left circular analyzer infront of the detector, respectively

Iin(ηc) incident radiance angular distributionI�(θ) angular distribution of the scattered intensity of a

system of N particlesI�(x, y) intensity of light transmitted by an RPSI|| and I⊥ intensities of the transmitted (scattered) light polar-

ized in parallel or perpendicular to linear polar-ization of the incident light, respectively

I(θ) angular distribution of the scattered light by a parti-cle, W/cm2sr

I(2ω) SHG signal intensityI0(λ) spectrum of the incident lightI0 incident light intensity, W/cm2

Ib intensity of the uniform background lightIc(x,y) intensity of light transmitted in the forward direc-

tion (the specular component)IF|| and IF⊥ fluorescence intensities of light polarized in paral-

lel or perpendicular to the exciting electric fieldvector

I2f(t) TPEF instant intensity collected by the optical sys-tem⟨

I2f

⟩CW

time-averaged over any period of time T, the TPEFintensity per a single molecule at CW laser exci-tation

IHP(x, y, z0) intensity distribution in the hologram plane (HP)Ipar and Iper intensity images for light polarized in parallel or

perpendicular to linear polarization of the inci-dent light, respectively

Ir(r) and Is(r) intensity distributions of the reference and signalfields, respectively

IR and IS intensity distributions of the reference and objectfields, respectively

Irest and Itest light intensity detected when an object is at rest(brain tissue or skeletal muscle) or test (inducedbrain activity, cold or visual test, or training)

Is(x, y) intensity of the scattered componentIsp mean intensity of speckles<Ix,y> mean value of CCD intensity counts at pixel (x, y)

over n framesJ flux of matter, mol/s/cm2


Nomenclature xix

J0 zero-order Bessel functionJ1 first-order Bessel functionJS dissolved matter fluxJW water fluxk = 2π/λ wavenumberka acoustic wave vectorkET rate constant of nonradiative energy transfer to adja-

cent moleculeskF rate constant of the fluorescence transition to ground

state S0 (including its vibrational states)K image contrastK, S Kubelka–Munk parametersKϕ(�x) correlation coefficient of phase fluctuations of the

boundary fieldkB Boltzmann constantkbvo modification factor for reducing the crosstalk

between changes in blood volume and oxygena-tion

kG gas heat conductivity, W/Kki(ω) imaginary part of the photon-density wave vector,

1/cmkIC rate constant of internal conversion to ground state S0

kISC rate constant of intersystem crossing from singlet totriplet state T1

kr(ω) real part of the photon-density wave vector, 1/cmkT heat conductivity, W/KKt(x, y) temporal contrast of intensity fluctuations of laser

scattered light at pixel (x, y)l thickness of a thin membraneL total mean path length of a photon, cmL tissue slab thickness, cmL = Dλ/2l period of interferential fringes (D is the mean dis-

tance between eye nodal plane and retina)LD phenomenological coefficient characterizing the

interchange flux induced by osmotic pressureLφ correlation length of the phase fluctuations of the

scattered fieldl0 amplitude of longitudinal harmonic vibrationsLc correlation length of the inhomogeneities (random

relief)lc coherence length of a light sourceld = μeff

−1 diffusion length, cmle depth of light penetration into a tissue


xx Nomenclature

Lp phenomenological coefficient indicating that volu-metric flux can be induced by increasing hydro-static pressure

Lpd phenomenological coefficient indicating, on onehand, the volumetric flux that can be inducedfor a membrane by osmotic pressure, and on theother, the efficiency of the separation of watermolecules and dissolved matter

lph = μ−1t photon mean free path, cm

ls = μ−1s scattering length, cm

lT length of thermal diffusivity (thermal length), cmltr = (μ′

s + μa)−1 photon transport mean free path (MFP), cmM molecular weightM optical magnificationm ≡ ns/n0 relative refractive index of the scatterersM = I1/I0 intensity modulation depth, defined as the ratio

between the intensity at the fundamental fre-quency, I1, and the unmodulated intensity, I0

M normalized 4 × 4 scattering matrix (intensity orMueller’s matrix) (LSM)

M0 zero moment of the power density spectrum, S(ν),of the intensity fluctuations

M1 first moment of the power density spectrum, S(ν),of the intensity fluctuations

Mac(x, f x) amplitude envelope of the reflected photon densitystanding wave at frequency fx

Mdc(x) spatially varying dc amplitudemI intensity modulation depth of the incident lightMij LSM elements, i, j = 1– 4, 16 elementsMij LSM element normalized to the first elementMij

0 LSM elements of an isolated particlemRBC relative index of refraction of RBCMq mass of the charge of the molecule capable

for oscillations at its own frequency at lightexcitation

mt amount of dissolved matter at moment tm∞ amount of dissolved matter at the equilibrium statemU ≡ acdetector/dcdetector modulation depth of scattered light intensityn relative mean refractive index of tissue and sur-

rounding median(ω) = n′(ω) − i·n′′(ω) complex refractive indexn′(ω) real part of index of refractionn′′(ω) = α(ω)·c/ω imaginary part of index of refractionn mean refractive index of the scattering medium


Nomenclature xxi

N number of scatterers (particles)N = θ/2π fringe order (θ is the optical phase)N0 number of scatterers in a unit volumeN1(z) = z · μex

s average number of scattering events experienced byexcitation light before it reaches the fluorophore(z is the distance of fluorophore location)

N2(z) = z · μems average number of scattering events experienced by

the emitted light before it exits the medium (z isthe distance of fluorophore location)

N outside vector normal to ∂Gn2f rate of two-photon excitationn0 refractive index of ground mattern0 average background index of refractionnc refractive index of collagen fibersncp refractive index of cytoplasmne extraordinary refractive indexnf refractive index of tissue fibers (collagen and

elastin)ng0 refractive index of the ground material of a tissueng1 effective (mean) group refractive index of a tissueng2 group refractive index of the homogeneous refer-

ence medium (air)ng group refractive indexngs group refractive index of scatterersnH2O refractive index of waterN i = f RBCi/VRBCi number of RBCs in a unit volume of bloodN int = [arcsin(λ/2l)]−1 density of interferential fringes per degree of the

view angle (angular resolving power of the eyeor retinal visual acuity)

nis refractive index of the ISFnnc refractive index of cell nucleusno ordinary refractive indexnor refractive index of cell organellesNp number of particle diametersns refractive index of scattering centers (particles)ns refractive index of a scattering particle, determined

by averaging refractive indices of tissue compo-nents

nsc average refractive index of eye scleraNsp number of speckles within the receiving apertureNA numerical aperture of the objective or fibern(x, y) spatial variations in the refractive index of the

random phase screennt average refractive index of the tissue


xxii Nomenclature

O(x, y, z = z0) object waveOD optical densityosm osmolarityp packing dimensionp porosity coefficientP laser beam power, WP induced polarizationP(t) instantaneous power of the radiation within illumi-

nated area APa coefficient of permeabilityPave = (τp · f p)Ppeak average powerP0 average incident power, WPC = V/I = [Q2 + U2]1/2/I degree of circular polarizationPFL= (IF|| − IF⊥)/(IF|| + IF⊥)

degree of linear polarization of fluorescence

PL = (I|| – I⊥)/(I|| + I⊥) degree of linear polarizationPr

L (λ) residual polarization degree spectraPmin minimal detectable signal powerp(I) intensity probability density distribution functionp(s) distribution function of photon migration paths in

the mediump(s, s′) = p(θ) scattering phase function (probability density func-

tion for scattering in the direction, s′, of a photontravelling in direction s), 1/sr

pGK(θ) Gegenbauer kernel phase function (GKPF)pHG(θ) Henyey–Greenstein phase function (HGPF)Ppeak peak powerPR and PS powers of the reference and object beams of OCT

interferometerPI polarization degree imageP1

n (cos θ) Legendre polynomialsp(�L) probability density distribution function of relief

variationsp(r, t) acoustic waveP(3) third-order polarizationpix pixel sizeq charge of molecule capable of oscillations at its own

frequency at light excitationq spatial modulation frequency of fringesq scattering vector|q| value of scattering vectorq(r) source function (i.e., number of photons injected

into the unit volume)


Nomenclature xxiii

Q, U, and V the extents of horizontal linear, 45 deg linear,and circular polarization, respectively

Qa asymmetry parameter of intensity fluctuationsqb blood perfusion rate (1/s), defined as the vol-

ume of blood flowing through unit volumeof tissue in one second

Qs, Qs(asph, ns, nI) factor of scattering efficiencyR(x, y, z = z0) reference waver transverse spatial coordinater = I||−I⊥

I||+2I⊥ polarization anisotropy

rF = (IF|| − IF⊥)/(IF|| + 2 IF⊥) fluorescence polarization anisotropyR(φ) Stokes rotation matrix for angle φr radius vector of a scatterer or a given point at

which the radiance is evaluated, cmR radius of membrane (of a cell or tumor

necrotic core)R(z) backscattering or reflectance in OCTr⊥||(τ) cross-correlation function (correlation coeffi-

cient) for two polarization statesR||(λ) and R⊥(λ) reflectance spectra at parallel and perpendicu-

lar orientations of polarization filtersR reflection operatorR 4 × 1 response vector corresponding to the

four retarder/analyzer settingsRa reflectance from the backward surface of the

sample impregnated by an agentRθ(λ) spectrum of light scattered under the angle

(θ+ dθ)r0 radius of the incident light beam, cmRbd distance between the axis of exciting laser

beam and the acoustic detector, cmRd diffuse reflectanceRd(k) diffuse reflectance of spatially modulated

photon density wavesRF = [(n − l)/(n + l)]2 coefficient of Fresnel reflectionRG gas cell radius, cmrh hydrodynamic radius of a particleRo dimension (radius for a cylinder form) of a

bio-object, cmrp radius of the pinholerRBC radius of RBCrs radius of the scattered beam in the observation

plane


xxiv Nomenclature

Rs reflectance from the backward surface of the controlsample

rsd distance between light source and detector at thetissue surface (source–detector separation), cm

R(η′c, ηc) reflection redistribution function

Rp(ω) complex reflection coefficient (p-polarization)RL(ω) reflection losses at the boundaries of the sampleRT�CS osmotic pressures total photon path length (or mean path length of a

photon)S hemoglobin oxygen saturationS heat source term, W/m3

S sample areaSD surface of detectionS Stokes vectorSs Stokes vector of the scattered lightSi Stokes vector of the incident lights and s′ directions of photon travel or unit vectors for inci-

dent and scattered waves|s| = 2ksin(θ/2) magnitude of the scattering wave vector, k = 2πn/λ0

S0 unit vector of the direction of the incident waveS1 unit vector of the direction of the scattered waveS(r, s) incident light distribution at ∂GS(f ) power spectrum of intensity fluctuations of the

speckle fieldS(q) structure factorS3(θ) 3D structure factorS2(θ) 2D structure factorS(ω) spectrum of intensity fluctuationsS1−4 elements of the amplitude scattering matrix

(S-matrix) or Jones matrixSr(t) surface radiometric signalS(t) describes the shape of the irradiating pulsesO2 or SO2 hemoglobin saturation with oxygenT absolute temperatureT exposure time, sT(r) change in tissue temperature at point rT(η′

c, ηc) transmission redistribution functionT(ω) transmission spectrum on terahertzT0(ω) medium transmission spectrum through which the

THz pulse is travellingt time, st0 spatially independent amplitude transmission of the

RPS


Nomenclature xxv

t1 first moment of the distribution function, f (t, t′);time interval of an individual scattering act, s

t2 = l/(μtc) average interval between interactions, sTa acoustic wave periodTa arterial blood temperature, Ktb blood temperatureTc(λ) collimated transmission spectrumTc collimated transmittanceTd diffuse transmittanceTs and Te temperature of the tissue surface and environment,

respectivelyts(x, y) amplitude transmission coefficient of an RPST t = Tc + Td total transmittanceT t(λ) total transmission spectrumTθ(λ) transmission spectrum when a measuring system

with a finite angle of view is used (collimated lightbeam with the addition of a forward-scatteredlight in the angle range 0 to θ is detected)

U(r) total radiant energy fluence rate, W/cm2

〈U〉 averaged amplitude of the output signal of thehomodyne interferometer

Um maximum of the total radiant energy fluence rate,W/cm2

V illuminated volumeV volume of the tissue sampleV(t) =

∫H(x, y, t)dxdy momentary volume of the cell

v velocity of motion of the object with respect to thelight beam

VC volume of collagen fibersVe volume of an erythrocyteVF flow velocityVM molecular volumevsh shear rateV(z) contrast of average intensity fringesV� phase velocity of a photon-density wave, cm/sV0 contrast of the interference pattern in the initial laser

beamva velocity of acoustic waves in a medium, m/sV I contrast of the intensity fluctuationsvp radius (in optical units) of conjugate pinholes of a

confocal microscopic systemVP contrast of the polarization imageVRBC RBC volume, μm3

V rms root-mean-square speed of moving particles


xxvi Nomenclature

Vs velocity of a moving particleVS partial mole volumes of dissolved mattervsh shear rateVV parameter directly proportional to the flow velocityVW partial mole volumes of waterw laser (Gaussian) beam radius (or radius of a cylinder

illuminated by a laser beam), cmwH radius of the beam at 1/e, at a probing depth of OCT

in the absence of scattering, cmwp probing laser beam radius, cmw0 radius of the Gaussian beam waist, cmx0 fixed point at the plane where speckles are observedx = 2πa/λ size (diffraction) parameter z linear coordinate

(depth inside the medium), cmZ normalized phase matrixz0 = (μ′

s)−1 transport scattering length, cm

Greekα(z) reflectivity of the sample at depth of zα(ω) absorption coefficient on terahertzαHb spectrally dependent coefficient of the proportional-

ity of hemoglobin imaginary refractive index onits concentration

αi incidence angle of the beam, angular degrees

β coefficient of volumetric expansion, 1/Kβ modulation depth of photoelectric signal of the

interferometerβ factor that accounts for the conversion of optical

power to the photodetector current〈β〉 orientation averaged first molecular hyperpolariz-

abilityβsb parameter of self-beating efficiency� Grüneisen parameter (dimensionless, temperature-

dependent factor proportional to the fraction ofthermal energy converted into mechanical stress)

�eff effective shear rate�T relaxation parameterγ = cP/cV ratio of specific heat capacitiesγ11(�t) degree of temporal coherence of light�ψ phase shift in a measuring interferometer, degrees�a half-width of the radii distribution�Evib = hνvib energy of the molecular vibration state


Nomenclature xxvii

�F width of the averaged spectrum�k wavenumber shift�L = �(nh) optical length (relief) variations�n difference in refractive indices�n = (ncell – n0) difference between the average refractive index of

the cell and the environment�noe difference in refractive indices due to birefringence

of form�p change of pressure, Pa�p hydrostatic pressure, Pa�Rr(λ) differential residual polarization spectra�V change of illuminated volume caused by local tem-

perature increase, m3

�w change of radius of a cylinder illuminated by a laserbeam caused by local temperature increase, cm

�x linear shift of the center of maximal diffuse reflec-tion, cm

�z longitudinal displacement of the object�T local temperature increase, ◦C�T optical clearing (enhancement of transmittance)�xT amplitude of mechanical oscillations, cm<�n> mean refractive index variation�� phase shift relative to the incident light modulation

phase (phase lag), degrees��0 initial phase due to the instrumental response�φHP (x, y, z0) =φR(x, y, z0) − φO(x, y, z0)

phase difference between waves O and R in planez = z0

�θ angular width of the coherent peak in backscatter,angular degrees

�λ bandwidth of a light source�ξ change in variable�� I(r) deterministic phase difference of the interfering

waves��I(r) random phase difference��I(r) time-dependent phase difference related to the

motion of an object�ϕs(x, y, z0) phase change attributable to the object<�r2(τ)> mean-square displacement of a particle within time

interval τ�TS temperature change of a sample, ◦C�TG temperature change of a surrounding gas, ◦C�t time shift of the transmitted pulse peak⟨�V2

⟩second moment of the particle velocity distribution

(mean square velocity)


xxviii Nomenclature

δ = 2π d�n/λ0 phase delay (retardance) of optical fieldδ penetration depth of the field into tissue or fluidδCCD = pix/M resolution of CCD cameraδF = VFτL motion distortion due to cell displacement during

the exposure or the time between the two probepulses

δn and δd parameters related to the average contributions perphoton free path and scattering event, respec-tively, to the ultrasonic modulation of light inten-sity

δoe = 2π d�noe/λ0 phase delay of optical field due to birefringenceδOPT = 0.61λ/NA optical resolution of the microscope objectiveδPT image resolutionδT ≡ lT = (4aTτL)1/2 thermal resolutionδp(ω) amplitude of harmonically modulated pressure, Paδp(t) time-dependent change of pressure, Pa∂G boundary surface of domain G∂n/∂p adiabatic piezo-optical coefficient of the tissue�zopt optical path lengthε(ω) dielectric function (permittivity)ε0 low-frequency permittivityεab absorption coefficient, measured in mol−1 cm−1

εdλ extinction coefficient of deoxyhemoglobin, mea-

sured in mol−1 cm−1

εoλ extinction coefficient of oxyhemoglobin, measured

in mol−1 cm−1

ελ extinction coefficient at wavelength λ, in mol−1

cm−1

εHbO2 (λi) and εHbR(λi) molar extinction coefficients of oxyhemoglobin anddeoxyhemoglobin, respectively

φ(x) spatially modulated phase due to the objectφO0 (x, y, z0) phase of the object wave itselfη absolute viscosity of the mediumη(a) or η(2a) radii (a) or diameter (2a) distribution function of

scatterersηc cosine of the polar angleηF, η = η(λem) fluorescence quantum yieldηq quantum efficiency of the detectorη′(2a) correlation-corrected distribution η(2a)θ scattering angle, angular degreesθI angle between the wave vectors of the interfering

fieldsθGK

rnd GKPF random scattering angleθHG

rnd HGPF random scattering angle


Nomenclature xxix

κ coefficient taking into account the collection effi-ciency of the fluorescent photons

= σscaσext

= μsμt

albedo for single scattering (characterizes the rela-tion of scattering and absorption properties of atissue)

′ = μ′s

μa+μ′s

transport albedo� photon-density wavelength, cmI spacing of interference fringesλ = λ0/n wavelength in the scattering medium, nmλ0 wavelength of the light in vacuum, nmλ1f wavelength necessary to excite the fluorescence at

single-photon absorptionλ2

∼= 2λ1f wavelength necessary to excite the fluorescence attwo-photon absorption

λexc and λem wavelengths of excitation and emission, respec-tively

λp wavelength of the probe beam, nmμ′

a absorption coefficient at the thermal radiation emis-sion wavelength, 1/cm

μa absorption coefficient, 1/cmμb volume-averaged backscattering coefficient,

1/cm srμeff = [3μa(μ′

s + μa)]1/2 effective attenuation coefficient or inverse diffusionlength, 1/cm

μ′eff =

√μ2

eff + k2x + k2

y scalar attenuation coefficient of spatially modulatedphoton density waves

μge change in dipole moment between ground andexcited states

μn n-order statistical moment (n = 1,2,3,. . . ,)μ′

s = (1−g)μs reduced (transport) scattering coefficient, 1/cmμs scattering coefficient, 1/cmμex

s scattering coefficient of the excitation light, 1/cmμem

s scattering coefficient of the emitting light, 1/cmμt = μa + μs extinction coefficient (interaction or total attenua-

tion coefficient), 1/cmμtr = μa + μ′

s transport coefficient|μ(z)| modulus of the transverse correlation coefficient of

the complex amplitude of the scattered fieldνI exponential factor of the spatial intensity fluctua-

tionsξ = x or t spatial or temporal variableξI characteristic depolarization length for linearly

(i = L) and circularly (i = C) polarized lightρ medium density, kg/m3


xxx Nomenclature

ρ polarization azimuthρ distance from collimated sourcesρa volume density of absorbers, 1/cm3

ρb blood density (kg/m3)ρG gas density, kg/m3

ρs volume density of the scatterers, 1/cm3

ρ(s) probability density function of the optical pathsσ half-width of particle size distributionσ = – (Lpd/Lp) molecular reflection coefficient(σ1 – σ2) difference in the in-plane principle stressσ2 two-photon absorption cross section, GMσabs absorption cross section of a particle, cm2

σabs specific absorption coefficient, cm−1

σb effective backscattering cross sectionσext extinction cross section of a particle, cm2

σf photon absorption cross sectionσh standard deviation of the altitudes (depths) of inho-

mogeneitiesσI standard deviation of the intensity fluctuationsσL standard deviation of relief variations (in optical

lengths)σm width of the skewed logarithmic distribution func-

tion for the volume fraction of particles of diam-eter 2a

σs(2ai) optical cross section of an individual particle withdiameter 2ai and volume vi, cm2

σsca scattering cross section of a particle, cm2

σsca specific scattering coefficient, cm−1

�sca scattering cross section for the system of particles,cm

σφ standard deviation of the phase fluctuations of thescattered field

σ2I variance of the intensity fluctuationsσ2

s spatial variance of the intensity in the speckle pat-tern

σ2U variance of the output signal of the homodyne

interferometerσx,y standard deviation of the CCD intensity counts at

pixel (x, y) over the n framesτ delay time, sτ lifetime of the excited state, sτ = ∫ s

0 μtds optical thicknessτa = 1/μac average travel time of a photon before being

absorbed, s


Nomenclature xxxi

τc correlation time of intensity fluctuations in the scat-tered field, s

τd, τoa time delay between optical and acoustical pulses, sτL duration of a laser pulse, sτNR nonradiative relaxation time, sτp pulse duration, sτPH time to response of the photodetector, sτr time constant of rotational diffusion, sτRT characteristic rise time, sτTA temperature-averaging time within the biological

cellτth time delay for the thermal lens technique, sτT thermal relaxation time, sτ−1

B ≡ �T characterizes the random (Brownian) flowτ−1

S∼= 0.18GV |q| ltr characterizes the directed flow

�(x, y) random phase shift introduced by the RPS at the (x,y) point

�p(ω) phase lag of harmonically modulated pressure, degφ(t) phase shift defined by a scatterer positionϕ angle of observation and azimuthal angle, angular

degϕ volume fraction of particlesϕd deflection angle of a probe laser beam, angular

degreesχ(n) nth order nonlinear susceptibility[χ(3)

nonres + χ(3)res

]third-order optical susceptibility, presented as a sum

of the nonresonant and resonant contributions�(z) heterodyne efficiency factor� solid angle, sr�v frequency of harmonic vibrationsω = 2πf modulation frequency, 1/sωa fundamental acoustic frequencyωge energy difference between the ground and excited

statesωp packing factor of a medium filled with a volume

fraction f s of scatterers(ωt − θ) phase of the photon-density wave


Acronyms

ac alternating currentADC amplitude- (or analog-) digital convertorAF autocorrelation functionAF autofluorescenceAHA α-hydroxy acidALA aminolevulinic acidAO acousto-opticalAOD acousto-optical deflectorAOM acousto-optic modulatorAOT acousto-optic tomographyAPD avalanche photodetectorALA δ-aminolevulinic acidATR attenuated total reflectionATR-FTIR attenuated total reflectance Fourier transform infraredAW acoustic wavesBEM boundary-element methodBSA bovine serum albuminBW birefringent wedgesCARS coherent anti-Stokes Raman scatteringCBF cerebral blood flowCCD charge-coupled deviceCDI coherent detection imagingCEA carotid endarterectomyCFD constant-fraction discriminatorCIE Commission Internationale de l’Eclairage (the French title

of the International Commission on Illumination)CIN cervical intraepithelial neoplasiaCIS carcinoma in situCM confocal microscopycmOCT correlation map OCTCMOS complementary metal-oxide semiconductorCNT carbon nanotube

xxxiii


xxxiv Acronyms

CP-OCT cross-polarization OCTCPU central processing unitCRI contrast of refractive indexCSF cerebrospinal fluidCT computed tomographyCUDA Compute Unified Device ArchitectureCW continuous waveCyt-c cytochrome cDBM double-balanced mixerdc direct currentDCF double-clad fiberdcOCT double correlation OCTDCS diffusion-correlation spectroscopyDeoxyHb deoxyhemoglobinDG delay generatorDHM digital holographic microscopeDIS double integrating sphereDLP digital light processingDMD digital micromirror deviceDMSO dimethyl sulfoxideDNA deoxyribonucleic acidDOCP degree of circular polarizationDOCT Doppler OCTDOLP degree of linear polarizationDOP degree of polarizationDOPA 3,4-dihydroxyphenylalanineDOPE dioleoylphosphatidylethanolamineDPF differential path length factorDPS OCT differential phase-sensitive OCTDPSS diode pumped solid stateDT diffusion theoryDTC disseminated tumor cellDWS diffusion wave spectroscopyEB Evans BlueEDL extensor digitorum longusEDTA ethylenediaminetetraacetic acidEEM excitation–emission mapENT ear, nose, and throatESCC esophageal squamous cell carcinomaESR erythrocyte sedimentation rateFAD flavin dinucleotideFD frequency domainFDA Food and Drug AdministrationFD-LUM frequency-domain luminescence


Acronyms xxxv

FD-OTR frequency-domain OTRFD-PTR-LUM frequency-domain photothermal radiometry luminescenceFDPM frequency-domain photon migrationFDTD finite-difference time domainFF-OCT full-field OCTFFT fast Fourier transformFG function generatorFLIM fluorescence lifetime imaging microscopyFLMA fractional laser microablationFMN flavin mononucleotideFOV field-of-viewFRAP fluorescence recovery after photobleachingFWHM full-width half-maximumGFP green fluorescent proteinGHb glycated hemoglobinGK Gegenbauer kernelGKPF Gegenbauer kernel phase functionGM Goeppert MayorGNP gold nanoparticleGNR gold nanorodGNT golden carbon nanotubeGPM goniophotometric measurementsGPU graphics processing unitGRIN gradient indexHCM human cervical mucusHct hematocritHDL high-density lipoproteinH&E hematoxylin and eosinHEM human epidermal membraneHG Henyey−GreensteinHGPF Henyey–Greenstein phase functionHP hologram planeHPD hematoporphyrin derivativeHPM Hilbert phase microscopyHRS hyper-Rayleigh scatteringHWHM half-width half-maximumIAD inverse adding-doublingIC25 Infracyanine 25ICG indocyanine greenIF intermediate frequencyIFS interfibrillar spacingIMC inverse Monte CarloIMS intermolecular spacingIOC immersion optical clearing


xxxvi Acronyms

IQ in-phase quadratureIR infraredIS integrating sphereKDP kalium dihydrophosphateKMM Kubelka–Munk modelLASCA laser speckle contrast analysisLAT lung adenocarcinoma tumorLBG lung benign granulomatosisLD laser diodeLDA laser Doppler anemometerLDI laser Doppler imagingLDL low-density lipoproteinLDM laser Doppler microscopeLED light-emitting diodeLID lattice of islet damageLIPT laser-induced pressure transientLITT laser-induced interstitial thermal therapyLO local oscillatorLPF low-pass filterLSCC lung squamous cell carcinomaLSI laser speckle imagingLSLO line-scanning laser ophthalmoscopeLSM light-scattering matrixLSMM laser scattering matrix meterLSS light scattering spectroscopyLVDS low-voltage differential signalingMAR modified amino resinMB methylene blueMBG mean blood glucoseMC Monte CarloMCA multi-channel analyzerM-CARS multiplex coherent anti-Stokes Raman scatteringMCML Monte Carlo modeling of photon transport in multilayered tissuesMCP-PMT multichannel plate-photomultiplier tubeMED minimal erythema doseMFP mean free path lengthMIM multispectral imaging micropolarimeterMIR middle infraredMNP magnetic nanoparticleMO micro-objectiveMONSTIR multichannel optoelectronic near-infrared system for time-resolved

image reconstructionMPM multiphoton microscopy


Acronyms xxxvii

MPS maximum permissible exposureMPT multiphoton tomographyMR magnetic resonanceMRI MR imagingMSOAT multispectral optoacoustic tomographyMTF modulation transfer functionMTT meal tolerance testNA numerical apertureNAD nicotinamide adenine dinucleotideNAD+ oxidized form of NADNADH, NAD·H reduced form of NADNADP·H reduced form of NAD phosphateNIR near infraredNIRS near infrared spectroscopyNL normal lungNP nanoparticleOA optoacousticOAT OA tomographyOCA optical clearing agentOCE optical coherence elastographyOCI optical coherence interferometryOCM optical coherence microscopyOCP optical clearing potentialOCT optical coherence tomographyOCTSS OCT signal slopeOD optical densityOFDI optical frequency-domain imagingOGTT oral glucose tolerance testOMA optical multichannel analyzerOMAG optical microangiographyOPD optical path differenceOPO optical parametric oscillatorOR-PAM optical resolution PAMOT optothermalOTR optothermal radiometryOxyHb oxyhemoglobinPA photoacousticPAM photoacoustic microscopyPBS phosphate buffered solutionPC personal computerPD photodetectorPDF probability distribution functionPDMD phase-delay measurement devicePDT photodynamic therapy


xxxviii Acronyms

PDWFCS photon-density wave fluctuation correlation spectroscopyPEG polyethylene glycolPG propylene glycolPHA pulse-height analysisPhS-OCT phase-sensitive OCTPhS-SSOCT phase-stabilized swept-source OCTPM polarization-maintainingPMT photomultiplier tubePOS polyorganosiloxanePPG polypropylene glycolPpIX Protoporphyrin IXPRS polarized reflectance spectroscopyPSF point-spread functionPS-OCT polarization-sensitive OCTPS-OLCR phase-sensitive optical low-coherence reflectometerPT photothermalPTFC PT flow cytometryPTI PT imagingPTM PT microscopyPT-OCT photothermal OCTPTR PT radiometryPVA-C polyvinyl alcohol cryogelPVDF polyvinyldenefluoridePY Percus–YevickQD quantum dotQELS quasi-elastic light scatteringRA-SHG random access second-harmonic generationRBC red blood cellRC relative contrastRCM reflection confocal microscopyRC-PACT ring-shaped confocal photoacoustic computed tomographyRF radio frequencyRGA Rayleigh–Gans approximationRI refractive indexrms root mean squareRNA ribonucleic acidRNFL retinal nerve fiber layerROI region of interestRPS random phase screenRSODL rapid scanning optical delay lineRTE radiative transfer equationRTT radiation transfer theoryRTV room-temperature vulcanizingRVA retinal visual acuity


Acronyms xxxix

SAW surface acoustic waveSC stratum corneumSD-OCM spectral-domain OCMSD-OCT spectral-domain OCTSEM standard error of the meanSERS surface-enhanced Raman scatteringSF spatial filterSFD spatial-frequency domainSFDI spatial frequency-domain imagingSHG second harmonic generationSIV statistical intensity variationSL sonoluminescenceSLD superluminescent diodeSLM spatial light modulatorSLN sentinel lymph nodesSLT SL tomographySMF skeletal muscle fibersSMI spatially modulated imagingSMLB spatially modulated laser beams-MTF spatial modulation transfer functionSNR signal-to-noise ratioSOCS skull optical clearing solutionSOI scattering orientation indexSPD sonophoretic deliverySPEF single-photon excitation fluorescenceSPR spatially resolved reflectanceSPS spatial phase shifts-PSF spatial point-spread functionSRR spatially resolved reflectanceSSB single sidebandSSOCT swept-source OCTSSS superior sagittal sinusST Staphylococcus toxinSTFT short time Fourier transformsvOCT Speckle variance OCTSWI-OCT shear wave imaging OCTTA thermoacousticTAC time-to-amplitude convertorTD time-domainTDM time division multiplexTDM transillumination digital microscopyTEWL transepidermal water lossTGS thermal gradient spectroscopyTHb total hemoglobin


xl Acronyms

TMP trimethylolpropanolTMR transverse microradiographyt-MTF temporal modulation transfer functionTOAST time-resolved optical absorption and scattering tomographyTPEF two-photon-excited fluorescencet-PSF temporal point-spread functionTRS time-resolved spectroscopyUHP ultra-high performanceUS ultrasoundUV ultravioletVLDL very low density lipoproteinVOA variable optical attenuatorWBC white blood cellWP Wollaston prismVRTE vector radiative transfer equationVTW virtual transparent windowWDM wavelength division multiplexWHO World Health OrganizationWMC “white” Monte Carlo


Preface to the First Edition

Many up-to-date medical technologies are based on recent progress in physics,including optics.1−102 An interesting example relevant to the topic of this tutorialis provided by computer tomography.1,4 X-ray, magnetic resonance, and positron-emission imaging techniques are extensively used in high-resolution studies of bothanatomical structures and local metabolic processes. Another safe and technicallysimple tool currently in use is diffuse optical tomography.1, 3, 4, 6, 15, 28, 71

From the viewpoint of optics, biological tissues and fluids (blood, lymph,saliva, mucus, gastric juice, urine, aqueous humor, and semen) can be separatedinto two large classes.1–40, 40–69, 92–97, 101 The first class includes strongly scattering(opaque) tissues and fluids, such as skin, brain, vessel walls, eye sclera, blood, andlymph. The optical properties of these tissues and fluids can be described withinthe framework of a model of multiple scattering of scalar or vector waves in arandomly nonuniform absorbing medium. The second class consists of weaklyscattering (transparent) tissues and fluids, such as cornea, crystalline lens, vitreoushumor, and aqueous humor of the front chamber of the eye. The optical proper-ties of these tissues and fluids can be described within the framework of a modelof single scattering (or low-step scattering) in an ordered isotropic or anisotropicmedium with closely packed scatterers with absorbing centers.

The vector nature of light waves is especially important for transpar-ent tissues, although much attention has recently focused on the investi-gation of polarization properties of light propagating in strongly scatteringmedia.3, 5, 6, 8–10, 23, 28, 43, 59–64, 69, 70 In scattering media, the vector nature of lightwaves is manifested as the polarization of an initially nonpolarized light beam or asthe depolarization (generally, change in the character of polarization) of an initiallypolarized beam propagating in a medium. Similar to coherence properties of a lightbeam reflected from or transmitted through a biological object, polarization param-eters of light can be employed as a selector of photons originating from differentdepths in an object.

The problems of optical diagnosis and spectroscopy of tissuesare concerned with two radiation regimes: continuous wave and timeresolved.1, 3, 4, 6, 12, 14, 15, 28, 31, 71, 92 The latter is realized by means of the expo-sure of a scattering object to short laser pulses (∼10−10 to 10−12 s) and the

xli


xlii Preface to the First Edition

subsequent recording of scattered broadened pulses (time-domain method), orby irradiation with modulated light, usually in the frequency range 50 to 1000MHz, and recording the depth of modulation of scattered light intensity and thecorresponding phase shift at modulation frequencies (frequency-domain or phasemethod). The time-resolved regime is based on the excitation of the photon-densitywave spectrum in a strongly scattering medium, which can be described in theframework of the nonstationary radiation transfer theory (RTT). The continuousradiation regime is described by the stationary RTT.

Many modern medical technologies employ laser radiation and fiber opticdevices.1–7 Because the application of lasers in medicine has both fundamentaland technical purposes, the problem of coherence is critical for the analysis of theinteraction of light with tissues and cell ensembles. On one hand, this problemcan be considered in terms of the loss of coherence due to the scattering of lightin a randomly nonuniform medium with multiple scattering, or to the change inthe statistics of speckle structures of the scattered field. On the other hand, thisproblem can be interpreted in terms of the appearance of an amplified, coher-ent, sharply directed component in backscattered radiation under conditions whena tissue is probed with an ultrashort laser pulse.1, 3, 73, 74 The coherence of lightis of fundamental importance for the selection of photons that have experiencedfew or zero scattering events, as well as for the generation of speckle-modulatedfields from scattering phase objects with single and multiple scattering.1, 3, 75–77

Such approaches are important for coherent tomography, diffractometry, holog-raphy, photon-correlation spectroscopy, laser Doppler anemometry, and speckleinterferometry of tissues and fluxes of biological fluids.1, 3, 5, 15, 22, 28, 76–83 The use ofoptical sources with short coherence length creates new opportunities in coherentinterferometry and tomography of tissues, organs, and blood flows.1, 3, 8, 17, 18, 77, 84

The transparency of tissues reaches its maximum in the near infrared (NIR),which is associated with the fact that living tissues do not contain strong intrin-sic chromophores that absorb radiation within this spectral range. Light penetratesinto a tissue for several centimeters, which is important for the transillumination ofthick human organs (such as brain or breast). However, tissues are characterized bystrong scattering of NIR radiation, which prevents one from obtaining clear imagesof localized inhomogeneities arising in tissues owing to various pathologies; e.g.,tumor formation, local increase in blood volume caused by a hemorrhage, orgrowth of microvessels. Strong scattering of NIR radiation also imposes certainrequirements on the power of laser radiation, which should be sufficient to ensurethe detection of attenuated fluxes. Special attention in optical tomography andspectroscopy is focused on the development of methods for the selection of image-carrying photons or the detection of photons providing the information concerningthe optical parameters of the scattering medium. These methods employ the resultsof fundamental studies devoted to the propagation of laser beams in scatteringmedia.1, 3, 4, 6, 15, 28, 31, 71, 92

Another important area in which deep tissue probing is practiced is reflectingspectroscopy, e.g., optical oxymetry for the evaluation of the degree of hemoglobin


Preface to the First Edition xliii

oxygenation in working muscular tissue, the diseased neonatal brain, or the activebrain of adults.1, 3, 4

This tutorial is primarily concerned with recently developed light-scatteringtechniques for quantitative studies of tissues and cell ensembles. It discusses theresults of theoretical and experimental investigations into photon transport in tis-sues and describes methods for solving direct and inverse scattering problems forrandom media with multiple scattering and quasi-ordered media with single scat-tering, to model different types of tissue behavior. The theoretical considerationis based on stationary and nonstationary radiation transfer theories for stronglyscattering tissues, Mie theory for transparent tissues, and the numerical MonteCarlo method, which is employed for the solution of direct and inverse problemsof photon transport in multilayered tissues with complicated boundary conditions.

These are general approaches extensible to the examination of a large numberof abiological scattering media. Many known methods of scattering media optics(e.g., the integrating sphere technique) were perfected when used in biomedicalresearch. Concurrently, new measuring systems and algorithms for the solution ofinverse problems have been developed that are useful for scattering media opticsin general. Moreover, the improvement of certain methods was undertaken onlybecause they were needed for tissue studies; this is especially true of the diffusephoton-density wave method, which is promising for the examination of manyphysical systems: aqueous media, gels, foams, air, and aerosols.

Based on such fundamental optical phenomena as elastic and quasi-elastic(static and dynamic) scattering, diffraction, and interference of optical fields andphoton-density waves (intensity waves), we will discuss optical methods andinstruments that offering promise for biomedical applications. Among these arespectrophotometry and polarimetry; time-domain and frequency-domain spec-troscopy and imaging systems; photon-correlation spectroscopy; speckle interfer-ometry; coherent topography and tomography; phase, confocal, and heterodynemicroscopy; and partial coherence interferometry and tomography.

I am grateful to Terry Montonye, Donald O’Shea, Alexander Priezzhev, BarryMasters, and Rick Hermann for their valuable suggestions and comments onpreparation of this tutorial.

I am very thankful to Andre Roggan, Lihong Wang, and Alexander Oraevskyfor their valuable comments and constructive criticism of the manuscript.

I greatly appreciate the cooperation and contribution of all my colleagues,especially D.A. Zimnyakov, V.P. Ryabukho, S.S. Ul’yanov, I.L. Maksimova, V.I.Kochubey, S.R. Uts, I.V. Yaroslavsky, A.B. Pravdin, G.G. Akchurin, I.L. Kon, E.I.Zakharova (Galanzha), A.A. Bednov, A.A. Chaussky, S.Yu. Kuz’min, K.V. Larin,I.V. Meglinsky, A.A. Mishin, I.S. Peretochkin, and A.N. Yaroslavskaya.

I am very thankful to attendees of my short courses on biomedical optics,which I have giving during SPIE Photonics West International Symposia since1992; for their good questions, fruitful discussions, and critical evaluations ofpresented materials. Their responses were very valuable for preparation of thisvolume. I am especially grateful to Michael DellaVecchia, Hatim Carim, Sandor


xliv Preface to the First Edition

Vari, M. Pais Clemente, Haishan Zeng, Leon Sapiro, and Zachary Sacks, who havebeen my good friends and colleagues for many years.

Prolonged collaboration with the University of Pennsylvania, my fruitful dis-cussions with Britton Chance, Shoka Nioka, Arjun Yodh, David Boas, and manyothers were very helpful in writing this book.

My joint chairing with Halina Podbielska, Ben Ovryn, and Joe Izatt of theSPIE Conference on Coherence Domain Optical Methods in Biomedical Scienceand Clinical Applications was also very helpful.

The original part of this work was supported within the program “LeadingScientific Schools” of the Russian Foundation for Basic Research (project # 96-15-96389), USA–Russia CRDF grant RB1-230, and ISSEP grants p97-372, p98-768,and p99-703 within the program “Soros Professors.”

I would like to thank all of my numerous colleagues and friends all over theworld who kindly sent me reprints of their papers, which were used in this tuto-rial and greatly simplified my task, especially Y. Aizu, J.D. Briers, Z. Chen, B.Devaraj, A.F. Fercher, M. Ferrari, J.G. Fujimoto, M.J.C. van Gemert, E. Gratton,J. Greve, A.H. Hielscher, S.L. Jacques, R.G. Johnston, G.W. Kattawar, M. Keijzer,S.M. Khanna, A.Ya. Khairulllina, A. Knüttel, J.R. Lakowicz, M.W. Lindner, Q.Luo, R.L. McCally, W.P. van de Merwe, G. Müller, F.F.M. de Mul, M.S. Patterson,B. Pierscionek, H. Rinneberg, P. Rol, W. Rudolph, B. Ruth, J.M. Schmitt, W.M.Star, R. Steiner, H.J.C.M. Sterenborg, L.O. Svaasand, J.E. Thomas, B.J. Tromberg,A.J. Welch, and J.R. Zip.

I would like to say a few words in memory of Pascal Rol, my good friend andcolleague with whom I have organized many SPIE meetings. Pascal died suddenlyon January 10, 2000. The reader will find many of his excellent results on scle-ral tissue optics in this tutorial. He has made many outstanding contributions tobiomedical optics, and I will always remember him as a good scientist and friendlyperson.

I am very thankful to Ruth Haas, Erika Wittmann, and Sue Price for theirassistance in editing and production of the book, and to S.P. Chernova and E.P.Savchenko for their help in the preparation of the figures.

Last, but not least, I express my gratitude to my wife, Natalia, and all my familyfor their support, understanding, and patience.

Valery TuchinApril 2000


Preface to the Second Edition

This is the second edition of the tutorial on Tissue Optics: Light Scattering Methodsand Instruments for Medical Diagnosis, first published in 2000. The last sevenyears since the printing of the first edition of the book have seen intensive growth ofresearch and development into tissue optics, particularly in the field of tissue diag-nostics and imaging.103−144 Further developments in light-scattering techniqueshave been made for the quantitative evaluation of optical properties of normal andpathological tissues and cell ensembles. New results on theoretical and experimen-tal investigations into light transport in tissues have been found, as have methodsfor solving direct and inverse scattering problems for quasi-ordered media andrandom media with multiple scattering. A few specific fields, such as optical coher-ence tomography (OCT),108−111,115,116,126,127,129,130,136,142 and polarization-sensitivetechnologies,129,130,135,136,138,139 which are very promising for optical medical diag-nostics and imaging, have developed rapidly over the last few years. The opticalclearing method, based on reversible reduction of tissue scattering through refrac-tive index matching of scatterers and ground matter, has also been of great interestfor research and application since the last edition.129,132,136,139,140 Further develop-ments in Raman and vibrational spectroscopies104,105,123,130,132,136,143 and multipho-ton microscopy114,119,122,130,132,136,137 applied to morphology and the functioning ofliving cells and tissues have been provided by many research groups.

This new edition of this book is conceptually the same as the first. It is alsodivided into two parts: Part I describes the fundamentals and basic research oftissue optics, and Part II presents optical and laser instrumentation and medi-cal applications. The author has corrected misprints, updated the references, andadded some new results, primarily on measurements of tissue optical properties(Chapter 2) and polarized light interaction with turbid tissues (Section 1.4). Recentresults on polarization imaging and spectroscopy techniques (Chapter 7), and onOCT developments and applications (Chapter 9) are also overviewed. Materials oncontrolling tissue optical properties (Chapter 5) and optothermal and optoacousticinteractions of light with tissues (Section 1.5) are updated. Brief descriptions offluorescent, nonlinear, and inelastic light scattering spectroscopies are provided inChapter 1.

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xlvi Preface to the Second Edition

I am grateful to Sharon Streams for her suggestion to prepare the second edi-tion of the tutorial and for her assistance in editing of the book. I also would liketo thank Merry Schnell for her assistance on the final stage of book editing andproduction.

I am very thankful to attendees of my short courses “Coherence, LightScattering, and Polarization Methods and Instruments for Medical Diagnosis,”“Tissue Optics and Spectroscopy,” “Tissue Optics and Controlling of TissueOptical Properties,” and “Optical Clearing of Tissues and Blood,” which I havegiven during SPIE Photonics West Symposia, SPIE/OSA European Conferenceson Biomedical Optics, and OSA CLEO/QELS Conferences over the last sevenyears, for their stimulating questions, fruitful discussions, and critical evaluationsof presented materials. Their responses were very valuable for preparation of thisedition. My joint chairing with Joseph A. Izatt and James G. Fujimoto of theSPIE Conference on Coherence Domain Optical Methods and Optical CoherenceTomography in Biomedicine also was very helpful.

The original part of this work was supported within Russian and inter-national research programs by grant N25.2003.2 of President of RussianFederation “Supporting of Scientific Schools,” grant N2.11.03 “Leading Research-Educational Teams,” contract No. 40.018.1.1.1314 “Biophotonics” of the Ministryof Industry, Science and Technologies of RF, grant REC-006 of CRDF (U.S.Civilian Research and Development Foundation for the Independent States ofthe Former Soviet Union) and the Russian Ministry of Education, the RoyalSociety grants for joint projects between Cranfield University (UK) and SaratovState University, grants of National Nature Science Foundation of China (NSFC),grant of Federal Agency of Education of RF No. 1.4.06, RNP.2.1.1.4473, CRDFgrants BRHE RUXO-006-SR-06 and RUB1-570-SA-04, and by Palomar MedicalTechnologies Inc., MA.

I greatly appreciate the cooperation, contributions, and support of all my col-leagues from Optics and Biomedical Physics Division of Physics Departmentand Research-Educational Institute of Optics and Biophotonics of Saratov StateUniversity, especially A.N. Bashkatov, I.V. Fedosov, E.I. Galanzha, E.A. Genina,I.L. Maksimova, I.V. Meglinski, V.I. Kochubey, V.P. Ryabukho, A.B. Pravdin, G.V.Simonenko, Yu.P. Sinichkin, S.S. Ul’yanov, D.A. Yakovlev, and D.A. Zimnyakov.

I would like to thank all my numerous colleagues and friends all over the worldfor collaboration and sending materials which were used in this tutorial and mademy work much easy, especially P.E. Andersen, J.F. de Boer, S.A. Boppart, Z. Chen,P.M.W. French, J.G. Fujimoto, V.M. Gelikonov, P. Gupta, C.K. Hitzenberger, X.H.Hu, J.A. Izatt, S.L. Jacques, A. Kishen, S.J. Kirkpatrick, A. Knüttel, J.R. Lakowicz,K.V. Larin, G.W. Lucassen, Q. Luo, A. Mahadevan-Jansen, B.R. Masters, K.Meek, M. Meinke, G. Müller, F.F.M. de Mul, R. Myllylä, L. Oliveira, M. PaisClemente, L.T. Perelman, A. Podoleanu, A.V. Priezzhev, F. Reil, J. Rodriguez, H.Schneckenburger, A.M. Sergeev, A.N. Serov, N.M. Shakhova, B.J. Tromberg, T.Troy, L.V. Wang, R.K. Wang, A.J. Welch, A.N. Yaroslavskaya, I.V. Yaroslavsky,P.V. Zakharov, and V.P. Zharov.


Preface to the Second Edition xlvii

I express my gratitude to my wife, Natalia, and all my family, especiallyto my daughter, Nastya, and grandchildren, Dasha, Zhenya, and Stepa, for theirindispensable support, understanding, and patience during my writing this book.

Valery TuchinJune 2007


Preface to the Third Edition

The idea to publish the third edition of this book was stimulated by severalfactors and strongly supported by SPIE Press staff. A couple of years ago, SPIEPress received requests to republish this book in Russian by Fizmatlit Publishers(Moscow) and in Japanese by Optronics (Tokyo). Since the second edition ofthe English language book was issued seven years ago, and accounting for rapiddevelopments in the field of tissue optics and corresponding optical medical instru-mentation, the author offered to provide the further updates of this book to SPIEPress before its translation. In addition, the book structure was changed to pro-vide more convenient and readable presented materials. The third edition contains14 chapters instead of 9, as in the second edition. In addition, chapters relatedto optical coherence tomography, digital holography and interferometry, control-ling of optical properties of tissues, nonlinear spectroscopy, and imaging weresubstantially updated.

Since the second edition of Tissue Optics, many other monographs, specialissues of journals, and conference proceedings have been published related to tis-sue optics and biophotonics. This highlights the urgency of this research field andeducation, as well as the growing market for biomedical optics, medical lasersand fibers, optical biosensors, high-speed digital cameras, other devices for medi-cal diagnostics and treatment, and skill training.6,116,118,137,145−210 These books andjournals address similar issues to those discussed in this monograph; in many ways,they are essentially complementary to Tissue Optics and can be recommended formore in-depth study of selected topics.

The previous editions of Tissue Optics contained two glossaries on (1) physics,statistics, and engineering; and (2) medicine, biology, and chemistry. These glos-saries have been considerably updated and were recently published as a separatebook, V.V. Tuchin, Dictionary of Biomedical Optics and Photonics, SPIE Press(2012) (see Ref. 210). Therefore, the third edition does not contain Glossariesbecause the reader can use this published dictionary instead.

The book is intended for researchers, teachers, and graduate and undergradu-ate students specializing in the physics of living systems, biomedical optics andbiophotonics, laser biophysics, and applications of lasers in biomedicine. This

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l Preface to the Third Edition

monograph can be useful as a textbook for students of physical, engineering,biological, and medical specialties.

Acknowledgments

The original materials included in the monograph were obtained with the finan-cial support of many Russian Federation (RF) and International grants andresearch programs, such as grants of the President of RF “Supporting of ScientificSchools” (00-15-96667, 25.2003.2, 208.2008.2, 1177.2012.2, 703.2014.2); grant2.11.03/1.4.09 “Leading Research-Educational Teams;” Russian and Internationalgrants of Russian Foundation for Basic Research (RFBR) (98-02-17997, 03-02-17359, 05-08-50318-a, 06-02-16740-a, 08-02-92224-NNSF-a (RF-China),13-02-91176-NNSF-a (RF-China), 10-02-90039-Bel-a, 11-02-00560-a, 11-02-12248-ofi-m, 12-02-92610-RS-a), and 14-02-00526-a); grants of RF Ministryof Science and Education 2.1.1/4989 and 2.2.1.1/2950; RF Governmentalcontracts 40.018.1.1.1314 “Biophotonics,” 02.740.11.0484, 02.740.11.0770,02.740.11.0879, 11.519.11.2035, 12.740.11.0871, 12.740.11.0871, 12.740.11.1156, 14.B37.21.0728, 14.B37.21.0563, 14.512.11.0022; grants of U.S. CivilianResearch and Development Foundation for the Independent States of theFormer Soviet Union (CRDF) (BRHE RUXO-006-SR-06; Next Step to theMarket Program, RUB1-570-SA-04; BP1M06 RUX0-006-SR-06; RUB1-2932-SR-08); the Royal Society grants for joint projects between Keele University,Cranfield University, St. Andrews University, (UK) and Saratov State University,2002–2006, 2012–2014; grant 224014 Photonics4life-FP7-ICT-2007-2; grantsof National Nature Science Foundation of China (NSFC); collaborativeprojects of Palomar Medical Technologies Inc., MA, USA; FiDiPro grant ofTEKES, Finland (40111/11); SCOPES Project (IZ74ZO_137423/1-2011-2014,Switzerland, Russia, and Uzbekistan); grant 14.Z50.31.0004 of the RF Governmentto support scientific research projects implemented under the supervision ofleading scientists; The Tomsk State University Academic D.I. Mendeleev FundProgram; and grants 14-15-00186 and 14-15-00128 of the Russian ScienceFoundation.

Many results presented in this monograph on modeling of tissue optical prop-erties were provided by Irina L. Maximova, who was a very talented scientist andwho passed away too early, in 2013.

The author expresses his deep gratitude to J.T. Alander, G.B. Altshuler,P. Andersen, R.R. Anderson, S. Andersson-Engels, V.A. Bochko, S.A. Boppart,E. Borisova, A.V. Bykov, M.E. Darvin, A. Diaspro, V.A. Doubrovsky, A. Douplik,D.D. Duncan, M. Fedorov, J.G. Fujimoto, E.I. Galanzha, S.L. Jacques,I.K. Ilev, J.A. Izatt, V.V. Kalchenko, T.G. Kamenskikh, V.A. Khanadeev,B.N. Khlebtsov, N.G. Khlebtsov, B.-M. Kim, M. Kinnunen, M.Yu. Kirillin,K. Kordás, J. Lademann, K.V. Larin, I.V. Larina, M.J. Leahy, P. Li, Q. Luo,L.I. Malinova, D. Matthews, I.V. Meglinski, O. Minet, R. Myllylä, T. Myllylä,M.M. Nazarov, L. Oliveira, F. Pavone, L. Perelman, R. Pini, A.P. Popov,J. Popp, A.V. Priezzhev, J. Qu, D.D. Sampson, A.P. Savitsky, A.M. Sergeev,


Preface to the Third Edition li

J. Spigulis, A.P. Shkurinov, O. Sydoruk, S. Tanev, A. Tárnok, G.S. Terentyuk,V.Yu. Toronov, B. Tromberg, S.R. Utz, P. Valisuo, A. Vitkin, L. Wang,R. Wang, B.C. Wilson, M. Wolf, A.N. Yaroslavsky, I.V. Yaroslavsky, V.P. Zharov,D. Zhu, and all his colleagues in the Saratov State University and the Instituteof Precise Mechanics and Control of RAS, especially to D.A. Agafonov,G.G. Akchurin, Yu.A. Avetisyan, A.N. Bashkatov, V.L. Derbov, L.E. Dolotov,I.V. Fedosov, E.A. Genina, V.I. Kochubey, A.S. Kolesnikov, E.A. Kolesnikova,V.V. Lychagov, A.B. Pravdin, V.P. Ryabukho, O.V. Semyachkina-Glushkovskaya,G.V. Simonenko, Yu.P. Sinichkin, Yu.S. Skibina, A.V. Solovieva, P.A. Timoshina,N.A. Trunina, D.K. Tuchina, E.S. Tuchina, M.A. Vilensky, D.A. Yakovlev,A.N. Yakunin, I.Yu. Yanina, A.A. Zanishevskaya, O.S. Zhernovaya, andD.A. Zimnyakov for collaboration, discussion of the results and valuablecomments.

I would like to express my gratitude to Eric Pepper and Tim Lamkins fortheir suggestion to prepare the third edition of the book and to Dara Burrows forassistance in editing the book.

I am grateful to my wife, Natalia Tuchina, and entire family for theirexceptional patience and understanding.

Valery V. TuchinDecember 2014


Part I: Introduction to TissueOptics


Chapter 1

Optical Properties of Tissueswith Strong (Multiple)Scattering

This first chapter introduces the problem of light (laser beams) transport withinstrongly (multiply) scattering tissues, such as skin, breast, brain, and vessel wall.Basic principles and theoretical descriptions using radiation transfer theory orMonte Carlo (MC) simulation are considered. The propagation of short pulses andphoton-density diffusion waves in scattering and absorbing media is analyzed, andthe prospects of using these methods for tissue spectroscopy and tomography arediscussed.

1.1 Propagation of Continuous Wave Light in Tissues

1.1.1 Basic principles and major scatterers and absorbers

Biological tissues are optically inhomogeneous and absorb media whose aver-age refractive index is higher than that of air. This is responsible for the partialreflection of radiation at the tissue/air interface (Fresnel reflection); the remain-ing part penetrates the tissue. Multiple scattering and absorption are responsiblefor the broadening and eventual decay of a laser beam as it travels through atissue, whereas bulk scattering is a major cause of the dispersion of a largefraction of radiation in the backward direction. Therefore, light propagationwithin a tissue depends on the scattering and absorption properties of its compo-nents: cells, cell organelles, and various fiber structures.1–3, 6, 15, 129, 130, 134, 135, 138, 172,

183, 195–197, 200 The size, shape, and density of these structures; their refractiveindex relative to the tissue ground substance; and the polarization state ofthe incident light all play important roles in the propagation of light intissues.1–3, 6, 15, 129, 130, 134, 135, 138, 172, 183, 195–197, 200, 211–219

In view of the great diversity and structural complexity of tissues, the devel-opment of adequate optical models that account for the scatter and absorption oflight is often the most complex step of a study. Two approaches are currently

3


4 Chapter 1

used for tissue modeling. In the framework of the first approach, tissue ismodeled as a medium with a continuous random spatial distribution of opti-cal parameters; the second approach considers tissue as a discrete ensemble ofscatterers.1–3, 6, 15, 129, 130, 134, 138, 195–197, 220, 221 The choice of approaches is dictatedby both the structural specificity of the tissue under study and the manner oflight-scattering characteristics that are to be obtained.

Most tissues are composed of structures with a wide range of sizes, and canbe described as a random continuum of the inhomogeneities of the refractive indexwith a varying spatial scale.220, 221 In particular, phase contrast microscopy has fre-quently been used to show that the structure of refractive index inhomogeneities inmammalian tissues is similar to that of frozen turbulence.220 This fact is of funda-mental importance for understanding the peculiarities of light propagation in tissue,and may be a key to solving the inverse problem of tissue structure reconstruction.This approach is applicable for tissues with no pronounced boundaries betweenelements that feature significant heterogeneity. The process of scattering in thesestructures may be described under certain conditions by using the model of a phasescreen.75, 136, 221–224

The second approach to tissue modeling is its representation as a system ofdiscrete scattering particles. In particular, this model has been advantageouslyused to describe the angular dependence of the polarization characteristics of scat-tered radiation.129, 135, 169, 195, 211, 212, 214, 216 Blood is the most important biologicalexample of a disperse system that entirely corresponds to the model of discreteparticles.48, 101, 129, 205, 225

Biological media are often modeled as ensembles of homogeneous sphericalparticles, because many cells and microorganisms, particularly blood cells, are sim-ilar in shape to spheres or ellipsoids. A system of noninteracting spherical particlesis the simplest tissue model. Mie theory rigorously describes the diffraction of lightin a spherical particle.214, 226 The development of this model takes into account thestructures of the spherical particles; namely, the multilayered spheres and thosewith radial nonhomogeneity, anisotropy, and optical activity.169, 172, 211, 212

Because connective tissue consists of fiber structures, it is most appropriatelymodeled by a system of long cylinders. Muscular tissue, skin dermis, dura mater,eye cornea, and sclera belong to this type of tissue, essentially formed by collagenfibrils. The solution to the problem of light diffraction in a single homogeneous ormultilayered cylinder is also well understood.214

The sizes of cells and tissue structure elements vary, from a few tenths ofnanometers to a few tenths of micrometers.47, 58, 94–96, 129, 130, 172, 215–219, 227–272 Bloodcells (erythrocytes, leukocytes, and platelets) exhibit the following parameters. Anormal erythrocyte in plasma has the shape of a concave–concave disc with a diam-eter varying from 7.1 to 9.2 μm, a thickness of 0.9–1.2 μm in the center and1.7–2.4 μm on the periphery, and a volume of 90 μm3. Leukocytes are formedlike spheres, with a diameter of 8–22 μm. Platelets in the bloodstream are bicon-vex disk-like particles with diameters ranging from 2 to 4 μm. Normally, bloodhas approximately 10 times as many erythrocytes as platelets and approximately30 times as many platelets as leukocytes.


Optical Properties of Tissues with Strong (Multiple) Scattering 5

Figure 1.1 Major organelles and inclusions of the cell (see Ref. 129) (a); mitochondrionstructure (b).

Most other mammalian cells have diameters in the range of 5–75 μm. In theepidermal layer, the cells are large (with an average cross-sectional area of approx-imately 80 μm2) and quite uniform in size. Fat cells, each containing a single lipiddroplet that nearly fills the entire cell, and therefore results in eccentric placementof the cytoplasm and nucleus, have a wide range of diameters, from a few micronsto 50–75 μm. Fat cells may reach a diameter of 100–200 μm in pathological cases.

A wide variety of structures within cells determine tissue light scattering (seeFig. 1.1). Cell nuclei are on the order of 5–10 μm in diameter, mitochondria∼1–2 μm, lysosomes and peroxisomes ∼20 nm. Structures within variousorganelles have dimensions from a few nanometers up to a few hundred nanome-ters. Usually, scatterers in cells are not spherical. The models of prolate ellipsoidswith a ratio of the ellipsoid axes between 2 and 10 are more typical.

The hollow organs of the body are lined with a thin, highly cellular surfacelayer of epithelial tissue, which is supported by underlying, relatively acellularconnective tissue. In healthy tissues, the epithelium often consists of a single,well-organized layer of cells with en face diameter of 10–20 μm and height of


6 Chapter 1

Figure 1.2 Microphotograph of the isolated normal intestinal epithelial cells (a) and intesti-nal malignant cell line T84 (b). Note the uniform nuclear size distribution of the normalepithelial cell (a) in contrast to the T84 malignant cell line, which at the same magnificationshows larger nuclei and more variation in nuclear size (b). Solid bars equal 20 μm in eachpanel (from Ref. 187).

25 μm (see Fig. 1.2). In dysplastic epithelium, cells proliferate and their nucleienlarge and appear darker (hyperchromatic) when stained.216 Enlarged nuclei areprimary indicators of cancer, dysplasia, and cell regeneration in most humantissues.

In fibrous tissues or tissues containing fiber layers (cornea, sclera, dura mater,muscle, myocardium, tendon, cartilage, vessel wall, or retinal nerve fiber layer)and composed mostly of microfibrils and/or microtubules, typical diameters of thecylindrical structural elements are 10–400 nm. Their length ranges from 10–25 μmto a few millimeters.

The dominant scatterers in an artery may be the fibers, cells, or subcellularorganelles. Muscular arteries have three main layers. The inner intimal layer con-sists of endothelial cells with a mean diameter of less than 10 μm. The medial layerconsists mostly of closely packed smooth muscle cells with a mean diameter of15–20 μm; small amounts of connective tissue, including elastin, collagenous, andreticular fibers as well as a few fibroblasts, are also located in the media. The outeradventitial layer consists of dense fibrous connective tissue that is largely com-posed of collagen fibers 1–12 μm in diameter and thinner elastin fibers, 2–3 μm indiameter.

Two other examples of complex scattering structures are myocardium and theretinal nerve fiber layer. The myocardium primarily consists of cardiac muscle,



which is composed of myofibrils (approximately 1 μm in diameter) that, in turn,consist of cylindrical myofilaments (6–15 nm in diameter) and aspherical mito-chondria (1–2 μm in diameter). The retinal nerve fiber layer comprises bundlesof unmyelinated axons that run across the surface of the retina. The cylindricalorganelles of the retinal nerve fiber layer are axonal membranes, microtubules,neurofilaments, and mitochondria. Axonal membranes, like all cell membranes,are thin (6–10 nm) phospholipid bilayers that form cylindrical shells enclosing theaxonal cytoplasm. Axonal microtubules are long, tubular polymers of the proteintubulin with an outer diameter of ≈25 nm, inner diameter of ≈15 nm, and length of10–25 μm. Neurofilaments are stable protein polymers with a diameter of ≈10 nm.Mitochondria are ellipsoidal organelles that contain densely involved membranesof lipid and protein. They are 0.1–0.2 μm thick and 1–2 μm long.

For some tissues, the size distribution of the scattering particles may be essen-tially monodispersive; for others, it may be quite broad. Two opposite examplesare transparent eye cornea stroma, which has a sharply monodispersive distribu-tion, and turbid eye sclera, which has a rather broad distribution of collagen fiberdiameters.129, 130 There is no universal distribution size function that describes alltissues with equal adequacy. In optics of dispersed systems, Gaussian, gamma,or power size distributions are typical.237 Polydispersion for randomly distributedscatterers can be resolved by using gamma distribution or the skewed logarithmicdistribution of scatterer diameters, cross sections, or volumes.61, 129, 220, 222, 231, 238

In particular, for turbid tissues such as eye sclera, the gamma radii distributionfunction is applicable.61, 238

Absorbed light is converted to heat or radiated in the form of fluorescence; itis also consumed in photobiochemical reactions. The absorption spectrum dependson the type of predominant absorption centers and water content of tissues (seeFigs. 1.3–1.7). Absolute values of absorption coefficients for typical tissues liein the range 10−2 to 104 cm−1.1–4, 6, 9–15, 28, 29, 31, 37–42, 56, 57, 72, 86–91 In the ultraviolet

Figure 1.3 Absorption spectrum of water (see Ref. 56).


8 Chapter 1

Figure 1.4 Molar attenuation spectra for solutions of major visible light-absorbing humanskin pigments: 1, DOPA-melanin (H2O); 2, oxyhemoglobin (H2O); 3, hemoglobin (H2O);4, bilirubin (CHCl3).57

Figure 1.5 Transmittance spectrum of a 3-mm-thick slab of female breast tissue. A spec-trometer with an integrating sphere was used. The contributions of absorption bands of thetissue components are marked: 1, hemoglobin; 2, fat; 3, water (see Ref. 50).

(UV) and infrared (IR) (λ ≥ 2000 nm) spectral regions, light is readily absorbed,which accounts for the small contribution of scattering and the inability of radiationto penetrate deeply into tissues (only through one or two cell layers). Short-wavevisible light penetrates typical tissues as deeply as 0.5–2.5 mm, whereupon itundergoes an e-fold decrease in intensity. In this case, both scattering and absorp-tion occur, with 15–40% of the incident radiation being reflected. In the wavelengthrange of 600–1600 nm, scattering prevails over absorption and light penetrates to adepth of 8–10 mm. Simultaneously, the intensity of the reflected radiation increasesto 35–70% of the total incident light (owing to backscattering).

Light interaction with a multilayer and multicomponent skin is a very com-plicated process.57 The horny skin layer (stratum corneum) reflects approximately5–7% of the incident light. A collimated light beam is transformed to a diffuse



Figure 1.6 UV absorption spectra of major chromophores of human skin [1, DOPA–melanin, 1.5 mg % in H2O; 2, urocanic acid, 104M in H2O; 3, DNA, calf thymus,10 mg % in H2O (pH = 4.5); 4, tryptophan, 2 × 104M (pH = 7); 5, tyrosine, 2 × 104M(pH = 7)].57

Figure 1.7 Absorption spectra of skin and aorta; spectra of tissue components: water(75%), epidermis, melanosome, and whole blood are also presented; diagnostic lasers andtheir wavelengths as well as diagnostic/therapeutic window and wavelength ranges suitablefor superficial and deep spectroscopy are shown (adapted from Ref. 36).

beam by microscopic inhomogeneities at the air/horny layer interface. A majorpart of reflected light results from backscattering in different skin layers (stratumcorneum, epidermis, dermis, blood, and fat). The absorption of diffuse light by skin


10 Chapter 1

pigments is a measure of bilirubin content, hemoglobin concentration and its satu-ration with oxygen, and the concentration of pharmaceutical products in blood andtissues; these characteristics are widely used in the diagnosis of various diseases(see Fig. 1.4). Certain phototherapeutic and diagnostic modalities take advantageof the ready transdermal penetration of visible and near infrared (NIR) light insidethe body in the wavelength region corresponding to the therapeutic or diagnosticwindow (600–1600 nm) (Fig. 1.7).

Another example of heterogeneous multicomponent tissue is a female breast(which is principally composed of adipose and fibrous tissues). The absorptionbands of hemoglobin, fat, and water are clearly visible in the in vitro measuredspectrum of the 3-mm slab of breast tissue presented in Fig. 1.5.50 Measurementwas done using the integrating sphere spectrometer. There is a wide windowbetween 700 and 1100 nm, and narrow windows at approximately 1300 and1600 nm, where the lowest percentage of light is attenuated.

Solid tissues such as ribs and the skull, as well as whole blood, are also eas-ily penetrable by visible and NIR light.1–4, 6, 9–16, 36, 91, 129, 130 The relatively suitabletransparency of skin for long-wave UV light (UV-A) depends on DNA, tryptophan,tyrosine, urocanic acid, and melanin absorption spectra, and underlies selectedmethods of the photochemotherapy of skin tissues using UV-A irradiation (seeFig. 1.4).3, 6, 10, 57, 86, 129, 130

A collimated (laser) beam is attenuated in a thin tissue layer of thickness d inaccordance with the exponential Bouguer–Beer–Lambert law:37

I(d) = (1 − RF)I0 exp(−μtd), (1.1)

where I(d) is the intensity of transmitted light, measured by using a distant pho-todetector with a small aperture (online or collimated transmittance), W/cm2;RF is the coefficient of Fresnel reflection; at the normal beam incidence, RF =[(n − l)/(n + l)]2; n is the relative mean refractive index of tissue and surroundingmedia; I0 is the incident light intensity, W/cm2;

μt = μa + μs (1.2)

is the extinction coefficient (interaction or total attenuation coefficient), 1/cm,where μa is the absorption coefficient, 1/cm, and μs is the scattering coefficient,1/cm. Strictly speaking, Eq. (1.1) is valid only for a highly absorbing media whenμa >>μs.

The extinction coefficient is connected with the extinction cross section σext as

μt = ρsσext, (1.3)

where ρs is the density of particles (tissue and cell compounds). For a system ofparticles with absorption,

σext = σsca + σabs (1.4)

and

μs = ρsσsca, μa = ρsσabs. (1.5)



The average scattering cross section per particle can be presented in a suitable formfor experimental evaluations:214

σsca = (λ2/2π)(1/I0)∫ π

0I(θ) sinθdθ, (1.6)

where I0 is the intensity of the incident light, I(θ) is the angular distribution ofthe scattered light by a particle, and θ is the scattering angle. For macroscopicallyisotropic and symmetric media, the average scattering cross section is indepen-dent of the direction and polarization of the incident light. The average extinction,σext, and absorption, σabs, cross sections are also independent of the direction andpolarization of the incident light.

The probability that a photon incident on a small volume element will surviveis equal to ratio of the scattering and extinction cross sections, and is called thealbedo for single scattering, �:

� = σsca

σext= μs

μt. (1.7)

The albedo ranges from zero for a completely absorbing medium to unity for acompletely scattering medium.

The mean free path (MFP) length between two interactions is denoted by

lph = 1

μt. (1.8)

1.1.2 Theoretical description

To analyze light propagation under multiple scattering conditions, it is assumed thatabsorbing and scattering centers are uniformly distributed across the tissue. UV-A,visible, or NIR radiation is normally subject to anisotropic scattering, character-ized by a clearly apparent direction of photons undergoing single scattering, whichmay be attributable to the presence of large cellular organelles [mitochondria,lysosomes, and inner membranes (Golgi apparatus)].3, 58, 85, 95, 96, 129, 130, 135, 216–219

When the scattering medium is illuminated by unpolarized light and/or theintensity of multiply scattered light needs to be computed singly, a sufficientlystrict mathematical description of continuous wave (CW) light propagation in amedium is possible in the framework of the scalar stationary radiation transfertheory (RTT).1, 3, 6, 12–16, 129, 130, 135, 136, 196, 197, 211, 212, 273, 273–289

This theory is valid for an ensemble of scatterers located far from one anotherand has been successfully used to decipher certain practical aspects of tissue optics.The main stationary equation of RTT for monochromatic light has the form1

∂I(r, s)

∂s= −μtI(r, s) + μs

∫4π

I(r, s′)p(s, s′)d�′, (1.9)

where I(r, s) is the radiance (or specific intensity) – average power flux density at apoint r in the given direction s (W/cm2sr); p(s, s′) is the scattering phase function,


12 Chapter 1

1/sr; and d�′ is the unit solid angle about the direction s′, sr. It is assumed thatthere are no radiation sources inside the medium. With the existence of a radiationsource inside the medium, the source term, S(r, s), should be added to the right partof this equation or accounted for when formulating the boundary conditions.

The scalar approximation of the radiative transfer (transport) equation (RTE)is not accurate when the size of the scattering particles is much smaller than thewavelength, but provides acceptable results for particles comparable to and largerthan the wavelength.212, 276 There is ample literature on the analytical and numericalsolutions of the scalar RTE.1, 3, 15, 129, 130, 196, 197, 276–289

If radiative transport is examined in a domain G ∈ R3, and ∂G is the domainboundary surface, then the boundary conditions for ∂G can be written in thefollowing general form:

I(r, s)∣∣(s·n)<0 = (1

/μt)S(r, s) + R I(r, s)

∣∣(s·n)>0, (1.10)

where r ∈ ∂G, n is the outside normal vector to ∂G, S(r, s) is the incident lightdistribution at ∂G, and R is the reflection operator. When both absorption andreflection surfaces occur in domain G, conditions analogous to Eq. (1.10) mustbe given at each surface.

For practical purposes, integrals of the function I(r, s) over certain phase spaceregions (r, s) are of greater value than the function itself. Specifically, opticalprobes of tissues frequently measure the outgoing light distribution function at themedium surface, which is characterized by the radiant flux density or irradiance(W/cm2):

F(r) =∫

(s·n)>0I(r, s) (s · n)d�, (1.11)

where r ∈ ∂G.In problems of optical radiation dosimetry in tissues, the measured quantity is

actually the total radiant energy fluence rate U(r). It is the sum of the radiance overall angles at point r and is measured by watts per square centimeter:

U(r) =∫

4πI(r, s)d�. (1.12)

The phase function, p(s, s′), describes the scattering properties of the medium;in fact, it is the probability density function for scattering in direction s′of a photontraveling in direction s. In other words, it characterizes an elementary scatteringact. If scattering is symmetric relative to the direction of the incident wave, thenthe phase function depends only on scattering angle θ (angle between directionss and s′), i.e.,

p(s, s′) = p(θ). (1.13)

The assumption of random distribution of scatterers in a medium (i.e., theabsence of spatial correlation in the tissue structure) leads to normalization∫ π

0p(θ)2π sinθdθ = 1. (1.14)



In practice, the phase function is usually accurately approximated with the aidof the postulated Henyey–Greenstein function:1, 3, 12–16, 70, 129, 130, 230

p(θ) = 1

4π· 1 − g2

(1 + g2 − 2g cos θ)3/2, (1.15)

where g is the scattering anisotropy parameter (mean cosine of scattering angle θ)

g ≡ 〈cos θ〉 =∫ π

0p(θ) cos θ · 2π sin θdθ. (1.16)

The value of g varies in the range from −1 to 1:211, 212 g = 0 corresponds toisotropic (Rayleigh) scattering, g = 1 to total forward scattering (Mie scatteringat large particles), and −1 to total backward scattering.

The integro-differential Eq. (1.9) is too complicated to be employed for theanalysis of light propagation in scattering media. Therefore, it is frequently sim-plified by representing the solution in the form of spherical harmonics. Thissimplification leads to a system of (N + 1)2 connected differential partial deriva-tive equations known as the PN approximation. This system is reducible to asingle differential equation of order (N + 1). For example, four connected dif-ferential equations reducible to a single diffusion-type equation are necessary forN = 1.283–289 This has the following form for an isotropic medium:

(∇2 − μ2eff) U(r) = −Q(r), (1.17)

where

μeff = [3μa(μ′s + μa)]

1/2 (1.18)

is the effective attenuation coefficient or inverse diffusion length, μeff = 1/ld,1/cm;

Q(r) = 1

DSd(r), (1.19)

D = 1

3(μ′s + μa)

(1.20)

is the photon diffusion coefficient, cm; to convert this to cm2/s, it should bemultiplied by c, the velocity of light in the medium, cm/s;

μ′s = (1 − g)μs (1.21)

is the reduced (transport) scattering coefficient, 1/cm; Sd(r) is the source function(i.e., the number of photons injected into the unit volume); for the isotropic lightsource, S(r, s) is independent of s:

S(r, s) = 1

4πSd(r). (1.22)


14 Chapter 1

A collimated source in a multiple scattering medium can be effectively convertedinto an isotropic source.196

The transport mean free path of a photon (cm) is defined as

ltr = 1

μtr= 1

μa + μ′s

, (1.23)

where μtr = μa + μ′s is the transport coefficient.

The transport mean free path (TMFP) in a medium with anisotropic single scat-tering significantly exceeds the MFP in a medium with isotropic single scatteringltr � lph [see Eq. (1.8)]. The TMFP ltr is the distance over which the photon losesits initial direction. Figure 1.8 illustrates the random walk migration of a photon inthe multiple scattering medium and defines photon MFP, lph, and TMFP, ltr.

Diffusion theory provides a satisfactory approximation in the case of a smallscattering anisotropy factor, g ≤ 0.1, and large albedo, � → 1. For many tis-sues, g ≈ 0.6 − 0.9, and can be as large as 0.990 − 0.999; for example, forblood.48, 49, 87, 129 This significantly restricts the applicability of the diffusionapproximation. It is argued that this approximation can be used at g < 0.9, whenthe optical thickness, τ, of an object is on the order of 10–20:

τ =∫ d

0μtds, (1.24)

where d is the tissue depth (thickness) in the direction s.

Figure 1.8 Multiple scattering. MFP and TMFP definitions: MFP ∼= 1/μs(μs � μa), TMFP∼= 1/μ′

s(μ′s � μa), and < cos θ >= 0.90, i.e., < θ >≈ θ1 ≈ θ2 ≈, . . . , ≈ θ10 ≈ 26 deg and

μs′ = μs(1 − g) = 0.10μs (a). Illustration of photon random walk of TMFP step size;scattering particles are shown as lighter disks, small arrows show directions of pho-ton migration between consecutive elementary interaction acts with scattering and largearrows showing the direction of effective photon migration as a result of multiplescattering (b). For a more anisotropic phase function (larger g-factor), more elemen-tary scattering steps are needed to transfer photon distribution to isotropic distribution;http://omlc.ogi.edu/classroom/ece532/class3/musp.html.



However, the diffusion approximation is inapplicable for beam input near theobject’s surface, where single or low-step scattering prevails. When a narrow lightbeam is normally incident upon a semi-infinite turbid medium with anisotropicscattering, it can be considered as converted into an isotropic point source at thedepth of one transport MFP ltr [Eq. (1.23)] below the surface. The strength of thispoint source is the original source strength multiplied by the transport albedo:285

�′ = μ′s

μa + μ′s

. (1.25)

It was confirmed that diffusion theory is accurate for describing photon migra-tion in infinite, homogeneous, turbid media.34, 46, 51, 93, 196, 198, 283, 290–298 However,although another procedure for diffusion equation derivation, described in Refs. 34,51, and 283, leads to the basic Eq. (1.20), it provides a more general expression forphoton diffusion coefficient:

D = 1

3(μ′s + aμa)

, (1.26)

where a is the numerical coefficient depending on the form of the diffusionequation (on scattering anisotropy factor).

Systematic approximation schemes lead to recommendations34, 51, 283 of a =0, 1/5, 1/3, and 1. Any of these a values agrees significantly better with randomwalk simulations than the diffusion equation at a = 0, with a = 1/3 slightly betterthan the other two.283 Because values a = 1/5 and a = 1 lead to the wrong pulse-front propagation speeds, and only the intermediate value a = 1/3 gives the correctspeed, the photon-diffusion coefficient should be determined in the form283

D ∼= 1

3μ′s + μa

. (1.27)

This expression in general provides a better agreement between the diffusion equa-tion and RTE, but in practice, it is useful only for relatively highly absorbing tissuesor tissue components when μa/μ

′s > 0.01.291

For accurate use of diffusion theory, one must accurately convert the nar-row light beam into isotropic photon sources that must be sufficiently deep inthe medium, comparable with photon transport length, ltr; and the absorptioncoefficient, μa, should be much lower than the reduced scattering coefficient,μ′

s.196, 290

Thus, for the case of homogeneous tissue where μ′s � μa, photon migration

at CW irradiation is accurately described by a diffusion model with total radi-ant energy fluence rate, U(r), decaying exponentially away from a point source,according to Refs. 275 and 299:

U(r) = P

4πDrexp(−μeffr), (1.28)

where r is the distance away from the source, P is the power of the source, and theother parameters are defined above.


16 Chapter 1

Figure 1.9 Optical system focused on tissue surface provides imaging due to collectingdiffuse (scattered) light, radiated by real or virtual light sources inside tissue; geometry indiffusion model with extrapolation border, which is apart from the tissue surface (z = 0) ondistance zb (see Ref. 299).

When an imaging system is viewing down on a homogeneous slab of tis-sue with an embedded light source (for instance, excited fluorescence), as shownin Fig. 1.9, the radiance observed at the tissue surface can be calculated fromEqs. (1.9), (1.17), and (1.28) with appropriate boundary conditions. The extrap-olated boundary condition is often used because it is simple and can be provedby numerical modeling and measurements.296, 299 As shown in Fig. 1.9, an imagesource is reflected about a plane located a distance

zb= 2D1 + Reff

1 − Reff, (1.29)

from the tissue-surface extrapolated boundary. Here, Reff is the effective reflectioncoefficient averaged over all angles of incidence at the boundary, which can befound by integrating the Fresnel reflection coefficient over all incident angles;296

and D is the diffusion coefficient [see Eq. (1.20)]. The photon fluence at theextrapolated boundary is the sum of the contribution from the source and its image

U(z = 0) = P

4πD

[1

r1e−μeffr1 − 1

r2e−μeffr2

]. (1.30)

The radiance, I(r, s), in tissue along a unit vector s is given by296

I(r, s) = 1

4π

[U(r) − 3D(∇U(r)) · s

]. (1.31)

Using Eq. (1.30) and its normal derivative, ∂U/∂z

z=0, the surface radiance iscalculated from Eq. (1.31) as299

Iz=0 = 1

4π

(P

4πD

){1

r1e−μeffr1 − 1

r2e−μeffr2

+3D

[d

r21

(μeff + 1

r1

)e−μeffr1 + d + 2zb

r22

(μeff + 1

r2

)e−μeffr2

]}, (1.32)



where r1 = √ρ2 + d2, r2 = √

ρ2 + (d + 2zb)2, and d is the source depth (seeFig. 1.9).

Measurement of diffusely reflected light is often used to infer bulk tissue opti-cal properties for the aims of tissue spectroscopy and imaging. To provide suchmeasurements, an adequate calculating algorithm should be derived. The diffusionequation, solved subject to boundary conditions at the interfaces, is one basis forthe calculation algorithm.46, 93, 296–298 As already discussed, these boundary con-ditions are derived by considering Fresnel’s laws of reflection and balancing thefluence rate and photon current crossing the interface. For the source term mod-eled as a point scattering source at a depth of one TMFP, ltr, and an extrapolatedboundary approach satisfying the boundary condition (see Fig. 1.9), the spatiallyresolved steady-state reflectance per incident photon, R(rsd), is expressed as297, 298

R(rsd) = FU4π

{ltr

(μeff + 1

r1

)exp(−μeffr1)

r21

+ (ltr + 2zb)(μeff + 1

r2

)exp(−μeffr2)

r22

}+ FF

4πD

{exp(−μeffr1)

r1− exp(−μeffr2)

r2

},

(1.33)

where rsd is the distance between light source and detector at the tissue surface

(source–detector separation), cm; r1 =√

l2tr + r2sd; r2 =

√(ltr + 2zb)2 + r2

sd; D isthe diffusion coefficient [Eq. (1.20)]; zb is the distance to the extrapolated boundary[Eq. (1.29)]; parameters FU and FF represent the fractions of the fluence rate andflux, which exit the tissue across the interface. These values are obtained by inte-gration of the radiance over the backward hemisphere297 and depend on refractiveindex mismatch on the boundary. For the tissue phantom (polystyrene), the valuesof FU and FF were 0.089 and 0.239 for air, and 0.169 and 0.406 for water abovethe phantom.298

Certain limitations to the diffusion theory, particularly connected with baddescription of the fluence rate if one reaches the source, can be overcome whenit is modified on the basis of an accurate but simple Grosjean’s equation, whichdescribes the light distribution in infinite isotropically scattering turbid media.293

A new diffusion approximation to the RTE for a scattering medium with a spatiallyvarying refractive index is derived in Ref. 295.

Now, let us briefly review other solutions of the transport equation. Thefirst-order solution is realized for optically thin and weakly scattering media(τ < 1, � < 0.5) when the intensity of a transmitting (coherent) wave is describedby Eq. (1.1) or a similar expression:284

I(s) = (1 − RF)I0 exp(−τ), (1.34)

where the incident intensity, I0 (W/cm2), is defined by the incident radiant fluxdensity or irradiance [see Eq. (1.11)], F0, and a solid angle delta function pointedin the direction �0 : I0 = F0δ(� − �0).

Given a narrow beam (e.g., a laser), this approximation may be appliedto denser tissues (τ > 1, � < 0.9). However, certain tissues have � ≈ 1 in thetherapeutic/diagnostic window wavelength range, which makes the first-orderapproximation inapplicable even at τ � 1.


18 Chapter 1

A more strict solution of the transport equation is possible by the discrete ordi-nates method (multiflux theory), in which Eq. (1.9) is converted into a matrixdifferential equation for illumination along many discrete directions (angles).275

This approximates an exact solution as the number of angles increases. Asdiscussed previously, the fluence rate can be expanded in powers of sphericalharmonics, separating the transport equation into the components for spherical har-monics. This approach also leads to an exact solution, provided that the numberof spherical harmonics is sufficiently large. For example, a study of tissues usedup to 150 spherical harmonics,300 and the resulting equations were solved by thefinite-difference method.301 However, this approach requires tiresome calculationsif a sufficiently exact solution is to be obtained. Moreover, it is hardly suitable forδ-shaped phase scattering functions.284

The P3 approximation, which expresses the radiance algebraically in a trun-cated series of Legendre polynomials, is a solution to the RTE [see Eq. (1.9)].Star was the first to use the advances in computer power to compare the P3approximation to Monte Carlo calculations in slab geometry.302, 303 Further devel-opment of the P3 approximation for spherical geometry, which is more practicalfor application in tissue study, is described in Ref. 304.

Tissue optics extensively employs simpler methods for the solution of transportequations; e.g., the two-flux Kubelka–Munk theory305 or three, four, and seven fluxmodels.56, 275, 284 Such representations are natural and very fruitful for laser tissueprobing. Specifically, the four-flux model306 actually represents two diffuse fluxestraveling to meet each other (Kubelka–Munk model) and two collimated laserbeams, the incident beam and that reflected from the rear boundary of the sample.The seven-flux model is the simplest three-dimensional (3D) representation of scat-tered radiation and an incident laser beam in a semi-infinite medium.56 Of course,its simplicity and expeditious calculation of the radiation dose or rapid determi-nation of tissue optical parameters (solution of the inverse scattering problem) isachieved at the expense of accuracy.

1.1.3 Monte Carlo simulation techniques

The development of new methods for solving forward and inverse radiation trans-fer problems in media with arbitrary configurations and boundary conditions iscrucial for reliable layer-by-layer measurements of laser radiation inside tissues,and necessary for practical purposes such as diffuse optical tomography and thespectroscopy of biological objects. The Monte Carlo (MC) method appears tobe especially promising in this context; it is widely used for the numerical solu-tion of the RTT equation in different fields of knowledge (such as astrophysicsor atmosphere and ocean optics).307, 308 It has additionally been applied to tis-sue optics.1–3, 12–16, 29, 33, 41, 48, 129, 135, 196, 197, 290, 306, 309–373 The method is based on thenumerical simulation of photon transport in scattering media. Random migrationsof photons inside a sample can be traced from their input until absorption or out-put. Known algorithms allow a few tissue layers with different optical propertiesto be characterized, along with the final incident beam size and the reflection of



light at interfaces. Typical examples of multilayer tissues are skin, vascular, urinarybladder, and uterine walls.

Despite its high accuracy and universal applicability, the MC method hasone major drawback: due to the statistical nature of modeling, it consumes toomuch computation time to trace a large number of photons to achieve accept-able variance. MC simulations are especially computationally expensive when theabsorption coefficient is much lower than the scattering coefficient of the media, inwhich photons may propagate over a long distance before being absorbed.

Depending on the problem to be solved, the MC technique is used to simulateeither the diffuse reflectance or transmittance for one wavelength or for a wholespectrum; other optical characteristics at various experimental geometries also canbe modeled.1–3, 12–16, 29, 33, 41, 48, 129, 135, 196, 197, 290, 306, 309–373 Because the implicit pho-ton capturing technique is used during MC simulation, a photon packet with aninitial weight of unity is launched perpendicularly to the tissue surface along thelight beam direction for the problem of pencil beam propagation, and isotropicallyfor the problem of light distribution of an isotropic light source inserted into a tis-sue. Other geometries are also possible. Next, a step size is chosen statistically byusing the expression198

l = − ln(ξ)

μa + μs, (1.35)

where ξ is a random number equidistributed between 0 and 1 (0 < ξ ≤ 1). Becauseof absorption in the system, the photon packet loses some of its weight at the endof each step. The amount of weight lost is the photon weight at the beginning ofthe step multiplied by (1 − �), where � is the albedo [see Eq. (1.7)]. The pho-ton with the remaining weight is scattered. A new photon direction is statisticallydetermined by a phase function [see Eq. (1.13)], which, according to the scatteringanisotropy factor, g, can be determined in the form of the Henyey–Greenstein pos-tulated function [see Eq. (1.15)]. A new step size is then generated by Eq. (1.35)and the process is repeated. When the photon does try to leave the medium, theprobability of an internal reflection is calculated by using Fresnel’s equation.296, 327

When the photon weight is lower than a preset threshold (usually 10−4), a form ofRussian roulette is used to determine whether the photon should be terminated orpropagated further with increased weight. If the photon packet crosses the sur-face boundary into the ambient medium, the photon weight contributes to thediffuse reflectance or transmittance. If a reflection occurs, then the photon packet isreflected the appropriate distance back into the medium and migration continues.Otherwise, the migration of that particular photon packet halts, and a new pho-ton is launched into the medium at the predefined source location. Multiple photonpackets are used to obtain statistically meaningful results; at present, 1–100 millionphoton packets are usually used. For example, 3D MC code, designed for photonmigration through complex heterogeneous media, allows one to obtain a signal-to-noise ratio greater than 100 for up to distances of 30 mm by using a 1 mm2 detectorwith 108 photons propagated within 5–10 hours of computing on a computer with1 GHz CPU.342


20 Chapter 1

Although advanced computer facilities and software systems have reducedthe necessary time, further developments in laser diagnostic and therapeutic toolsrequire more effective, relatively simple, and reliable algorithms of the MCmethod. For instance, the condensed MC method allows one to obtain the solutionfor any albedo based on the results of modeling for a single albedo, which substan-tially facilitates computation.320 Additionally, the development of very economicalhybrid models currently underway is intended to combine the accuracy of the MCmethod with the high performance of diffusion theories or approximating analyticexpressions.290, 319, 326, 327

The original MC code, allowing one to obtain information required to recon-struct an internal structure of highly scattering objects with size of 1000 scatteringlengths or more, was recently designed based on the path-integration techniqueand Metropolis algorithm.374, 375 The path-integral apparatus first suggested byFeynman for the alternative description of quantum mechanics can also be usedto describe the movement of photons in a turbid medium as if they are particlesundergoing collisions at a given collision frequency with mean deflection in trajec-tory per collision.376–382 The integral over all possible paths using a set of nestedintegrals is called a path integral. This approach offers analytical solutions to theRTE in the framework of Perelman’s approximation that is valid for relatively weakscattering.377 The path-integral model described in Ref. 376 is derived from firstprinciples and does not include Perelman’s approximation. The path-integral tech-nique was applied to numerical calculations in the model of a photon random walkwithin a 3D discrete grid.382 In the context of the MC approach, the path-integraltechnique may be viewed as an extreme form of variance reduction, in which,instead of determining the most likely paths by random sampling, the path-integralformalism sets out to identify them directly.374–376 Therefore, the elimination ofuninformative photon paths from the calculations may provide a few-orders-highercalculation rate.374, 375

Let us consider human skin optics as an example.6, 37, 38, 57, 306, 315, 316, 318, 321–325,

333, 334, 340, 343, 383–388 To calculate distributions of the radiant flux density, F(r), andthe total radiant energy fluence rate, U(r), by the MC method [see Eqs. (1.11) and(1.12)], let us represent the skin as a plane multilayer scattering and absorbingmedium (Fig. 1.10) with a laser beam falling normally onto its surface. Let usfurther assume that each ith layer is characterized by the following parameters:μai; μsi; pi(θ); thickness, di; and refractive index of the filler medium, ni. A moregeneral approach to MC simulation, which accounts for the interfaces between thedermal layers as quasi-random periodic surfaces and spectral skin response, is alsoavailable.340, 343

Using the MC algorithm described in Refs. 306, 318, and 323–325 to simulatethe distribution of Gaussian light beams in the skin (see Fig. 1.10 and Table 1.1), thetotal fluence rate at wavelengths of 337, 577, and 633 nm was obtained, as shownin Fig. 1.11, along with the dependencies of the maximum total radiant energy flu-ence rate, Um, and the maximum fluence rate area, D|| × D⊥, on the incident beamradius, r0, at 633 nm (Fig. 1.12). D|| and D⊥ are defined at the 1/e2 level of U alongand across the incident light beam, respectively. It is clear that the illumination



Figure 1.10 Model of the human skin (see Ref. 306).

maximum is formed at a certain depth inside the tissue and that the total fluencerate at the point of maximum Um may be significantly higher than that in the mid-dle of the beam incident to the surface of the medium (U0). This was noticed bymany authors (for instance, Refs. 1, 3, 6, 37, and 303), who emphasized the strongcorrelation between the Um/U0 ratio and the optical properties of the medium, theincident beam radius, and boundary properties. It appears from Fig. 1.12(b) that anincrease in the incident beam radius leads to a broadening of the illuminated area

Table 1.1 Optical parameters of skin (see Refs. 6 and 306).

N Skin layer λ, nm μa, cm−1 μs, cm−1 g n d, μm

1 Epidermis 337 32 165 0.72 1.5 100577 10.7 120 0.78 1.5633 4.3 107 0.79 1.5

2 Dermis 337 23 227 0.72 1.4 200577 3.0 205 0.78 1.4633 2.7 187 0.82 1.4

3 Dermis with 337 40 246 0.72 1.4 200plexus 577 5.2 219 0.78 1.4superficialis 633 3.3 192 0.82 1.4

4 Dermis 337 23 227 0.72 1.4 900577 3.0 205 0.78 1.4633 2.7 187 0.82 1.4

5 Dermis with 337 46 253 0.72 1.4 600plexus 577 6 225 0.78 1.4profundus 633 3.4 194 0.82 1.4


22 Chapter 1

Figure 1.11 Results of Monte Carlo simulation of the total radiant energy fluence rate dis-tribution, U (W/cm2), in skin irradiated by Gaussian laser beams with different wavelengths(λ = 633, 577, and 337 nm), equal radius on the skin surface (r0 = 1.0 mm), and equalintensity at the beam center (U0 = 1W/cm2) (see Ref. 6). z is the linear coordinate (depthinside the skin); r is the coordinate across the light beam or along the skin surface.

inside the tissue, with the enhancement rate in the transversal direction exceedingthat along the beam.

For practical purposes, such calculations for the human skin and other mul-tilayered soft tissues are necessary to correctly choose the irradiation doses forphotochemical, photodynamic, and photothermal therapy of cancer and many otherdiseases and the for laser coagulation of the superficial blood vessels or transscleralcyclophotocoagulation.2, 3, 10–16, 22, 29, 32, 33, 37, 57, 72, 90, 91, 303, 323–325, 386–394

In particular, based on the results of MC simulation presented in Figs. 1.11and 1.12, attenuation of a wide laser beam of intensity I0 at depths z > ld = 1/μeff

[see Eq. (1.18)] in a thick tissue may be described as

I(z) ≈ I0bs exp(−μeffz), (1.36)

where bs accounts for additional irradiation of upper layers of a tissue due tobackscattering (photon recycling effect). Thus, the depth of light penetration into atissue is

le = ld[ln bs + 1]. (1.37)

Typically, for tissues bs = 1–5 for a beam diameter of 1–20 mm.303, 391 Thus,when wide laser beams are used for irradiating highly scattering tissues with lowabsorption, CW light energy is accumulated in tissue owing to the multiplicity ofchaotic long-path photon migrations. A highly scattering medium works as a ran-dom cavity, providing the capacity of light energy. The light power density withinthe superficial tissue layers may substantially (up to fivefold) exceed the incidentpower density, causing overdosing during photodynamic therapy or overheating atinterstitial laser thermotherapy. On the other hand, the photon recycling effect canbe used for more effective irradiation of undersurface lesions at relatively smallincident power densities.



Figure 1.12 Parameters of the maximum illumination area as functions of the incident beamradius. A beam with a Gaussian profile, wavelength 633 nm, power 25 mW. 1, total illumi-nation in the center of the incident beam U0; 2, maximal total illumination Um; 3, Um/U0(a). 1, size of the maximally illuminated area (at the 1/e2 level) along the beam axis, D||;2, size of the maximally illuminated area (at the 1/e2 level) across the beam axis D⊥ (b)(see Ref. 306).

Most current and recently developed MC studies have used the publicallyavailable MCML code (developed by Wang and Jacques) or its modified ver-sion.196, 290, 319, 326, 327 The MCML is based on the reduction of photon weightvariance; i.e., the weight of each photon packet during the propagation within amedium is exponentially attenuated according to scattering and absorption coeffi-cients of the medium. When the actual weight, W, becomes too small, the so-calledRussian roulette technique is applied, which gives each photon packet a chance,m, to survive with weight of m × W. This approach was originally used forcounting fluence rate distribution and intends to balance the energy of incidentradiation with that of radiation absorbed and scattered within the medium. Thisassignment of additional weight to randomly selected photon packets results inunjustified increasing of their path lengths within the medium. This affects thefinal distribution of the photon paths and adds uncertainty to the method.


24 Chapter 1

Another approach, which combines the statistical weight scheme with the sim-ulation of effective optical photon paths, is used in Ref. 338. The simulation isbased on modeling a large number of possible trajectories of the photon packets,from the area of photon injection into the medium to the site where the photonpackets leave the medium. The initial and final states of the photons are entirelydetermined by the source and detector geometries, numerical apertures, spatialdistribution of the intensity of incident light, and detector sensitivity. Assumingthe independence of absorption and scattering along the photon trajectory allowsthese events to be separately simulated. Therefore, during propagation withina medium, the weight of each photon packet is attenuated only due to partialreflection and/or refraction on the medium boundaries; i.e., total internal reflec-tion is taken into account.348 Thus, by accumulating a sufficient number of photonpackets (∼106 − 108) between source and detector areas, the statistical weight ofeach photon packet is recalculated by exponential attenuation according to its totalpath length and absorption coefficient of the medium. This allows for rapid recal-culation of the intensity for a set of the medium absorption assigned for particularwavelengths. Thus, spectra of human skin and other biological tissues, fluores-cence spectra, and optical coherence tomography (OCT) images, can be easilysimulated. The great advantages of this approach are that the time for simulationis independent of the absorption of the medium and that this modeling avoids theenergy conservation problem occurring in roulette-based MC techniques. With fur-ther recent developments, this MC approach has been generalized for a number ofapplications and is available online.370, 371

MC simulation is widely used for calculating the fluorescence of biological tis-sues. Models proposed in Refs. 347 and 349 suggest that the fluorescence emitteduniformly from scattering centers in random directions. The algorithm describedin Ref. 350 takes into account the spatial distribution of fluorophores in tissue,using skin as a particular example. MC algorithms for calculating the reflectancespectra of the skin can be found in Refs. 338 and 340, and in Ref. 351 for clearedskin. Coherent effects in multiple-scattering media were included in MC simula-tion by the authors of Refs. 352 and 353. An MC algorithm for modeling imagetransformation in a dispersive medium is presented in Ref. 359. The simulationof two-dimensional (2D) OCT images accounting for polarization, coherence oflight, and formation of speckles can be found in Refs. 362 and 367. The firstobject-oriented unified MC algorithm using CUDA NVIDIA GPU technology,which is suitable for many applications in tissue optics and biophotonics, includ-ing the calculation of skin color, reflection spectra, and polarization characteristics,is described in Ref. 370. It can also be found in Wikipedia and other onlinesources (www.biophotonics.ac.nz).

The migration of photons in human head tissues studied by the MC methodhas been described in Ref. 342. A detailed comparison of three different MC mod-els was conducted in Ref. 354. An efficient MC algorithm for the description oflaser Doppler flowmetry of blood in the skin is presented in Ref. 365. An MCMLalgorithm has been adapted for GPU parallel computing by the authors of Ref.364 (included in Wikipedia). A quantitative description of the optical properties of



blood using the inverse MC algorithm (IMC) has been given in Refs. 230, 345,and 346. Data were obtained for the absorption and scattering coefficients (μa

and μs), and for the scattering anisotropy factor, g, of human blood in differentphysiological states. Additionally, an IMC algorithm was developed for the anal-ysis of optical parameters of blood in flow.48 The observed changes in the opticalproperties of blood in flow were attributed to the deformation, distribution, andorientation of red blood cells due to shear stresses in the flow of these particles.However, conventional MC algorithms309–311, 318, 327, 348, 356–358 cannot account forthe real interaction of photons with erythrocytes. In particular, they cannot quan-titatively describe the observed phenomena or reliably determine the scatteringanisotropy factor. Obviously, because of the complex shape of the erythrocyte, scat-tering of a photon from an erythrocyte depends on the incident angle of the photonon the red blood cell. The erythrocyte is also deformed during its movement, whichfurther complicates the interaction of photons with the cell. In Refs. 357 and 358,an MCML algorithm using the Henyey–Greenstein phase function was proposedto model the scattering of photons by erythrocytes. Detailed studies of the influ-ence of the scattering phase function in MC simulations are presented in Refs. 360and 361.

To overcome these problems, a promising approach is based on a detailedaccount of the interaction of photons with cells, designated the photon-cell interac-tive MC (pciMC) algorithm, which tracks photon migration in the region outsideand inside the cell without the need for the macroscopic scattering phase functionor scattering anisotropy factor.368 In this MC algorithm, 3D doubly concave ery-throcytes are determined by the input parameters, including volume, shape, andhematocrit. Because erythrocyte dimensions are much larger than the wavelengthof the probing light, and hemoglobin is uniformly distributed within the cell, theinteraction of photons with an erythrocyte is described by geometrical optics. Thus,this MC algorithm accounts for changes in the nature of the scattering of photonscaused by changes in cell volume, its shape and orientation, and the hemoglobincontent in the cell.

IMC algorithms used for reconstructing the optical parameters of biologi-cal tissues and the rate of blood flow in the vessels by measuring static anddynamic reflection spectra can be found in reviews.344, 372 They are also presentedin Chapter 7, devoted to the description of methods and algorithms for determiningthe optical parameters of biological tissues.

1.2 Short Pulse Propagation in Tissues

1.2.1 Basic principles and theoretical background

Based on the time-dependent RTT, it is possible to analyze the time responseof scattering tissue. This analysis is critical to provide a rationale for non-invasive optical diagnostic methods by using the time-resolved measurementof reflectance and transmittance in tissues.1, 3, 6, 31, 42, 44, 71, 92, 129, 130, 139, 196, 197, 206, 290,

291, 294, 296, 374–382, 395–428 In its general form, the time-dependent RTT equation fortime-dependent radiance (or specific intensity), I

(r, s, t

), can be written as395, 427


26 Chapter 1

Figure 1.13 Ultrashort laser pulse propagating through random medium spreads into adiffuse component, a snake with zigzag paths, and a ballistic component (see Ref. 1).

∂

∂SI(r, s, t

) + μtt2∂

∂tI(r, s, t

) = −μt I(r, s, t

)+

μs ×∫

4π

[∫ t

−∞I(r, s, t

)f(t, t′

)dt′

]p(s, s′) d�′ + S

(r, s, t

). (1.38)

Compared with the CW equation [Eq. (1.9)], the following notation is intro-duced into Eq. (1.38): t is time; t2 = l/(μtc) is the average interval betweeninteractions, where c is the velocity of light in the medium; f (t, t′) describes thetemporal deformation of a δ-shaped pulse following its single scattering, and canbe represented in the form of an exponentially decaying function

f (t, t′) = 1

t1exp

(− t − t′

t1

), (1.39)

where t1 may be a function of r; and t1 is the first moment of the distributionfunction f (t, t′), which describes the time interval of an individual scattering act att1 → 0, f (t, t′) → δ(t – t′). The radiance, I(r, s, t), in Eq. (1.38) contains two compo-nents: attenuated and diffuse incident radiation. This equation meets the boundaryconditions [see Eq. (1.10)] at (r, s) → (r, s, t).

When probing the plane-parallel layer of a scattering medium with an ultra-short laser pulse, the transmitted pulse consists of a ballistic (coherent) component,a group of photons having zigzag trajectories, and a highly intensive diffuse com-ponent (see Fig. 1.13).1, 3, 6, 31 Both unscattered photons and photons undergoingforward-directed single step scattering contribute to the intensity of the ballisticcomponent (composed of photons traveling straight along the laser beam). Thiscomponent is subject to exponential attenuation with increased sample thickness[see Eq. (1.1)]. This accounts for the limited utility of ballistic photons for practicaldiagnostic purposes in medicine.

The group of snake photons with zigzag trajectories includes photons that haveeach experienced only a few collisions. They propagate along trajectories that devi-ate only slightly from the direction of the incident beam and form the initially



Figure 1.14 Typical schemes for time-resolved tissue studies (see Ref. 1): recording trans-mitted photons (a), backscattering regime (b). A, probing beam; B, detected radiation. Thedark area in the center of the scattering layer is a local inhomogeneity (tumor). Spatial andtemporal photon distributions in the medium are shown.

arriving part of the diffuse component. These photons carry information about theoptical properties of the random medium and the parameters of any foreign objectthat they may encounter during their progress.

The diffuse component is very broad and intense because it contains the bulkof incident photons after they have participated in many scattering acts, and there-fore, migrate in different directions and have different path lengths. Moreover, thediffuse component carries information about the optical properties of the scatter-ing medium, and its deformation may reflect the presence of local inhomogeneitiesin the medium. The resolution obtained by this method at a high light-gatheringpower is much lower than in the method measuring straight-passing photons. Twoprobing schemes are conceivable, one recording transmitted photons and the othertaking advantage of their backscattering (see Fig. 1.14).

In the diffusion approximation (valid at μa � μ′s), if the tissue is homogeneous

and semi-infinite, the size of both the source and detector is small compared withthe distance, rsd, between them at the tissue surface, and the pulse may be regardedas single, then the light distribution is described by the time-dependent diffusionequation398, 399 (

∇2 − cμaD−1 − D−1 ∂

∂t

)U(r, t) = −Q(r, t) , (1.40)

which is, in fact, the generalization of the CW [Eq. (1.17)]. The diffusion equationis equivalent to the equation for thermal conductivity.412 The solution of Eq. (1.40)yields the following relation for the number of backscattered photons at the surfacefor unit time and from unit area R(rsd, t):398, 399

R(rsd, t) = z0

(4πD)3/2 t−5/2 exp

(−r2

sd + z20

2Dt

)exp(−μact) , (1.41)


28 Chapter 1

correspondingly, for transmittance,

T(rsd, d, t) = (4πD)−3/2t−5/2 exp

(− r2

sd

4Dt

){(d − z0)exp

[−d − z0)2

4Dt

]

−(d + z0)exp

[−d + z0)2

4Dt

]+ (3d − z0)exp

[−3d − z0)2

4Dt

]

−(3d + z0)exp

[−3d + z0)2

4Dt

]}exp(−μact), (1.42)

where z0 = (μ′s)

−1 and d is the tissue thickness.In practice, μa and μ′

s are estimated by fitting Eqs. (1.41) or (1.42) withthe shape of a pulse measured by the time-resolved photon counting technique.Experimentally measured optical parameters of many tissues and model mediaobtained by the pulse method can be found in Refs. 1, 3, 6, 12–15, 31, 88, 89,129, 130, 139, 206, 342, 372, 399–415, and 426. An important advantage ofthe pulse method is its applicability to in vivo studies, owing to the possibilityof the separate evaluation of μa and μ′

s by using a single measurement in thebackscattering or transillumination regimes. A search is underway for more ade-quate approaches to describing tissue responses to laser pulses (see, for instance,Refs. 206, 291, 292, 295, 296, 374–382, and 417–428). Many publications aredevoted to image transfer in tissues and the evaluation of the resolving powerof optical tomographic schemes making use of the first-transmitted photons ofultrashort pulses.1, 3, 6, 71, 129, 130, 139, 342, 396, 397, 405–410, 420, 423–428

1.2.2 Techniques for time-resolved spectroscopy and imaging

The primary principle of enhanced viewing through turbid medium (tissue) usinga time-resolved approach is accurately illustrated in Fig. 1.15.1, 31 A contrastimage of an object in a scattering medium can be provided by electronic oroptical time-gating of the earliest-arriving, minimally scattered light (ballisticand snake photons), which contains geometric information.1, 3, 31, 71, 139 The typicaloptical schemes using the selection of the earliest-arriving photons are pre-sented in Figs. 1.16 and 1.17. The first group of schemes (see Fig. 1.16) usesthe electronic time-gating procedure. The time-correlated single-photon countingtechnique explores a high-repetition-rate picosecond laser (for example, a cavity-dumped mode-locked dye laser). Upon the detection of the first arriving photons,the time delay is measured with a time-to-amplitude converter [see Fig. 1.16(a)],and a histogram of the arrival times is created by using a large number of lowenergy pulses. The time resolution for such a technique is limited to approximately50 ps. For more energetic pulses from lasers with a lower repetition rate, the usageof streak cameras allows for a time resolution down to 1 ps [see Fig. 1.16(b)]. Ifa Synchroscan streak camera is employed, a high repetition rate source with lowenergy pulses can even be used.

The second group of techniques uses optical nonlinear effects to select photons(see Fig. 1.17).1 For a scheme with an optical Kerr gate, an energetic laser is used.



Figure 1.15 Gated viewing through tissue. Enhanced spatial resolution is obtained byselecting “early” light only (see Ref. 1).

Figure 1.16 Techniques for electronically gated viewing (see Ref. 1).

Part of the pulse is transmitted into the tissue and part is used to open the shutter byutilizing the optical Kerr effect (the cell with CS2) [see Fig. 1.17(a)]. Because thegate width is determined only by the length of the laser pulse, subpicosecond gatetimes can be achieved. The Raman amplifier gating technique also uses energeticlaser pulses. A Stokes wave generated by stimulated Raman scattering in a gas cell


30 Chapter 1

Figure 1.17 Gated-viewing technique using nonlinear optical phenomena (see Ref. 1): CS2is the optical Kerr cell filled by CS2; KDP is the nonlinear crystal for frequency doubling.

is used to probe the tissue [see Fig. 1.17(b)]. The low-intensity transmitted lightis amplified in a Raman amplifier, which, in turn, is pumped by an ultrashort laserpulse. This pulse has the proper time delay to strobe on the desired early tempo-ral part of the light under investigation. The third scheme uses a time-correlatedfrequency doubling technique and is frequently used in optical autocorrelators formonitoring laser pulse characteristics [see Fig. 1.17(c)]. It can be directly used foroptical gating of signal photons.

1.2.3 Coherent backscattering

The use of ultrafast laser pulses generates a local peak of intensity backscatteredwithin a narrow solid angle, owing to scattered light interference.31, 73, 74 In theexact backward direction, the intensity of the scattered light is normally twice thediffuse intensity. This coherence interference arises from the time reversal sym-metry among various scattered light paths in the backscattering direction. Thisphenomenon is known as weak localization. The profile of the angular distributionof the coherent peak depends on the transport mean path, ltr, and the absorptioncoefficient, μa. The angular width of the peak is directly related to ltr:74

�θ ≈ λ/(2πltr). (1.43)



The backscattered coherent peak occurs when the probing laser pulse is shorterthan 20 ps in many hard and soft tissues, such as human fat tissue; lung cancertissue; normal and cataractous eye lens; and myocardial, mammary, and dentaltissues.74

1.3 Diffuse Photon-Density Waves

1.3.1 Basic principles and theoretical background

The frequency-domain (FD) method has been proposed for photon migrationstudies in scattering media. This method is designed to evaluate the dynamicresponse of scattered light intensity to modulate the incident laser beam inten-sity in a wide frequency range, usually in tissue research using 50 to 1000MHz.1, 3, 4, 6, 10, 52, 53, 71, 129, 130, 139, 206, 411, 412, 427–465 The FD method measures themodulation depth of scattered light intensity, mU ≡ ACdetector/DCdetector (seeFig. 1.18), and the corresponding phase shift relative to the incident light modula-tion phase, �� (phase lag). Compared with the time-domain (TD) measurementsdescribed earlier, this method is more simple and reliable in terms of data interpre-tation and immunity from noise. This is because FD equipment involves amplitudemodulation at low peak powers and slow rise time [compare Figs. 1.18(a) and1.18(b)], and hence, smaller bandwidths than TD instruments; higher signal-to-noise ratios are also attainable. Medical FD equipment is more economic andportable, and can be built on the basis of measuring devices used in optical telecom-munication systems and in studies of optical fiber dispersion.4, 139, 456 However, theFD technique suffers from the simultaneous transmission and reception of signalsand requires special attempts to avoid unwanted crosstalk between the transmittedand detected signals. The current measuring schemes are based on heterodyning ofoptical and transformed signals.1, 3, 4, 6, 10, 52, 53, 71, 129, 130, 139, 411–416, 427–451, 462, 463

The development of the theory underlying this method resulted in the discoveryof a new type of wave: photon-density waves or waves of progressively decayingintensity. Microscopically, individual photons make random migrations in a scat-tering medium, but collectively, they form a photon-density wave at modulationfrequency ω that moves away from a radiation source (see Figs. 1.18 and 1.19).Diffuse waves of this type are well known in other fields of physics (for example,thermal waves are excited upon absorption of modulated laser radiation in vari-ous media, including biological5, 6, 25). Photon-density waves possess typical waveproperties, e.g., they undergo refraction, diffraction, interference, dispersion, andattenuation.1, 3, 4, 6, 52, 53, 71, 129, 130, 139, 411, 427, 429, 433–436, 439–441, 462

In strongly scattering media with weak absorption far from the walls and asource or receiver of radiation, light distribution may be regarded as a decayingdiffusion process described by the time-dependent diffusion equation for pho-ton density [see Eq. (1.40)]. When a point light source with harmonic intensitymodulation is used, placed at the point r = 0,

I(0, t) = I0[1 + mI exp(jωt)], (1.44)

where mI is the intensity modulation depth of the incident light.


32 Chapter 1

Figure 1.18 Schematic representation of the time evolution of the light intensity measuredin response to a very narrow light pulse (a) and a sinusoidally intensity-modulated lighttransversing an arbitrary distance in a scattering and absorbing medium (b). (a) If themedium is strongly scattering, there are no unscattered components in the transmittedpulse. (b) The transmitted photon density wave retains the same frequency as the incomingwave in the medium. The reduced amplitude (ACdetector) and shift of modulation phase(��) of the transmitted wave arises mostly from attenuation related to scattering. Thedemodulation is the ratio ACdetector/DCdetector normalized to the modulation of the source

ACsource/DCsource (see Ref. 440).

The solution of Eq. (1.40) for a homogeneous infinite medium can be presentedin the following form:71

U (r, t) = Udc(r) + Uac (r,ω) exp(jωt) , (1.45)

where

Udc = I0

4πcDrexp

(− r

ld

), (1.46)

Uac (r,ω) = Uac (r,ω) exp{−ikr (ω) r} , (1.47)



Figure 1.19 Schematic representation of propagation of photons in scattering mediainduced by a CW (a), pulse (b), and sinusoidally intensity-modulated light sources (c) (seeRef. 441).

Uac (r,ω) = mI

[I0

4πcDr

]exp {−ki (ω) r} , (1.48)

ω = 2πν is the modulation frequency, ld = μeff−1 is the diffusion length [see

Eq. (1.18)], and kr(ω) and ki(ω) are the real and imaginary parts of the photon-density wave vector, respectively:

k = kr − iki = −i

[μac + iω

cD

]0.5

, (1.49)

kr,i = 1

ld

{[1 + (ωτa)

2]0.5 ∓ 1

2

}0.5

, (1.50)

μac = 1

τa, (1.51)

where τa is the average travel time of a photon before it is absorbed.An alternating component of this solution is an outgoing spherical wave with

its center at the point r = 0, which oscillates at modulation frequency ν andundergoes a phase shift relative to the phase value at point r = 0 equal to

�� = kr(ω)r. (1.52)

Constant and time-dependent components of the photon-density wave fall with dis-tance as exp(–r/ld) and exp[– ki(ω)r], respectively. The length of a photon-densitywave is defined by


34 Chapter 1

�� = 2π

kr= 2π

ω

{2c2Dμa

(1 + [

1 + (ωτa)2]0.5

)}0.5, (1.53)

and its phase velocity is

V� = ��ν. (1.54)

It follows that photon-density waves are capable of dispersion.For biomedical applications, particularly optical mammography, we can easily

estimate that, for ω/2π = 500 MHz, μ′s = 15 cm−1, μa = 0.035 cm−1, and c =

(3.1010/1.33) cm/s, the wavelength is �s∼= 5.0 cm and the phase velocity is Vs

∼=1.77 × 109 cm/s.

For weakly absorbing media, when ωτa � 1,

�2� = 8π2 cD

ω, (1.55)

V2� = 2cDω, (1.56)

mU (r,ω) ≡ Uac (r,ω)

Udc (r)= mI exp

(r

√μa

D

)exp

(−r

√ω

2cD

), (1.57)

��(r,ω) = r( ω

2cD

)0.5. (1.58)

It is clearly follows from Eq. (1.57) that to support transport of a photon-densitywave in a medium, light scattering is needed (see first exponential term); incontrast, high scattering decays a photon density wave (see second exponentialterm).

Measuring mU(r,ω) and ��(r,ω) allows one to separately determine thetransport scattering coefficient, μ′

s, and the absorption coefficient, μa, and toevaluate the spatial distribution of these parameters.

1.3.2 Principles of FD spectroscopy and imaging of tissues

Evidently, there is a close relationship between the two time-resolved methods forthe assessment of optical properties of tissues. In the case of pulse probing of ascattering medium, Fourier instrumental or computer-aided analysis of scatteredpulses allows us to simultaneously obtain the amplitude-phase responses of themedium for a continuous set of harmonics.1, 3, 4, 71, 139, 206, 412, 427–429, 437 Figure 1.20illustrates the typical behavior of the amplitude-phase response in a tissue-likephantom (whole or diluted milk).71 Such characteristics are useful for the spec-troscopic examination of tissues, e.g., for in vivo evaluation of hemoglobinoxygenation449, 466 or blood glucose level.467–469

The spatial resolution available using photon-density waves is crucial forthe visualization of macro-inhomogeneities. Theoretical considerations illustratedby Fig. 1.21 for two absorbing macro-inhomogeneities in a scattering mediumprovide evidence that their separate identification is feasible if the accuracy ofthe phase and wave amplitude measurements is not less than 1.0 and 2.0%,



Figure 1.20 Amplitude (a) and phase (b) responses of a model medium [unskimmed (1, 3)and 40% diluted (1.2) milk] obtained by the Fourier transformation of experimental pulseresponses; 1, 2, recording transmitted pulses, 2-cm-thick cuvette; 3, backscattering regime(large volume of unskimmed milk). The distance between irradiating and detecting opticalfibers is rsd = 2 cm (see Ref. 71).

respectively.436, 458 The predicted resolving power of diffuse tomography usingphoton-density waves is close to 1 mm; i.e., it is comparable to that of positronemission and magneto-resonance tomography.4, 411 Important advantages of opti-cal tomography are technical simplicity, enhancement of an object’s contrast byusing molecular dyes, and visualization of local metabolic processes.

Figure 1.22 presents images of tumor-containing female breast tissue outlinedby contour lines for μa and μ′

s, which were obtained by exposure to modulatedvisible and NIR radiation.71 The tumor is readily discernible because of its highabsorption and scattering coefficients.

In principle, a record-breaking resolving power of less than 1 mm can beachieved by taking advantage of the interference of photon-density waves excitedby spaced sources.4, 53, 428, 458, 470 Not only high spatial resolution, but also high con-trast and low sensitivity to the movements and geometry of the object under study,should be provided to achieve a high-quality image. A tissue immersion techniquecan be used to improve image quality.4, 53, 129, 428, 452, 456, 458, 470 When the imagedtissue is surrounded by a medium of matching scattering and absorption proper-ties, a uniform transillumination image is obtained, and the maximum dynamicrange is available to examine variations within the tissue. In addition, this allowsone to eliminate the influences of boundary conditions and geometry for objectswith complex shapes and structures. It also allows one to achieve optical match-ing of the probe laser beam with the tissue to considerably reduce the influenceof external and internal movements (breathing, heartbeats, or muscle tremors) of


36 Chapter 1

Figure 1.21 Theoretical distributions of the relative phase shift and intensity modulationat 200 MHz in an irradiated system of two absolute absorbers (balls 0.5 cm in diameter)placed in a homogeneous scattering medium (μ′

s = 10 cm−1, μa = 0.02 cm−1). The sourceis located at the origin and the absorbers located at points (–2, 4) and (2, 4) (see Ref. 436).

Figure 1.22 Reconstructed optical images of human cancerous breast tissue obtained byexposure to modulated radiation in the visible and NIR wavelength regions. Image outlinedby contour lines for the absorption coefficient μa (10−2 cm−1) (a). Same for the trans-port scattering coefficient μ′

s (cm−1) (b). The tumor is located near the point (70, 10); thecoefficients have relative values (see Ref. 71).



the object during the imaging process, and to calibrate measurements using well-known optical properties of the immersion medium. Sometimes, such a simpletechnique is a satisfactory alternative for more sophisticated imaging techniquesbased on multifrequency analysis.

Apart from the visualization of macro-inhomogeneities of breast tissues, theFD method is useful for examining other tissue, e.g., brain and lungs. It alsoprovides insights into many physiological processes dependent on oxygen con-sumption by tissues and organs and related hemodynamic changes. One of the mostimportant areas of application may be the evaluation of the oxygen distributionin a functioning brain.4, 411, 428, 429 Another example is the monitoring of neoplas-tic growth patterns, including enhanced blood volume and blood deoxygenation,increased intracellular organelle content, and tissue calcification, which may becritical for the differentiation between benign and malignant tumors.411, 428, 429

To conclude, it should be emphasized that high tissue density occasionallynecessitates considering the time interval of an individual scattering act, t1 [seeEqs. (1.38) and (1.39)], which may prove comparable to the mean time intervalbetween interactions, t2.427, 455 Moreover, the widely used diffusion approxima-tion imposes important constraints on the analysis of the optical properties oftissues. Therefore, the development of more universal models of photon-densitywave dispersion is in progress using new MC algorithms.427–429, 455

1.4 Spatially Modulated Light Propagation in Tissues

1.4.1 Introduction

As we have discussed, light transport in tissues is a complex process owing tomultiple scattering and absorption. Thus, at the core of every optical techniquefor quantitative tissue characterization is the ability to separate optical absorp-tion from optical scattering effects by the detection of a remitted or transmittedlight field. This remission (or transmission) is a function of time and space, yield-ing two general classes of quantitative techniques: time resolved and spatiallyresolved measurements, respectively (see Fig. 1.23). As we already discussed,time-resolved measurements are further broken down into TD and FD techniques:the first measuring the temporal point-spread function (t-PSF), or spreading of apropagating pulse in time (see Section 1.2),31, 72 and the latter measuring the tem-poral modulation transfer function (t-MTF), or the attenuation and phase delayof a periodically varying photon density wave (see Section 1.3).435, 437, 438, 440, 441

The TD and FD share an exact Fourier transform equivalency, although eachhas its compromises when considering real-life hardware and model-fittingconstraints.

In diffuse optics, spatially resolved measurements have been generally limitedto multidistance measurements, tracking the spatial dependence of a reflected ortransmitted light field generated from a point-like illumination, for which opticalfibers are often used. Here, the spatial point-spread function (s-PSF) is character-ized by the spatial dependence of a reflected or transmitted light field generated


38 Chapter 1

Figure 1.23 Four measurement domains characterizing scattering tissues: time domain(top left), time frequency domain (bottom left), real spatial domain (top right), and spatialfrequency domain (bottom right) (see Ref. 479).

at a point-like illumination [see Section 1.1 and Eq. (1.33)].285, 298 The Fouriertransform equivalent to the real spatial domain is the spatial-frequency domain(SFD). In diffractive optics, spatially structured illumination techniques are usedfor manipulating optical images (see, for example, Ref. 471). Spatially modulatedlaser beams have been effectively used in studies of scattering objects, includingsamples of tissues and blood (see Section 8.3).472, 473 This technique was primarilyapplied to investigate low-scattering objects or thin tissue slices and blood layers.However, it was successfully approved for the investigation of whole cataractoushuman eye lenses at averaging of interferential fringes (see Section 13.7).472, 473

The interactions of spatially modulated light beams with diffuse media aredescribed in Refs. 474–483. Typically, these are not laser beams, but insteadbeams from low-cost incoherent conventional white light sources. Such interac-tions are discussed in the framework of application to quantification and imagingof strongly scattering tissues. Spatially modulated imaging (SMI) provides awide-field mapping of turbid media in the SFD. The spatial modulation transferfunction (s-MTF) of a turbid medium encodes both depth and optical propertyinformation, enabling both quantitation and tomographic imaging of the spa-tially varying medium optical properties.479 References 474–483 present detailedexposition and validation of the ability of SMI to quantitatively recover opticalproperties of homogeneous tissues. Similarly to time-resolved methods, the SMImethod can be described analytically using diffusion-based theory, or numeri-cally by using Monte Carlo simulations in the framework of a transport-basedapproach. The optical properties of tissues can be recovered by analysis withthe analytic diffusion model using an inversion method, such as the least-squaresmultifrequency fitting algorithm or the more rapid two-frequency lookup tableapproach.474–483



1.4.2 Theory and measurement of diffuse light spatial frequencyspectrum

1.4.2.1 Diffusion approximation

The concept of temporally modulated scalar photon-density waves induced inturbid media is well developed and features a wide spectrum of biomedicalapplications, including quantifying the optical properties of tissues and biomed-ical imaging. The major properties of temporal photon-density waves, such asdispersion, diffraction, and interference, have been demonstrated, thoroughly stud-ied, and used in practice (see Section 1.3). At the same time the concept ofspatially modulated photon-density waves, which can be considered as standingwaves, has primarily been accepted as a theoretical concept (i.e., as the Fouriertransform representation of spatial point sources and perturbations), rather thana practical measurement modality employing periodic illumination, despite cer-tain experimental achievements in tissue studies.472, 473 In this section, followingRef. 479, we will formulate the basic principles behind the generation of spa-tially modulated photon-density plane waves and describe their properties by usingspatial-frequency spectral representation. For the initial approximation, diffusiontheory will be used to determine valid analytical expressions for relatively largealbedo and small spatial frequencies; in the following subsections, based on MCmodeling of the transport equation, the results will be extended to low albedo andhigh spatial frequency regimes.

The time-independent form of the diffusion equation for a homogeneousmedium is given by Eq. (1.17). For semi-infinite geometry of the medium and anormally incident periodically modulated plane wave, as shown in Fig. 1.24, thesource function, Sd, from Eq. (1.17) can be presented in the following form:

Sd = Sd0 (z) cos (kxx + α) cos(kyy + β

)(1.59)

Figure 1.24 Schematic of modulated illumination source (in the x-direction only) and theresulting modulated internal fluence rate with the same frequency and phase (see Ref. 479).


40 Chapter 1

with spatial frequencies fx = (kx/2π) and fy = (ky/2π), and spatial phases α and β,extending infinitely in the tangential spatial dimensions, x and y, with somearbitrary dependence on depth, z.

If medium response is proportional to the input intensity (i.e., medium is lin-ear), this sinusoidal modulation will initiate a diffuse fluence rate with the samefrequency and phase:

U = U0 (z) cos (kx x + α) cos(ky y + β

). (1.60)

According to symmetry considerations for light normally incident onto a homoge-neous medium, there should be no lateral phase shift.477 Insertion of Eqs. (1.59)and (1.60) into Eq. (1.17) yields a one-dimensional (1D) second-order Helmholtzequation for the fluence rate as a function of depth, z:

d2

dz2U0 (z) − μ′2

eff U0(z) = −Sd0 (z)

D, (1.61)

where

μ′eff =

√μ2

eff + k2x + k2

y ≡ 1

δ′eff

. (1.62)

Here, a plane wave with both x and y modulation initiates a photon density wavepropagating with scalar attenuation coefficient μ′

eff. Although spatial anisotropymay exist in real tissues, for simplicity, we will focus on the characteristics of a 1Dprojection to understand scalar photon density wave attenuation in multiply scat-tering media. Consequently, the subsequent discussion considers a single nonzerospatial frequency along the x dimension only, k = kx, with constant illuminationalong y (ky = 0). A more complex anisotropic diffusion model for the trans-port of spatially modulated beams was also described,483 which showed that theeffects of anisotropy are independent from volumetric scattering and absorption ofa medium; thus, inclusions of isotropic and anisotropic scattering structures can beseparated.

At zero spatial frequency (k = 0), the effective light penetration depth into ascattering medium, δ′

eff, is equivalent to that of a planar (unmodulated) illumina-tion, δeff = (1/μeff). In general, however, μ′

eff (and δ′eff) are functions of both optical

properties and spatial frequency of illumination. The 1D form of Eq. (1.61) impliesthat the amplitude of the periodic wave, U0(z), is independent of the tangential spa-tial dimensions x and y. Because this equation is identical to the diffusion equationfor a planar illumination, we can use the existing planar geometry solutions ofEq. (1.17) by simply substituting μeff with the new μ′

eff term.To study planar photon-density wave reflectance, the expression derived in

Ref. 484 for an extended light source can be used:

Sd0 (z) = P0 μ′s exp(−μtr z) , (1.63)

where P0 is the incident optical power. Conceptually, this represents a spatiallydistributed but angularly isotropic source introduced via scattering of a collimated,forward-directed beam. The solution for the resulting fluence rate is



U0(z) = 3P0 �′(μ′

eff/μtr)2 − 1

exp(−μtr z) + C exp(−μ′

eff z)

, (1.64)

where �′ is the reduced albedo [see Eq. (1.25)], and C is a constant deter-mined by the choice of a boundary condition. Using the partial current boundarycondition,296 where the flux, j, is established proportional to the fluence at theinterface z = 0:

j

∣∣∣∣z→0+ ≡ −∇U|z→0+

3μtr= −AU

∣∣∣∣z→0+

, (1.65)

where the coefficient of proportionality

A = 1 − Reff

2 (1 + Reff), (1.66)

and effective reflection coefficient are determined by a mismatch of mean refractiveindex of the scattering medium related to surroundings, n, that for tissues primarilydepends on dispersion of the water/protein mixture:

Reff ≈ 0.0636n + 0.668 + 0.710

n− 1.440

n2. (1.67)

Constant C then becomes

C = − 3P0 �′ (1 + 3A)((μ′

eff/μtr)2 − 1

) (μ′

eff/μtr + 3A) , (1.68)

yielding the diffuse reflectance, Rd(k), as

Rd (k) = − j |z→0+

P0= 3A �′((

μ′eff/μtr

) + 1) (μ′

eff/μtr + 3A) . (1.69)

Although this formulation is for a pure 1D sinusoidal illumination pattern, anarbitrary illumination function can be modeled through linear superposition ofsinusoids in both the x and y directions. For a given set of optical parameters, thefunction Rd(k) specifies the diffuse s-MTF of the medium (see Fig. 1.23). The sim-plicity of Eq. (1.69) allows for the qualitative analysis of its properties. First, thespatial frequency dependence of Rd in the SFD is an inverse polynomial function ofa single, positively valued ratio, μ′

eff/μtr, which fully describes the low-pass spatialfiltering properties of homogeneous turbid samples within a steady-state diffusionprocess:

μ′eff

μtr=

√μ2

eff + k2

μ2tr

=√

3μa

μtr+ k2

μ2tr

. (1.70)


42 Chapter 1

For

k = 0 → μ′eff

μtr= √

3 (1 − �′),

k � μeff → μ′eff

μtr= k

μtr. (1.71)

The low- and high-frequency modes have differential sensitivity to absorption andscattering properties, respectively. At k = 0, Rd is solely a function of the reducedalbedo. In the additional limit of zero absorption, μ′

eff/μtr → 0 and Rd → 1, imply-ing that all incident photons are reflected back out of the turbid medium. Atlow spatial frequencies (k � μeff), the absorption has a maximal effect on thereflectance. Approaching the high-frequency mode (k � μeff) the denominatorμtr(≈μ′

s in the diffusion limit) becomes the only source of optical contrast. Bothlimits involve a ratio with respect to the transport coefficient, highlighting thenatural length scale of light transport, ltr = 1/μtr, the transport MFP.

The preceding fluence and reflectance expressions can be written in the dimen-sionless form of units of the transport spatial frequency, μtr, by the substitutions

μa = (μa · ltr), k = (k · ltr), and z = (z/ltr), where μ′eff =

(3μa + k2

)1/2and �′ ∼=(

1 − μa). The diffusion approximation to the radiative transport equation is valid

when

μ′s � μa (1.72)

and owing to the anisotropic nature of light scattering, has been observed to beaccurate approximately when

ρ � ltr, (1.73)

where ρ describes the distance from collimated sources. Depending on the mea-surement technique (modality, geometry, and calibration method) and chosenmetric of accuracy, the practical minimal limit of ρ is approximately in the rangeof 3ltr to 4ltr.288, 485 The spatial frequency analog of ltr is the transport spatial fre-quency, exactly equal to the transport spatial frequency (or transport coefficient),μtr = fx,tr = (ktr/2π). If we relate the inverse of ρ as a metric of spatial frequency,then Eq. (1.73) can be rewritten as

fx � μtr ≡ 1/ltr. (1.74)

Therefore, in diffuse approximation, accurately predicted maximal spatial fre-quency should be in the range from 1/(3ltr) to 1/(4ltr), or from 0.25μtr to 0.33 μtr.Both albedo and source distance requirements of the diffusion approximation limitthe ratio μ′

eff/μtr to much lower than 1.

1.4.2.2 Monte Carlo simulation

For a more explicit description of spatially modulated beam transportation in typ-ical tissues with a high scattering, it is desirable to derive solutions of a forward



problem in the SFD that are valid for a greater range of both albedo and spatial fre-quency than in diffusion theory. A few transport-based approaches are available,including both direct numerical solution of the radiative transfer equation275, 486

and statistical Monte Carlo simulation.41, 196, 319, 326, 327 The authors of Ref. 479used “white” Monte Carlo (WMC) simulations487, 488 of a collimated point sourceillumination to generate predictions of the spatially resolved, steady-state diffusereflectance, Rd(ρ), for a given set of optical properties μa, μs, and g. This s-PSFprovides an impulse medium response, and spatial frequency domain spectrum ofdiffuse reflectance, Rd(k), is found by Fourier transformation of Rd(ρ). For a radi-ally symmetric function such as Rd(ρ), the 2D Fourier transform in the x–y planereduces to a 1D Hankel transform of zero order:479

Rd(k) = 2π∫

ρJ0(kρ) Rd(ρ) dρ, (1.75)

where J0(kρ) is the zeroth-order Bessel function of the first kind. At simulations,ρ is binned in n finite intervals, �ρi. Then, Rd(k) is calculated as a series of theseintervals:

Rd(k) = 2π∑n

i=1ρiJ0(kρi) Rd(ρi) �ρi. (1.76)

In Ref. 479, the WMC data were generated by using 107 photons and a detectorwith numerical aperture of 0.22. In all simulations, the index of refraction, n, andanisotropy factor, g, were set to 1.33 and 0.71, respectively, for direct comparisonwith the Liposyn phantom experiments. All radial bins had a spacing of �ρ = 0.09mm, making the maximum spatial frequency greater than 5 mm−1.

1.4.2.3 Results of simulation

Diffuse reflectance curves on spatial frequency (mm−1) calculated on the basis ofdiffusion approximation (dashed lines) and MC simulations (solid lines) are plot-ted in Fig. 1.25 (top) for varying values of ltr at a constant ratio (μ′

s/μa) = 100 (orconstant �′ = 0.99).479 It is clear that as ltr increases (or μtr decreases), the diffuses-MTF is rescaled toward lower spatial frequencies, indicating that lower frequencycontent is preserved. This scaling with ltr is consistent with experimental results,479

in which high-scattering samples can retain very sharp (high frequency) reflectancefeatures. For example, reflectance from point illumination is more localized ina high-scattering medium (such as Spectralon) than in a low-scattering medium(such as in vivo tissue). Moreover, the frequency scaling of Rd(fx) varies directlywith μtr or inversely with ltr. This scaling of μtr and fx is directly evident in theμ′

eff/μtr ratio of Eqs. (1.70) and (1.71) (diffusion approximation); thus, all five dif-fusion curves will coincide perfectly if plotted versus normalized spatial frequency,(fx/fx,tr) = (fx/μtr) = (fx·ltr). This behavior is also accurately retained in the MC pre-dictions. Therefore, it is convenient to present the reflectance curves on normalizedspatial frequency, (fx/fx,tr). It is also convenient that μtr =1 mm−1 (ltr = 1 mm) isan accurate approximate transport coefficient for many biological tissues, so forthe high-albedo curves, fx,tr can be interpreted as ∼1 mm−1 spatial frequency.


44 Chapter 1

Figure 1.25 Diffuse reflectance versus spatial frequency (mm−1) for varying values of ltr,using both Monte Carlo simulations (solid lines) and the diffusion approximation (dashedlines), demonstrating accuracy of the diffusion approximation within 12% for fx = (2ltr)−1 =0.5μtr (a). Diffuse reflectance versus normalized spatial frequency (fx/fx,tr = fx·ltr) forvarying albedo (μ′

s/μa ratio), using both Monte Carlo simulations (solid lines) and the dif-fusion approximation (dashed lines), demonstrating degrading accuracy of diffusion withdecreasing albedo (b) (see Ref. 479).

The comparison of diffusion approximation and MC modeling of reflectancecurves shows that the diffusion solution slightly overestimates low-frequency com-ponents and underestimates the high-frequency components of the reflectance (seeFig. 1.25). This is partially due to the use of a simple, mono-exponential extendedsource function [Eq. (1.63)]. Analytical solutions that preserve higher-order spatialmoments of the source are available in the literature.489, 490 They can be accountedfor in calculations to improve the precision of diffuse approximation. By defining



the diffusion approximation error as the percent difference of the diffusion theoryprediction from MC, a diffusion error of 12% was found for fx ≤ (2ltr)−1 = 0.5μtr

at (μ′s/μa) = 100.

Data presented in Fig. 1.25(b) allow further comparison between the transportand diffusion models when the albedo is decreasing [(μ′

s/μa) ratio ranging from30 to 3]. In the figure, the diffuse reflectance is presented versus normalized spatialfrequency, fx,tr. In this case, as before, diffusion theory overestimates reflectanceat low spatial frequencies and underestimates reflectance at high frequencies. Alldiffusion theory curves converge at high frequency [(fx/fx,tr) ∼ 1], while an absoluteoffset between curves remains in the MC simulation.

For low frequencies (below 0.5·μtr), the diffusion approximation error remainslower than 16% at (μ′

s/μa) = 30 (�′ = 0.97). For the lower albedo, the absolutevalues of diffusion reflectance are inaccurate, positively, and negatively biased atlow and high frequencies, respectively. In measurements, however, the usage ofa reference calibration sample (with known optical properties determined from amore rigorous approach) allows one to correct these types of errors. For example,the calibrated measurements of samples with ±25% difference of optical proper-ties (μ′

s/μa) between the samples and reference phantom allows the observationof < 10% error down to (μ′

s/μa) = 10 for all frequencies.479 This result suggeststhat, through measurement calibration with the help of a reference phantom of sim-ilar albedo, one can still achieve quantitatively accurate results from the diffusionapproximation.

1.4.2.4 Measurement, imaging, and calibration

The diffuse s-MTF of a scattering system can be measured in a transmission orreflection geometry. In practice, the illumination must be a superposition of ac(spatially modulated) and dc (planar) reflectance terms (i.e., it is impossible toilluminate with a negative scalar intensity):479

S = S0

2

[1 + M0 cos(2πfx x + α)

], (1.77)

where S0, M0, fx, and α are the illumination source intensity, modulation depth,spatial frequency, and spatial phase, respectively. In this simple case, the patternis constant in the orthogonal y direction. In reflection mode, the diffusely reflectedintensity, I, is a sum of ac (Iac) and dc (Idc) components:

I = Iac + Idc, (1.78)

where the measured ac component of the reflected intensity, Iac, has the view

Iac = Mac (x, fx) · cos (2πfx x + α) . (1.79)

Here, Mac(x, fx) represents the amplitude envelope of the reflected photon densitystanding wave at frequency fx. The Mac can be a function of position, x, as shownschematically in Fig. 1.26 (top). Multiple Mac(x, fx) curves can be sampled in par-allel at each y pixel row by using a 2D camera, allowing for simultaneous spatialsampling of millions of reflectance values.


46 Chapter 1

Figure 1.26 Schematic of modulated reflectance (a) and demodulated ac and dc ampli-tudes (b) (see Ref. 479).

Various signal processing schemes can be used for signal demodulation andobtaining Mac(x, fx). One can employ a simple time-domain amplitude demodulationmethod,471 based on the illumination of a sinusoid pattern measured three times atthe same spatial frequency, with phase offsets of α = 0, (2/3)π, and (4/3)π radians.Then, Mac(x, fx) can be calculated algebraically at each spatial location, xi, by

MAC (xi, fx) =√

2

3

{[I1 (xi) − I2 (xi)]

2 + [I2 (xi) − I3 (xi)]2

+ [I3 (xi) − I1 (xi)]2}1/2

, (1.80)

where I1, I2, and I3 represent the Iac image values at each location with shifted spa-tial phases. This differencing approach is convenient, because (1) it automaticallyremoves features common to all three images, including the average image noiseand digitization offset; (2) it does not require knowledge of the spatial frequency,removing potential spatial calibration errors; and (3) it provides an automatic sub-traction of any constant ambient light present in each acquired image. The spatiallyvarying dc amplitude, Mdc(x), can be calculated as before with fx = 0, or at anyfrequency of illumination by using

Mdc (xi) = 1

3[I1 (xi) + I2 (xi) + I3 (xi)] . (1.81)

Figure 1.26 shows a schematic of a spatially varying modulated reflectance (top)and its demodulated ac and dc amplitude (bottom) components.



In the FD, measurement of Mac(xi, fx) is the product of (1) the source intensity,I0, (2) the MTF of the illumination and imaging optical system, s-MTFsystem, and(3) the true turbid system s-MTF, Rd(xi, fx):

Mac (xi, fx) = I0 · MTFsystem (xi, fx) · Rd (xi, fx) . (1.82)

Therefore, it is possible to simultaneously calibrate for the absolute intensity of thesource and the s-MTFsystem of the imaging system by performing a reference mea-surement, Mac,ref(x, fx), on a tissue phantom of known optical properties. Usinga measured value for the phantom diffuse reflectance, Rd,ref,pred(fx), the diffusereflectance of the tissue sample under investigation at each spatial location canbe written as

Rd(xi, fx) = Mac (xi, fx)

Mac,ref (xi, fx)· Rd,ref,pred (fx) . (1.83)

This direct division-based correction for the system frequency response is anadvantage of the SFD measurement over other spatially resolved measurements,avoiding deconvolution of the optical system s-PSF in the real spatial domain,which can amplify measurement noise and uncertainties. However, the surfaceprofile of the sample and the phantom should ideally be identical or numericallycompensated by using surface profilometry.479

For a given modulation frequency, there are two unknowns in Eq. (1.69): μa

and μ′s, which are needed for spectroscopic predictions or tomography. To sepa-

rate absorption and scattering coefficients, measurements should be conducted fora few (at least two) spatial frequencies. This is clear in a lookup table (Fig. 1.27),where Rd(dc) and Rd(ac) correspond to diffuse reflectance measurements at zeroand nonzero spatial frequencies f 1 and f 2, respectively. Lines correspond to con-stant absorption and reduced scattering coefficients. As an example, the dottedlines in Fig. 1.27 show that if Rd (0 mm−1) = 0.55 and Rd (0.5 mm−1) = 0.06,then μa ≈ 0.03 and μ′

s ≈ 1.4 mm−1, respectively. The remarkably strongly orthog-onal relationship between the absorption and scattering contour lines indicates theability to separate absorption and scattering coefficients with maximal sensitiv-ity. This is attributable to the large frequency range spanned by 0 and 0.5 mm−1

(dc and ac) frequencies. Correspondingly, as the x- and y-axis frequencies becomecloser to one another, these lines will become less orthogonal, and inversion cou-pling between absorption and scattering coefficients will increase. Again, both acand dc measurements can easily be obtained with only three phase projections ofa single illumination frequency [see Eqs. (1.80) and (1.81)], allowing for rapid,high-resolution imaging of absorption and scattering contrast.

1.4.3 Spatially modulated spectroscopy and imaging of tissues

1.4.3.1 Inverse problem solution

The spectroscopy and imaging of tissues with absorption or scattering contrastare determined by inverse problem solving for the reconstruction of tissue opti-cal parameters from measurements of diffuse reflectance and/or transmittance. In


48 Chapter 1

Figure 1.27 Two-frequency (dc versus ac) lookup table for rapid calculation of opticalproperties, generated from diffusion model forward problem solution. Gray lines indi-cate constant absorption; black lines indicate constant reduced scattering coefficient.Dotted lines demonstrate the lookup method, translating dc and ac values into μa and μ′

sparameters (see Ref. 479).

Ref. 479, two inversion methods are considered to calculate the absorption andreduced scattering coefficients from measurements of diffuse reflectance. The firstis based on a “sweep” in spatial frequency space, analogous to the broadbandfrequency domain photon migration approach (see Section 1.3),491 producing anoverdetermined set of measurements that can be fitted to Eq. (1.69) via least-squares minimization. The second is more rapid and based on a two-frequencylookup table method (see Fig. 1.27), which uses cubic spline interpolation (the“griddata” method in MATLAB) of forward-model data at two spatial frequen-cies. On typical personal computers, this method is capable of millions of lookupcalculations per second.

In Fig. 1.28, the entire data-mining process using in vivo forearm data ispresented as an example of data receiving and processing. Intensity data at each fre-quency (three phase images per frequency) are demodulated, calibrated, and fittedby using Eqs. (1.80), (1.83), and (1.69), respectively. Data are processed separatelyfor each pixel, generating spatial maps of tissue optical properties (absorption andscattering coefficients).

In contrast to other spatially resolved methods, the SMI technique acquirescoincident, axial projection measurements of optical contrast to quantify the opticalproperties at each x–y spatial position, allowing robust measurement of the average



Figure 1.28 Flow chart of SMI data processing. Intensity data at each frequency (threephase images per frequency) are demodulated, calibrated, and fit using Eqs. (1.80), (1.83),and (1.69), respectively. Data are processed separately for each pixel, generating spatialmaps of optical properties. Images are plotted within three standard deviations of the indi-vidual image mean to make them visually comparable. This image highlights the differentialcontrast in diffuse reflectance (Rd) versus spatial frequency (fx ), the basis for separationabsorption and scattering (see Ref. 479).

properties. Compared to point illumination measurements, the SMI technique sam-ples only the low spatial frequency moments of the s-MTF. However, these lowfrequencies (<1 mm−1) are sufficient for separate detection of absorption and scat-tering coefficients. In addition, the SMI technique has reduced sensitivity to theuncertainty inherent in measuring high-frequency spatial moments (i.e., reflectanceclose to the light source).

1.4.3.2 Experimental studies of tissue phantoms

To characterize the precision and accuracy of the SMI technique for measuringhomogeneous absorption and reduced scattering coefficients, 16 tissue phantomswere constructed by using a single batch of Liposyn lipid emulsion and water-soluble nigrosin dye stock solutions for controlling the scattering and absorbingproperties, respectively.479 In the first eight phantoms, the absorption coefficient,μa, was varied over two orders of magnitude (logarithmically spaced within 0.002mm−1 ≤ μa ≤ 0.12 mm−1) with a constant scattering coefficient: μ′

s = 0.97 mm−1.In the second set of eight phantoms, the reduced scattering coefficient, μ′

s, waslinearly varied: 0.32 mm−1 ≤ μ′

s ≤ 1.8 mm−1, while the absorption coefficientremained constant at μa = 0.0046 mm−1. These values were calculated based oninfinite geometry, multifrequency (50 to 500 MHz), multidistance (10 to 25 mm)FD photon migration measurements296 of a Liposyn/nigrosin phantom.


50 Chapter 1

Thirty spatial frequencies of illumination were chosen between 0 and0.13 mm−1 on SMI measurements of each phantom, corresponding to a total of90 images per phantom (three spatial phases per frequency). The interfrequencyspacing was chosen to accurately capture the s-MTF shapes of all phantoms,with finer spacing at low frequencies and coarser spacing at high frequencies.All measurements were taken at the wavelength of 660 nm with an approximate75 × 75 mm2 illumination area, a 50 × 50 mm2 camera field of view, and anintegration time of 100 ms. The individual phantoms were measured in a random-ized order, and measurements were repeated three times to allow for statisticalaveraging.

Modulation images of the ac reflectance were obtained at each frequency byusing Eq. (1.80). At full CCD resolution, the pixel-by-pixel demodulation approachresulted in approximately 250,000 separate measurements of reflectance per spatialfrequency, highlighting the statistical power of the technique. Because the phan-toms under study were expected to be highly homogeneous, 20 × 20 pixel binningwas performed on each image to speed computation, resulting in low-resolution,15 × 15 pixel modulation images. The resulting 30 images provided quantitativeac amplitude measurements at each of the 100 spatial locations within the field ofview. For calibration, a single phantom from the entire set of 16 was chosen as thereference. Using the known optical properties of the reference (determined fromFD photon migration measurements), a model-based prediction for the reflectance,Rd,ref,pred(fx), was calculated. Then, for each spatial frequency and each spatiallocation, Rd(fx) was calculated by using Eq. (1.83).

The diffusion model [see Eq. (1.69)] was used to reconstruct values of μa andμ′

s using both least-squares minimization by a simplex search algorithm (“fmin-search” MATLAB) and the two-frequency lookup table approach using the lowest(0 mm−1) and highest (0.13 mm−1) spatial frequencies. For each phantom, thespatial sampling point was separately analyzed, generating images of recoveredabsorption and scattering values. Because these were homogeneous samples, themean and standard deviation were calculated to represent each optical propertyimage result, characterizing the accuracy and precision of SMI, respectively.

The average measured diffuse reflectance versus spatial frequency is presentedin Fig. 1.29. This figure also shows, using solid dots, the absorption and scatter-ing variation measurement sets [Figs. 1.29(a) and 1.29(b), respectively]. In solidblack lines, the corresponding fits using the diffusion-based reflectance model[Eq. (1.69)] are shown. The absorption experiment data demonstrate that increasingthe absorption causes a decrease in reflectance. Because the sensitivity to absorp-tion change (absorption contrast) primarily resides in the low-frequency regime, thescattering data indicate that increased scattering causes an increase in reflectanceamplitude and a rescaling to higher spatial frequencies (i.e., a decrease in ltr), withcontrast apparent at all spatial frequencies. All model-based fits of Fig. 1.29 (solidlines) demonstrate excellent agreement with the data, with typical errors less than0.02. This is particularly satisfying, because all measurements were calibrated witha single reference phantom. The largest model–data deviation appears in the high-frequency range of the lowest scattering phantom (μ′

s = 0.32 mm−1, ltr ≈ 3 mm).



Figure 1.29 Liposyn experiment data (black circles) fit to the SFD diffusion model ofEq. (1.69) (gray lines). As absorption increases, reflectance at low spatial frequenciesdecreases dramatically, while high-frequency data show little sensitivity to absorption con-trast (a). Increasing scattering generates an increase in reflectance, with scattering contrastobserved at all frequencies (b). All results show excellent visual agreement betweenmeasurement data and diffusion fits (see Ref. 479).

This is consistent with the ltr plots of Fig. 1.25, where model breakdown is expectedat or before fx = 1/(2ltr), or 0.16 mm−1.

In the absorption variation experiment, recovered versus expected absorptionshows excellent linearity over two orders of magnitude, ranging from high to lowalbedo [from (μ′

s/μa) = 500 to (μ′s/μa) = 8]. Similar linearity is observed in the

scattering variation experiment, albeit with slightly more fluctuation. In this case,reconstructed absorption values demonstrate less than 15% deviation from theexpected value, except in the lowest scattering (largest ltr) case. Standard deviationsof the recovered 15 × 15 pixel optical property maps are mostly less than 1%, indi-cating both high precision of measurements and phantom spatial uniformity overthe field of view.

Table 1.2 summarizes the average percent deviation for multifrequency (30-frequency fitting) and two-frequency lookup table inverse models that demonstrate

Table 1.2 Summary of recovered average optical properties for absorption and scatteringvariation experiments of Liposyn/nigrosin tissue phantoms. Overall accuracies of recoveredabsorption and reduced scattering coefficients are approximately 6 and 3%, respectively(see Ref. 479).

Absorption experiment Scattering experiment

Average error, % 30-frequency fit 2-frequency fit Average error, % 30-frequency fit 2-frequency fitμa error 4.74 4.85 μa error 7.51 11.4μ′

s error 2.98 2.29 μ′s error 3.05 10.2


52 Chapter 1

the accuracy of all recovered values for Liposyn/nigrosin phantoms.479 On average,6% and 3% deviation occurred in absorption and reduced scattering coefficients,respectively. The two-frequency lookup table errors are generally comparable tothose of the multifrequency method. However, in tissue measurements, with theirspatial heterogeneity, the multifrequency technique is expected to provide a morestable measure of the average optical properties.

The largest errors are observed for the lowest values of absorption and scatter-ing. As a planar imaging modality, the SMI technique samples relatively superficialvolumes; therefore, short photon paths lose sensitivity to low absorption andlow scattering contrast, where the length scales of photon interaction are verylong.

To further understand the volume effects connected with the lateral and in-depth photon migration, which are of great importance for the interpretation oftissue images, a contrast-resolution study using heterogeneous tissue phantoms wasperformed.479 Eight homogeneous gelatin phantoms were fabricated using nigrosinas the absorber and Liposyn as the scattering agent. Heterogeneous phantoms wereassembled by placing two gelatin slabs of differing optical properties adjacent toone another. Gelatin phantoms with a 300% step in either absorption (μa1 = 0.01mm−1, μa2 = 0.03 mm−1; μ′

s1,2 = 1.0 mm−1) or scattering (μa1,2 = 0.02 mm−1;μ′

s1 = 0.5 mm−1, μ′s2 = 1.5 mm−1) were measured at 660 nm, both directly and

through a 2-mm homogeneous layer with optical properties of μa = 0.01 mm−1,μ′

s = 0.5 mm−1. Both were calibrated by a homogeneous phantom with opticalproperties of μa = 0.02 mm−1 and μ′

s = 1.0 mm−1. SMI measurements were con-ducted for nine spatial frequencies between 0 and 0.11 mm−1 and used to calculateoptical property maps by using least-squares regression of the diffusion reflectancemodel.

Recovered optical property spatial profiles for absorption and scattering mediawere averaged over the vertical direction. The results reveal a diffuse edge-responsefunction that is both depth and optical property dependent. For both absorption andscattering variation experiments, degradation of the spatial resolution and quan-titative contrast through the homogeneous layer compared to that at the surfacewas observed. Specifically, the measured contrast values through the homogeneouslayer are only approximately 15% and 5% of those at the surface for absorptionand scattering, respectively. Defining spatial resolution as the distance at whichthe edge-response contrast is reduced by 90%, the resolution of absorption andscattering contrast was found to be 0.3 and 0.05 mm, respectively, for surface per-turbations, and 0.5 and 0.25 mm, respectively, for perturbations 2 mm beneath thesurface.

Although these characteristics suggest the capability to resolve optical contraston small spatial scales, actual performance is also dependent on illumination spa-tial frequency and noise in the measuring system. In general, at a given depth, thedepth resolution to scale with the measurement precision and number of frequen-cies (number of sources), and x–y resolution to scale with the number of spatialsampling points (number of detectors), are expected.492



1.4.3.3 Summary

The theoretical framework and instrumental platform for SFD measurement in tur-bid tissues were designed and proved by simulations and tissue phantom studies.479

Analytic diffusion and MC-based transport forward models were carefully com-pared, and quantitative measurements of a variety of phantoms were performed.This method is principally contactless and needs no illuminating or detecting ofoptical fibers. This combination of advantages makes it particularly suited to theimaging of static and dynamic processes in in vivo tissues, especially for medi-cal diagnostics. The method can easily be extended to multispectral imaging forthe quantitative functional mapping of both intrinsic and extrinsic tissue chro-mophores476, 481, 482, 493 (responsible for functional state of a tissue) with in-depthresolution and accounting for multilayer tissue structure. The spatial anisotropy oftissue optical properties, such as those of skin,495 also can be studied by the SMImethod. Reference 483 showed that the SMI method allows one to separate theinclusions of isotropic and anisotropic scattering structures of tissues in diffusereflectance, which, with evidence, provides new diagnostic perspectives.

1.5 Conclusion

Presented in this chapter is the description of low-intensity light interaction (nothermal effects) with tissues; this basically depends on light scattering and absorp-tion by the different structures of biological tissues, which, in turn, determine lighttransmittance and reflectance. It is possible to design and build practical opticalmeasuring techniques and instrumentation for the quantification of tissue opticalparameters and imaging associated with the spatial variations of optical parameters.Optical radiation (CW, pulsed, and modulated in intensity over time and space) istypically used in these techniques. The developed theoretical approaches allow forthe recovery of the true NIR absorption spectra of tissues, despite the strong tissuescattering, and thus, for the monitoring of metabolic processes in the living bodyvia evaluation of blood oxygenation, total hemoglobin, and water content in thetissue. Thais makes it possible to study brain and muscle activity to assess tumorstatus, for instance, in the course of photodynamic therapy.

Tomographic imaging of pathological inclusions in tissues is based on bothabsorption and scattering contrast. Because absorption is directly related to theoccurrence of metabolic reactions in the tissues, it is possible to be measured byfunctional imaging with a resolution in both space and time.

In addition to those presented in this chapter, the literature also describes spec-troscopic methods and instruments, and imaging techniques based on spatiallyresolved,496–511 pulse,511–542 and temporal484, 485, 491, 511, 543–554 CWs and standingphoton-density waves.474, 476, 478, 479, 481, 493 Some of the methods and instrumentsfor spectroscopy and imaging of tissues described in these papers will be presentedin Chapters 10 and 11.


Chapter 2

Propagation of Polarized Lightin Tissues

The structure and anisotropy of tissues, specificity of light scattering by a particle,and polarization phenomena are described. The major polarization characteristicsof polarized light, methods and techniques for its detection, and interactions with arandom single scattering medium as a tissue model are presented. The vector equa-tion of radiative transfer theory and Monte Carlo modeling of tissue polarizationproperties are discussed. This chapter provides certain examples of polarizationsensitive studies for tissue phantoms, highly scattering tissues, and whole bloodlayers.

2.1 Introduction

Up to this point, we have ignored the vector nature of light transport in scatteringmedia, such as tissues, because we assumed it to be rapidly depolarized duringpropagation in a randomly inhomogeneous medium. It is a common belief thatthe randomness of tissue structure results in fast depolarization of light propa-gating in tissues. Therefore, polarization effects are usually ignored. However,in certain tissues and cell structures (transparent tissues, such as eye tissues,cellular monolayers, mucous membrane, and superficial skin layers), the degreeof polarization of transmitted or reflected light remains measurable even whenthe tissue has a considerable thickness. In this situation, information about thestructures of tissues and cell ensembles can be extracted from the registered depo-larization degree of initially polarized light, the polarization state transformation,or the appearance of a polarized component in the scattered light.3, 5, 6, 59, 67–70,

105, 129, 135, 138, 150, 153,166, 176, 211, 212, 214,215, 221, 224, 225, 232, 278, 555–749

Regarding practical implications, polarization techniques are believed to gen-erate simplified schemes of optical medical tomography, compared with time-resolved methods, and to provide additional information about the structure oftissues.555–749

55


56 Chapter 2

2.2 Tissue Structure and Anisotropy

Many biological tissues are optically anisotropic.3, 6, 9, 10, 24, 29, 43, 59–70, 97, 127–130, 135,

138, 153, 166, 176, 216,217, 234, 246, 247, 323,609–663, 666–671, 680, 684–687, 690–732, 737, 738 Tissue bire-fringence primarily results from the linear anisotropy of fibrous structures thatform the extracellular media. The refractive index of a medium is higher along thelength of a fiber than along the cross section. A specific tissue structure is a sys-tem composed of parallel cylinders that create a uniaxial birefringent medium withthe optic axis parallel to the cylinder axes. This is called birefringence of form.A large variety of tissues exhibit form birefringence, including eye cornea, ten-don, cartilage, eye sclera, dura mater, testis, muscle, nerve, retina, bone, teeth, andmyelin. All of these tissues contain uniaxial and/or biaxial birefringent structures.For instance, bone and tooth are mineralized structures originating from hydrox-yapatite crystals, which play an important role in hard tissue birefringence. Inparticular, dental enamel is an ordered array of such crystals surrounded by a pro-tein/lipid/water matrix.65, 66, 97, 153, 635, 637, 638 Fairly well-oriented hexagonal crystalsof hydroxyapatite, approximately 30–40 nm in diameter and up to 10 μm inlength, are packed into an organic matrix to form enamel prisms (or rods) withan overall cross section of 4–6 μm. Enamel prisms are roughly perpendicular tothe tooth surface. Tooth dentin is a complex structure, honeycombed with denti-nal tubules, which are shelled organic cylinders with a highly mineralized shell.Tubule diameters are 1–5 μm, and their number density is in the range of (3–7) ×106 cm−2.65, 66, 97, 153, 635, 750,751

Tendon consists mostly of parallel, densely packed collagen fibers arrangedin parallel bundles interspersed with long, elliptical fibroblasts. In general, tendonfibers are cylindrical in shape, with diameters ranging from 20 to 400 nm.246, 247

The ordered structure of collagen fibers running parallel to a single axis makestendon a highly birefringent tissue.

Arteries have a more complex structure than tendons. The medial layer pri-marily consists of closely packed smooth muscle cells with a mean diameter of15–20 μm. Small amounts of connective tissue, including elastin, collagenous,and reticular fibers, as well as a few fibroblasts, are also located in the media.The outer adventitial layer consists of dense fibrous connective tissue. The adven-titia is largely composed of collagen fibers, 1–12 μm in diameter, and thinnerelastin fibers, 2–3 μm in diameter. As with tendon, the cylindrical collagen andelastin fibers are primarily ordered along one axis, thus causing the tissue to bebirefringent.

Myocardium, on the other hand, contains fibers oriented along two differentaxes. Myocardium mostly consists of cardiac muscle fibers arranged in sheets thatwind around the ventricles and atria. In pigs, the myocardium cardiac muscle iscomprised of myofibrils (approximately 1 μm in diameter) that, in turn, consistof cylindrical myofilaments (6–15 nm in diameter) and aspherical mitochondria(1–2 μm in diameter). Myocardium is typically birefringent because the refractiveindex along the axis of the muscle fiber is different from that in the transversedirection.246, 247


Propagation of Polarized Light in Tissues 57

Figure 2.1 Models of tissue birefringence: system of long dielectric cylinders (a), system ofthin dielectric plates (b) (see Ref. 654).

Form birefringence arises when the relative optical phase between the orthog-onal polarization components is nonzero for forward-scattered light. After multipleforward scattering events, a relative phase difference accumulates and a delay (δoe)similar to that observed in birefringent crystalline materials is introduced betweenorthogonal polarization components. For organized linear structures, an increasein phase delay may be characterized by a difference (�noe) in the effective refrac-tive index for light polarized along, and perpendicular to, the long axis of thelinear structures. The effect of tissue birefringence on the propagation of linearlypolarized light is dependent on the angle between the incident polarization orien-tation and the tissue axis. Phase retardation, δoe, between orthogonal polarizationcomponents is proportional to the distance, d, traveled through the birefringentmedium:628

δoe = 2πd�noe

λ0. (2.1)

A medium of parallel cylinders is a positive uniaxial birefringent medium [�noe

= (ne − no) > 0], with its optic axis parallel to the cylinder axes [see Fig. 2.1(a)].Therefore, a case defined by an incident electrical field directed parallel to thecylinder axes will be called “extraordinary,” and a case with the incident electricalfield perpendicular to the cylinder axes will be called “ordinary.” The difference(ne − no) between the extraordinary and ordinary indices is a measure of thebirefringence of a medium composed of cylinders. For the Rayleigh limit (λ >>cylinder diameter), the form birefringence becomes611, 614

�noe = (ne − no) = f1f2(n1 − n2)2

f1n1 + f2n2, (2.2)

where f 1 is the volume fraction of the cylinders; f 2 is the volume fraction of theground substance; and n1, n2 are the corresponding indices. For a given indexdifference, maximal birefringence is expected for approximately equal volume


58 Chapter 2

fractions of thin cylinders and ground material. For systems with large diametercylinders (λ << cylinder diameter), the birefringence reaches zero.614

For a system of thin plates [see Fig. 2.1(b)], the following equation isobtained:226

n2e − n2

o = − f1f2(n1 − n2)

f1n21 + f2n2

2

, (2.3)

where f 1 is the volume fraction occupied by the plates; f 2 is the volume fractionof the ground substance; and n1, n2 are the corresponding indices. This impliesthat the system behaves like a negative uniaxial crystal with its optical axis alignednormally with the plate surface.

Form birefringence is used in biological microscopy as an instrument for study-ing cell structure. The sign of the observed refractive index difference is the particleshape closest to that of the rod or plate, and if n1 and n2 are known, one canassess the volume fraction occupied by the particles. To separate the birefrin-gence of the form and the particle material, the refractive indices of the particlesand the ground substance should be matched, because form birefringence vanisheswith n1 = n2.

Linear dichroism (diattenuation), i.e., different wave attenuation for twoorthogonal polarizations, is defined in systems formed by long cylinders or platesby the difference between the imaginary parts of the effective indices of refrac-tion. Depending on the relationship between the sizes and the optical constantsof the cylinders or plates, this difference can take both positive and negativevalues.226

Reported birefringence values for tendon, muscle, coronary artery,myocardium, sclera, cartilage, and skin are on the order of 10−3 (see, forinstance, Refs. 612, 621, 622, and 624–628). The measured refractive index varia-tions for the fast and slow axes of rabbit cornea show that its birefringence varieswithin the range of 0 at the apex, or top of the cornea, to 5.5 × 10−4 at the baseof the cornea, where it attaches to the sclera.610, 616 The predominant orientationof collagenous fibers in different regions of the cornea results in birefringenceand dichroism.615 Based on experimental results, it has been assumed that thebirefringent portions of the corneal surface all have a relatively universal fast axislocated approximately 160 deg from the vertical axis, defined as a line that runsfrom the apex of the cornea through the pupil.616

A new technique—polarization-sensitive optical coherence tomography (PSOCT)—allows for the highly precise measurement of linear birefringence in turbidtissue.135, 624–628, 630 The following data have been reported using this technique: forrodent muscle, 1.4 × 10−3 (Refs. 627 and 628); for normal porcine tendon, (4.2 ±0.3) × 10−3, and for thermally treated (90◦C, 20 s) porcine tendon, (2.24 ± 0.07) ×10−3 (Ref. 630); for porcine skin, 1.5 × 10−3 – 3.5 × 10−3 (Ref. 630); for bovinecartilage, 3.0 × 10−3 (Ref. 630); and for bovine tendon, (3.7 ± 0.4) × 10−3 (Ref.625). This birefringence provides 90% phase retardation at a depth on the order ofseveral hundred micrometers.



Figure 2.2 Examples of chiral aggregates of spherical particles.

For 1-mm-thick myocardium tissue samples of rat, ex vivo measurements usingthe Mueller matrix meter (633/635 nm), with follow-up decomposition of themeasured matrix needed for the separate determination of optical activity, bire-fringence, and dichroism, phase retardation δoe [see Eq. (2.1)], were ∼1.5 rad forhealthy tissue, only ∼0.1 rad for tissue in the infarctus region, and approximately0.5 rad after treatment of infarct with stem cells.669, 721, 731

The magnitudes of birefringence and diattenuation are related to density andother properties of collagen fibers, whereas the orientation of the fast axis indicatesthe orientation of collagen fibers. The amplitude and orientation of birefringencein the skin and cartilage are not as uniformly distributed as in tendon. In otherwords, the density of collagen fibers in skin and cartilage is not as uniform asin tendon, and the orientation of collagen fibers is not distributed in as orderly afashion.630

In addition to linear birefringence and dichroism (diattenuation), many tissuecomponents show optical activity. In polarized light research, the chirality of amolecule, which stems from its asymmetric molecular structure, results in manycharacteristic effects, generically called optical activity.642, 646 A well-known man-ifestation of optical activity is the ability to rotate the plane of linearly polarizedlight about the axis of propagation. The amount of rotation depends on the chiralmolecular concentration, the path length through the medium, and the light wave-length. For instance, chiral asymmetricality encoded in the polarization propertiesof light transmitted through a transparent medium enables very sensitive and accu-rate determination of glucose concentration. Tissues containing chiral componentsdisplay optical activity.616, 640, 641, 713–723, 731 Interest in chiral turbid media is drivenby the attractive possibility of noninvasive in situ optical monitoring of the glucosein diabetic patients.105, 138, 713–723, 731 Within turbid tissues, however, where scatter-ing effects dominate, the loss of polarization information is significant and thechiral effects due to the small amount of dissolved glucose are difficult to detect.

In complex tissue structures, chiral aggregates of particles, particularly spher-ical particles, may be responsible for tissue optical activity (see Fig. 2.2). Moresophisticated anisotropic tissue models can also be constructed. For example, theeye cornea can be represented as a system of plane anisotropic layers (plates,i.e., lamellas), each composed of densely packed long cylinders (fibrils) [seeFig. 2.1(a)] with their optical axes oriented along a spiral (see Fig. 3.3). Thisfibrillar-lamellar structure of the cornea is responsible for linear and circulardichroism and its dependence on the angle between lamellas.615


60 Chapter 2

Figure 2.3 Geometry of the scattering of light by a particle located at the origin (see Ref.214). The incident light beam is parallel to the z-axis. A detector is located distance r fromthe origin along vector S1.

2.3 Light Scattering by a Particle

Let us now consider the transformation of any polarization type (linear, circular,or elliptical) in a scattering medium with typical tissue parameters and comparethe penetration depth of circular and linear polarization in different media. Tothis end, let us examine a monochromatic plane wave incident on an isolatedscatterer.43, 135, 214, 215 The geometry needed to describe the scattering of light bya particle is shown in Fig. 2.3. The incident monochromatic plane wave comesfrom below and travels along the positive z-axis. Some of the light is scattered bythe particle along the direction indicated by vector S1 toward a detector located adistance, r, from the particle. The scattering direction is defined by the scatteringangle, θ, and azimuthal angle, ϕ. The scattering plane is originated by vector S1

and the z-axis. The electrical field of the incident light is in the x–y plane and canbe resolved into components that are parallel, E‖i, and perpendicular, E⊥i, to thescattering plane. The electrical field vector and intensity of the incident light beamare given by

Ei = E‖i + E⊥i, (2.4)

Ii = ⟨E‖iE

∗‖i + E⊥iE

∗⊥i

⟩, (2.5)

where the asterisk denotes complex conjugation and the angular brackets denote atime average.



The electrical field of the scattered light wave is perpendicular to S1 and canbe resolved into components E‖s and E⊥s, which are parallel and perpendicular,respectively, to the scattering plane. The scattered electrical field vector is given by

Es = E‖s + E⊥s. (2.6)

There is a linear relationship between the incident and scattered field compo-nents, defined by Eqs. (2.4) and (2.6):43, 135, 214, 215

[E‖s

E⊥s

]= eik(r−z)

−ikr

[S2 S3

S4 S1

] [E‖i

E⊥i

], (2.7)

where k = 2π/λ is the wave number; λ = λ0/n is the wavelength in the scatteringmedium; n is the mean refractive index of the scattering medium; λ0 is the wave-length of the light in vacuum; i = √−1; r is the distance from the scatterer to thedetector; and z is the position coordinate of the scatterer. The complex numbersS1−4 represent the elements of the amplitude scattering matrix (S-matrix) or Jonesmatrix.43, 135, 214, 215, 226, 655–661 They each depend on scattering and azimuthal anglesθ and ϕ, and contain information about the scatterer. Both amplitude and phasemust be measured to quantify the amplitude scattering matrix. Matrix elementscan be directly measured by using a two-frequency Zeeman laser, which producestwo laser lines with a small frequency separation (approximately 250 kHz) andorthogonal linear polarizations,215 or by the OCT technique.135, 630

2.4 Description and Detection of Polarized Light

Definitions of polarized light, its properties, as well as production and detec-tion techniques, are extensively described in the literature.135, 211, 212, 214, 215,

226, 280, 655–660, 665–670, 731, 740–748 Polarization refers to the pattern described by theelectric field vector as a function of time at a fixed point in space. When the elec-trical field vector oscillates in a single, fixed plane all along the beam, the lightis categorized as linearly polarized. This linearly polarized wave can be resolvedinto components that are parallel and perpendicular to the scattering plane [seeEqs. (2.4) and (2.6), and Fig. 2.3]. If the plane of the electrical field rotates, thelight is characterized as elliptically polarized, because the electrical field vectortraces out an ellipse at a fixed point in space as a function of time. If the ellipsehappens to be a circle, the light is characterized as circularly polarized. The con-nection between phase and polarization can be understood as follows: circularlypolarized light consists of equal amounts of linear, mutually orthogonal polarizedcomponents that oscillate exactly 90 deg out of phase. In general, light of arbitraryelliptical polarization consists of unequal amplitudes of linearly polarized compo-nents; the electrical fields of the two polarizations oscillate at the same frequency,but have some constant phase difference.

Light of arbitrary polarization can be represented by four numbers knownas the Stokes parameters: I, Q, U, and V, where I refers to the irradi-ance or intensity of the light; the parameters Q, U, and V represent the


62 Chapter 2

extents of horizontal linear, 45 deg linear, and circular polarization, respec-tively.135, 211, 212, 214, 215, 226, 655–660, 665–670, 731, 740–748

In polarimetry, the Stokes vector, S, of a light beam is constructed based onsix flux measurements obtained with different polarization analyzers in front of thedetector:

S =

⎛⎜⎜⎝

IQUV

⎞⎟⎟⎠ =

⎛⎜⎜⎝

IH + IV

IH − IV

I+45◦ − I−45◦IR − IL

⎞⎟⎟⎠, (2.8)

where IH, IV, I+45◦ , I−45◦ , IR, and IL are the light intensities measured with a hori-zontal linear polarizer, vertical linear polarizer, +45 deg linear polarizer, −45 deglinear polarizer, right circular analyzer, and left circular analyzer in front of thedetector, respectively. Because of the relationship IH + IV = I+45◦ + I−45◦ = IR + IL

= I, where I is the intensity of the light beam measured with no analyzer in front ofthe detector, a Stokes vector can be determined by four independent measurements,for example, IH, IV, I+45◦ , and IR:

S =

⎛⎜⎜⎝

IH + IV

IH − IV

2I+45◦ − (IH + IV)2IR − (IH + IV)

⎞⎟⎟⎠ . (2.9)

From the Stokes vector, the degree of polarization (P), the degree of linearpolarization (PL), and the degree of circular polarization (PC) are derived as

P =√

Q2 + U2 + V2

I, (2.10)

PL =√

Q2 + U2

I, (2.11)

PC =√

V2

I. (2.12)

If the degree of polarization (DOP) of a light field remains at unity after transfor-mation by an optical system, this system is nondepolarizing; otherwise, the systemis depolarizing.

The values of the normalized Stokes parameters, which correspond to certaintypes of polarization, are presented in Table 2.1.

The Mueller matrix, M, of a sample transforms an incident Stokes vector, Sin,into the corresponding output Stokes vector, Sout, as

Sout = MSin. (2.13)

Obviously, the output Stokes vector varies with the state of the incident beam,but the Mueller matrix is determined only by the sample and the optical path.



Table 2.1 Polarization types (see Refs. 6 and 215).

Stokes Horizontal Vertical +45◦ −45◦ Right Leftparameter (linear) (linear) (linear) (linear) (circular) (circular)

I 1 1 1 1 1 1Q 1 −1 0 0 0 0U 0 0 1 −1 0 0V 0 0 0 0 1 −1

Conversely, the Mueller matrix can fully characterize the optical polarization prop-erties of the sample. The Mueller matrix can be experimentally obtained frommeasurements with different combinations of source polarizers and detection ana-lyzers. In the most general cases, a 4 × 4 Mueller matrix has 16 independentelements; therefore, at least 16 independent measurements must be acquired todetermine a full Mueller matrix.

The normalized Stokes vectors for the four incident polarization states, H,V, +45◦, and R, are, respectively,

SHi =

⎛⎜⎜⎝

1100

⎞⎟⎟⎠, SVi =

⎛⎜⎜⎝

1−100

⎞⎟⎟⎠, S+45◦i =

⎛⎜⎜⎝

1010

⎞⎟⎟⎠, SRi =

⎛⎜⎜⎝

1001

⎞⎟⎟⎠, (2.14)

where H, V, +45◦, and R represent horizontal linear polarization, vertical linearpolarization, +45 deg linear polarization, and right circular polarization, respec-tively. We may express the 4 × 4 Mueller matrix as M = [M1 M2 M3 M4], whereM1, M2, M3, and M4 are four column vectors of four elements each. The fouroutput Stokes vectors corresponding to the four incident polarization states, H, V,+45◦, and R, are denoted by SHo, SVo, S+45◦ o, and SRo, respectively. These fouroutput Stokes vectors are experimentally measured based on Eq. (2.9) and can beexpressed as ⎧⎪⎪⎨

⎪⎪⎩

SHo = MSHi = M1 + M2

SVo = MSVi = M1 − M2

S+45◦o = MS+45◦i = M1 + M3

SRo = MSRi = M1 + M4

. (2.15)

The Mueller matrix can be calculated from the four output Stokes vectors:661

M = 1

2×[

SHo + SVo,SHo − SVo,−2S+45◦o(SHo + SVo),2SRo − (SHo + SVo)](2.16)

In other words, at least four independent Stokes vectors must be measured todetermine a full Mueller matrix, and each Stokes vector requires four independentintensity measurements with different analyzers.


64 Chapter 2

2.5 Light Interaction with a Random Single-Scattering Media

In terms of the electrical field components, the Stokes parameters from Eqs. (2.8)and (2.9) are given by

I = ⟨E||E∗

|| + E⊥E∗⊥⟩

Q = ⟨E||E∗

|| − E⊥E∗⊥⟩

U = ⟨E||E∗

⊥ + E⊥E∗||⟩

(2.17)

V = ⟨i(E||E∗

⊥ − E⊥E∗||)

⟩.

All Stokes parameters have the same dimension: energy per unit area per unittime per unit wavelength. For an elementary monochromatic plane or sphericalelectromagnetic wave,211

I2 ≡ Q2 + U2 + V2. (2.18)

For an arbitrary light beam, as in the case of a partially polarized quasi-monochromatic light that is attributable to the fundamental property of additivity,the Stokes parameters for the mixture of the elementary waves are sums of therespective Stokes parameters of these waves. Thus, Eq. (2.18) is replaced by theinequality:211, 214

I2 ≥ Q2 + U2 + V2. (2.19)

The DOP, degree of linear polarization (DOLP), and degree of circularpolarization (DOCP) for the incident and scattered light are defined by Eqs. (2.10)–(2.12). In particular, for the DOLP (PL) and the DOCP (PC) of the scattered light,we have

PL = (I|| − I⊥)

(I|| + I⊥)=

√Q2

s + U2s

Is, (2.20)

PC =√

V2s

Is. (2.21)

In the far field, the polarization of the scattered light is described by the Stokesvector, Ss, connected with the Stokes vector of the incident light, Si [see Eq. (2.13)],by the matrix equation214

Ss = M · Si, (2.22)

where M is the normalized 4 × 4 scattering matrix (intensity or Mueller matrix):

M =

⎡⎢⎢⎣

M11 M12 M13 M14

M21 M22 M23 M24

M31 M32 M33 M34

M41 M42 M43 M44

⎤⎥⎥⎦ . (2.23)



Elements of the light-scattering matrix (LSM) depend on the scattering angle,θ, the wavelength, and the geometrical and optical parameters of the scatterers. M11

is measured when the incident light is unpolarized, the scattering angle dependenceof which is the phase function of the scattered light. It provides only a fraction ofthe information that is theoretically available from scattering experiments. M11 ismuch less sensitive to chirality and long-range structure than certain other matrixelements.214, 215 M12 refers to the DOLP of the scattered light; M22 displays the ratioof depolarized light to the total scattered light (a good measure of the nonsphericityof scatterers); M34 displays the transformation of 45◦ obliquely polarized incidentlight to circularly polarized scattered light (which is uniquely characteristic fordifferent biological systems); the difference between M33 and M44 is an accuratemeasure of the nonsphericity of scatterers.

In addition to the DOLP, defined by Eqs. (2.10)–(2.12), (2.20), and (2.21),diattenuation (linear dichroism) is introduced as

DA = P21 − P2

2

P21 + P2

2

=√

M212 + M2

13 + M214

M11, (2.24)

where P1 and P2 are the principal coefficients of the amplitude transmission for thetwo orthogonal polarization eigenstates.

In general, all 16 elements of the LSM are nonzero. However, there are onlyseven independent elements (out of 16) in the scattering matrix of a single parti-cle with fixed orientation, and nine relations, which connect the others.211, 212 Forscattering by a collection of randomly oriented scatterers, there are 10 independentelements.

The LSM for macroscopically isotropic and symmetric media has the well-known block-diagonal structure274

M(θ) =

⎡⎢⎢⎣

M11(θ) M12(θ) 0 0M12(θ) M22(θ) 0 0

0 0 M33(θ) M34(θ)0 0 −M34(θ) M44(θ)

⎤⎥⎥⎦ . (2.25)

It follows that only eight LSM elements are nonzero and only six of these areindependent. Moreover, there are special relationships for two specific scatteringangles, 0 and π:211

M22(0) = M33(0), M22(π) = −M33(π),

M12(0) = M34(0) = M12(π) = M34(π) = 0, (2.26)

M44(π) = M11(π) − 2M22(π).

Rotationally symmetric particles have an additional property:211

M44(0) = 2M22(0) − M11(0). (2.27)


66 Chapter 2

The structure of the LSM further simplifies for spherically symmetric particles,which are homogeneous or radially inhomogeneous (composed of isotropic materi-als with a refractive index depending only on the distance from the particle center),because in this case,211

M11(θ) ≡ M22(θ), M33(θ) ≡ M44(θ). (2.28)

The phase function, i.e., the M11 element, for symmetric scattering relative to thedirection of the incident wave, depends only on the scattering angle, θ, and satisfiesthe following normalization condition [see Eq. (1.14)]:211, 214

2π∫ π

0M11(θ) sin θdθ = 1, (2.29)

that corresponds to assumption of random distribution of scatterers in a medium.The scattering anisotropy parameter (mean cosine of θ) or the asymmetry

parameter of the phase function [see Eq. (1.16)] is now expressed as

g ≡ 〈cos θ〉 = 2π∫ π

0M11(θ) cos θ sin θdθ (2.30)

If a particle is small with respect to the wavelength of the incident light, its scatter-ing can be described as the reemission of a single dipole. This Rayleigh theory isapplicable under the condition that m(2π a/λ) � 1, where m is the relative refrac-tive index of the scatterers; (2π a/λ) is the size parameter; a is the radius of theparticle; and λ is the wavelength of the incident light in a medium.214 For the vis-ible and NIR light and scatterers with a typical (for biological tissue) refractiveindex relative to the ground matter, m = 1.05–1.11, the maximum particle radiusmust be approximately 12–14 nm for Rayleigh theory to remain valid. For this the-ory, the scattered irradiance is inversely proportional to λ4 and increases as a6; theangular distribution of the scattered light is isotropic.

The Rayleigh−Gans or Rayleigh−Debye theories address the problem of cal-culating the scattering by a special class of arbitrarily shaped particles. Theserequire |m − 1| � 1 and (2π a′/λ)|m − 1| � 1, where a′ is the largest dimension ofthe particle.129, 211, 212, 215 These conditions mean that the electrical field inside theparticle must be close to that of the incident field and that the particle can be viewedas a collection of independent dipoles that are all exposed to the same incident field.A biological cell might be modeled as a sphere of cytoplasm with a higher refrac-tive index (ncp = 1.37) relative to that of the surrounding water medium (nis = 1.35);then m = 1.015, and for NIR light, this theory is valid for particle dimensions up toa′ = 0.8–1.0 μm. This approximation has been applied extensively to calculationsof light scattering from suspensions of bacteria.215 It can be applied for describinglight scattering from cell components (mitochondria, lysosomes, and peroxisomes)in tissues due to their small dimensions and refraction.58, 96, 216–219, 229, 232

The Fraunhofer diffraction approximation is useful for describing the forwardscattering caused by large particles (on the order of 10 μm).215 According to thistheory, the scattered light has the same polarization as that of the incident light andthe scatterer pattern is independent of the refractive index of the object. For small



scattering angles, the Fraunhofer diffraction approximation can accurately repre-sent the change in irradiance as a function of particle size. Thus, this approachis applicable in laser flow cytometry. The structures in a biological cell, such ascell membrane, nuclear texture, and granules in the cytoplasm, can be detected byvariations in optical density. An optical Fourier transform of the diffraction patterncan be performed by a lens. Spatial variations in optical density in the object planeare converted by Fourier transform into spatial frequency variations in the Fouriertransform plane in the rear focal plane of the lens.215 If the optical density changesslowly across the object, the Fourier transform places most of the scattered lightnear zero angles (low spatial frequency) in the Fourier transform plane. This is anaccurate model of a cell with clear cytoplasm (constant optical density). If the opti-cal density changes rapidly across the object, the Fourier transform moves moreof the energy to larger scattering angles (higher spatial frequency) in the Fouriertransform plane. This is an accurate model of a cell with highly granular cytoplasm(rapid changes in optical density across the cytoplasm). It was shown that the trans-forms of abnormal cells have significantly higher spatial frequency than those ofnormal cells, particularly single cells in cervical smears. Fourier optical micro-scopes were developed for such studies. The technique is applicable for a positivephotographic transparency of a cell, single cells on slides, and cells in flows.215

Mie or Lorenz-Mie scattering theory is an exact solution of Maxwell’s elec-tromagnetic field equations for a homogeneous sphere.214, 226 In the general case,light scattered at a particle becomes elliptically polarized. For spherically symmet-ric particles of an optically inactive material, the Mueller scattering matrix is givenby Eqs. (2.25) and (2.28). Mie theory has been extended to arbitrary coated spheresand arbitrary cylinders.211, 212, 215 In Mie theory, the electromagnetic fields of theincident, internal, and scattered waves are each expanded in a series.226 A lineartransformation can be made between the fields in each region. This approach canalso be used for nonspherical objects such as spheroids.211, 212 The linear trans-formation is called the transition matrix (T-matrix). The T-matrix for sphericalparticles is diagonal.

Thus far, Stokes vectors have been defined for the case of a monochromaticplane wave, and the Mueller matrix has been defined for single scattering. Theseconcepts have been generalized for more complicated situations. The Stokes vec-tor was defined for a quasi-monochromatic wave.273 Then, in the case of partiallypolarized light, the inequality described by Eq. (2.19) is valid.214

When Mueller matrices from an ensemble of particles differing in size, ori-entation, morphology, or optical properties are added incoherently, six of thepreviously mentioned equalities became inequalities.593 For an ensemble of inter-acting particles in the single-scattering approximation,5, 6, 10, 654 LSM elements havethe form

Mij(θ) = M0ij(θ)NFint(θ), (2.31)

where M0ij are the LSM elements of an isolated particle, N is the number of scatter-

ers, and Fint(θ) is the interference term, taking into account the spatial correlationof particles. The normalized elements (Mij/M11) in a monodisperse system weakly


68 Chapter 2

depend on whether the spatial correlation of scatterers is considered, and this ratiois similar to that for isolated particles.654

2.6 Vector Radiative Transfer Equation

As already shown, the majority of tissues are turbid media showing strong scatter-ing and much weaker absorption (up to two orders less than scattering in visible andNIR). Moreover, in their natural state (unsliced), tissues are rather thick. Therefore,multiple scattering is a specific feature of a wide class of tissues.1–3, 6, 24, 31, 129, 130, 135

Polarization effects of light propagation through various multiply scatteringmedia, including tissues, are fully described by the vector RTE.59, 211, 212, 556–578

The RTT originated as a phenomenological approach based on considering thetransport of energy through a medium filled with a large number of particles andensuring energy conservation.274–277 This medium, composed of discrete, sparsely,and randomly distributed particles, is treated as continuous and locally homoge-neous. As discussed above, the concept of single scattering and absorption by anindividual particle is replaced in this subsection by the concept of single scatteringand absorption by a small homogeneous volume element. In the framework of theRTT, the scattering and absorption of the small volume element follow from theMaxwell equations and are given by incoherent sums of the respective character-istics of the constituent particles; the result of scattering is not the transformationof a plane incident wave into a spherical scattered wave but, rather, the transfor-mation of the specific intensity vector (Stokes) of the incident light into that of thescattered light.212

For macroscopically isotropic and symmetric plane-parallel scattering media,the vector radiative transfer equation (VRTE) can be substantially simplified asfollows:212

dS(r,ϑ,ϕ)

dτ(r)= −S(r,ϑ,ϕ)+�(r)

4π

∫ +1

−1d(cos ϑ′)

∫ 2π

0dϕ′Z(r,ϑ,ϑ′,ϕ − ϕ′)S(r,ϑ′,ϕ′),

(2.32)where S is the Stokes vector defined by Eq. (2.8); r is the position vector; ϑ,ϕ are the polar (zenith) and azimuth angles, respectively, characterizing incidentdirection;

dτ(r) = ρ(r)〈σext(r)〉ds (2.33)

is the optical path length element; ρ is the local particle number density; 〈σext〉 isthe local ensemble-averaged extinction coefficient; ds is the path length elementmeasured along the unit vector of the direction of light propagation; � is the singlescattering albedo; ϑ′, ϕ′ are the polar (zenith) and azimuth angles, respectively,characterizing scattering direction; Z is the normalized phase matrix:

Z(r,ϑ,ϑ′,ϕ − ϕ′) = R(�)M(θ)R(�), (2.34)



where M(θ) is the single scattering Mueller matrix, defined by Eq. (2.13); θ is thescattering angle; and R(φ) is the Stokes rotation matrix for angle φ:

R(φ) =

⎡⎢⎢⎣

1 0 0 00 cos 2φ − sin 2φ 00 sin 2φ cos 2φ 00 0 0 1

⎤⎥⎥⎦ . (2.35)

Every Stokes vector and Mueller matrix is associated with a specific referenceplane and coordinates. In Mie theory, the Mueller matrix of a single scattering eventis defined in the scattering plane that is formed by the incident light and scatteredlight vectors (see Fig. 2.3). For a general coordinate system associated with thisscattering plane, the z-axis is along the direction of photon propagation. The x-axis is within the reference plane and is perpendicular to the z-axis. The y-axis isperpendicular to both the z-axis and the reference plane.

A local coordinate system is associated with each incident photon packet, andits Stokes vector, Sin, is associated with this local coordinate system. The localcoordinate system of the photon before scattering is (x, y, z). After the scatteringevent, the photon propagates along the z′-axis with q as the polar scattering angleand j as the azimuth angle. The scattering plane is formed by the z-axis and z′-axis,which is the new reference plane.

Equation (2.8) is used to calculate the Stokes vector of the scattered light.Because the Mueller matrix of the scattering event is defined in the reference plane[see Eq. (2.13)], we first need to transform the Stokes vector of the incident light tothe coordinate system associated with the reference plane. This transformation canbe accomplished by rotating the local coordinate system (x, y, z) by φ about thez-axis, where the rotation matrix is defined by Eq. (2.35). The new Stokes vector isobtained by

S′in = R(φ)Sin. (2.36)

The local coordinate system of the photon packet is tracked in the process. Thetransformation can be divided into two steps. The first step is rotating the (x, y, z)system by φ about the z-axis, and the second step rotating the coordinate by qabout the rotated y-axis to achieve (x′, y′, z′). After the transformation, the z′-axisis aligned with the new light vector. The transformation matrix is

⎡⎣ x′

y′z′

⎤⎦ =

⎡⎣ cos θ 0 − sin θ

0 1 0sin θ 0 cos θ

⎤⎦

⎡⎣ cosφ sinφ 0

− sinφ cosφ 00 0 1

⎤⎦

⎡⎣ x

yy

⎤⎦ . (2.37)

After a photon packet passes through the turbid medium, its Stokes vector isrecorded and accumulated. The local coordinate system is tracked in the simula-tion. To record the Stokes vector, the local coordinate system of each photon packet


70 Chapter 2

needs to be transformed into the laboratory coordinate system. In the laboratorycoordinate system (e1, e2, e3), the local photon coordinate can be written as

⎡⎣x

yz

⎤⎦ =

⎡⎣e1x e2x e3x

e1y e2y e3y

e1z e2z e3z

⎤⎦

⎡⎣e1

e2

e3

⎤⎦ . (2.38)

To transform the photon Stokes vector from the local into the laboratory coordinatesystem, the local coordinate system is rotated by its z-axis so that the new x-axislies within the (e2, e3) plane in the laboratory coordinate. The rotation angle is

φ = tan−1(e1x/e1y). (2.39)

The rotation matrix and the new Stokes vector can be obtained from Eqs. (2.35)and (2.36).

The phase matrix, Eq. (2.34), links the Stokes vectors of the incident and scat-tered beams, specified relative to their respective meridional planes. To computethe Stokes vector of the scattered beam with respect to its meridional plane, onemust calculate the Stokes vector of the incident beam with respect to the scatter-ing plane, multiply it by the scattering matrix (to obtain the Stokes vector of thescattered beam with respect to the scattering plane), and then compute the Stokesvector of the scattered beam with respect to its meridional plane. This procedureinvolves two rotations of the reference plane: � = −φ; � = π − φ, and � = π +φ; � = φ. The scattering angle, θ, and angles � and � are expressed via the polarand azimuth incident and scattering angles:

cos θ = cos ϑ′ cos ϑ + sin ϑ′ sin ϑ cos(ϕ′ − ϕ), (2.40)

cos � = cos ϑ − cos ϑ′ cos θ

sin ϑ′ sin θ, (2.41)

cos � = cos ϑ′ − cos ϑ cos θ

sin ϑ sin θ. (2.42)

The first term on the right-hand side of the VRTE [Eq. (2.32)] describes thechange in the specific intensity vector over the distance, ds, caused by extinctionand dichroism; the second term describes the contribution of light illuminatinga small volume element centered at r from all incident directions and scat-tered in the chosen direction. For real systems, the form of the VRTE tendsto be rather complex and often intractable. Therefore, a wide range of analyti-cal and numerical techniques have been developed to solve the VRTE. Becausethe important property of the normalized phase matrix, Eq. (2.34), is dependenton the difference between the azimuthal angles of the scattering and incidentdirections rather than on their specific values,212 an efficient analytical treat-ment of the azimuthal dependence of the multiply scattered light is possible,using a Fourier decomposition of the VRTE. The following techniques and their



combinations can be used to solve the VRTE: transfer matrix method, singulareigenfunction method, perturbation method, small-angle approximation, adding-doubling method, the matrix operator method, invariant embedding method, andMC method.129, 135, 138, 211, 212, 279, 280, 556–580

When the medium is illuminated by unpolarized light and/or only the inten-sity of multiply scattered light needs to be computed, the VRTE can be replacedby its approximate scalar counterpart. In this case, in Eq. (2.32), the Stokesvector is replaced by its first element (i.e., radiance) [see Eq. (1.9)] and thenormalized phase matrix by its (1, 1) element (i.e., the phase function) [seeEq. (1.13)]. The scalar approximation is not accurate when the size of the scatter-ing particles is much smaller than the wavelength, but provides acceptable resultsfor particles comparable to and larger than the wavelength.212, 276 Ample litera-ture1, 3, 15, 129, 130, 196, 277, 280–282 describes the analytical and numerical solutions ofthe scalar RTE [Eq. (1.9)].

2.7 Monte Carlo Simulation

The MC method, which is widely used for the numerical solution of the RTT equa-tion306–309 in different fields (such as astrophysics or atmosphere and ocean optics)appears to be especially promising for the solution of direct and inverse radiationtransfer problems for media with arbitrary configurations and boundary conditions,particularly for the purposes of medical polarization optical tomography and spec-troscopy.1, 3, 15, 41, 129, 135, 306–309, 362, 370, 561, 569,573–581, 669, 716, 718, 723, 731 The method isbased on the numerical simulation of photon transport in scattering media. Randommigrations of photons inside a sample can be traced from their input untilabsorption or output occurs.

The straightforward simulation using the MC method has the following advan-tages: (1) one can employ any scattering matrix; (2) there are no obstacles for theuse of strongly forward directed phase functions or experimental single-scatteringmatrices; (3) the polarization calculation requires only a twofold increase in com-putation time over that needed for the evaluation of intensity; (4) any reasonablenumber of detectors can be accounted for without noticeable increase in the com-putation time; (5) there are no difficulties in determining the radiation parametersinside the medium; (6) it is possible to model media with complex geometry inwhich radiance depends not only on the optical depth, but also on the transversecoordinates.

The liability of the obtained results to statistical variations on the order of afew percent at an acceptable computation time is the primary disadvantage of theMC technique. For a twofold increase in the accuracy, a fourfold increase in thecomputation time is necessary. The MC method is also impractical for great opticaldepths (τ > 100).

A few MC codes for modeling polarized light propagation through a scatter-ing layer are available in the literature (see, for example, Refs. 561, 569, 573, 574,575, 576, 577, 578, 579, 669, 716, 718, 723, and 731). To illustrate this MC simu-lation technique, we will discuss the algorithm described in Ref. 578 and applied to


72 Chapter 2

model the angular dependencies of scattering matrix elements. Let a flux of photonswithin an infinitely narrow beam be incident exactly upon the center of the spheri-cal volume filled by the scattering particles. The path of a single photon migrationin the medium is accounted for in a computer simulation process. In this case, thephotons are considered as ballistic particles. Different events possible in the courseof photon migration are estimated by the appropriate probability distributions. Inthe model under study, the photons would either be elastically scattered or absorbedfollowing collision with the medium particles. A certain outcome of every event isfound by a set of uniformly distributed random numbers. The probability of scat-tering in the given direction is determined in accordance with scattering by a singleparticle. It is possible to specify the cross section of scattering and values of thescattering matrix elements for every photon interaction with a scatterer.

When an incident photon enters a scattering layer, it is allowed to travel afree path length, l. The l value depends on the particle concentration, ρ, and anextinction cross section, σext. The l is a random quantity that takes any positivevalues with the probability density p(l):

p (l) = ρσexte−ρσextl. (2.43)

The particular realization of l is dictated by the value of a random number, ξ, thatis uniformly distributed over the interval [0, 1]:

∫ l

0p(l)dl = ξ. (2.44)

Substituting Eq. (2.43) into Eq. (2.44) yields the l value of the certain realizationin the form

l = − 1

ρσextln ξ. (2.45)

If l is larger than the thickness of the scattering system, then this photon is detectedas transmitted with no scattering. If, having passed l, the photon remains withinthe scattering volume, then the possible events of photon–particle interaction(scattering or absorption) are randomly selected.

Within the spherical system of coordinates, the probability density of photonscattering along the direction specified by θ between the directions of the incidentand scattered photons and by angle φ between the previous and new scatteringplanes is given as

p(θ,φ) = Is(θ,φ) sin θ∫ 2π0

∫ π

0 Is(θ,φ) sin θd θdφ, (2.46)

where Is(θ, φ) is the intensity of the light scattered in the direction (θ, φ) withrespect to the previous direction of the photon, defined by angles ϑ and ϕ [seeEqs. (2.32) and (2.33)]. For spherical particles, this intensity is given by the Mieformulas with allowances for the state of polarization of each photon. An integral



Is(θ, φ) over all scattering directions, similar to Eq. (1.6), determines the scatteringcross section:

σsca =∫ 2π

0

∫ π

0Is(θ,φ) sin θdθdφ. (2.47)

The probability density of photon scattering along the specified direction, p(θ, φ),depends on the Mueller matrix of the scattering particle, M(θ, φ) (a single scat-tering matrix), and the Stokes vector, S, associated with the photon [Eqs. (2.8) and(2.22)]. The M(θ, φ) links the Stokes vectors of the incident [Si (0, 0)] and scat-tered [Ss (θ, φ)] light. For spherical scatterers, the elements of this matrix may befactorized:

M(θ,φ) = M(θ)R(φ). (2.48)

The single scattering matrix, M(θ), of spherical particles has the form describedby Eqs. (2.25) and (2.28). The elements of this matrix are given by the Mie formu-las,214, 226 which are functions of θ and diffraction parameter x = 2π a/λ, where a isthe radius of the spherical particle and λ is the wavelength in the medium.

The matrix R(φ) describes the transformation of the Stokes vector under rota-tion of the plane of scattering through angle φ, which is defined by Eq. (2.35).Thus, the intensity of the light scattered by spherical particles is determined by theexpression

Is(θ,ϕ) = [M11(θ)Ii + (Qi cos 2ϕ + Ui sin 2ϕ)M12(θ)] , (2.49)

where Qi and Ui are components of the Stokes vector of the incident light [seeEqs. (2.8) and (2.17)]. As it follows from this equation, probability p(θ, φ) [Eq.(2.46)], unlike the scattering matrix [Eq. (2.48)], cannot be factorized; it appears tobe parametrized by the Stokes vector associated with the scattered photon. In thiscase, one should use a rejection method to evaluate p(θ, φ).

The following method of generating pairs of random numbers with p(θ, φ)may be used.578 In 3D space, the function p(θ, φ) specifies a certain surface. Thevalues (θ, φ) corresponding to the distribution p(θ, φ) are chosen by using the fol-lowing steps: first, a random direction (θξ, φξ) with a uniform spatial distributionis selected, and the values of the random quantities θξ and φξ, distributed over theintervals (0, π) and (0, 2π), respectively, are found from the equations

cos θξ = 2ξ − 1, φξ = 2πξ, (2.50)

where ξ is a random number uniformly distributed over the interval (0,1). Second,

the surface specified by the function p(θ, φ) is surrounded by a sphere of radius�

R,

equal to the maximum value of p(θ, φ), and a random quantity, rξ = ξ�

R, is gen-erated. Third, the direction (θξ, φξ) is accepted as the random direction of photonscattering at this stage, provided that the condition rξ ≤ p(θξ, φξ) is satisfied.In the opposite case, steps 1 and 2 are repeated.


74 Chapter 2

The migration of the photon in the scattering medium can be described bya sequence of transformations for the related coordinate system. Each scatteringevent is accompanied by a variation in the Stokes vector associated with the pho-ton. The new Stokes vector, Sn+1, is a product of the preceding Stokes vector,transformed to the new scattering plane, and the Mueller matrix, Mk(θ), of thescattering particle:

Sn+1 = Mk(θ)Rn(φ)Sn, (2.51)

where matrix Rn(φ) [see Eq. (2.35)] describes the rotation of the Stokes vectoraround the axis specifying the direction of propagation of the photon before theinteraction.

For the chosen scattering direction, the Stokes vector is recalculated by usingEqs. (2.22), (2.25), (2.28), (2.51), and expressions for elements of the single-scattering Mueller matrix for a homogeneous sphere made of an optically inactivematerial.135, 214, 226 The value thus obtained is renormalized so that the intensityremains equal to unity. Thus, the Stokes vector associated with the photon onlycontains information about the variation in the state of polarization of the scat-tered photon. Real intensity is determined by the number of detected photons inthe chosen direction within the detector aperture.

The above procedure is repeated as long as the photon appears to be outside thescattering volume. In this case, if the photon propagation direction intersects thesurface of the detector, the photon is detected. Upon detection, the Stokes vector isrotated from the current plane of the last scattering to the scattering plane of the lab-oratory coordinate system. The obtained values are accumulated in the appropriatecells of the detector, whose number is defined by the photon migration direction.Furthermore, with registering, the photon is classified in accordance with the scat-tering multiplicity and the length of a total path. For every unabsorbed photon, thedirection and the coordinates of a point at which it escapes the scattering volume,as well as the number of scattering acts it has experienced, are also recorded. Thespatial distribution of radiation scattered by the scattering volume can be obtainedwith regard to polarization by analyzing the above data for a sufficiently greatnumber of photons.

To determine the full LSM of an object, it is necessary to detect the lightscattering of four linearly independent states of polarization of the incident light,S1i, S2i, S3i, and S4i. This allows the following system of linear equations to beconstructed:

CM′ = S′, (2.52)

where M′ is the column matrix composed of found matrix elements of the LSMof the object, and S′ is the 16-element vector containing the Stokes vector ele-ments recorded upon light scattering for the four independent states of the incidentlight polarization. The transformation matrix, C, is determined by the choice ofthe initial set of the Stokes vectors of the incident light. Having solved this sys-tem of Eq. (2.52) for the set of Stokes vectors, S1i = (1,1,0,0), S2i = (1,−1,0,0),



Figure 2.4 Angular distributions of the total scattering intensity for multiply scattering sys-tems of spherical particles having relative refractive index m = 1.2 and uniformly distributedwithin a spherical volume at volume fraction f = 0.01: particles with small radius, a = 50 nm,diameter of the system is equal to (1) 1, (2) 2, and (3) 20 mm (a); and particles with largeradius, a = 300 nm, diameter of the system is equal to (1) 0.002, (2) 0.2, and (3) 2 mm(b); the infinitely narrow unpolarized light beam is incident exactly upon the center of thescattering volume in the zero angle direction (not shown); the wavelength is 633 nm (seeRef. 578).

S3i = (1,0,1,0), and S4i = (1,0,0,1), one finds the desired LSM of the object,M′ = M:

M = 1

2

⎡⎢⎢⎣

I1 + I2 I1 − I2 2I3 − (I1 + I2) 2I4 − (I1 + I2)Q1 + Q2 Q1 − Q2 2Q3 − (Q1 + Q2) 2Q4 − (Q1 + Q2)U1 + U2 U1 − U2 2U3 − (U1 + U2) 2U4 − (U1 + U2)V1 + V2 V1 − V2 2V3 − (V1 + V2) 2V4 − (V1 + V2)

⎤⎥⎥⎦ , (2.53)

where the elements of the Stokes vectors of the scattered light obtained in each ofthese four cases are denoted as Sn = (In, Qn, Un, Vn), (n = 1, 2, 3, 4). As a result, onemay calculate the angular dependencies for all elements of the LSM with allowancefor the contributions of multiple scattering.

The simulation was performed for the systems of spherical particles with a rela-tive index of refraction, m = 1.2, which are uniformly distributed within a sphericalvolume at volume fraction f = 0.01.578 In the calculations, the illuminating beamwas assumed to be infinitely narrow and incident exactly upon the center of thescattering volume in the zero angle direction; the scattered radiation was detectedat different scattering angles in the far zone by a detector with the full angular aper-ture of 1 deg in the scattering plane and 5 deg in a plane that is perpendicular to thescattering plane.

The calculated angular distributions of the total scattering intensity for differ-ent scattering systems of spherical particles with small radius, a = 50 nm, or largeradius, a = 300 nm, are presented in Fig. 2.4. The average multiplicity of scatter-ing of the detected radiation increases with increasing dimensions of the scatteringsystem. For systems of small particles at illumination in the visible range (633 nm),


76 Chapter 2

an approximation of Rayleigh scattering is applicable. For rather small dimensionsin a scattering volume of 1 mm of diameter, the contribution of single scatter-ing is predominant. This follows from the intensity angular dependence, which israther isotropic [Fig. 2.4(a)]. As the dimensions of the scattering system increase,the fraction of contributions of the higher multiplicity scattering also increase.For a 20-mm-diameter system, the detected light contains noticeable contributionsfrom scattering of the 10th–20th multiplicity. With a further increase in the systemdimensions, most of the incident light is scattered in the backward direction andthe scattering intensity in the forward half-plane vanishes. For this reason, begin-ning from a certain value, the dimensions of the scattering system hardly affect theshape of the diagram of scattering multiplicity distribution.

Systems composed of particles with a size on the order of the wavelength[Fig. 2.4(b)] also show an increase in the contributions of higher-order scatteringwith increased dimensions of the scattering system. The system transforms fromthe forward to backward directed scattering modes at rather small thickness: 2 mmdiameter.

As shown, the intensity of unpolarized light at the higher scattering multi-plicity weakly depends on the scattering angle and carries almost no informationabout the size of the scattering particles. Systems of small particles at triple scat-tering may already be considered as nearly isotropic, whereas angular distributionsfor the large particles, strongly elongated in the forward direction at single scat-tering, remain anisotropic for sufficiently high scattering multiplicity [four to sixscattering events for the system of 0.2 mm diameter; Fig. 2.4(b)].

The view of the LSM elements’ angular dependences under the conditionsof multiple scattering differs substantially from that for the LSM of a single-scattering system. Figures 2.5 and 2.6 show that multiple scattering flattens theangular dependences of the LSM elements. The solid line shows the result of calcu-lation of a normalized LSM for an isolated spherical particle with a similar radiusand relative index of refraction. All elements of the LSM are normalized to theM11 element (total scattering intensity) along the given direction, and M11 is pre-sented in the plot as normalized to unity in the forward direction; its actual intensitydistributions are presented in Fig. 2.4.

Because the single scattering angular distribution for particles with sizes sub-stantially exceeding the Rayleigh limit is strongly asymmetric, the scatteringintensity at large angles is very low. For this reason, one must trace the trajec-tories of a great number of photons to obtain satisfactory accuracy in this angularrange. Therefore, to demonstrate the fine structure of the angular dependence ofthe matrix elements, it is necessary to use 107–108 photons in the simulation.575, 578

For the scattering by particle suspensions in a spherical volume of small diam-eter, almost all detected photons are singly scattered. An increase in the opticalthickness considerably enhances the contribution of multiple scattering. The angu-lar dependences of the LSM elements have a form similar to the single-scatteringLSM, provided that the optical thickness of the scattering system, τ, does notexceed unity for the systems of large particles, considered to be 10 or above forsystems of small particles.



Figure 2.5 MC simulation: the angular distributions of the LSM elements for multiple scat-tering systems of small spherical particles (a = 50 nm, m = 1.2) uniformly distributed withina spherical volume (f = 0.01); diameter of the system is equal to 1 mm (•), 2 mm (�), and20 mm (©); the solid line shows the results of calculations in the approximation of singlescattering; the infinitely narrow unpolarized light beam is incident exactly upon the centerof the scattering volume in the zero angle direction (not shown); the wavelength is 633 nm(see Ref. 578).

The multiple-scattering intensity (element M11) for a volume of large diameterdecreases with increasing scattering angle more slowly than the single-scatteringintensity. As the cell diameter further increases, backward scattering becomes pre-dominant (see Figs. 2.4–2.6). In the systems of small particles (see Fig. 2.5), thegrowth of multiple scattering contributions is accompanied by a gradual decrease in


78 Chapter 2

Figure 2.6 MC simulation: the angular distributions of the LSM elements for multiple scat-tering systems of large spherical particles (a = 300 nm, m = 1.2) uniformly distributed withina spherical volume (f = 0.01); diameter of the system is equal to 0.002 mm (•), 0.2 mm (�),and 2 mm (©); the solid line shows the results of calculations in the approximation of singlescattering; the infinitely narrow unpolarized light beam is incident exactly upon the centerof the scattering volume in the zero angle direction (not shown); the wavelength is 633 nm(see Ref. 578).

the magnitude of all elements except for M11; i.e., the form of the LSM approachesthat of the ideal depolarizer. In particular, the magnitudes of elements M12 andM21 decrease in nearly the same way; elements M33 and M44 also decrease inmagnitude, but M44 decreases faster. As a result, multiple scattering generates a



difference in the detected values of elements M33 and M44, even for the systemsof spherical particles. The values of element M22 become smaller than unity; thisdecrease is more substantial in the range of scattering angles close to 90 deg. Thus,the manifestation of the effect of multiple scattering in monodisperse systems ofspherical particles, which is revealed in the appearance of nonzero values of thedifference |M33−M44| and |1−M22|, is similar to the manifestation of the effect ofnonsphericity of the scatterers observed under conditions of single scattering.224

For large particle systems, the multiple scattering also decreases the magni-tudes and smoothes the angular dependences of the normalized elements of theLSM (see Fig. 2.6). The corresponding angular dependences, compared to the LSMof small particles, show the following specific features: the minimum value of ele-ment M22 is reached not at 90 deg, but rather at large scattering angles; the finestructures of angular dependences for all elements are smeared even in the presenceof a small fraction of the multiply scattered light; and, finally, the very importantresult that, in the limit of high scattering multiplicity, element M44, unlike otherelements, tends to 0.5 rather than to zero for all scattering angles. This form ofthe LSM means that the radiation scattered by large particles holds the preferen-tial circular polarization at higher scattering multiplicities. This result may serve asa confirmation of the preferential survival of different types of polarization underconditions of multiple scattering for different sizes of scattering particles or tissuestructures.59, 557, 560, 650

The process of multiple scattering of the photons during their migration is con-sidered as a series of successive rotations of their coordinate systems, determinedby the scattering planes and directions. Because these rotations are random, thedetected photons will be randomly polarized; hence, the detected light will be par-tially depolarized. The depolarization will increase with the increasing multiplicityof scattering. For moderate optical thicknesses (0.2 mm, f = 0.01), the depolariz-ing ability is strongly different for different directions. The scattered light may bealmost completely polarized in the region of small scattering angles, completelydepolarized at large angles (θ = 120 deg), and partly polarized in the backwarddirection. The angular range of the strongest depolarization corresponds to theangle at which element M22 acquires minimum values (see Fig. 2.6).

The simulated dependences allow one to estimate the limits of applicabilityof the single-scattering approximation when interpreting the results of experimen-tal studies of disperse scattering systems. It follows from these simulations thatmodifications to the LSM of monodisperse systems of spherical particles due tothe effects of multiple scattering have much in common with modifications to theLSM of singly scattering systems upon deviation in the shape of the particles fromspherical. This fact imposes serious limitations on the application of the measuredLSM of biological objects for inverse problem solving to determine particle non-sphericity. The appropriate criteria to distinguish the effects of multiple scatteringand particle nonsphericity have to be developed.

The comparison of MC simulation accounting for all orders of multiple scatter-ing with the analytical double-scattering model indicated no essential change in thebackscattering polarization patterns.562, 563 This is because the primary contribution


80 Chapter 2

stems from near-double-scattering trajectories in which light suffers two wide-angle scatterings and many near-forward scatterings among multiple-scattering tra-jectories. The contributions of such multiple but near-double-scattering trajectoriesare obviously accurately approximated by the contributions of the correspondingdouble-scattering trajectories.

The preceding MC technique for photon trajectory modeling is well suited tothe simulation of multiple scattering effects in a system of randomly arranged par-ticles. Furthermore, this scheme allows for an approximate approach to describethe interference effects caused by space particle ordering. To this end, one shouldinclude the interference of scattered fields in calculations of the single-scatteringMueller matrix and integral cross sections for a particle. In other words, at thefirst stage, one accounts for the interference effects for simulation of the single-scattering properties, then uses these properties in the MC simulation of multiplescattering. This approach is admissible if the size of a region of local particleordering is substantially smaller than the mean free photon path length.

In general, for polarized light propagated in a strongly scattering medium,the multiple scattering decreases the magnitudes and smoothes the angular depen-dences of the normalized LSM elements, characterizing polarized light interactionwith the medium. For media composed of large particles, specified by a highdegree of single scattering anisotropy or considerable photon transport length, thescattered radiation holds the preferential circular polarization at higher scatteringmultiplicities. This theoretical result serves as a confirmation of the preferentialsurvival of different types of polarization under conditions of multiple scatteringfor different sizes of scattering particles or tissue structures.

2.8 Strongly Scattering Tissues and Phantoms

Given the known character of the Stokes vector transformation for each scatter-ing act, the state of polarization following multiple light scattering in a highlyscattering medium can be found by using various approximations of the multiplescattering theory or the MC method. For small particles, the effects of multiple scat-tering are apparent as a broken symmetrical relationship between LSM elements[see Eqs. (2.25)–(2.28)], M12(θ) �= M21(θ), M33(θ) �= M44(θ), and a significantreduction in linear polarization of the light scattered at angles close to π/2.662

For a system of small spatially uncorrelated particles, the degree of linear(i = L) and circular (i = C) polarization in the far region of the initially polarized(linearly or circularly) light transmitted through a layer of thickness d is defined bythe relation557

Pi∼= 2d

lssin h(ls/ξi) · exp(−d/ξi), (2.54)

where ls =1/μs is the scattering length,

ξi = (ζi · ls/3)0.5 (2.55)

is the characteristic depolarization length for a layer of scatterers, d >> ξi, ζL =ls/[ln(10/7)], ζC = ls/(ln2).



Figure 2.7 Semilogarithmic dependencies of the degree of polarization ratio, PL/PC, on d/ltrfor three ka values, k = 2π/λ. The solid line corresponds to Rayleigh scattering (ka << 1)and dashed lines indicate a correspondence between experimental findings and Eq. (2.48)at ls = ltr. The experimental points are measurements for aqueous suspensions of polysty-rol latex spherical particles having diameter 0.22 (�) and 1.05 (©) μm, λ0 = 670 nm (seeRef. 557).

As demonstrated from Eq. (2.54), the characteristic depolarization length forlinearly polarized light in tissues that can be represented as ensembles of Rayleighparticles is approximately 1.4 times greater than the corresponding length for cir-cularly polarized light. One can employ Eq. (2.54) to assess the depolarizationof light propagating through an ensemble of large-scale spherical particles whosesizes are comparable to the wavelength of incident light (Mie scattering). For thispurpose, one should replace ls with the transport length, ltr ∼= 1/μ′

s [see Eq. (1.23)],and account for the dependence on the size of scatterers in ζL and ζC. With growthin the size of scatterers, the ratio ζL/ζC changes. It decreases from ∼1.4 to 0.5 as2πa/λ increases from 0 to ∼4, where a is the radius of scatterers and λ is the wave-length of the light in the medium; it remains virtually constant at the level of 0.5when 2πa/λ grows from ∼4 to 15.

MC numerical simulations and model experiments in aqueous latex suspen-sions with particles of various diameters demonstrate that there are three regimesof dependence of the ratio of DOLP to the circular polarization for transmittedlight, PL/PC, on d/ltr (Fig. 2.7).557 In the Rayleigh range, PL/PC grows linearlywith the increase of d/ltr. In the intermediate range, this ratio remains constant.In the range of Mie scattering, this quantity decreases linearly. Such behaviorof this quantity is associated with the transition of the system under study fromisotropic to anisotropic scattering. Qualitatively, the physical mechanism behindthe change in depolarization is associated with the fact that a considerable proba-bility of backward scattering in each event of light–medium interaction (isotropicscattering) does not distort linear polarization, whereas backward scattering forcircular polarization is equivalent to the reversal of polarization direction (similarto a reflection from a mirror); i.e., it is equivalent to depolarization. For the samereason, in the case of a strongly elongated scattering phase function, the degree of


82 Chapter 2

circular polarization in an individual scattering event (anisotropic scattering) forlight propagating in a layer should remain nonzero for lengths greater than theDOLP.

These arguments also follow from the above MC simulation of polarized lightinteraction with multiply scattering systems578 and experimental works.641, 650 Forexample, at high scattering multiplicities, the radiation scattered by large particlesholds the preferential circular polarization (LSM element M44 is far from zero forall scattering angles, as shown in Fig. 2.6). At multiple scattering, the LSM fora monodisperse system of randomly distributed spherical particles is modified tobe approximately identical to the single-scattering LSM of a system containingnonspherical particles or optically active spheres.578

Thus, different tissues or the same tissues in various pathological or functionalstates should display different responses to a probe with linearly and circularlypolarized light. This effect can be employed for both optical medical tomographyand for determining optical and spectroscopic parameters of tissues. As followsfrom Eq. (2.54), the depolarization length in tissues should be similar to the meantransport path length, ltr, of a photon, because this length characterizes the distancewithin which the direction of light propagation, and consequently, the polarizationplane of linearly polarized light, becomes totally random after many sequentialscattering events.

Because ltr is determined by the parameter g, characterizing the anisotropyof scattering, the depolarization length should also substantially depend on thisparameter. Indeed, the experimental data in Ref. 583 demonstrate that the depolar-ization length, lp, of linearly polarized light, which is defined as the length withinwhich the ratio I||/I⊥ decreases to 2, displays such a dependence. The ratio men-tioned above varied from 300 to 1, depending on the thickness of the sample andthe type of tissue (Fig. 2.8). These measurements were performed within a nar-row solid angle (∼10−4 sr) in the direction of the incident laser beam. The valuesof lp differed considerably for the white matter of brain and tissue from the cere-bral cortex: 0.19 and 1.0 mm for λ = 476–514 nm, and 0.23 and 1.3 mm for λ =633 nm, respectively. Human skin dermis (bloodless) has depolarization lengths of0.43 mm (λ = 476–514 nm) and 0.46 mm (λ = 633 nm). The depolarization lengthat λ = 476–514 nm decreases in response to a pathological change in the tissue ofthe aortal wall: 0.54 mm for normal tissue, 0.39 mm for a stage of tissue calcifica-tion, and 0.33 mm for a stage of necrotic ulcer. Whole blood with a low hematocritis characterized by a considerable depolarization length (approximately 4 mm) atλ = 633 nm, which is indicative of the dependence on parameter g, whose value forblood exceeds the values of this parameter for tissues of many other types and canbe estimated as 0.966–0.997.2, 40, 48, 230

In contrast to depolarization, the attenuation of collimated light is determinedby the total attenuation coefficient, μt [see Eq. (1.1)]. For many tissues, μt ismuch greater than μs

′. Therefore, in certain situations, it is impossible to detectpure ballistic photons (photons that do not experience scattering), but the forwardscattered photons retain their initial polarization and can be used for imaging.584, 585



Figure 2.8 Dependence of the depolarization degree (I||/I⊥) of laser radiation (He-Ne laser,λ = 633 nm; Ar laser, λ = 476/488/514 nm) on the penetration depth for brain tissue (grayand white matter) (a) and whole blood (low hematocrit) (b), see Ref. 583. Measurementswere performed within a small solid angle (10−4 sr) along the axis of a laser beam1 mm in diameter. A strong influence of fluorescence was seen in blood irradiated by theAr laser.

This is illustrated by Figs. 2.9 and 2.10, which present experimental data for thedecay of the DOLP, PL [see Eq. (2.20)], obtained for a gelatin gel–milk phantom (amodel of bloodless dermis) within a broad wavelength range,77, 586 and for varioustissues and blood as a function of light transmission.650 The kink in the characteris-tics of polarization decay [Fig. 2.9(b)], which can be observed for a small thicknessof 0.6 mm, can be attributed to the transition of a medium to the regime of multiplescattering.

The authors of Ref. 587 experimentally demonstrated that laser radiationretains linear polarization on the level of PL ≤ 0.1 within 2.5ltr. Specifically, forskin irradiated in the red and NIR ranges, they determined μa

∼= 0.4 cm−1, μs′ ∼=

20 cm−1, and ltr ∼= 0.48 mm. Consequently, light propagating in skin can retainlinear polarization within a length of approximately 1.2 mm. This optical path ina tissue corresponds to a time delay on the order of 5.3 ps, which provides anopportunity to produce polarization images of macro-inhomogeneities in a tissuewith a spatial resolution equivalent to that achieved by the selection of photonsusing more sophisticated time-resolved techniques. In addition to the selectionof diffuse-scattered photons, polarization imaging makes it possible to eliminatespecular reflection from the surface of a tissue, which allows this technique toimage microvessels in facile skin and to detect birefringence and optical activity insuperficial tissue layers.138, 588, 590, 590, 594, 595

Polarization imaging is a new direction in tissue optics.36, 129, 135, 138, 556–559,

560–580, 583–636, 640, 641, 647–654, 662, 663, 666, 670–673, 675–678, 680, 684, 687–695, 701, 709–712, 721, 726, 728,

731, 737, 749 The most prospective approaches for polarization tissue imaging, par-ticularly linear polarization degree mapping, 2D backscattering Mueller matrix


84 Chapter 2

Figure 2.9 Polarization spectra of light transmitted in the forward direction (a) and the rel-evant dependencies on layer thickness d for a gelatin gel–milk (20%) phantom (b) (seeRef. 586).

measurements, polarization-sensitive OCT, and the full-field polarization-speckletechnique, will be discussed in this and following chapters.

The registration of 2D polarization patterns for the backscattering of apolarized incident narrow laser beam is the basis for the polarization imagingtechnique.587, 594, 595 The major informative images can be received by using thebackscattering Mueller matrix approach.563, 573–579, 592, 593, 597–599 To determine each



Figure 2.10 Degree of linear polarization in different tissues as a function of the sampleoptical transmittance, Iout/Iin ≡ T, on 633 nm. Each point is an average of three measure-ments (see Ref. 650). The error bars representing standard deviation of measurements aresmaller than the symbols.

Figure 2.11 Schematic diagram of the experimental setup for polarization imaging (seeRefs. 563 and 593): LS, 10 mW He-Ne laser (633 nm); F1, 10% neutral density filter;PO1, polarization optics (set 1); L1, focusing lens (f = 10 cm); M1, mirror; S, sample; PO2,polarization analyzer optics (set 2); L2, imaging lens system; CCD, imaging camera.

of the 16 experimental matrix elements, a total of 16 images should be taken atvarious combinations of input and output polarization states.

A schematic view of the experimental setup used for collecting the diffusebackscattered images is shown in Fig. 2.11.563, 593 A collimated laser light beam ispolarized via various polarization optics (PO1) (linear and circular polarizers) toobtain the desired input polarization. This polarized light is focused through a hole(approximately 2 mm in diameter) in a mirror (M1) mounted onto the sample at45 deg. The diffusely backscattered light from the sample is then imaged througha polarization analyzer (PO2) by using a cooled 12-bit CCD camera. The polariza-tion analyzer consists of a variety of optics, which were interchanged to analyze


86 Chapter 2

Figure 2.12 Experimental and Monte Carlo backscattered Mueller matrix (see Refs. 563and 593): The individual images are represented by a two-letter combination that denotesthe input polarizer and output analyzer orientation (see Fig. 2.11). HV denotes horizontalinput polarized light and a vertical polarization analyzer; V, vertical; H, horizontal; P, +45 deg;M, –45 deg; R, right; L, left; and O, open polarization optics or none. The approximate sizeof each image is 1.6 × 1.6 cm2. The tissue-like phantom was composed of a suspension of2.02 μm polystyrene spheres in water: μ′

s ∼= 12 cm−1, g = 0.912, μa ≈ 0.

specific states of polarization (vertical; horizontal; ±45 deg linear; and left, right,circular) for a respective image used to reconstruct the Mueller matrix.

To determine each of the 16 experimental matrix elements, a total of 49 images(49 – 16 = 33 are dependent) were taken at various combinations of input andoutput analyzer polarization states.563, 593 Each of the 16 experimental elements wascalculated by adding or subtracting a series of images. Each image was collectedby using an exposure time of 1.7 s, averaging out the speckle effect (the estimatedcorrelation time of the laser-induced speckles was generally on the order of 10 ms).

A comparison of the measurements of the Mueller matrix elements with theMC calculations is presented in Fig. 2.12.563, 593 For the MC simulations, the aver-age number of collisions per photon trajectory was 10. This figure clearly showssatisfactory agreement between the experimental and calculated patterns, particu-larly azimuthal dependence. For the suspensions studied, the transport MFP, ltr, isapproximately 1 cm. It appears that for distances that exceed two transport MFPs,the azimuthal dependence of the images becomes less pronounced because multi-ple scattering tends to randomize the polarization state of the light. It was shownboth theoretically and experimentally that only seven matrix elements are indepen-dent; the rest can be obtained by simple rotations. The nature of such symmetryis quite general: the scattering medium should be invariant under rotations aroundthe initial laser beam direction and should contain an ensemble (or a finite numberof different ensembles) of identical (possibly asymmetric) scatterers in random



orientations.563, 593 The polarization images of tissue-like phantom, cancerous andnoncancerous cell suspensions, and living tissues (human skin and bone) are pre-sented in Refs. 563, 565, 566, 567, 568, 569, 574, 687, 688, 689, 690, 691, 692,677, 680, 684, 689, 690, 691, 692, 693, 696, 703, 704, 710, 711, 712, 726, 728,731, and 737.

In media containing large-scale scatterers (a common tissue model), depo-larization is a higher-order effect (∼θ4, θ < 1) than polarization (∼θ2).70 In theliterature, the polarization state of multiply scattered light is analyzed either underconditions of spatial diffusion of photons, when the angular spectrum of radiationis virtually isotropic (see, for example, Refs. 276, 605, and 662), or in the caseof small-angle scattering in media with large-scale inhomogeneities.70, 278, 557, 662

Following Ref. 70, the analysis of polarization state in the case of small-angularmultiple scattering is important for many problems pertaining to the optical diagno-sis of biological media that can be represented as random systems with long-rangecorrelation of fluctuations of dielectric permittivity. These systems display coherentscattering effects73, 74, 603 or may be expected to show fluctuations of polariza-tion similar to those in disordered media with large-scale inhomogeneities.604–608

Coherent effects at multiple scattering of polarized light were studied theoreticallyin Refs. 733, 739, and 752.

In weakly absorbing media showing small-angular multiple scattering, thedegree of linear polarization for a Henyey–Greenstein phase function [seeEq. (1.15)] is described by the following formula:70

PL = − [(μ′

s z)4/2θ2] ·[√

1 + (θ/μ′s z)2 − 1

]2

· [1 + (θ/μ′s z)2] . (2.56)

This means that in a very small angle range (θ << μ′sz), the degree of polarization

does not depend on the depth (z):

PL = −θ2/8. (2.57)

At the wings of the scattering angle dependence (θ >> μ′sz), it tends to

PL = −θ2/2, (2.58)

which equals the degree of polarization of singly scattered light.


Chapter 3

Discrete Particle Models ofTissue

In this chapter, discrete particle models of tissues are presented. Optical modelsof biotissue with basic single and low-order scattering are analyzed, in whichboth orderly and randomly distributed scatterers are considered. As examples,three types of eye tissues are shown with different structure and turbidity, suchas cornea, healthy or cataract lens, and sclera. Basic principles of transmission,reflection, and scattering spectra formation are discussed. The Mueller matrix ele-ment measurements applied for diagnostics and monitoring of biological tissue andcell pathology are presented.

3.1 Introduction

Although it follows from the preceding discussion that the optical properties oftissue are related to its microstructure and refractive index distribution, the natureof the relationship should be discussed in more detail. It has been shown that thecontribution of mitochondrial and spatial variations in the refractive index of cellsand other tissue components, such as collagen and elastin fibers, to the scatteringproperties of tissue can be estimated theoretically and experimentally.58, 85, 96, 220, 222

However, there is still no quantitative model that relates the microscopic prop-erties of cells and other tissue components to the scattering coefficients of bulktissue. Ideally, such a model should be able to predict the absolute magnitudesof optical scattering coefficients as well as their wavelengths and angle depen-dencies.222 To be useful for inverse problem solving, the model should provideinsight into how the scattering properties are influenced by the numbers, sizes,and arrangement of the tissue components. This section presents a framework fora particulate model of soft tissue that satisfies at least a few of these require-ments. The model was developed by the authors of Ref. 222. We will discuss theirpaper.

89


90 Chapter 3

3.2 Refractive-Index Variations of Tissue

Soft tissue is composed of closely packed groups of cells entrapped in a net-work of fibers through which water percolates. At a microscopic scale, the tissuecomponents have no pronounced boundaries. They appear to merge into a con-tinuous structure with spatial variations in the refractive index. To model sucha complicated structure as a collection of particles, it is necessary to resort to astatistical approach.

It has been shown that the tissue components that contribute most to the localrefractive-index variations are the connective tissue fibers (bundles of elastin andcollagen), cytoplasmic organelles (mitochondria, lysosomes, and peroxisomes),cell nuclei, and melanin granules.58, 220, 222 Figure 3.1 shows a hypothetical indexprofile formed by measuring the refractive index along a line in an arbitrary direc-tion through a volume of tissue. The widths of the peaks in the index profile are pro-portional to the diameters of the elements, and their heights depend on the refrac-tive index of each element relative to that of its surroundings. In accordance withthis model, the origin of the index variations will be represented by a statisticallyequivalent volume of discrete particles having the same index but different sizes.

The refractive indices of tissue structure elements, such as the fibrils, interstitialmedium, nuclei, cytoplasm, organelles, and tissue itself, can be derived by usingthe law of Gladstone and Dale, which states that the resulting value represents anaverage of the refractive indices of the components related to their volume fractionsas follows:654, 753

n =∑N

i=1nifi

∑ifi = 1, (3.1)

where ni and fi are the refractive index and volume fraction of the individualcomponents, respectively, and N is the number of components.

The statistical mean index profile in Fig. 3.1 illustrates the nature of the approx-imation implied by this model. The average background index is defined as theweighted average of refractive indices of the cytoplasm (cp) and the interstitialfluid (is), ncp and nis, as

n0 = fcpncp + (1 − fcp)nis, (3.2)

Figure 3.1 Spatial variations of the refractive index of a soft tissue. A hypothetical indexprofile through several tissue components is shown, along with the profile through a statisti-cally equivalent volume of homogeneous particles. The indices of refraction labeling of theprofile are defined in the text (see Ref. 222).


Discrete Particle Models of Tissue 91

where fcp is the volume fraction of the fluid in the tissue contained inside the cells.Literature data presented in Ref. 58 allow one to estimate ncp = 1.367 and nis =1.355. Because approximately 60% of the total fluid in soft tissue is contained inthe intracellular compartment, it follows from Eq. (3.2) that n0 = 0.6 · (1.367) +0.4 · (1.355) = 1.362. The refractive index of a particle can be defined as the sumof the background index and the mean index variation <�n>,

ns = n0 + <�n>, (3.3)

which can be approximated by another volume-weight average,

<�n> = ff(nf − nis) + fnc(nnc − ncp) + for(nor − ncp). (3.4)

Here, the subscripts f, is, nc, cp, and or refer to the fibers, interstitial fluid, nuclei,cytoplasm, and organelles, which were identified above as the major contributorsto index variations. The terms in parentheses in this expression are the differencesbetween the refractive indices of the three types of tissue components and theirrespective backgrounds; the multiplying factors are the volume fractions of the ele-ments in the solid portion of the tissue. The refractive index of the connective-tissuefibers is approximately 1.47 (see Table 7.2), which corresponds to approximately55% hydration of collagen, its primary component. The nucleus and cytoplasmicorganelles in mammalian cells that contain similar concentrations of proteins andnucleic acids, such as mitochondria and ribosomes, have refractive indices that liewithin a relative narrow range (1.38–1.41).58 Taking this into account and assum-ing that nnc = nor = 1.40, the mean index variation can be expressed in terms ofthe fibrous-tissue fraction, ff, only:

<�n> = ff(nf − nis) + (1 − ff)(nnc − ncp). (3.5)

Collagen and elastin fibers compose approximately 70% of the fat-free dry weightof the dermis, 45% of the heart, and 2–3% of the nonmuscular internal organs (seeRefs. 14–16 in Ref. 222). Therefore, depending on tissue type, ff may be as smallas approximately 0.02 or as large as 0.7. For nf − nis = 1.470 − 1.355 = 0.115and nnc − ncp = nor − ncp = 1.400 − 1.367 = 0.033, the mean index variationsthat correspond to these two extremes are <�n> = 0.02 · (0.115) + (1 − 0.02) ·(0.033) = 0.035 and <�n> = 0.7 · (0.115) + (1 − 0.7) · (0.033) = 0.09.

3.3 Particle Size Distributions

For certain tissues, the size distribution of the scattering particles may be essen-tially monodispersive; for others, it may be quite broad. Two opposite examplesare transparent eye cornea stroma, which has a sharply monodispersive distribu-tion, and turbid eye sclera, which has a rather broad distribution of collagen fiberdiameters.129 There is no universal distribution size function that describes all tis-sues with equal adequacy. In the optics of dispersed systems, Gaussian, gamma,or power size distributions are typical.237 Polydispersion for randomly distributedscatterers can be considered by using the gamma distribution or skewed logarithmic


92 Chapter 3

distribution of scatterer diameters, cross sections, or volumes.61, 129, 220, 222, 231, 238

In particular, for turbid tissues such as eye sclera, the gamma radii distributionfunction is applicable:61, 238

η(a) = aμ exp(−μβ), (3.6)

where σ/am = 2.35μ−0.5, β = a/am, σ is the half-width of the distribution; and am

is the more probable scatterer radius.A two-phase system composed of an ensemble of equally sized small particles,

and a minor fraction of larger particles, provides an accurate model of pathologicaltissue, e.g., a cataractous lens.239

For epithelial cells and their nuclei scattering structures, lognormal size dis-tributions of spherical or slightly prolated ellipsoidal particles are characteristicas232

η(a) = (1/aσ√

2π) exp{−[(ln(a) − ln(am)]2/2σ2}. (3.7)

In particular, for epithelial cells and their nucleus components, two lognormal sizedistributions for small and large spherical scatterers with the following parameterswere found in a certain line of rat prostate carcinoma cells:232 am1 = 0.012μm,σ1 = 1.15μm and am2 = 0.59μm, σ2 = 0.43μm.

To describe the scattering characteristics of a particle with a complex shape,unlike a sphere or long cylinder, certain special procedures can be applied, suchas the method of T-matrices.211, 212, 232 Complexly shaped scatterers, like cellsthemselves, may be modeled as aggregates of spherical particles.

The scattering centers in turbid tissue have a wide range of dimensions and tendto aggregate into complex forms suggestive of fractal objects. The skewed logarith-mic distribution function, as the most plausible on physical grounds, is extensivelyused in particle-size analysis. The skewed logarithmic distribution function for thevolume fraction of particles of diameter 2a is222

η(2a) = Fv

Cm(2a)3−Df exp

[−{ln(2a) − ln(2am)}2

2σ2

], (3.8)

where

Cm = σ√

2π(2am)4−Df exp[(4 − Df)

2σ2/2]

is the normalizing factor;

Fv =∫ ∞

0η(2a)d(2a)

is the total volume fraction of the particles, and quantities 2am and σ establishthe center and width of the distribution, respectively; Df is the (volumetric) fractaldimension.

In the limit of an infinitely broad distribution of particle sizes,

η(2a) ≈ (2a)3−Df . (3.9)



For 3 < Df < 4, this power-law relationship describes the dependence of the vol-ume fractions of subunits of an ideal mass fractal on their diameter, 2a. Thesesize distributions expand the size distributions described by Eqs. (3.6) and (3.7) toaccount for the fractal properties of tissues.

Scatterers in the epidermal layer of the skin also exhibit a lognormal size dis-tribution, whereas the spatial fluctuations in the index of refraction of dense fibroustissues, such as the dermis and many other tissues, follow a power law.107, 231

3.4 Spatial Ordering of Particles

A discrete particle ensemble is characterized by the packing density, or in otherwords, by the volume fraction occupied by particles. Evidently, in addition toparticle size, the volume fraction of particles is essential for the optical proper-ties of an ensemble due to its influence on the refractive index distribution [seeEqs. (3.1)–(3.5)], optical anisotropy [see Eqs. (2.2) and (2.3)], and other struc-tural characteristics. The volume fraction of particles for a certain tissue may beexperimentally found using electron micrographs of tissue slices. Estimation of thevolume fraction occupied by scattering particles may also be accomplished by theweighting of native tissue and dry rest.

The volume fraction occupied by the scattering particles in tissues, such asmuscle, cornea, sclera, and eye lens, covers 20 to 40%. Conventionally, 1 mm3

of whole blood contains (4 − 5) × 106 erythrocytes, (4 − 9) × 103 leukocytes, and(2 − 3) × 105 platelets. Cells represent 35–45% of the blood volume. The volumefraction, f, of erythrocytes in the blood is called the hematocrit (Hct). For normalblood, Hct = 0.4. The remaining 60% of the blood volume is mostly plasma: anessentially transparent water solution of salts.

Most tissues are comprised of cellular and subcellular structures located inclose proximity. In general, densely packed structures are likely to exhibit cor-relation scattering, an effect that has been observed, for instance, in corneastroma.63, 129, 644, 645, 647, 648 Cornea is comprised of individual collagen fibrils thatare closely packed and parallel in a lamella. If each fibril in the lamella scat-tered light independently, then the scattering cross section of the lamella wouldbe the product of the cross section of a single fibril and the number of fibrils inthe lamella. If all corneal fibers scattered light independently, the cornea wouldscatter 90% of incident light and we would essentially see nothing. However,the fibrils do not scatter independently and the coherent scattering (interference)effects cannot be neglected. Accordingly, correlated polarization effects can beobserved.63, 129, 647–650 For example, in spherical particle suspensions, as the parti-cle concentration increases beyond a concentration at which independent scatteringcan be assumed, the degree of polarization increases (rather than decreases) as thescatterer concentration increases.649, 650

Thus, the spatial organization of particles forming a tissue plays a substan-tial role in the propagation of light. As mentioned above, with very small packingdensities, incoherent scattering occurs by independent particles. If the volumefraction occupied by the particles is equal to or greater than 0.01–0.1, coherent


94 Chapter 3

concentration effects appear. The concentration of scattering particles is adequate,in most tissues, to allow spaces between individual scatterers that are comparableto their sizes. However, if the particle-size distribution is rather narrow, then densepacking entails a certain degree of order in the arrangement of the particles.

Spatial ordering is of utmost importance in optical eye tissue.63, 64, 129, 615,

644, 645, 647, 648 In a large variety of other tissues, spatial ordering is also inherent toa certain degree, particularly in tendon, cartilage, dura mater, skin, or muscle. Thehigh degree of order in densely packed scatterers ensures superior transmissionin the cornea and eye lens. Tissue structures with statistically ordered periodicalvariations in the index at characteristic scales of light wavelength, like photoniccrystals,652 exhibit high-transmission spectral regions and bands for which thepropagation of electromagnetic waves is forbidden. The position and depth ofthese bands depends on the size, refractive index, and spatial arrangement of thescattering particles.

To account for the interparticle correlation effects, which are critical for sys-tems with volume fractions of scatterers higher than 1–10% (when dependent onparticle dimensions), the following expression is valid for the packing factor of amedium filled with a volume fraction, fs, of scatterers with different shapes:214

ωp = (1 − fs)p+1

[1 + fs(p − 1)]p−1, (3.10)

where p is a packing dimension that describes the rate at which the empty spacebetween scatterers diminishes as the total density increases. The packing of spher-ical particles is accurately described by packing dimension p = 3. The packing ofsheet-like and rod-shaped particles is characterized by dimensions that approach1 and 2, respectively. The elements of tissue have many different shapes andmay simultaneously exhibit cylindrical and spherical symmetry, and the packingdimension may lie anywhere between 1 and 5. When one calculates the opti-cal coefficients at high concentrations of particles, the size distribution, η(2a)[Eqs. (3.6)–(3.9)], should be replaced by the correlation-corrected distribution:222

η′(2a) = [1 − η(2a)]p+1

[1 + η(2a)(p − 1)]p−1η(2a). (3.11)

Most of the observed scattering properties of soft tissue that are explained in thismodel treat tissue as a collection of scattering particles whose volume fractions aredistributed according to a skewed lognormal distribution, modified by a packingfactor to account for correlated scattering among densely packed particles.222

3.5 Scattering by Densely Packed Particle Systems

Because of the spatial correlation of individual scatterers, it is necessary to con-sider the interference of multiply scattered waves. Particle re-radiation in thedensely packed disperse system induces a distinction between an effective opti-cal field in a medium and the incident field. Under these conditions, the statistical



theory of multiple wave scattering seems to be highly promising for describingthe collective interaction between an ensemble of particles and electromagneticradiation.75, 654, 754

The rigorous theory of wave multiple scattering is constructed on the basisof fundamental differential equations for the fields, followed by using statisticalconsiderations.75 The total field, E(r), at point r is the sum of the incident field,Ei (r), and the scattered fields from all particles with regard to their phases:

E (r) = Ei (r) +∑N

j=1Es

j (r) , (3.12)

where Esj (r) is the scattered field of the jth particle. The field scattered by the

jth particle is defined by the parameters of this particle and by the effective fieldincident on the particle.

Twersky has derived a closed system of integral equations describing the pro-cesses of multiple scattering.755 A rigorous solution in general form has not yetbeen found for this problem. In actual calculations, various approximations areexploited to average Eq. (3.12) over statistical particle configurations. For example,the quasi-crystalline approximation proposed by Lax756 for densely packed mediais used most efficiently in tissue optics.654 Averaging of Eq. (3.12) over statisti-cal particle configurations results in an infinite set of equations that is truncated atthe second step by applying the quasi-crystalline approximation. The closed sys-tem of equations obtained for the effective field is reduced to a system of linearequations by expansion in terms of vector spherical or cylindrical harmonics. Theexplicit expressions757, 758 for the expansion coefficients involve the radial distri-bution function as well as the Mie coefficients for a single particle. The equalityto zero for the determinant of this system of linear equations yields the dispersionrelation for the effective propagation constant, keff, of this medium.759 For the sys-tems of particles whose sizes are small compared to the wavelength, the expressionfor keff obtained in this manner has the form654, 757

k2eff = k2 + 3fy

Dk2

[1 + i

2

3

k2a2y

DS3(θ = 0)

], (3.13)

where

y = n21 − n2

0

n21 + 2n2

0

, D = 1 − fy, S3 (θ = 0) = 1

1 − H3, H3 = −24f

(α

3+ β

4+ δ

6

),

(3.14)

in which f is the volume fraction occupied by particles with radius a and refractiveindex n1, and the α, β, and δ values are found according the approximation of hardspheres:

α = (1 + 2f )2

(1 − f )4 ,β = −6f(1 + 0.5f )2

(1 − f )4 , δ = 1

2f(1 + 2f )2

(1 − f )4 . (3.15)


96 Chapter 3

The calculated effective index of refraction,654

neff = n′eff + in′′

eff, (3.16)

is complex, even if the particles and the surrounding base substance exhibit nointrinsic absorption. The imaginary part of the effective index of refraction, n′′

eff,describes the energy diminishing for an incident plane wave due to scattering in alldirections. The transmittance of this layer with thickness z is

T = exp(−4π

λn′′

effz). (3.17)

The quantity 4πλ

n′′eff is the extinction coefficient, μt. The value of the imaginary

part of the effective index of refraction grows with higher radiation frequency forthese systems, and nonmonotonously depends on the particle concentration in thelayer. As a result, the transmittance of the disperse layer decreases for small par-ticle concentrations with a greater concentration of particles, and starting at f ≈0.1, the transmittance grows, and the clearing effect takes place. The real portionof the effective index of refraction in this approximation is essentially independentof the wavelength and alters monotonously with growing particle concentrationto approach the refractive index of particles. The near ordering in the scatter-ers’ arrangement with greater concentration not only provides conditions for themanifestation of the secondary scattered wave interference, but also changes theregime of propagation of noncoherent multiply scattered light.760 This may beaccompanied by the concentration effects of clearing and darkening.

The optical softness of tissues enables one to employ an expansion in calcu-lation by scattering multiplicities with restricting by low orders. In Ref. 761, anexpression was obtained for the effective index of refraction of the eye cornea,modeled by a system of cylindrical scatterers in the form of expansion by scat-tering multiplicities, and the effects of polarization anisotropy were analyzed withrespect to the double scattering contributions.

Using the theory of multiple scattering, Twersky762 succeeded in deriving theapproximate expressions for absorption, μa, and scattering, μs, coefficients describ-ing light propagation in the blood. The blood hematocrit, Hct, is related to theerythrocyte concentration, ρ, and to the volume of an erythrocyte, Ve, by thefollowing ratio:275, 762

ρ = Hct/Ve. (3.18)

Thus, μa is

μa = (Hct/Ve)σa. (3.19)

For sufficiently small values of Hct (Hct < 0.2), the scattering coefficient is givenby the equation

μs = (Hct/Ve)σs. (3.20)



For Hct > 0.5, the particles become densely packed and the medium is almosthomogeneous. In this case, the blood may be considered as a homogeneousmedium containing hemoglobin, in which scattering particles formed by plasmasurrounding red blood cells are embedded. Within the limit of Hct → 1, plasmaparticles disappear and the scattering coefficient should tend to zero. This resultsin the following approximate equation for μs:275, 763

μs ≈ Hct(1 − Hct)

Veσs, (3.21)

where the coefficient (1 − Hct) regards the scattering termination with Hct → 1.However, the absolute dense packing (Hct = 1) is not attainable in reality; forexample, for the hard sphere approximation, Hct may not exceed 0.64. Consideringthis fact and keeping in mind the physiological conditions, the effect of cell packingon light scattering might be described by a more complex function:

μs = (Hct/Ve)σsF(Hct), (3.22)

where the packing function F(Hct) accounts for physiological conditions of redblood cells, particularly, cell deformability at high concentration.

Although the equations from Twersky’s wave-scattering theory755, 762 agreereasonably well with measured optical density data for a whole blood layer,763

researchers have resorted to curve-fitting techniques for evaluating the parame-ters in Twersky’s equations. Additionally, this theory does not describe the spatialdistribution of the reflected and transmitted light, and therefore, does not accom-modate light detectors and sources that do not share a common optical axis. Bycontrast, the radiative transfer theory discussed above — particularly its more sim-ple diffusion approximation — overcomes the limitations of the wave-scatteringtheory; but to be applied to densely packed tissues, this theory should accountfor particle interaction and size distribution effects. The combination with othertheories describing particle interactions and the usage of empirical data can be con-sidered as a fruitful and practical approach for modeling the optical properties oftissues.

For example, using the diffusion theory, Steinke and Shepherd763 have cor-rected the dependence [Eq. (3.21)] of μs for a thin blood layer on Hct, asfollows:

μs ≈ (Hct/Ve)σs(1 − Hct)(1.4 − Hct). (3.23)

Using the concept of a combination of photon-diffusion theory and parti-cle representation of a tissue, a micro-optical model that explains most of theobserved scattering properties of soft tissue has been developed.222 The modeltreats the tissue as a collection of scattering particles whose volume fractions aredistributed according to a skewed lognormal distribution modified by a packingfactor, p, to account for correlated scattering among densely packed particles [seeEqs. (3.8), (3.9), and (3.11)]. Assuming that the waves scattered by the individualparticles in a thin slice of the modeled tissue volume are added randomly, then


98 Chapter 3

the scattering coefficient of the volume can be approximated as the sum of thescattering coefficients of the particles of a given diameter as

μs =∑Np

i=1μs(2ai), (3.24)

where

μs(2ai) = η(2ai)

viσs(2ai), (3.25)

Np is the number of particle diameters; η(2ai) is the volume fraction of particles ofdiameter 2ai [see Eqs. (3.8), (3.9), and (3.11)]; σs(2ai) is the optical cross sectionof an individual particle with diameter 2ai and volume νi. The volume-averagedphase function, (p(θ)) (and scattering anisotropy parameter, g), of the tissue slice isthe sum of the angular-scattering functions, pi(θ) (and anisotropy parameters, gi),of the individual particles weighted by the product of their respective scatteringcoefficients:

p(θ) =∑Np

i=1μs(2ai)pi(θ)∑Np

i=1μs(2ai); (3.26)

g =∑Np

i=1μs(2ai)gi(2ai)∑Np

i=1μs(2ai). (3.27)

The reduced scattering coefficient is usually defined as μ′s = μs(1 − g). The

volume-averaged backscattering coefficient can be defined as the sum of the parti-cle cross sections weighted by their angular-scattering functions, evaluated at 180deg:

μb =∑Np

i=1

η(2ai)

viσs(2ai)pi(180◦). (3.28)

The product of μb (cm−1/sr) and the thickness of the tissue slice yield the fractionof incident irradiance backscattered per unit solid angle in the direction opposite tothe incident light.

The evaluation of the model by applying Mie theory to a collection of sphereswith a wide range of sizes produced a set of parameters for the distribution andpacking of the particles: volumetric fractal dimension, Df = 3.7; mean refractiveindex of tissue grounds, n0 = 1.352; mean refractive index of scatterers (particles),ns = 1.420; total volume fraction of the particles, Fν = 0.2; center of particle sizedistribution, 2am = 1.13μm; width of this σ = 2μm; and packing factor, p = 3[see Eqs. (3.3) and (3.8)–(3.11)]. These parameters yield credible estimates ofthe scattering coefficients and scattering anisotropy parameters of representativesoft tissues. Table 3.1 summarizes the optical properties predicted by the modelat three wavelengths (633, 800, and 1300 nm) for a soft tissue containing dif-ferent dry-weight fractions of connective tissue fibers (ff = 0.03, 0.3, and 0.7).The coefficients μs, μ′

s, μb, and g were computed for specific parameters of the



Table 3.1 Optical coefficients of model tissues with three different dry-weight fiber fractions(f f), for Df = 3.7 (see Ref. 222).

Wavelength, nm 633 800 1300

f f 0.03 0.3 0.7 0.03 0.3 0.7 0.03 0.3 0.7μs, cm−1 105 224 402 69 146 274 29 63 119μ′

s, cm−1 8.0 20 45 5.7 14 32 3.0 7.5 16.5μb, cm−1/sr 0.8 2.2 5.0 0.5 1.3 3.1 0.3 0.9 2.0g 0.92 0.91 0.89 0.92 0.90 0.88 0.90 0.88 0.86

particle system. In general, these calculations accurately fit the experimental datafor in vitro and even in vivo measurements of the optical parameters of softtissues.

By using the model to describe soft tissue, the authors of Ref. 222 have shownthe following: (1) as an optical medium, tissue is best represented by a volume ofscatterers with a wide distribution of sizes; (2) fixing the total volume fraction ofparticles and their refractive indices places upper and lower bounds on the mag-nitude of the scattering coefficient; (3) the scattering coefficient decreases with anapproximate wavelength of μs ∼ λ2−Df for 600 ≤ λ ≤ 1400 nm, where Df is thelimiting fractal dimension; and (4) scatterers in tissue with diameters between λ/4and λ/2 are the dominant backscatterers, and those that cause the greatest extinctionof forward-scattered light have diameters between 3λ and 4λ.

As it follows from Ref. 107, Df is highly dependent on the discretizationof continuous size distribution. In the 10-sphere discrete model by Schmitt andKumar,222 a fractal dimension between 3 < Df < 4 was found, in contrast tothe model described by Wang,107 of spheres ranging from 5 to 30,000 nm inintervals of 5 nm; ranges of fractal dimension such as 4 < Df < 5 were deter-mined. In Wang’s model, the scattering coefficient decreases with wavelength asμs ∼ λ3−Df for 600 ≤ λ ≤ 1500 nm; therefore, both models produce similar powerlaws for dependence of the scattering coefficient on the wavelength, which rangesfrom μs ∼ λ−1 to μs ∼ λ−2. The magnitude of the scattering coefficient increasesas the fractal dimension decreases because the larger particles, which have thelargest optical cross sections, contribute relatively more to the total optical crosssection of the tissue. Wang’s model also confirms that particles with diametersbetween λ/4 and λ/2 are the dominant backscatterers; however, in comparison tothe model by Schmitt and Kumar, it predicts a wider range of scatterer diameters forwhich the greatest extinction of forward scattering is characteristic, i.e., between λand 10λ.

The reduced scattering coefficient decreases with an increase in wavelength inaccordance with a power law that was experimentally demonstrated in an in vitrostudy for normal, dehydrated, and coagulated human aorta as764, 765

μ′s ∝ λ−h. (3.29)

Experimental data for normal human (control) and processed samples of humanaorta are presented in Table 3.2. At direct heating (100◦C), h was reduced from 1.38


100 Chapter 3

Table 3.2 Power relationship between wavelength and reduced scattering coefficient, h[see Eq. (3.29)], and significance of h values for control and experimental reduced scatteringspectra (400–1300 nm) for human aorta, obtained from t-test (rms values in parentheses)(see Refs. 764 and 765).

Description hcontrol hexper Significance, %

Dehydration 1.15 (0.10) 1.22 (0.13) ∼15Heating at 60◦C 1.21 (0.12) 1.28 (0.04) ∼25Heating at 70◦C 1.30 (0.01) 1.10 (0.10) <5Heating at 100◦C (direct heating) 1.38 (0.11) 1.06 (0.07) <5Heating at 100◦C (wrapped heating) 1.26 (0.08) 1.03 (0.05) <5

to 1.06 for the normal and heated tissue samples, respectively. An in vitro study ofrat skin impregnated with glycerol also showed a power wavelength dependenceof the reduced scattering coefficient in the range 500–1200 nm with h = 1.12 fornormal skin, and with subsequent decreases in h with increased time in glycerol(mostly dehydration effect).766 These values were 1.09 for 5 min, 0.85 for 10 min,0.52 for 20 min, and 0.9 for the rehydrated sample.

In vivo backscattering measurements for human skin and underlying tissuesalso have demonstrated the power law for the wavelength dependence of thereduced scattering coefficient:767

μ′s = qλ−h(cm−1, λ in μm). (3.30)

In particular, for reflectance spectra from the human forearm in the wavelengthrange 700–900 nm, constants q and h were determined as 5.50 ± 0.11 and 1.11± 0.08, respectively. From Mie theory, it follows that the power constant, h, isrelated to an average size of the scatterers: the Mie-equivalent radius, aM. Once his determined, this radius can be derived from767

h = −1109.5 a3M + 341.67 a2

M − 9.36961 aM − 3.9359 (aM < 0.23 μm) (3.31)

h = 23.909 a3M − 37.218 a2

M + 19.534 aM − 3.965 (0.23 < aM < 0.60 μm).

(3.32)

These relations were determined for a relative refractive index between spheresand the surrounding medium, m = 1.037. The in vivo measured constant, h = 1.11,leads to an aM value of 0.30 μm, which is approximately two times smaller thanthe mean radius (0.57 μm) used in the previously discussed model of a collectionof packed spheres with a wide range of sizes.222

3.6 Optical Properties of Eye Tissues

3.6.1 Optical models

3.6.1.1 Structure of eye tissues

Healthy tissues of the anterior human eye chamber (e.g., the cornea and lens; seeFig. 3.2) are highly transparent for visible light because of their ordered structure



Figure 3.2 Diagram of the human eye showing the locations of cornea, lens, sclera, andother eye components (see Ref. 776). (See color plates.)

and the absence of strongly absorbing chromophores. Scattering is an importantfeature of light propagation in eye tissues. The size and the distance between scat-terers are smaller than or comparable to the wavelength of visible light, and therelative refractive index of scatterers is equally small (soft particles). Typical eyetissue models are long, round dielectric cylinders (corneal and scleral collagenfibers) or spherical particles (lens protein structures) having a refractive index, ns;they are randomly (or quasi-orderly) (sclera and opaque lens) or regularly (trans-parent cornea and lens) distributed in the isotropic base matter with refractiveindex n0 < ns.3, 10, 24, 61, 63, 64, 77, 129, 238, 609, 611, 614, 615, 644, 645, 647, 648, 651, 652, 768–801 Lightscattering analysis in eye tissue is often possible by using a single scattering modelowing to the small scattering cross section (soft particles).

Let us first consider the structure of the cornea and the sclera in more detail,to demonstrate tissues with different size distributions and spatial ordering ofscatterers.3, 129, 644, 768–780 The cornea is the frontal section of the eye’s fibrous cap-sule; its diameter is approximately 10 mm. The sclera is a turbid opaque tissuethat covers nearly 80% of the eye and serves as a protective membrane to retaineye shape and to provide, along with the cornea, counteraction against internal andexternal forces. Both tissues are composed of collagen fibrils immersed in a groundsubstance.644, 768–773, 777–780 The shape of the fibrils is similar to that of a cylinder.


102 Chapter 3

Figure 3.3 Schematic illustration of the lamellar organization of the cornea stroma. Thediagram also depicts how keratocytes are interspersed between lamellae (see Ref. 645).

They are packed in bundles like lamellae. Within each lamella, all fibers are nearlyparallel with each other and with the lamella plane. Fibrils and lamellar bundles areimmersed within an amorphous ground (interstitial) substance containing water,glycosaminoglycans, proteins, proteoglycans, and various salts. The glycosamino-glycans play a key role in regulating the assembly of the collagen fibrils, as wellas in tissue permeability to water and other molecules.779 The indices of refractionfor the fibers and ground substance differ markedly.

The structural elements that give the cornea the strength to preserve itsproper curvature while withstanding intraocular pressure (14–18 mm Hg) arelocated within its stromal layer, which constitutes 0.9 of the cornea’s thick-ness.644, 645, 657, 770, 774–776 The stroma is composed of several hundred successivelystacked layers of lamellae (see Fig. 3.3), which vary in width (0.5–250 μm) andthickness (0.2–0.5 μm), depending on the tissue region770 (three sequential lamel-lae are shown in Fig. 3.4). A few flat cells (keratocytes) are dispersed betweenthe lamellae, which occupy only 0.03–0.05 of the stromal volume. Each lamella iscomposed of a parallel array of collagen fibrils. Human corneal thickness averages0.52 mm.

Although the cornea fibril diameters vary from 25 to 39 nm in differentmammals, the fibrils are quite uniform in diameter within each species.770, 771, 779

Spacing between fibril centers is equal to 45–65 nm; intermolecular spacing withinfibrils is in the range of 1.56–1.63 nm.771 The fibrils in the human cornea havea uniform diameter of approximately 30.8 ± 0.8 nm with similar periodicity totwo diameters, 55.3 ± 4.0 nm, and rather high regularity in the organization offibril axes about one another (see Fig. 3.4). The intermolecular spacing is 1.63 ±0.10 nm.771 Thus, the stroma has at least three levels of structural organization: thelamellae that lie parallel to the cornea’s surface; the fibrillar structure within eachlamella that consists of small, parallel collagen fibrils with uniform diameters thathave some degree of order in their spatial positions; and the collagen molecularultrastructure.



Figure 3.4 Collagen fibrils in the human cornea have a uniform diameter and are arrangedin the same direction within the lamellae (see Ref. 770). K is the keratocyte (×32,000,scanning electron microscopy).

The sclera contains three layers: the episclera, the stroma, and the laminafusca.769 The stroma is the thickest layer of the sclera. The thickness of the scleraand the arrangement of scleral collagen fibers show regional (limbal, equatorial,and posterior pole region) and aging differences. In the scleral stroma, the collagenfibrils exhibit a wide range of diameters, from 25 to 230 nm (see Fig. 3.5).770 Theaverage diameter of the collagen fibrils increases gradually from approximately 65to 125 nm in the innermost and outermost parts of the sclera, respectively;778 themean distance between fibril centers is approximately 285 nm.780 Collagen inter-molecular spacing is similar to that in the cornea; in bovine sclera, particularly, itis equal to 1.61 ± 0.02 nm.779

These fibrils are arranged in individual bundles in a parallel fashion, but morerandomly than in the cornea; moreover, within each bundle, the groups of fibersare separated from each other by large, empty lacunae randomly distributed inspace.770 Collagen bundles show a wide range of widths (1 to 50 μm) and thick-nesses (0.5 to 6 μm) and tend to be wider and thicker toward the inner layers. Theseribbon-like structures are multiply cross-linked; their length can be a few millime-ters.769 They cross each other in all directions, but remain parallel to the scleralsurface. The episclera has a similar structure, with more randomly distributed andless compact bundles than in the stroma. The lamina fusca contains a larger amountof pigments, primarily melanin, which are generally located between the bundles.


104 Chapter 3

Figure 3.5 Collagen fibrils in the human sclera (see Ref. 770). Scleral collagen fibrils dis-play various diameters, which are much larger than those in the cornea. Mf is the microfibril(×18,000, scanning electron microscopy).

The sclera itself does not contain blood vessels, but has a number of channels thatallow arteries, veins, and nerves to enter or exit the eye.769

The thickness of the sclera is variable. It is thicker at the posterior pole (0.9to 1.8 mm) and thinnest at the equator (0.3 to 0.9 mm), and ranges from 0.5 to0.8 mm at the limbus. Hydration of the human sclera can be estimated as 68%.Approximately 75% of its dry weight is attributable to collagen; 10% is attributableto other proteins and 1% to mucopolysaccharides.769

When designing an optical model of a tissue, in addition to form, size, anddensity of the scatterers (fibrils) and thickness of the tissue, it is important tohave information about the refractive indices of the tissue components. FollowingRefs. 238, 769, 771, and 773, we can estimate the refractive index of the cornealand scleral fibrils (hydrated collagen), nc, using Eq. (3.2), which was written forthe average refractive index of the tissue, nt:

nc = nt − (1 − fc)nis

fc, (3.33)



where fc is the volume fraction of the hydrated collagen and nis is the refrac-tive index of the interstitial fluid. The refractive indices measured for thedry corneal collagen and interstitial fluid are: ndry

c = 1.547 and nis = 1.345 −1.357.644,645,647,769,771,773 The refractive index of the corneal stroma measured formany species is nt = 1.375 ± 0.005.771 Therefore, for nis = 1.356 and fc = 0.32,corresponding to tissue hydration of 76.2% and collagen content of 61.3% of thedry weight,771 it is easy to obtain the refractive index of the hydrated fibrils asnc = 1.415 by using Eq. (3.33). The direct measurement of the average refractiveindex of sclera using an Abbe refractometer gives nt = 1.385 ± 0.005 for λ = 589nm. Because of the similarly fibrous nature of the cornea and the sclera, it isexpected that at equal hydration, the refractive indices of scleral collagen and itsinterstitial fluid should be equal to these indices in the cornea. For nt = 1.385,nis = 1.345, and fc = 0.31, corresponding to tissue hydration of 68% and collagencontent of 75% of the dry weight, it follows from Eq. (3.33) that for the refractiveindex of the scleral fibrils, nc = 1.474. Changes in nc and fc with hydration can beevaluated from measurements of the refractive index and thickness of the collagenfilms.802

Although both tissues are composed of similar molecular components, theyhave different microstructures, and thus, very different physiological functions.The cornea is transparent, allowing for more than 90% of the incident light to betransmitted. The collagen fibrils in the cornea feature much more uniform size andspacing than those in the sclera, resulting in a greater degree of spatial order in theorganization of the fibrils in the cornea than in the sclera. The sclera of the eye isopaque to light; it scatters almost all wavelengths of visible light, and thus, appearswhite.

Light propagation in a densely packed disperse system can be analyzed byusing the radial distribution function, g(r), which statistically describes the spatialarrangement of particles in the system. Function g(r) is the ratio of the local numberdensity of the fibril centers at distance r from a reference fibril at r = 0 to thebulk number density of fibril centers.645 It expresses the relative probability offinding two fibril centers separated by distance r; thus, g(r) must vanish for valuesof r ≤ 2a (a is the radius of a fibril—fibrils cannot approach each other closer thantouching). The g(r) for a certain tissue may be calculated on the basis of tissueelectron micrographs (see Figs. 3.4 and 3.5).

The technique for the experimental determination of g(r) involves countingthe number of particles placed at a specified spacing from an arbitrarily choseninitial particle, followed by statistical averaging over the whole ensemble. In a two-dimensional case, particle number �N at the spacing from r to r + �r is related tofunction g(r) by the following equation:

�N = 2πρg (r) r�r, (3.34)

where ρ is the mean number of particles for a unit area.The g(r) was first found for rabbit cornea by Farrell et al.645 Figure 3.6(a)

depicts a typical result for a corneal regions, which was obtained by determiningthe ratio of the local mean density of the centers as a function of radii taken from


106 Chapter 3

Figure 3.6 Histograms of radial distribution functions g(r) obtained from electron micro-graphs of rabbit cornea (a) (see Ref. 645) and human sclera (b) (see Refs. 651 and 791).

700 fibril centers. Function g(r) = 0 for r ≤ 25 nm, which is consistent with afibril radius of 14 ± 2 nm, can be calculated from the electron micrograph. Thefirst peak in the distribution provides the most probable separation distance, whichis approximately 50 nm. The value of g(r) is essentially unity for r ≥ 170 nm,indicating that the fibril positions are correlated over no more than a few of theirnearest neighbors. Therefore, a short-range order exists in the system.

Similar calculations for several regions of the human eye sclera651, 791 are illus-trated in Fig. 3.6(b). Electron micrographs from Ref. 770, averaged for 100 fibrilcenters, were processed (see Fig. 3.5). Function g(r) for the sclera was obtained onthe basis of the spatial distribution of the fibril centers, neglecting discrepancy intheir diameters. Some noise is attributable to the small volume of statistical aver-aging. The obtained results present evidence of the presence of a short-range orderin the sclera, although the degree of order is less pronounced than in the cornea.Function g(r) = 0 for r ≤ 100 nm, which is consistent with the mean fibril diameterof ≈100 nm derived from the electron micrograph (see Fig. 3.5).770 The first peakin the distribution gives the most probable separation distance, which is approxi-mately 285 nm. The value of g(r) is essentially unity for r ≥ 750 nm, indicating ashort-range order in the system. The short-range order, which is characterized bya ratio of this specific distance (decay of spatial correlation) to the most probableparticle separation distance, (750/285) ≈ 2.7, is smaller than the similar ratio forthe cornea, (170/50) = 3.4.

The spatial density (refractive index) fluctuations of a tissue can also beanalyzed by resolving 2D profiles of refractive index variations into Fouriercomponents, which provides a basis for detailed and quantitative descriptions of the



microstructure.772, 780 These Fourier components represent the predominant spatialdensity fluctuations and structural ordering. A comparable study of human corneaand sclera has shown that the cornea reveals much less collagen fibril spacing andgreater spatial order than the sclera.

The eye lens is another example of a tissue in which the short-range spatialorder is crucially important. Because of its high index of refraction and trans-parency, a lens focuses light to form an image at the retina (see Fig. 3.2). Theeye lens material exhibits a certain viscosity that is capable of altering its radius ofcurvature, and thus its focal length, through the action of accommodating mus-cles. The healthy human lens is a coherent structure containing approximately60% water and 38% protein.782–790 The lens consists of many lens fiber cells. Thepredominant dry components of a mammalian lens are three kinds of structuralproteins designated α-, β-, and γ-crystallins; their combined weight accounts forapproximately 33% of the total weight of the lens.793 The crystalline lens growsthroughout life and additionally undergoes a variety of biochemical changes as oneages. These changes include the possibility of age-related cataract formation, lead-ing to greatly increased light scatter and coloration, and eventually to lens opacity.Photo-oxidation of lens proteins by chronic UV, UVA, or visible light results inoxidized forms of these proteins, which crosslink to other proteins, causing opaci-ties or pigment formation.794 With pulse or CW UVA illumination of the eye lens,there is a probability of the aggregation of crystallins via bimolecular interactionof photoactivated protein molecules.799–801

Light scattering is caused by random fluctuations in the refractive index.These fluctuations can be density or optical anisotropy fluctuations.64, 609, 613, 614,

621, 782, 784, 788 Fluctuations in the refractive index due to density may arise becauseof (1) aggregation of lens proteins, (2) microphase separation (cold-inducedcataract), or (3) syneresis (water is released from the bound state in the hydra-tion layers of lens proteins and becomes bulk water; this increases the refractiveindex difference between the lens proteins and the surrounding fluid). Analyses ofpolarized light scattering of human cataracts have shown that 15% to 30% of theturbidity results from optical anisotropy fluctuations.

Eye lens transparency can be explained by short-range ordering in the packingstructure of the lens proteins. This idea was first suggested by Benedek.794 Theprimary role among the ocular lens proteins is played by water-solubleα-crystallin,which has a shape that is almost spherical and a diameter of approximately 17 nm.Studies of lens transparency, birefringence, and optical activity are critical for theearly diagnosis of cataracts.704, 782–790, 793–798

The types of fiber cell disruption attributable to cataract formation includeintracellular globules, clusters of globules, vacuoles with wholly or partiallyremoved contents, clusters of highly curved cell membranes, and odd-shapeddomains of high or low density.790 These spherical objects are variable in size(often in the range 100 to 250 nm) and occur in clusters that create potentialscattering centers.


108 Chapter 3

Table 3.3 Structural and optical properties of human eye tissues [refractive index of theground (interstitial) substance, n0 = 1.345].

Tissue Model Tissue thick-ness, mm

Diameter ofscatterers, nm

Refractive indexof scatterers, ns

Multiplicity ofscattering

Cornea Monodispersive systemof regularly distributedlong dielectric cylinders

0.46–0.52 30.8 ± 0.8 1.470 Single orlow-step

Sclera Polydispersive systemof randomly distributedlong dielectric cylinders

0.3–1.8 25–230 1.474 Multiple

Normal lens Monodispersive systemof regularly distributeddielectric spheres

5.0 20–200 1.380 Single orlow-step

Cataractlens

Two-phase system ofrandomly distributeddielectric spheres

5.0 200–2000 1.40–1.48 Low-stepor multiple

Optical models of the eye tissues have the following specific features:

1. Optical inhomogeneity generates light scattering.2. The mean distance between scatterers and their dimensions is less than or

comparable to the wavelength.3. Scattering particles are “soft;” i.e., the refractive index of their material,

ns, is similar to the refractive index of the ground (interstitial) substance,n0(ns ≥ n0).

4. In the major cases, absorption is small.5. Transparent tissue has an approximately monodispersive and ordered struc-

ture.

The major structural characteristics of the human eye tissues are summarizedin Table 3.3.

3.6.1.2 Tissue ordering

A certain correlation exists between waves scattered by adjacent particles in adensely packed medium that has characteristic dimensions on the order of awavelength. Therefore, it is necessary to sum the amplitudes of scattered waveswith regard to their phase relations. The interference interaction may result in anessential alteration of the total scattered intensity, its angular dependence, or thepolarization characteristics of the scattered light, compared with similar quantitiesfor a system of noninteracting particles.

To illustrate light scattering in a correlated disperse system, we will use aradial distribution function, g(r), which is a statistical characteristic of the spa-tial arrangement of the scatterers129, 645 (see Fig. 3.6). Let us consider N sphericalparticles in a finite volume. The pair distribution function, gij(r), is proportionalto the conditional probability of finding a particle of type j at distance r from the



Figure 3.7 Diagram of the radial distribution function, g(r), which is proportional to theprobability of particle displacement at a certain distance r from an arbitrarily fixed particle(see Refs. 651 and 791).

origin, given that there is a particle of type i at the origin (Fig. 3.7).803 In a modelof mutually impenetrable (hard) spheres, the interparticle forces are zero, excepttwo neighbor particles cannot interpenetrate each other.

The arrangement of particles in a densely packed system is not entirely ran-dom. A short-range order can be observed that is relatively ordered when thedensity of the scattering centers is great and their size distribution is narrow. Nearthe origin of the coordinates, in the region within the effective particle diame-ter, function g(r) = 0, which indicates the impenetrability of a particle. Functiong(r) has a few maxima whose positions correspond to distances from the cho-sen particle to its first, second, and further neighbors. Nonzero values of minimaare indicative of particle distribution between various coordination spheres. It isobvious that the correlation between pairs of particles should be degraded with r;hence, lim

r→∞ g (r) = 1. Function g(r) is the ratio of the local number density of the

scattering centers at distance r from an arbitrary center to the bulk number density.The medium composed of N scatterers considered here is analogous to a mix-

ture of L types of particles in the study of statistical mechanics, by consideringthe dynamics and positions of the particles with regard to the interparticle forces.Studies have obtained the pair distribution functions by using various approximatetheories. One important result is based on the Percus–Yevick (PY) approximation.The analytical solution of this equation exists as applied to a model of hard spheres


110 Chapter 3

distributed in 3D space. To find the function of radial distribution, the MC methodis also used. The solution of the Ornstein–Zernice equation for the case of singlespecies has been solved by Wertheim.804 For the case of two species, the solutioncan be found in Ref. 805. For the general case of L species, the solution based ona generalized Wiener–Hopf technique is obtained by Baxter.806 The polydispersityof the real system is approximated by an L-step distribution function.

For monodisperse systems of spherical particles with diameter of 2a, g(r) isrepresented by an approximation of the hard spheres as follows:807

g (r) = 1 + 1

4πf

∫ ∞

0

H23 (z)

1 − H3 (z)

sin zx

zxz2dz, for x > 1, (3.35)

where x = r/2a,

H3 (z) = 24f∫ 1

0c3 (x)

sin zx

zxx2dx, c3 (x) = −α− βx − δx3, (3.36)

α = (1 + 2f )2

(1 − f )4 ,β = −6f(1 + 0.5f )2

(1 − f )4 , δ = 1

2f(1 + 2f )2

(1 − f )4 , (3.37)

f is the volume fraction of particles.Let us consider light scattering by a system of N spherical particles.654 In gen-

eral, the field affecting a particle differs from the field of the incident wave, Ei,because the latter also contains the total field of adjacent scatterers. Within thesingle-scattering approximation (Born’s approximation), the field affecting the par-ticle does not essentially differ from that of the initial wave. For cases in whichdouble scattering of the field affects the particle, one needs to take the sum ofthe initial field plus the single-scattered field, and continue from this point.75

For transparent tissues composed of optically soft quasi-regularly packed par-ticles, the use of the single-scattering approximation yields highly satisfactoryresults.10, 24, 63, 64, 77, 129, 199, 611, 614, 615, 645, 647, 648, 652, 773, 782, 784, 795, 796

A field scattered by a particle with the center defined by radius-vector rj differsfrom a field scattered by a particle placed at the origin of the coordinates by a phasemultiplier characterizing the phase shift of the waves. The phase difference is equalto (2π/λ)(S0 − S1)rj, where S0 and S1 are the unit vectors of the directions of theincident and scattered waves (see Fig. 2.3). The difference between these vectorsis called the scattering vector, q:

q = 2π

λ(S0 − S1). (3.38)

Considering that the wave vector module is invariable with elastic scattering, thevalue of the scattering vector is found as follows:

|q| ≡ q = 4π

λsin(θ/2), (3.39)



where θ is the angle between directions S0 and S1, i.e., the scattering angle. Theamplitude of a wave scattered by a system of N particles will be

Es =∑N

j=1Esj =

∑N

j=1E0je

iqrj , (3.40)

where E0j is the scattering amplitude of an isolated particle. The single-scatteringintensity for the given spatial realization of the N particle arrangement is

I = |Es|2 =∑N

j=1E0j

∑N

i=1E∗

0ieiq(rj−ri). (3.41)

For real systems, the only mean scattering intensity of an ensemble of particles isdetected; natural averaging is caused by thermal particle motion, finite measuringtime, and a finite area of a photodetector, thus,

〈I〉 =⟨∑N

j=1

∑N

i=1E0jE

∗0ie

iq(rj−ri)⟩

. (3.42)

The brackets show the averaging over all possible configurations of the particlearrangement in the system. This equation represents the sum of the two contribu-tions to the noncoherent scattered intensity. One defines the light distribution on theassumption that there is no interference of light scattered by various particles. Theother term regards the interference affecting the light field structure and dependson the degree of order in the particle arrangement characterized by g(r). For anisotropic system of identical spherical particles, we may write648

〈I〉 = |E0|2 NS3(θ), (3.43)

S3(θ) ={

1 + 4πρ∫ R

0r2

[g(r) − 1

] sin qr

qrdr

}, (3.44)

where q is defined by Eq. (3.39), ρ is the mean density of particles, and R is thedistance for which g(r)→1. Quantity S3(θ) is the 3D structure factor. This fac-tor describes the alteration of the angle dependence of the scattered intensity thatappears with a higher particle concentration (Fig. 3.8). To approximate the hardspheres used for the derivation of Eq. (3.44), the structure factor is defined as

S3(θ) = 1/

[1 − H3(q)], (3.45)

where H3(q) is defined by Eq. (3.36).For small particle concentrations, the approximation of the excluded volume

is applicable: g(r) = 0 for r values that are smaller than the particle diameter andreach unity over long distances. In this approximation, the structure factor for asystem of spherical particles takes the form that was first discovered by Dirack:654

S3(θ) = 1 − f �(qa) , (3.46)

where a is the particle radius and �(qa) is the function defined by the followingequation:

�(qa) = 3 (sin qa − qa cos qa)

(qa)3 . (3.47)


112 Chapter 3

Figure 3.8 Structure factor [S3(θ) − 1] [Eq. (3.44)] as a function of the scattering angle, θ,and particle radius, a; wavelength, 633 nm; volume fraction f = 0.4; relative refractive index,m = 1.105 (calculated by I. L. Maksimova).

Function �(qa) modulates the angular dependence of the scattering intensity bydiminishing its value at small angles and generating a diffusion ring at 10-degangles for particle dimensions comparable with the wavelength.

For the case of infinitely long, identically aligned cylinders with radius a andlight that is incident normally to their axes, the 2D structure factor is defined withinthe approximation of a single scattering, as follows:

S2 (θ) ={

1 + 8πa2ρ

∫ R

0

[g(r) − 1

]J0

(2πa

λr sin

θ

2

)dr

}, (3.48)

where R is the distance for which g(r)→1. Because the light is incident perpen-dicularly to the cylinder axis, the scattered light propagates only in the directionperpendicular to the axis.

For a very small concentration of particles, the structure factor is nearly aunit and the intensity of scattering by a disperse system is essentially a sum ofthe contributions of independent scatterers. For systems of small soft particles,the structure factor only changes slightly as a function of the scattering angle.Therefore, the particle interaction primarily reveals itself by a uniform decreasein scattering intensity in all directions for linearly polarized and unpolarized inci-dent light (see Fig. 3.9 and 3.10). For systems of large particles, the structure factoris noticeably less than a unit only in the region of small scattering angles (see Figs.3.11 and 3.12). The interference interaction of scatterers in certain angular bandsreduces the scattering intensity; in the other bands, the scattering intensity is raisedcompared with that for a system of the equivalent number of independent parti-cles (Fig. 3.12). In general, particle interaction makes the angular dependence ofthe scattering intensity more symmetric with less overall scattered intensity, andtherefore, allows much more collimated transmittance for both small and large softparticles.



Figure 3.9 Calculated angular dependences of the scattered intensity for a system of smallspherical particles, 20 nm radius; the incident wave is linearly polarized parallel to (a) orperpendicular to (b) the scattering plane; dotted line–independent particles; wavelength,633 nm; volume fraction, f = 0.1; relative refractive index, m = 1.105 (calculated by I. L.Maksimova).

Figure 3.10 Calculated angular dependences of the scattered intensity for a system ofsmall spherical particles, 50 nm radius; the incident wave is unpolarized; dotted line–independent particles; wavelength, 633 nm; volume fractions, f = 0.04 (a) and f = 0.1 (b);relative refractive index, m = 1.105 (see Ref. 654).

Scattering strongly deforms the spectral tissue characteristics because theextinction of transmitted light is defined not only by the absorption factor as afunction of the wavelength, but also by a light fraction taken away from the beamby scattering. The latter process complexly depends on the wavelength, structure,and size of particles.

The spectrum of collimated transmission of a disperse layer is interpreted asthe spectral dependence of a weaker coherent component of light. Determining thecoherent component of light, scattered at a system of inhomogeneities correlatedin the space, is a complicated physical task exhibiting all of the difficulties inherentin the problem of light propagation through a system of many bodies.807 Assumingthat the intensity of the coherent light component, Icoh, is reduced with a longerdistance, d, by the exponent law owing to scattering and absorption, disperse layer


114 Chapter 3

Figure 3.11 Calculated angular dependences of scattered intensity for a system of largespherical particles, 500 nm radius; the incident wave is linearly polarized parallel to (a) orperpendicular to (b) the scattering plane; dotted line–independent particles; wavelength,633 nm; volume fraction, f = 0.4; relative refractive index, m = 1.105 (calculated by I. L.Maksimova).

Figure 3.12 Calculated angular dependences of the scattered intensity for a system oflarge spherical particles, 500 nm radius; the incident wave is unpolarized; dotted line–independent particles; wavelength, 633 nm; volume fractions, f = 0.04 (a) and f = 0.4 (b);relative refractive index, m = 1.105 (see Ref. 654).

collimated transmittance can be described by the Bouguer–Beer–Lambert law [seeEq. (1.1)]:

Tcoh(λ0, d) ≡ [Icoh(λ0, d)/I0(λ0)] ∝ exp[−ρsσext(λ0)d], (3.49)

where σext is the extinction cross section of an individual particle of the layer [seeEq. (1.4)]. For small volume concentrations, ρs, this is equivalent to the extinctioncross section of an independent particle. For greater f values, quantity σext is deter-mined not only by the properties of single particles, but also by their concentration.Within the assumption that the absorption cross section, σabs, is independent of thepacking density, σext may be calculated as a sum of σabs for the independent parti-cle and the scattering cross section, σsca, obtained by accounting for the correlationof scatterers.



While measuring the scattered intensity angular distribution of the particle sys-tem, one calculates the scattering cross section of single particles of the system.Having integrated the scattering intensity over all directions in the space, the totalenergy scattered by the system can be found. The scattering cross section for thesystem of spherical particles is obtained similarly to Eq. (1.6); however, to cal-culate the scattering cross section of a single particle of the system, the scatteredintensity must be divided by the particle number, N, and corrected by using the 3Dor 2D structure factor, S3 [Eq. (3.44)] or S2 [Eq. (3.48)].

The scattering cross section for the system of rods (cylinder particles), �sca

(cm), illuminated by a plane incident wave of intensity I0 in the direction normalto the cylinder axis, is defined by numerical integration over all possible scatteringdirections in a plane perpendicular to the cylinder axis:214

∑sca

= 2π

λI0

∫ 2π

0I� (θ) dθ, (3.50)

where I�(θ) is the angular distribution of the scattered intensity of a system of Nparticles. Dividing �sca by N, one may determine σsca for a single particle of thesystem. For an interacting particle system, the result may differ substantially fromthe scattering cross section of an independent particle.

Even the scattering cross section for an independent particle sized on the orderof a wavelength has a very strong nonmonotonous dependence on the wavelength.Additionally, effects associated with dense packing have a substantial dependenceon the wavelength. As a result, the transmission spectra for a system of identicalparticles can differ greatly, depending on the packing density and its degree oforder. Wonderful examples include the transmission spectra of the cornea both inthe norm and with turbidity caused by a disrupted spatial degree of order and bythe appearance of regions denuded of fibrils, designated lakes.647

The extinction of a collimated incident beam due to scattering, even in systemsof nonabsorbing particles, would result in a substantial difference in transmittancein different spectral regions. The values of the real and imaginary parts of theindices of refraction depend weakly on the wavelength far from the absorptionbands; they may be assumed to be constant under calculation. In systems of smallnonabsorbing particles, the interference interaction causes the short-wavelengthtransmission spectrum boundary to shift to a smaller wavelength and a slightlysteeper spectrum.654 If a scattering system is formed by particles whose sizes arecomparable with the light wavelength, then the spectrum of this system would benonmonotonous, even with no absorption. In the vicinity of the absorption bands,the real and imaginary parts of the complex index of refraction of the particlesubstance show a pronounced spectral dependence, which determines the speci-ficity of transmission spectra for systems of differently sized particles, with theimaginary part of the refractive index usually described by the Lorentz contour.654

Scattering deforms the symmetric contour of the absorption line and the spectraappear essentially different for systems of small and large particles with varyingpacking densities.


116 Chapter 3

In general, this is typical for spectroscopy of tissue or blood when an absorbingband of a chromophore (hemoglobin) is detected on the background of the scat-tering part of the spectrum. For example, the problem of evaluating hemoglobinsaturation by oxygen in tissues is usually solved by excluding the scatteringpart of measured tissue spectra. The calculated transmission spectra addition-ally explain a phenomenon of substantial differences in spectra for whole blood,where hemoglobin with a high index of refraction and strong absorption bandis concentrated in erythrocytes (system of large particles with absorption), andfor hemolyzed blood, where only small particles (blood residuals such as cellskeletons) scatter light.

For a densely packed system of large weakly refracting particles, the followingequation was obtained in Ref. 754 within the approximation of hard spheres andneglecting of mutual particle radiation for the coherent transmission of a layer withthickness d:

Tcoh =[

1 − 2b

(1 + b)

σext

π · a2+ b2

(1 + b)2

2λ

π · a3σscaI1(0)

]d/2a

, (3.51)

where b = 1.5f × exp(1.5f ) and I1(0) is the intensity of forward scattering by anindividual particle of radius a. This formula is transformed into the Bouguer–Beer–Lambert law [see Eq. (3.49)] for scattering systems of noninteracting particles atthe rarefaction of the scattering layer.

Not only coherent weakened light, but also a portion of noncoherently scat-tered light is usually recorded in real experiments, owing to the finite angularaperture of the receiving unit. For this reason, a transmittance called the instru-mental transparency, which is found experimentally, is slightly different from thecoherent transmission, Tcoh.

For the first time, an approximation regarding the near-order degree of tissuearrangement has been used by the authors of Refs. 644, 645, and 647 to describelight propagation in the cornea by calculating its transmission spectrum. The nearorder in the arrangement of scattering particles and the related interference inter-action of scattered light are the course of high transparency of the human corneaand lens at their normal state.63, 64, 796

The light-scattering intensity angular dependences for systems of sphericaland cylindrical particles in the single scattering approximation are described byEqs. (3.43), (3.44), and (3.48). The structure factor that transforms these depen-dences is defined by the spatial particle arrangement, and is independent of the stateof light polarization. Therefore, for systems of identical particles, when the singlescattering approximation is valid, the angular dependences of all elements of theLSM are multiplied by the same quantity, accounting for interference interaction[see Eq. (3.43)]:

Mij(θ) = M0ij(θ)NS3(θ), (3.52)



Figure 3.13 Angular dependences of LSM elements for a binary mixture of sphericalparticles (see Ref. 648) calculated while taking into account particle interactions (solidlines) and neglecting cooperative effects (dashed lines). Particle diameters: 2a1 = 60 nmand a2 = 500 nm; volume fractions: f1 = 0.3 and f2 = 0.02; relative index of refraction,m = 1.07; wavelength, 633 nm.

where M0ij(θ) is the LSM element for an isolated particle. Consequently, the LSM

for the system of monodispersive interacting particles coincides with that of the iso-lated particle [see Eq. (2.25)] if normalization to the magnitude of its first element,M11, is used.

Unlike monodispersive systems, in differently sized, densely packed particlesystems, the normalization of the matrix elements to M11 does not eliminate theinfluence of the structure factor on the angular dependences of the matrix elements.In the simplest case of a bimodal system of scatterers, expressions analogous toEqs. (3.44) and (3.48) can be found by using four structural functions, g11(r),g22(r), g12(r), and g21(r), which characterize the interaction between particles ofsimilar and different sizes.648 A bimodal system formed by a great number ofequally sized small particles, and a minor fraction of coarse particles, providesan accurate model of pathological tissue, e.g., a cataract eye lens.

Figure 3.13 depicts the calculated results for the LSM elements of a binarymixture of spherical particles with two different diameters (60 and 500 nm) andcorresponding volume fractions of f1 = 0.3 and f2 = 0.02.648 For comparison, theangular dependences of LSM elements for the same binary mixture, at neglectingcooperative effects, have also been calculated. The figure shows that the normal-ized LSM elements of a dense binary mixture are substantially altered due tothe interference interaction. As a consequence, the results of the inverse problemsolution for the experimental LSM of a dense mixture while neglecting the coop-erative effects should yield an overestimated value for the relative fraction of largeparticles. The LSM variations attributable to cooperative effects feature a morecomplicated nature for a binary system whose two components are sized on theorder of the wavelength of incident light; thus, they could not be interpreted souniquely as those in the preceding case. Numerical estimates for binary systemsof different compositions show648 the effects under consideration to be of the mostcrucial importance for the LSM in the visible region for mixtures of particles with2a1 < 200 nm and 2a2 > 250 nm.


118 Chapter 3

Unlike the transmission spectra, the spectral dependences of the intensityof light scattered in different directions are poorly studied. This is related, onone hand, to experimental difficulties owing to the need for standard spectraldevices to be modernized. On the other hand, an additional problem of the correctcomparison of different experimental results arises while examining the scatter-ing spectra because the form of the scattering spectrum depends substantiallyon the macrogeometry of the sample and measuring system. Nevertheless, thescattering spectra are of great interest.47, 58, 94–96, 216–219, 229, 232, 236, 239, 272, 783, 808 Theauthors of Ref. 808 address the absorption and scattering spectra of the chestmuscle of a chicken in the visible range. The scattering spectra visually definethe observed tissue color and can be employed for quickly estimating its state.For example, one traditional method for eye ocular lens diagnostics assumesthe observation of varying color characteristics for light scattered at differentangles. Reference 809 provides the theoretical background for quantitative anal-ysis of scattering spectra and color formation by the eye lens (presented as amodel of a dispersive system of spherical particles with low absorption), andin vitro measured scattering spectra of the human eye lens. The age-relatedalterations of the eye lens particle composition and corresponding transmittanceand light scattering spectra are modeled239 and compared with experimentaldata from Ref. 783. The spectral characteristics vary most strongly with highpacking densities as the volume fraction occupied by particles exceeds 50%.For these dense systems, the considered approximation of single scattering isincorrect and it is necessary to account for the effects of re-radiation of theparticles.

3.6.2 Spectral characteristics

The collimated transmission spectrum of a tissue layer of thickness d and meandensity ρs of scattering particles with absorption is defined by Eq. (3.49), whereIcoh(λ0) is the spectrum of the transmitted intensity detected in a far field using apinhole; the scattering cross section, σsca, for a given scattering model can be calcu-lated by using Eq. (1.6) for the corresponding angular dependence of the intensityscattered by a particle, I(θ). In the framework of Mie theory, the scattering andabsorption cross sections, as well as the mean cosine of the scattering angle θ (fac-tor of scattering anisotropy g = 〈 cos θ〉) for a single particle, can be calculated byusing the following expressions:214

σsca = λ20

2πn20

∑∞n=1

(2n + 1)(|an|2 + |bn|2), (3.53)

σabs = λ20

2πn20

∑∞n=1

(2n + 1)[Re(an + bn) − (|an|2 + |bn|2)], (3.54)

g = λ20

πn20σsca

{∑∞n=1

2n + 1

n(n + 1)Re(anb∗

n) +∑∞

n=1

n(n + 2)

n + 1Re(ana∗

n+1 + bnb∗n+1)

}.

(3.55)



Here an and bn are Mie coefficients, which are functions of the relative complexrefractive index of particles:

m = ns (λ0)

n0 (λ0), (3.56)

ns(λ0) = n′s(λ0) + in′′

s (λ0), (3.57)

n0(λ0) is the refractive index of the dielectric ground (host) material, in whichscattering particles with refractive index ns(λ0) are inserted; the imaginary partof the complex refractive index of scatterer material is responsible for light lossesattributable to absorption; λ0 is the wavelength in a vacuum; and parameter

α = 2πan0

λ0, (3.58)

a is the radius of the scattering particle; an asterisk indicates that the complexconjugate is to be used;

an = ψn(α)ψ′n(mα) − mψn(mα)ψ′

n(α)

ξ(α)ψ′n(mα) − mψn(mα)ξ′

n(α), (3.59)

bn = mψ′(mα)ψn(α) −ψn(mα)ψ′n(α)

mψ′n(mα)ξn(α) −ψn(mα)ξ′

n(α), (3.60)

where ψn, ξn, ψ′n, and ξ′

n are the Riccati–Bessel functions of the first or secondtypes.

For example, for unpolarized collimated light incidence on a system of Mieparticles, the scattered intensity is defined as

I�(θ, λ0) ≈ N(|S1|2 + |S2|2

), (3.61)

where N is the number of spherical particles; S1 and S2 are the functions of thepolar scattering angle, θ, and can be obtained from Mie theory as

S1(θ) = ∑∞n=1

2n+1n(n+1) {anπn(cos θ) + bnτn(cos θ)} ,

S2(θ) = ∑∞n=1

2n+1n(n+1) {bnπn(cos θ) + anτn(cos θ)} .

(3.62)

The parameters πn and τn represent

πn(cos θ) = 1sinθP1

n(cos θ),

τn(cos θ) = ddθP1

n(cos θ),(3.63)

where P1n(cos θ) is the associated Legendre polynomial. The following recursive

relationships are used to calculate πn and τn:

πn = 2n−1n−1 πn−1 cos θ− n

n−1πn−2,

τn = nπn cos θ− (n + 1)πn−1,(3.64)


120 Chapter 3

and the initial values are {π1 = 1,π2 = cos θ,τ1 = cos θ, τ2 = 3 cos 2θ.

(3.65)

The coefficients an and bn are defined in Eqs. (3.59) and (3.60). Eqs. (3.43), (3.44),and (3.48) can be used to account for particle interaction. The simpler Eq. (3.51)can also be used.

In turn, the transmission spectrum when using a measuring system with a finiteangle of view (a collimated light beam is detected with the addition of a forwardscattered light in the angle range 0 to θ) is defined by

Tθ(λ0) = Tcoh(λ0) + 1

I0(λ0)

∫θ

I�(θ, λ0)d�, (3.66)

where � is the solid angle in steradians.The total transmission spectra, Tt(λ0), and the spectrum of light scattered under

the angle (θ+ dθ), Rθ(λ0), can be calculated by using the following definitions:

Tt(λ0) = Tcoh(λ0) + 1

I0(λ0)

∫2π

I�(θ, λ0)d�, (3.67)

Rθ(λ0) = 1

I0(λ0)

∫ θ+dθ

θ

I�(θ, λ0)d�. (3.68)

Corneal transmittance was calculated by using a model monodisperse system oflong dielectric nonabsorbing cylinders (fibrils) of 26 nm in diameter and withrefractive index nc = 1.470. The cylinders were regularly oriented parallel to thecorneal surface in the ground matter (n0 = 1.345). Figure 3.14 demonstrates thetransmittance anisotropy for linearly polarized radiation and the marked effect ofscattering on corneal transmittance in the UV spectral region. The corneal trans-parence in the visible range is explained by the high degree of its fibril arrangement,so the diffuse light intensity decreases owing to interference along all directions(destructive interference) except the incident light direction (constructive interfer-ence). The effect of scattering is the most essential in a short wavelength region anddefines small UV radiation transmittance of the cornea, which is approximately50% for 320 nm. In the UV range, light extinction is defined not only by scatter-ing; the absorption bands of water and proteins additionally provide very strongextinction (see Figs. 1.3 and 1.5).

Disordering of the fibril arrangement (for example, after keratotomy) resultsin a decrease in corneal transmission, especially for short wavelengths (Purkinje’seffect).63 Another essential feature of the cornea is the presence of a preferabledirection of the alignment of fibrils. The results of such anisotropy are form bire-fringence and dichroism of the cornea.63 The transmission spectrum substantiallydepends on the orientation of the polarization vector of the linear polarized lightrelative to the collagen fibrils; light polarized along fibrils is scattered more effec-tively. As follows from calculations and measurements presented in Fig. 3.14, theperipheral corneal polarization sensitivity in UV (320 nm) is approximately five-fold higher than in the red region (633 nm). In the Rayleigh limit (λ � 2a), form



Figure 3.14 Collimated transmittance spectra of the human cornea: III, I⊥, and I∗ are cal-culated spectra for two orthogonal states of linear polarization and unpolarized light. Lightpolarization is parallel, III, to the fibrils (calculations were made for the light normally inci-dent on the corneal surface; they are valid for the peripheral conical portion where the fibrilsare similarly oriented in tissue layers). The cornea is 0.46 mm thick, with a scatterer den-sity ρs = 3 × 1010 cm−2. The dotted line shows the experimental data for unpolarized light.The circles are measurements for two orthogonal states of polarization at λ = 633 nm (seeRef. 63).

birefringence is defined by Eq. (2.2). Birefringence can be high for small diametercylinders and zero for a system consisting of parallel cylinders with large diameters(2a ≥ λ).614

Comparative studies of the spatial distributions of the polarization parameterswithin the cornea of healthy volunteers and patients after laser vision correctionsurgery (LASIK) have shown that the degree of depolarization is not smoothlydistributed within the cornea, and that its level is higher in patients after surgerythan in healthy volunteers.706 In addition, for normal eyes, birefringence increasesmonotonically along the radius of the cornea (from the center to the periphery);however, postoperative eyes do not show this relationship. These changes in opticalpolarization properties show a significant modification of the corneal structure aftersurgical intervention.

The total and collimated (axial) experimental transmission spectra for thehuman cornea are presented in Fig. 3.15. They illustrate that the cornea scatterslight because the total and axial transmissions are not identical. Water absorptionpeaks are evident at 300, 980, 1180, 1450, 1900, and 2940 nm (see Fig. 1.3);810

they provide poor transmission in the cornea in UV and IR spectral regions.No age effect was found when corneal transmittance was measured in the spec-

tral range of 320 to 700 nm on 10 aphakia subjects (14 to 75 yrs).811 The average


122 Chapter 3

Figure 3.15 Total and axial (collimated) transmission through human cornea (see Ref. 810).

spectral transmittance derived from these measurements was modeled by the fol-lowing functions for total transmittance (acceptance angle close to 180 deg) andon-axis transmittance (acceptance angle on the order of 1 deg):

log Tt(λ0) = −0.016 − 21 · 108λ−40 , (3.69)

log Tc(λ0) = −0.016 − 85 · 108λ−40 , (3.70)

where λ0 is the wavelength in nanometers.The study of the transmission spectra in the wavelength range of 400–750 nm

of bovine corneal stroma in different physiological states, controlled by the alter-ation of NaCl concentration in the range from 10 to 1000 mM and by the addition ofsorbitol (300 mM), showed that the transmission spectra are determined by changesin the nature of tissue scattering.812 In particular, samples of stroma, stabilized forNaCl solutions in the range from 10 to 100 mM and being isotonic with respect tothe initial state in a stabilized buffer (154 mM NaCl, pH 7.4, degree of hydrationof 3.2) in the presence of sorbitol, were weakly transparent at 10 mM; with ele-vated NaCl concentration, their transparency was increased to normal at 154 mMof NaCl. On the other hand, hypertonic solutions (300–1000 mM of NaCl) led to aloss of transparency, with the increased concentration compared to the case of 154mM of NaCl. The intensity of scattered light as a function of wavelength is accu-rately described by the function ∼λ−3 for all small concentrations of NaCl from10 to 154 mM in the spectral range from 450 to 650 nm, but not for longer wave-lengths. However, in the case of hypertonic solutions (300–1000 mM), there was aweaker dependence on the wavelength of ∼λ−2, but in the wider wavelength rangeof 450–750 nm. The results may be caused by the change in the intermolecularforces responsible for the ordering of collagen fibers in the stroma, which vary due



Figure 3.16 Primary species in the human lens that absorb light transmitted by the cornea:protein-bounded tryptophan (TRP), 3-hydroxy-L-kynurenine-O-β-glucoside (3-HKG), andaged lens protein (AP) (see Ref. 794).

to the binding of chloride ions to the matrix of the cornea,812 as well as immersionproperties of sorbitol (see Chapter 9) and temporal aggregation–disaggregation ofthe particles. Transmission spectra of the eye tissues, including the cornea, can befound in Ref. 813.

The lens is less transparent than the cornea. The visible light passing throughthe human lens undergoes an appreciable degree of both scattering and absorptionby different chromophores, including protein-bound tryptophan, 3-hydroxy-L-kynurenine-O-β-glucoside (3-HKG), and age-related protein (responsible for lensyellowing in aged subjects) (Fig. 3.16).794 The 3-HKG content slightly decreaseswith age. In the single-scattering model under examination, absorption is takeninto account by introducing a complex refractive index for the scatterers24 [seeEq. (3.57)]:

ns(λ0) = n′s + in′′

s = n′s + i[tn′′

t (λ0) + kn′′k(λ0) + pn′′

p(λ0)], (3.71)

where the coefficients t, k, and p characterize the contribution of each chromophoreto absorption.

Age-related changes in the optical properties of the lens are, as a rule,attributable to the appearance of scatterers with increased diameters and refrac-tive index, and to the enhanced content of age-related protein.24, 64 Figure 3.17presents collimated transmittance spectra calculated by using “young” and “old”lens models. A remarkable difference between the short-wave portions of the twoprofiles is readily apparent. The total transmittance spectra experimentally obtainedfor senile and cataractous lenses are shown in Fig. 3.18.24 Age-related variations inthe composition of scatterers and absorbers lead to significant differences in scat-tering spectra. There is a qualitative correlation between the experimental findingsand the calculated values for both backscattering and scattering at 90 deg (see, forinstance, Fig. 3.19).24, 239, 783


124 Chapter 3

Figure 3.17 Collimated transmittance spectra of the human lens calculated for ordered(1, 3) and disordered (2, 4) scatterers. 1, 2, in the absence of absorption; 3, 4, with absorp-tion: Model of a “young” lens (diameter of scatterers 2a = 20 nm, n′ = 1.43, t = 0.003,k = 0.005, p = 0) (a). Model of an “old” lens (2a = 40 nm, n′ = 1.47, t = 0.003, k =0.002, p = 0.015) (b). Volume density of scatterers, fs = 0.3, n0 = 1.345; lens thickness,5 mm (see Refs. 24 and 239).

Figure 3.18 Experimental total transmittance spectra of isolated human lens for normallens of a 56-year-old subject and a cataractous lens (88 years). Measurements were madeon a spectrophotometer with an integrating sphere (see Ref. 24).

Calculations of the scattering spectra for the eye lens model based on the firstorder of multiple scattering theory (see Fig. 3.20), which accounts for the atten-uation of a singly scattered light intensity, and on in vitro measured experimentalscattering spectra within a whole human cataractous crystalline lens for a certainscattering angle and different locations of a measuring volume, also demonstratethe usefulness of scattering spectra for prediction of eye lens pathology.809



Figure 3.19 Calculated and experimental scattering spectra of the lens at 90 deg (relativeunits, experimental data from Ref. 783). Calculations were made for a mixture of orderedsmall particles (99%) having diameter 2a = 60 nm (t = 0.003, k = p = 0.03, n0 = 1.345,n′ = 1.47) and large disordered particles (l%) (2a = 600 nm, t = 0.003, k = 0, p = 0.1)(see Ref. 239).

Analysis of the extensive literature on studies of absorption and scattering ofthe eyes of young and aged people allowed the authors of Ref. 814 to identifyfive primary contributions to the formation of the transmission spectrum in the300–700 nm range for transparent tissues of the eye: cornea, lens, aqueous humorof anterior chamber, and vitreous. Two components are common to all types oftissue: Rayleigh scattering and absorption of tryptophan. Three additional contri-butions are unique to the lens; they are determined by the absorption of kynureninederivatives (mostly 3-HKG) and two ingredients found only in the aged lenses.All deposits, except for Rayleigh scattering, are described by spectral curves ofGaussian shape. Optical density, Dmedia(λ), for all eye media and their scatter-ing and absorbing components (five spectrally dependent and one independent ofwavelength) can be written as

Dmedia (λ) = dRL (age) × FRL (λ) + dTP (age) × FTP (λ) + dLY (age) × FLY (λ)

+dLOUV (age) × FLOUV (λ) + dLO (age) × FLO (λ) + dneutral, (3.72)

where Fi is the spectral dependence of each medium component; di is a factordependent on the age, defining the optical density; indices RL, TP, LY, LOUV, andLO denote Rayleigh scattering, tryptophan, the young lens, the aged lens (narrowband with a maximum absorption in the UV), and the aged lens (broad absorptionband with long wing absorption in the visible), respectively; dneutral is the coef-ficient accounting for independent wavelength contributions from absorption andscattering. Bands of water in this wavelength range are marginal, so their contri-bution is not considered in the form of the spectral dependence, although it shouldimpact dneutral.

The age-related dependence of the optical density Dmedia(λ) is quadraticbecause of the quadratic dependence on age for all transparent media of the eye:


126 Chapter 3

Figure 3.20 Scattering spectra calculated in the first order of multiple scattering theory(accounting for attenuation of a singly scattered light intensity within a sample) for differentangles: θ = (�) 149 deg and (�) 90 deg. The particle radius is 25 nm, the radius of thesystem is 5 mm, and the relative volume of the particles is 0.3. The elementary scatteringvolume of 1 mm2 is located at distance l = (1) 0.5 mm, (2) 0.6 mm, and (3) 0.7 mm (a). Theexperimental (symbols) and corresponding calculated (1–3) scattering spectra at an angleof 149 deg for a cataractous crystalline lens of a human eye for three different locations ofscattering volume: (∗, 1) in the vicinity of front surface, (+, 2) in the central part, and (×, 3)in the vicinity of a rare part of the crystalline lens (b) (see Ref. 809).

Dmedia (λ) = (0.446 + 0.000031 × age2

) × (400/λ)4

+14.19 × 10.68 × exp{− [0.057 × (λ− 273)]2}

+ (0.998 − 0.000063 × age2

) × 2.13 × exp{− [0.029 × (λ− 370)]2}

+ (0.059 + 0.000186 × age2

) × 11.95 × exp{− [0.021 × (λ− 325)]2}

+ (0.016 + 0.000132 × age2

) × 1.43 × exp{− [0.008 × (λ− 325)]2}

+ 0.111

.

(3.73)

For a wider field of view, dRL = 0.446 should be replaced by dRL = 0.225.814

A detailed study of the kinetics of UV-induced aggregation of the major pro-teins of the eye lens, such as α-, β-, and γ-crystallins in a mixture or separate,is presented in Refs. 799, 800 and 801. In Fig. 3.21, the experimental setupis shown for the study of UV laser photo-induced aggregation of crystallins inlens and model media.800, 801 For providing photo-induced protein aggregation, the



Figure 3.21 Computer-aided system for the study of UV laser-induced photoaggregationof crystallins in the eye lens and model systems (see Refs. 800 and 801): UV light source,XeCl-laser LPX-200 (Lambda Physik) (308 nm) with a pulse energy up to 450 mJ and apulse repetition rate up to 80 Hz; single-mode (TEM00) He-Ne laser (633 nm) of 10 mWand a beam divergence of 1.1 × 10−3 rad to measure the induced scattering in the dark-field (at blocking of the main beam by an opaque screen); UV energy meter, Gentec ED-200UV detector to measure the energy of the transmitted radiation at a wavelength of 308 nm;photodiode (633 nm) for dark-field measurements; and photodiode (308 nm) as a trigger forcomputer control.

XeCl-excimer laser operating at a wavelength of 308 nm was used as a light source.Simultaneously, the energy of the transmitted radiation at a wavelength of 308 nmwas measured with a detector, which was located in the vicinity of the cell with thelens or crystallin solution. In this case, the transmittance change was attributableto induced absorption and scattering at a wavelength of 308 nm (Fig. 3.22). Themeasurements were performed at room temperature 22◦C. To study the dynamicsof aggregation of crystallins induced by UV radiation, the intensity of the scat-tered light in a dark field was measured while protein solutions were probed by auniphase beam of a single mode (TEM00) He-Ne-laser with wavelength of 633 nm,power of 10 mW, and divergence of 1.1·10−3 rad.

In studies of induced scattering at a wavelength of 633 nm on a dose of UVirradiation (308 nm) for solutions of the full set of lens crystallins (α+ β+ γ),only β-crystallin and mixtures of α- and β-crystallins showed a different resistanceof crystallins to UV radiation and a chaperone function of α-crystallin, which alsohas the greatest resistance to UV radiation.

Studies of photo-induced aggregation of aqueous solutions of β-crystallins ledthe authors800, 801 to a physical model of the initial stage of crystallin aggregationinduced by mild UV (308 nm) and allowed them to describe the ability to formlarge aggregates. According to the experimental results,799–801 such characteristicsas frequency and energy density of UV laser pulses are the key factors determiningthe kinetics of aggregation. Namely, it was found that the dose of UV radiationrequired for aggregation of crystallins depends on the energy density and repeti-tion rate of laser pulses: the dose initially decreases significantly with the increase


128 Chapter 3

Figure 3.22 Changes in optical transmittance of a pig eye lens at a wavelength of 633 nmcaused by scattering induced by excimer laser (308 nm) via the radiation dose for two laserpulses with the different energy densities of 4.5 mJ/cm2 (1) and 11 mJ/cm2 (2), and pulserepetition rate of 10 Hz (see Ref. 799).

Figure 3.23 Dose dependence of the scattered light at a wavelength of 633 nm for a solu-tion of βL-crystallin at a fixed energy density 75 mJ/cm2 and different repetition rates oflaser pulses F of excimer laser (308 nm). The transmission curves (308 nm) of the proteinsolution are also shown (see Ref. 800).

of intensity (frequency), and then saturates (see Fig. 3.23). This effect is thoughtto be because the initial process of photo-induced aggregation occurs when twolight-activated protein molecules interact, and the photoactivated state has a finitelifetime.

As discussed above, eye sclera is a nontransparent turbid medium, at least inthe visible range. Figure 3.24 displays the experimental spectra obtained for threesamples of human sclera with different thicknesses, showing its poor transparencyfor visible light and sufficiently high transparency for wide bands in the NIR regionbetween absorption bands of water.768, 769 In addition, a dry scleral sample has hightransmittance within a very large spectral band, including visible and IR. The originof scleral spectra formation can be understood on the basis of light scattering by asystem of polydispersive irregularly arranged collagen cylinders immersed in the



Figure 3.24 Transmittance spectra of the human sclera (see Refs. 768 and 769): Totaltransmittance for three samples (a). Axial (collimated) transmittance for the same threesamples (b). Total transmittance of the dry sclera sample (c).


130 Chapter 3

ground substance with a lower refractive index.791, 792 For natural thickness of 0.7–0.8 mm, this tissue shows multiple scattering [Figs. 3.24(a) and 3.24(b)], but thetransition from multiple to low-step or even single scattering can be provided notonly by histological tissue cutting, but also by the dehydration of a whole tissuesample [Fig. 3.24(c)] or its impregnation by an immersion liquid.238, 791, 792 Thiscontrol of tissue scattering properties can be done in vivo; thus, this technology isvery attractive for many biomedical applications (see Chapter 9).

3.6.3 Polarization properties

It has already been shown that light propagation in opaque multiply scattering tis-sues depends not only on the scattering and absorption coefficients and scatteringphase function, but also on the polarization properties of the tissue. In turn, the lat-ter depends on the size, morphology, refractive index, and internal structure of thescatterers and the optical activity of the material.5, 6, 10, 43, 215, 273, 274, 815 The polar-ization properties of elastically scattered light are described by a 16-element LSM,with each element dependent on the wavelength, size, shape, and material of thescatterers [see Eqs. (2.22) and (2.23)].

For measurements of the LSM elements of transparent biological tissues andfluids, computer-controlled laser scattering matrix meters (LSMMs) were devel-oped3, 5, 6, 10, 43, 64, 135, 215, 592, 662, 663, 666–670, 684, 689, 693, 695, 701, 712, 715, 717, 731, 740–743, 745, 746,

816–820 The principle of operation of an LSMM5, 10, 816 (Fig. 3.25) is modulating thepolarization of the incident laser beam, followed by demodulating the scatteredlight (transformation of polarization to intensity modulation), as described by thefollowing matrix equation:

S = AF′MFPS0, (3.74)

where S and S0 are the Stokes vectors of the recorded and source radiation, respec-tively; P, A, and F, F′ are the Mueller matrices for linear polarizers and the phaseplates, placed ahead of and behind the scattering medium, respectively. As thephase plates are rotated, the intensity recorded by a photodetector, i.e., the firstelement of the Stokes vector, S, depends on time. By multiplying the matrices inEq. (3.74) and performing the appropriate trigonometric transformations, one canshow that the output intensity can be represented as a Fourier series:816

I = a0 +∑K

k=1(a2k cos 2kϕ+ b2k sin 2kϕ) , (3.75)

where

a2k =∑N

i=1I(ϕi) cos 2kϕi, b2k =

∑N

i=1I(ϕi) sin 2kϕi, (3.76)

I(ϕi) is the intensity of the scattered light detected by the photoreceiver for a cer-tain orientation of the fast axis of the first retarder, ϕi; and N is the number ofmeasurements per one rotation cycle of the first phase plate, F.

The coefficients of the series described by Eq. (3.75) are defined by the valuesof matrix M elements of the object under study, and their measurement ensures a



Figure 3.25 Scheme of laser scattering matrix meter (see text for details and Refs. 5, 10,and 816).

system of linear equations to determine matrix M. The number of equations andthe degree of stipulation for this system of equations are dependent on the choiceof the ratio between the rotation rates of the phase plates (retarders). An optimalchoice of the rotation rates relationship at 1:5 allows an optimally stipulated systemof linear equations [K = 12 equations to be derived to determine the M of the objectunder study using Eq. (3.75)].821

A scheme shown in Fig. 3.25 was designed with rotating retarders (λ/4-phaseplates) running comparatively simple software, which allows one to avoid manyof the experimental artifacts peculiar to dc measurements and systems utilizingelectro-optic modulators.43 The LSMM has a fixed polarizer (P) and analyzer(A), and two rotating-phase plates (F and F′) before and behind the sample. Thepolarizer and analyzer are aligned in parallel, and their transmission planes areorthogonal to the scattering plane; fast optical axes of F and F′ form an angle withthe scattering planes, ϕ and ϕ′; as a result, respective phase differences, δ andδ′, are induced. The ratio of the rotation rates of the phase plates was assumedequal to 1:5, i.e., ϕ′ = 5ϕ, because all 16 matrix elements are uniquely deter-mined in this case. The computer-controlled LSMM provides automatic scatteringangle scanning in the range 0 ÷ ±175 deg with a step of 4′ and accuracy of 5′′.A single-mode stable He-Ne laser (633 nm) was used as a light source. Computer-driven retarders provided N = 256 indications per rotation cycle of the first phaseplate, F [see Eq. (3.76)]. A photon-counting system was used with the photomul-tiplier tube (PMT), amplitude discriminator (clipping amplifier), and counter. FastFourier transform (FFT) analysis allowed all 16 S-matrix elements to be measuredand calculated for the fixed scattering angle during a time of approximately 1 swith accuracy of 3–5%.


132 Chapter 3

Figure 3.26 Experimental angular dependencies for LSM elements of a normal lens (5 hafter the death of a 56-year-old subject) (a) and a cataractous lens (5 h after the death ofan 88-year-old subject) (b) (see Ref. 24).

The measurement of angular dependencies of LSM elements in a humanlens shows significant differences for clear and opaque (cataractous) eyes (seeFig. 3.26). This difference may be caused by the appearance of large nonsphericalscattering particles due to the aggregation of high molecular-weight proteins.

The comparison of transmittance (see Fig. 3.18) and angular dependencies ofLSM elements measured at the same wavelength indicates that the latter are moresensitive to variations in the structure of scattering media. This allows for measuredLSM elements to be used for early diagnosis of structural changes in a tissue, e.g.,those caused by a developing cataract.

This inference can be illustrated by the results of direct model experimentspresented in Fig. 3.27.24, 463 The measurements were performed in α-crystallinsolutions (quasi-monodispersive particle fraction approximately 0.02 μm in diam-eter) from a freshly isolated calf lens (a contribution by J. Clauwaert, Universityof Antwerp, who also participated in the experiment) and in solutions of highmolecular-weight proteins (mean diameter 0.8 μm) from opaque lenses. The figureshows that measuring the indicatrices of LSM elements permits the identifica-tion of a coarsely dispersed fraction of scatterers that is difficult to achieve by



Figure 3.27 Angular dependences for LSM elements of α-crystallin solutions and a fractionof large-size scatterers isolated from cataractous lens. The relative volume concentrationsof α-crystallin, fp = 0.3, and the large-particle fraction f 2 ≡ W2 = 0 (τ = 99%), 5 × 10−5

(τ = 98%); 1.4 × 10−4 (τ = 94%); and 2.5 × 10−4 (τ = 90%), τ is the transmittance of the5-mm-thick solution at λ = 633 nm (see Refs. 24 and 463).

spectrophotometry because the corresponding decrease in sample transmittancedoes not exceed 1%.

Laser scattering matrix measurements may be employed for in vitro examina-tion of various eye tissues, from cornea to retina. In vivo measurements in the intacteye are equally feasible, provided a fast LSMM is used to exclude the sensorimotoreye globe response. In this case, structural information about selected eye tissuescan be obtained to diagnose cataract and other ophthalmologic disorders.

A survey of rabbit eye LSM has demonstrated that the aqueous humor in theanterior eye chamber is actually a transparent isotropic substance exhibiting weaklight-scattering properties (the intensity of scattered light does not exceed 1.5–2% of the incident light intensity) owing to the presence of dissolved organiccomponents. The results of an LSM study in the vitreous humor indicate thatits amorphous tissue does not affect the polarization of straight-transmitting light,


134 Chapter 3

Figure 3.28 Angular distributions of the normalized (to M11) LSM elements of the mono-layer of erythrocytes: experimental: M22 (1,3), M33 (5, 6), M12 (7), M21 (8); theoretical (Mietheory): M22 (2), M33 (4); for disc-like erythrocytes (3, 5, 7, 8) and spherocytes (1, 2, 4, 6)(from Ref. 69 with corrections).

offering the possibility of examining the ocular fundus and imaging the optic nervestructure, which is important for early diagnosis of glaucoma.234, 589, 600 On theother hand, certain pathological changes in the vitreous humor may be responsiblefor the alteration of LSM elements. Specifically, a minor intraocular hemorrhage iseasy to identify by virtue of conspicuous light scattering from erythrocytes.

The angular dependence of LSM elements in a monolayer of disk-shapedor spheroidal erythrocytes in relation to their packing density was examined inRef. 69. The angular dependence of matrix element M11 in both cell types wasinfluenced by the packing density in the angular scattering range of θ = 15–16 deg.The angular dependencies of elements M11, M22, M33, and M21 at θ = 110–170 degwere far more affected by the shape of the scatterers than by their concentration. Itwas possible to derive the refractive indices of erythrocytes from measurements ofthe magnitude of M12 at scattering angles θ≈ 140–160 deg. One study815 revealedthe strong susceptibility of angular dependencies of the LSM elements (M11 andM12) to the degree of erythrocyte aggregation in blood plasma.

An image polarimeter based on liquid crystal variable phase plates was used ina double pass upon reflection from the retina or in transmitted light for in vivo andin vitro studies of the polarization properties of the eye and, separately, the corneaand lens.701–706 During the in vivo eye studies of volunteers, phase delays causedby birefringent structures of the eye were calculated based on a set of spatiallyresolved Mueller matrices obtained from a series of 16 images of the retina withdouble pass.701, 702, 704 Results for the 2-mm pupil diameter showed that, althoughthe phase delay introduced by the eye double pass for all media varies from personto person, in general, for the central region of the cornea, there is such a patternthat the slow axis is directed along the line from the upper-temporal region to thelower-nasal, with ellipticity close to zero; this indicates the presence of linear bire-fringence.701 As the size of the pupil increases, the phase delay also increases, theeye birefringence remains linear, and the azimuthal angle changes with no cleartrend.



In vivo studies of depolarization at the same image polarimeter702 showed thatfor the central area of the images, DOP is equal to 0.85 and 0.70 for pupil sizesof 2 and 5 mm, respectively. The DOP is reduced to the edges of the image. Itwas found that the eye has no strong polarizing properties (average ∼0.25 in thecentral part), which is associated with the presence of a small circular birefringenceand dichroism. It was also shown that the reflection from the retinal layer, whichprimarily contributes to the reflection of light, does not depend on the state ofpolarization. However, in vitro studies703 in some mammalian corneas using thesame Mueller matrix image polarimeter, but in transmitted light, showed that thebirefringence of the cornea is almost linear. Although the very magnitude of thephase delay varies from sample to sample, its value is constant at the center andincreases toward the periphery of the cornea. Dichroism and polarizing strengthare small in magnitude. Spatial maps for the DOP show that the cornea generallydoes not completely depolarize the polarized incident light.

In Ref. 705, it was shown that the effect of depolarization of light in the nor-mal eyes of young people is usually small, but increases with age. This change isalso expected in the presence of certain pathologies and after refractive surgery.706

Depolarization affects the assessment of birefringence of eye tissues (cornea andretina).

In vitro studies of intact, aged human lenses (56 to 88 years)704 showed thatthe total phase delay is small and decreases from the center to the periphery of thelens. The birefringence is linear and decreases from the center along the radius.Dichroism and polarizing strength are small, but the degree of depolarization forstudied lenses was 35%.

In Refs. 822 and 823, linear dichroism of a retinal nerve fiber layer was stud-ied by the Mueller matrix method; from these measurements, its thickness wasdetermined. Measurements of the same group of corneal dichroism are presentedin Ref. 824.


Chapter 4

Optothermal, Optoacoustic,and Acousto-Optic Interactionsof Light with Tissues

Optothermal, optoacoustic, and acousto-optical interactions, as well as sonolu-minescence, in strongly scattering tissues are described, including their primarymechanisms. The chapter presents optothermal (photothermal) and discussion ofoptoacoustic (photoacoustic) techniques. The basics and applications of optother-mal and optoacoustic spectroscopies, tomography, and microscopy are described.Prospective applications and measuring techniques are discussed.

4.1 Basic Principles and Classification

The optothermal (OT) method detects the time-dependent heat gener-ated in a tissue via interaction with pulsed or intensity modulated opti-cal radiation.5, 6, 25, 196, 204, 825–913 This interaction induces several thermo-elasticeffects in tissue; in particular, it generates acoustic waves. The detectionof acoustic waves is the basis of optoacoustic (or photoacoustic) meth-ods.5, 6, 25, 196, 204, 828–862, 884, 885, 887–913 The informative features of this method allowone to estimate tissue thermal, optical, and acoustical properties that depend onpeculiarities of the tissue structure.

Three modes can be used for the excitation of tissue thermal responses:5,

6, 25, 196, 828

1. In the first mode, a pulse of light (usually pulsed laser) excites the sample,and the signal is detected in the time domain by using a fast detector attachedto a wideband amplifier. In this case, signal averaging and gating techniquesare used to increase the signal-to-noise ratio.

2. The second mode exploits an intensity-modulated (usually harmonic modu-lation) light source (high-intensity lamp or CW laser) and a low-frequencytransducer. The measurement is in the frequency domain; phase-sensitive

137


138 Chapter 4

detection (lock-in amplification of the signal at the modulation frequency) isused for noise suppression.

3. In the third mode, CW excitation generates a photochemical reaction, and theheat evolved through a particular reaction can be detected as a temperatureincrease.

In every case, the thermal waves generated by the heat release result in severaleffects that have generated various techniques:5, 6, 25, 196, 828

1. Optoacoustics (OA) or photoacoustics (PA) (direct or indirect sound wavegeneration),

2. Optothermal radiometry (OTR) or photothermal radiometry (PTR) (detec-tion of infrared thermal emission),

3. Photorefractive techniques: thermal blooming, thermal lensing, probe beamrefraction, interferometry, and deflectometry (detection of refractive indexgradients above and inside the sample),

4. Optogeometric techniques (surface deformation in solids, volume changesin fluids), and

5. Optical or laser calorimetry (temperature rise).

The term “optoacoustics” refers primarily to the time-resolved technique utiliz-ing pulsed lasers and measuring the profiles of pressure in tissue.5, 25, 829, 831, 832

Historically, the term “photoacoustics” was introduced to describe primar-ily spectroscopic experiments with CW-modulated light and a photoacousticcell.5, 828, 830, 833 However, due to recent intensive development of the methodand its distribution not only for solving spectroscopic problems but also fornoninvasive imaging of absorbing inhomogeneities hidden in highly scatter-ing tissue, the term “photoacoustics” has experienced wider distribution in theliterature.196, 204, 893–897, 899

A schematic representation of certain OT and OA techniques applied to tissuestudies is given in Fig. 4.1.6 An excitation laser beam falls onto the sample surface;the light wavelength is tuned to an absorption line of the tissue component of inter-est; and the optical energy is absorbed by the medium. In a condensed medium, thecollisional quenching rate in the component is significantly higher than the radia-tive rate; therefore, most of the energy transforms to heat. The time-dependentheating leads to all of the previously mentioned thermal and thermoelastic effects.In OA or PA techniques (see “1” in Fig. 4.1), a microphone or piezoelectric trans-ducer that is in acoustic contact with the sample is used as a detector to measure theamplitude or phase of the resultant acoustic wave.5, 6, 25, 196, 828–832 In the OTR tech-nique (see “2” in Fig. 4.1), distant IR detectors and array cameras are employed forestimating the temperature of the sample surface and its image.5, 6, 25, 827, 828, 863–874

Heating the medium changes its refractive index. Changes in the refractive index ofthe sample or surrounding gas can either be detected directly by means of an inter-ferometer, or by a probe laser beam that changes its shape (converging or diverging)


Optothermal, Optoacoustic, and Acousto-Optic Interactions of Light with Tissues 139

Figure 4.1 Schematic representation of some optothermal techniques used in tissue study(see Ref. 6): �TS is the temperature change of a sample; �TG is the temperature changeof a surrounding gas; dS is the thermoelastic deformation; ϕd is the deflection angle ofa probe laser beam. 1, OA/PA technique; 2, OTR technique; 3, thermal lens technique;4, deflection technique.

thermal lens, (see “3” in Fig. 4.1) or is deflected (see “4” in Fig. 4.1) when it passesthe region excited by the pump beam.875–881

The intensity of the signals obtained with any of these OT or OA techniquesdepends on the amount of energy absorbed and transformed into heat and on thethermoelastic properties of the sample and its surroundings. Assuming that nonra-diative relaxation is the primary process in light beam decay and that extinction isnot very high, μad � 1 (d is the length of a cylinder within the sample occupiedby a pulse laser beam), the absorbed energy can be estimated on the basis of Beer’slaw:5, 6, 25

ET∼= Eμad, (4.1)

where E is the incident pulse energy; μa is the absorption coefficient.Energy absorption causes an increase in the local temperature, �T , which is

defined by the relation5, 6, 25

�T = ET

cpVρ∼= Eμad

cpVρ= Eμa

πw2bcpρ

, (4.2)

where cp is the specific heat capacity for a constant pressure,

V = πw2bd

is the illuminated volume, wb is the laser beam radius, and ρ is the medium den-sity. Assuming adiabatic expansion of an illuminated (heated) volume at constantpressure, one can calculate the change in this volume:

�V = π(wb + �wb)2 d − πw2

bd = βV�T ∼= βEμad

cpρ, (4.3)


140 Chapter 4

where �wb is the change in the radius of a cylinder illuminated by a laser beamcaused by a local temperature increase, and β is the coefficient of volumetricexpansion.

This expansion induces a wave propagating in the radial direction with thespeed of sound. The corresponding change of pressure, �p, is proportional to theamplitude of mechanical oscillations, �xT ∼ �wb:

�p = 2πfacυacρ�xT ∼ facυacρ�wb, (4.4)

where fac is the frequency of acoustic oscillations and υac is the velocity of acousticwaves in a medium.

Using Eq. (4.4) and taking into account that �wb � wb, we can finally find:

�p ∼ fac

wb· βυac

cpμaE. (4.5)

Equations (4.2)–(4.5) present the principles of various OT/PT and OA/PA tech-niques. Information about the absorption coefficient, μa, at a specific wavelengthcan be obtained from direct measurements of the temperature change, �T (opticalcalorimetry), volume change, �V (optogeometric technique), or pressure change,�p (OA or PA techniques). Using the connections between the focal length of thethermal lens, fT, the deflection angle of a probe laser beam, ϕd, and the phase shiftin a measuring interferometer, �ψ, with sample �T , the approximate expressionsdescribing the photorefractive methods can be written in the following forms5, 6, 25

for a thermal lens technique:

1

fT≈ dp

dn

dT· �T

w2b

, (4.6)

for a probe beam deflection technique:

ϕd ≈ 1

n· dn

dT· �T , (4.7)

and for a phase shifting (interferometry) technique:

�ψ ≈ 2πdp

λp· dn

dT· �T , (4.8)

where dn/dT is the medium (tissue) refractive index temperature gradient; dp is thelength of the space where the exciting and the probe laser beams overlap; λp is thewavelength of the probe beam.

The effects under consideration are possible in gases, liquids, and solids.Usually, a tissue under study is surrounded by a gas (composition of gases, likeair) or a liquid (blood, cerebrospinal fluid, or aqueous humor); therefore, a vari-ety of OT/PT and OA/PA effects can be concurrently monitored owing to thetransport of optical intensity, thermal, and acoustic waves in this tissue and itssurroundings.5, 6, 25



The time delay between optical and thermal (acoustic) pulses is an importantparameter of OT/PT (or OA/PA) techniques, defining the signal-to-noise ratio. Forexample, the pulse OA/PA method can be characterized by the time delay betweenoptical and acoustical pulses:828

τoa∼= Rbd/υac, (4.9)

where Rbd is the distance between the axis of the exciting laser beam and theacoustic detector, and υac is the velocity of acoustic waves in a medium.

The time delay for the thermal lens technique is defined by the time of thermalwave propagation transverse to the probing laser beam with radius wp:828

τth ≈ (wp/2.4)2/aT, (4.10)

where

aT = kT/(ρcp) (4.11)

is the thermal diffusivity of the medium, kT is the heat conductivity, and ρ is thedensity of the medium. When the duration of a laser pulse, τL, is much shorter thanτth, focusing the probe laser beam allows one to improve the transit time of thismethod.

The values of thermal parameters (the heat conductivity, kT, and the specificheat capacity for a constant pressure, cp) and ρ for many tissues are given in Refs. 2and 87.

4.2 OA/PA Gas Cell Technique

The OA/PA gas cell technique was developed over 30–80 years of the last cen-tury for a highly sensitive spectroscopy of gases, because there is no need in longcells, as required in conventional absorption spectroscopy, to study media with lowabsorption. This is because the facility of the OA/PA technique to measure signalsis directly determined by the absorption coefficient, μa, and not by the product ofμalcell, where lcell is the length of the cell, as in conventional spectroscopy.25, 825 Inapplication to biomedical research, the gas cell technique can be useful, for exam-ple, in analyzing the composition of a patient’s exhaled breath. For molecular gassystems with prevailing rates of nonradiative relaxation of the excited states, thetime-dependent OA/PA signal for excitation by a pulse with the energy, E, has theform5, 6

δp(t) ≈ (γ− 1)[(Eμa)/(πR2G)]exp(−t/τT), (4.12)

where δp(t) is the time-dependent change in pressure and t is the time; γ = cp/cV,and cp and cV are the specific heat capacity for constant pressure and volume,respectively; RG is the gas OA/PA cell radius;

τT ≈ (RG/2.4)2/aT (4.13)


142 Chapter 4

is the thermal relaxation time of the OA/PA cell, and the thermal diffusivity ofthe medium is

aT = kG/(ρGcV), (4.14)

where ρG is the gas density and kG is the gas heat conductivity. For condensedmatter, aT is defined in Eq. (4.11).

The length of thermal diffusivity (thermal length) is an important parameter,which for pulse excitation is estimated as5, 6

lT ≈ (4aTτL)1/2, (4.15)

where τL is the duration of a laser pulse.

4.3 Modulated (Phase) OA/PA Technique

Quantitative OA/PA images and spectroscopic studies of tissues can be providedin a frequency-domain mode, when a laser beam of P intensity modulated at fre-quency ω irradiates the sample, and the acoustic detector registers the modulationamplitude, δp(ω), and phase lag, �p(ω), of the acoustic signal.5, 6, 25, 823, 833 In thiscase, the following expressions for δp(ω) and �p(ω) can be derived:5, 6, 25

δp(ω) ≈ (√

2/2)(γ− 1)[(Pμa)/(πR2G)]τT/[1 + (ωτT)2]1/2, (4.16)

�p(ω) ≈ −tan−1(ωτT), (4.17)

where τT is defined by Eq. (4.13). These expressions are applicable within the samelimits as Eq. (4.12); these notations also coincide with those of Eq. (4.12).

A gas cell OA/PA method is widely used to study the optical and thermalproperties of condensed materials (liquids and solids).5, 6, 25, 828, 830 Light intensitymodulated at frequencyω is absorbed by condensed matter and partially convertedinto heat, which induces perturbations of the surrounding gas pressure, which inturn, can be registered by a microphone. For a description of the PA signal, threecharacteristic lengths are usually used: the geometric d, the mean free path ofphoton lph

∼= 1/μa (when μa � μs), and the thermal (thermal diffusion) lT,

lT = (2aT/ω)1/2, (4.18)

where aT is defined by Eqs. (4.11) or (4.14), depending on the measuring methodin use. Six various modes of a gas-microphone method can be used, based on dif-ferent relations between these three lengths. Evidently, for optically and thermallythick samples (d > lT ≈ lph), the generated OA/PA signal can be saturated and suchsituations should be avoided.25 For a given sample, lT is defined by modulationfrequency,ω, or pulse duration [see Eq. (4.15)]. For optically and thermally trans-parent samples (d ≈ lph + lT), the OA/PA response also includes the back surfaceof the sample; therefore, other modes may be used in addition to the six alreadydiscussed.



When light is assumed to be absorbed at the sample surface and heat flow isapproximated by the one-dimensional model, the phase lag can be written in theform833

tan�p = tan(d/lT)1 + Rb exp(−2d/lT)

1 − Rb exp(−2d/lT), (4.19)

where Rb = (1 − b)/(1 + b); b = [(kTbρbcpb/kTρcp)]1/2; lT is the thermal diffusionlength of tissue [see Eq. (4.18)], and d is the geometric length of the sample(parameters of the backing material are denoted by subscript b).

Equation (4.19) shows that �p is linear with ω1/2, provided by Rb

exp(−2d/lT) � 1. This condition is generally fulfilled for thermally thick objects(d � lT). However, it is even valid for a thermally thin case if the effusivity of thesample and the backing material are similar (b ≈ 1):

�p ≈ d/lT ∼ ω1/2. (4.20)

In that case, the images reflect only the thermal diffusivity of the samples. TheOA/PA cell was employed in the laser imaging system described in Ref. 833. Ithas two plane glass windows separated by 1 mm with a silicone sheet spacer. Toensure surface absorption, a sample was covered with 5-μm-thick copper foil andplaced on the rear window. An intensity-modulated (970 Hz) light beam from anargon laser (200 mW) irradiated the sample from the foil side and was absorbed atits surface. Then, generated heat traveled through the sample and showed phase lagat the air/sample boundary, which was detected as the OA/PA signal with a micro-phone. Transparent liquid paraffin was injected between the sample and windowto prevent generation of the OA/PA signal on the foil surface. It also worked asa backing material. The sample was embedded in paraffin, sectioned to approxi-mately 5 μm thickness, and placed on copper foil. The observed area of the samplewas scanned in increments of 25 μm over 100 × 100 points transverse to a laserbeam focused up to 40 μm.

A few types of tissues were studied: a slice of a dog’s eye and a mouse’skidney. From OA/PA phase images, the thermal diffusivity for each point can beobtained. For example, the thermal diffusivity of the optical nerve was estimatedas 1.9 × 10−7m2/s. The accuracy of the measured thermal diffusivity was approx-imately a few tens of a percent, primary owing to the difficulty in determiningthe exact thickness. The calculated thermal diffusion length was approximately8 μm. Thus, lateral resolution was limited only by the laser beam diameter andthe minimal scanning step. This method may be interesting for examining therelationship between the thermal properties and physiological functions of naturalbiological microtextures, because, in principle, it requires no fixation. The methodis categorized as PA microscopy (PAM).

The basic principles of PAM are very simple.25, 834, 897, 904–908 A spatially coher-ent laser radiation serves as a probe beam that can be focused to at least 1 μm.The scanning of a focused laser beam across the object’s surface and registrationof the PA signal, induced by using a microphone or piezotransducer, provide thedistributions of optical, thermal, and acoustic properties of the object.


144 Chapter 4

PAM allows profiling of the object in depth. When the wavelength of the lightsource is changed, the penetration depth of the light is also changed, and the PAsignal is generated at different depths. It should also take into account the spectralproperties of absorbers and their distribution within the tissue. Another way ofdepth profiling is to change the modulation frequency. This property is specificand characteristic only for PAM. The depth of profiling is defined by the thermaldiffusion length of the medium [see Eq. (4.18)] for a given modulation frequency.For example, for a highly absorptive sample (μa ≈ 106cm−1), a PA signal can begenerated at different depths from 10−1 to 103 μm when the modulation frequencyis changed in the range from 100 MHz to 1 Hz.

4.4 Pulsed OA/PA

Measurement of the stress-wave profile and amplitude by using an OA/PA spec-trometer (see Fig. 4.2), combined with measurement of the total diffuse reflectance,allows one to separately extract both absorption and scattering coefficients of thesample. The absorption coefficient in a turbid medium can be estimated from theacoustic transient profile only if the subsurface irradiance is known. For turbidmedia irradiated with wide laser beams (>0.1 mm), the effect of backscatteringcauses a higher subsurface fluence rate than incident laser fluence (see, for exam-ple, Figs. 1.11 and 1.12 for skin). Therefore, the z-axial light distribution in tissueand the corresponding stress distribution have a complex profile, reaching maxi-mum at a subsurface layer. However, the stress amplitude adjacent to the irradiatedsurface, δp(0), and the stress exponential tail into the depth of the tissue samplecan be expressed as829, 830, 840 [see also Eq. (1.36)]

δp(0) = �μaE(0), at surface (z = 0), (4.21)

δp(z) = �μabsE0exp(−μeffz), for z >1/μeff, (4.22)

where

� = β(υac)2/cT (4.23)

is the dimensionless Grüneisen parameter; cT is the specific heat of the tissue; bs isthe factor that accounts for the effect of backscattered irradiance, which increasesthe effective energy absorbed in the subsurface layer; the factor exp(−μeffz)describes the exponential attenuation of optical radiation in the tissue; μeff isdefined in Eq. (1.18); E(0) is the subsurface irradiance; and E0 is the incident laserpulse energy at the sample surface (J/cm2); the remaining parameters are given inEqs. (4.2)–(4.5). Thus, the amplitude of OA/PA pressure depends on the density ofthe laser pulse energy and the optical parameters of the tissue.

For optically thick samples,831, 840

E(0) ≈ (1 + 7.1Rd)E0, (4.24)

where Rd is the total diffuse reflection.



Figure 4.2 Optoacoustic/photoacoustic spectrometer for in vitro measurement of opticalparameters of tissues (see Ref. 840): SHC, second harmonic converter (532 nm); THC,third harmonic converter (355 nm).

Figure 4.3 Scheme of an acoustic transducer (see Ref. 840).

The Grüneisen parameter, �, is a dimensionless, temperature-dependent factorproportional to the fraction of thermal energy converted into mechanical stress. Forwater, it can be expressed with an empirical formula840 as

� = 0.0043 + 0.0053T , (4.25)

where temperature, T , is measured in degrees Celsius; for T = 37◦C, � ≈ 0.2.Equations (4.21) and (4.22) are strictly valid only when the heating process is

much faster than the expansion of the medium. The stress is temporarily confinedduring laser heat deposition when the duration of the laser pulse is much shorterthan the time of stress propagation across the depth of light penetration in the tissuesample. Such conditions of temporal pressure confinement in a volume of irradiatedtissue are accurately fit to nanosecond excitation and allow for the most efficientpressure generation with the least distortion.831, 832, 840

The described OA/PA method and instruments presented in Figs. 4.2 and 4.3were successfully used measuring the optical parameters of certain tissues.840, 841

The primary advantage of this three-wavelength laser OA/PA spectrometer formeasuring tissue optical properties is the LiNbO3 acoustic detector (Fig. 4.3),which provides high sensitivity (∼100 nV/Pa) combined with a broad ultrasonic


146 Chapter 4

frequency range (to 300 MHz) and long-term stability, and thus, accurate absolutecalibration.840 From OA/PA measurements for the human aorta samples (advancedfibrous atheroma), tissue optical properties were evaluated as μa = 16.5, 3.53, and0.15cm−1, and μ′

s = 72.1, 36.5, and 4.85 cm−1 at wavelengths of 355, 532, and1064 nm for sample thicknesses of ∼3, 7, and 12 mm, respectively, and estimatedroot mean square (rms) values of the measurements of ∼10, 15, and 50%. Onecan measure the absorption and scattering coefficients by using a combinationof diffuse reflectance and OA/PA techniques.841 Those measurements at wave-length of 1064 nm gave μa = 0.53 ± 0.03 cm−1 and μ′

s = 7.56 ± 0.92 cm−1 fornative canine liver. For coagulated tissue, a 1.3-fold increase in absorption coef-ficient (μa = 0.71 ± 0.30 cm−1) and a 2.6-fold increase in scattering coefficient(μ′

s = 19.9 ± 6.2 cm−1) were observed. The determination of optical properties ofsoft tissue in the NIR using OA/PA spectroscopy is also described in Ref. 845.Data for the optical parameters received using the OA/PA method are given inTable 7.1.

A systematic outline of OA/PA techniques, starting with production andextending to the propagation and detection of OA/PA waves, is presented in Ref.887. The focus of this review was the production of acoustic waves with maximalamplitude and minimal distortion. Receiving the maximal amplitude is importantfor OA/PA spectroscopy; minimal signal distortion is the key to determining thedistribution of optical properties and imaging in tissues.

4.5 Grounds of OA/PA Tomography and Microscopy

The concept of OA/PA tomography (OAT/PAT)196, 204, 831, 832, 838, 839, 843, 846, 848–858,

860, 890, 891, 893–898, 904–951 is illustrated in Figs. 4.4 and 4.5. Short laser pulses ensurethe temporal confinement of the transient pressure generated in the irradiated vol-ume of tissue as a consequence of laser heating. This means that laser-inducedacoustic waves do not move noticeably during laser heating of a tissue volumeunder study. As a result, the substantial fraction of energy deposited in the tar-get volume (tumor) will generate an ultrasonic wave before it can escape at thespeed of sound, and the profile of the laser-induced pressure precisely resemblesthe distribution of absorbed laser energy.

If the duration of the optical pumping pulse is much shorter than the thermaldiffusion time, thermal diffusion can be neglected; this is known as the assumptionof thermal confinement. In this case, the acoustic wave, p(r, t), which reaches thedetector at position r and time t, is related to optical energy absorption, H(r, t), bythe following wave equation:196, 829, 890

∂2p(r, t)

∂ t2− ∇2p(r, t) = βυac

cT

∂H(r, t)

∂ t, (4.26)

where t = tυac; acoustic wave speed, υac, is assumed to be constant; H(r, t) is theheating function, defined as the thermal energy per time and volume deposited by



Figure 4.4 Principal schematic diagram of laser OA/PA imaging system for breast cancerdiagnostics in transmission mode (a) (see Refs. 832 and 838). Normalized temporal signalof PA pressure from the tissue phantom based on Intralipid; PA peak-to-peak (PP) signal isshown (b) (see Ref. 887). Temporal pressure profiles recorded upon laser irradiation of thebreast phantom with a small “tumor” (the upper profile) and the same profile filtered usinga MATLAB wavelet transform method (c) (see Refs. 832 and 838). The x-axis displays thetime of transient acoustic wave arrival at the transducer. The “time” axis can be convertedinto the “depth” axis because depth = time × speed of sound (1.5 mm/μs).


148 Chapter 4

Figure 4.5 Principal schematic diagram of laser OA imaging system for skin cancer diag-nostics in reflection mode (a) and OA signals (pressure transients) measured in vivo intumor tissue (solid line) and normal tissue (dashed line) in a mouse model of breast carci-noma (b) (see Refs. 832 and 838). During the experiment, tissues were compressed by anattached acoustic transducer; therefore, all depths appear slightly smaller than they actuallywere.

the light source in close proportion to the optical absorption coefficient of interest;and the other parameters were defined previously. Equation (4.26) can be rewrittenin terms of H(r, t) as

p(r, t) = βυac

4πcT

∫∫∫∂H(r′, t′)

∂t′dr′

|r − r′| , (4.27)

where t′ = t − ∣∣r − r′∣∣. The source term, H(r, t), can be further rewritten asthe product of purely spatial (optical absorption function) and purely temporal(function of laser energy) components, i.e.,

H(r, t) = I0A(r)S(t), (4.28)

where I0 is a scaling factor proportional to the incident radiation intensity; A(r)describes the optical absorption properties of the tissue at r; and S(t) describes theshape of the irradiating pulse. Substituting Eq. (4.28) into (4.27) results in

p(r, t) = I0βυac

4πcT

∫∫∫A(r′)

dS(t′)dt′

dr′

|r − r′| . (4.29)

This equation shows the solution to the forward problem: prediction of the pressureoutside the tissue if the absorption properties of the medium and the profile of thelaser pulse are known.

For imaging, the inverse problem needs to be solved. Exact inverse solutionsin planar, spherical, and cylindrical geometries are available (see references inRef. 890). These exact solutions are computationally intensive and can be approxi-mated to more efficient solutions in most cases.890 In practice, the distance between



the OA/PA sources and the detector is much longer than the wavelength of thehigh-frequency OA/PA waves that are useful for imaging. Under this condition,the following backprojection algorithm is a satisfactory approximate of an inversesolution:890

A(r) = C∫

SD

∫dSD cos(ϕD)

1

t

∂p(r0, t)

∂t

∣∣t=|r0−r|/υac , (4.30)

where C is a constant, SD is the surface of detection, and ϕD is the angle betweenthe normal of dSD and r − r0 (the vector pointing from a point of detection to apoint of reconstruction).

This is a modified backprojection of the quantity (1/t)[∂p(r0t)/∂t

]. This back-

projection is analogous to that in x-ray computed tomography (CT). In x-ray CT,backprojection is along the paths of x-ray propagation; as in OAT/PAT, backpro-jection is along spherical shells that are centered at the detector and have a radiusdetermined by the acoustic time of flight.

In contrast to photon-density waves, acoustic waves (AWs) can provide min-imally distorted diagnostic information from sufficient depths in tissue to thesurface of a human organ owing to their much lower (two to three orders) scat-ter in tissues than in optical waves.890 This is a key point in laser OA/PA imagingand is explained by the independence of its resolution to light scattering. In addi-tion, its low sensitivity to light scattering helps to create more homogeneous lightdistribution in the volume of diagnostic interest. Light as a carrier of tissue structureinformation is replaced with a transient AW, which resembles the initial profile oflight distribution and can convey this unaltered profile to the acoustic detector.Imaging contrast is based primarily on the optical properties of tissue (absorption),and imaging resolution is based primarily on the acoustic waves. Wideband ultra-sonic detection permits the accurate reproduction of the initial pressure distributionin the irradiated volume. Profiles of the detected pressure transients and the times oftheir arrival carry information about dimensions, optical properties, and locationsof tumors. Owing to the sensitive detection of AW (5 V/bar), a temperature increaseof only 0.1 mK in a 2-mm tumor located at a depth of 5 cm will be sufficient for thegeneration of pressure signals with amplitude of 10 times the noise level.831, 832, 838

Figures 4.4 and 4.5 present two types of OAT/PAT in transmission and reflec-tion modes. The first type can be applied in breast cancer diagnosis and thesecond in the detection of skin cancer. A matrix of fiber-optic bundles deliversNIR laser energy from a pulsed Nd-YAG laser to the surface of the breast [seeFig. 4.4(a)]. A matrix of piezoelectric transducers reads temporal profiles of laser-induced acoustic waves. An electronic system digitizes the detected signal profilesand amplifies, filters, and transmits them to a computer for further data processingand image reconstruction. As an example, Figs. 4.4(b) and 4.4(c) show pressureprofiles recorded for the breast phantom (turbid collagen gel with “tumor” insertedinto a 2-mm gel sphere colored with hemoglobin). The bipolar signal that origi-nated from a depth of approximately 5 cm represents a 2-mm spherical tumor. Theslope of the general pressure profile is attributable to the exponential decrease inlaser energy absorbed in the phantom medium. The normalized and filtered final


150 Chapter 4

Figure 4.6 Schematic of the OA/PA imaging system for breast cancer diagnostics (seeRef. 932).

signal is free of high-frequency noise and other distortions, and can be used forimage reconstruction. Reconstructed 3D images can be obtained after a minimumof two OA/PA signal matrixes are measured at 90 deg relative to each other.

The reflection-type OAT/PAT system contains a fiber-optic light delivery sys-tem with a single piezoelectric transducer, so that AWs can be detected at thesite of laser irradiation [see Fig. 4.5(a)].831, 832, 838 The emphasis in this imagingsystem is on high spatial resolution (up to several microns); therefore, the acous-tic detector bandwidth must be the widest possible (approximately 300 MHz).Correspondingly, the laser wavelength and pulse duration should be chosen togenerate pressure profiles with maximum contrast in tissue layers. Figure 4.5(b)shows z-axial profiles of transient pressure signals measured in vivo in a mouse.One mammary gland of the mouse had a tumor (duct carcinoma) located under-neath the skin with a diameter of approximately 5−6 mm and a thickness ofapproximately 0.5 mm (histology was performed after the experiments). The tumorfeatured advanced microcirculation developed around it as a sphere. Two surfacesof the tumor are depicted as two maxima in an OA/PA signal on the axial profile.To obtain 3D images, it is necessary to scan the OA/PA reflectometer along thearea of diagnostic interest.

The literature describes a variety of OA/PA tomographic and microscopicsystems,834, 837, 839, 843, 846, 848–860, 890, 891, 893–946 including endoscopic.947–952 One ofthese systems, an OA/PA mammograph developed at the University of Twente(the Netherlands), is presented in Fig. 4.6.932, 933 The OA/PA-sectional images of



Figure 4.7 X-ray mammography (a), ultrasound (b), and OA/PA slice images (c) of a 57-year-old woman with invasive ductal carcinoma. The interslice spacing between OA/PAimages is 1 mm with the first slice 9.5 mm below the illuminated breast surface (seeRef. 933).

the right breast of a 57-year-old woman with invasive ductal carcinoma with neu-roendocrine differentiation obtained by this OA/PA mammograph are shown inFig. 4.7(c). For comparison, an x-ray mammogram [Fig. 4.7(a)] and an ultrasoundimage [Fig. 4.7(b)] were taken. A general view of the tumor presented in theseimages shows that it is benign. OA/PA-sectional images [Fig. 4.7(c)] show that themost intense OA/PA signal is distributed in the form of a ring. This distributioncan be attributed to the strong absorption due to the high density of blood vesselsin the periphery of the tumor. The distance between adjacent layers of the image is1 mm; the first layer is separated by 9.5 mm below the illuminated breast surface.

Dark-field PAM with ultrasonic resolution was proposed to minimize the inter-ference caused by the strong PA signal generated by the surface structures ofbiological tissue under direct laser beam illumination.6, 891, 897 However, a majorlimitation of dark-field PAM is related to the low illumination of the object. Incontrast, in PAM with optical resolution (OR-PAM) (see Fig. 4.8), which usesa diffraction-limited focused laser beam, significant scattering and absorption oflight limits the penetration of radiation into tissue within approximately one opti-cal TMFP, ltr ∼ 1 mm. In this sense, OR-PAM relies on ballistic and quasi-ballisticphotons to achieve imaging, for which the presence of signals from the surface is


152 Chapter 4

Figure 4.8 Schematic of a bright-field OR-PAM system (a) and enlarged sketch demon-strating the bright-field illumination and acousto-optical confocal configuration (b) (seeRef. 897).

not overly critical. Therefore, the OR-PAM technique allows for the use of com-mercial bright-field microscopes, providing diffraction-limited focusing of opticalradiation.

As shown in Fig. 4.8(a), a dye laser pumped by an Nd-YLF laser is used as theexcitation source for OR-PAM.897 The duration of the laser pulse is 7 ns and thepulse repetition rate, controlled by an external trigger, can be up to 5 kHz. A beamof light from a dye laser is attenuated before passing through a spatial filter (SF)(aperture diameter of 25 μm), then focused by an objective (RMS4X, Thorlabs,Inc.) with numerical aperture (NA) of 0.1, effective focal length of 45 mm, andworking distance of 18.5 mm. The distance between the SF and the objective lensis approximately 400 mm. An optical splitter located between the SF and the objec-tive lens allows one to adjust the focus and the optical system through the eyepiece.Two rectangular prisms form a cube with a clearance between them of 0.1 mm.This gap is filled with silicone oil, which has a similar refractive index to that ofglass (1.4 and 1.5, respectively), but is much smaller than the acoustic impedanceof glass (0.95 × 106 and 12.1 × 106 N·s/m3, respectively). Thus, a layer of siliconeoil is optically transparent but has acoustic reflection, acting as a divider of opticaland acoustic beams. An ultrasonic transducer (V2022-BC, Olympus-NDT) with acenter frequency of 75 MHz, bandwidth of 80%, and active element 6.4 mm indiameter is attached to the vertical part of the bottom prism. A plano-concave lenswith a 5.2-mm radius of curvature and a 6.4-mm aperture is fixed to the bottom ofthe cube and serves as an acoustic lens (NA of 0.46 in the water and focus diameterof 27 μm). Because this lens also functions as a negative optical lens, its effect onthe optical beam is compensated by a positive optical lens placed at the top of the



cube. A lens with a high acoustic NA is immersed in the water tank. The windowat the bottom of the water tank is closed by a plate made from optically and acous-tically transparent polyethylene. The experimental animal is located under the tankwith water, so that the targeted area is directly under the transparent window. Foracoustic coupling, ultrasound gel (Clear Image, SonoTech) is superimposed on thearea under study.

The PA signal recorded by the ultrasonic transducer is first amplified to 48dB by two successive ZFL 500LN (Mini-Circuits) amplifiers, and digitized with aCompuScope 14,200 14-bit digital data acquisition board (Gage Applied Sciences).A 2D raster scan (x−y), in combination with a time-resolved ultrasonic signal,allows for 3D information. The 2D scanner is controlled by a separate computer,which also runs the computer for data collection and the pump laser. The initiationsignal is synchronized with the clock generator of the data acquisition board. Forsimplicity, raster scanning is provided by moving the water tank and the animal inthe horizontal plane (x−y). A one-dimensional PA signal (A-scan) for each hori-zontal pixel is recorded during 1 μs at a sampling rate of 200 MS/s (mega-samplesper second).

The image obtained by using the OR-PAM is formed by combining differentA-scans for PA signals with temporal resolution that can be represented as a 3Dimage, or a 2D cross-sectional image (B-scan), or an image of the projection of thesignal’s maximal amplitude.

Through the use of tunable dye laser in OR-PAM, it is possible to conductspectral measurements, which is important for visualizing the vascular system andquantifying the relative concentration of oxyhemoglobin (HbO2) and deoxyhe-moglobin (HbR) in individual microvessels, because the absorption spectrum ofhemoglobin depends on the degree of oxygenation. Considering that in the visibleregion of the spectrum, HbR and HbO2 are the two dominant absorbers in blood,the blood absorption coefficient can be calculated by the formula939

μa (λi) = εHbR (λi) · [HbR] + εHbO2 (λi) · [HbO2] , (4.31)

where μa (λi) is the blood absorption coefficient at wavelength λi; εHbR (λi) andεHbO2 (λi) are the molar extinction coefficients, and [HbR] and [HbO2] are theconcentrations of HbR and HbO2, respectively.

In addition, from PA measurements, the absorption coefficient, μa (λi), can bedetermined, because the PA signal, p (λi, x, y, z), is proportional to the product ofμa (λi) and the local density of optical energy, E (λi, x, y, z) [see (4.22)]. Assumingthat the optical energy density does not depend on the wavelength, μa (λi) inEq. (4.31) can be replaced by p (λi, x, y, z) to calculate [HbR] and [HbO2] in relativeterms. Because both εHbR (λi) and εHbO2 (λi) are well known,953 for determining theconcentrations of [HbR] and [HbO2], it is sufficient to provide measurements onlyfor two wavelengths. However, measurements for more wavelengths can improveaccuracy. Based on measured concentrations of [HbR] and [HbO2], the degree ofoxygen saturation, sO2, can be calculated as

sO2 = [HbO2]

[HbR] + [HbO2]. (4.32)


154 Chapter 4

Figure 4.9 Pseudo-color sO2 mapping of a microvascular network in a nude mouse earacquired in vivo by OR-PAM (see Fig. 4.8); a1–a3: arterioles of different diameters; v1–v3:venules of different diameters. PA: photoacoustic signal amplitude (see Ref. 897). (See colorplates.)

To demonstrate the possibility of in vivo quantification and imaging of sO2

in vessels, an athymic hairless mouse (Hsd: Athymic Nude-Foxn1NU, Harlan Co.;weight ∼20 g) was supplied with pure oxygen, and measurements were providedat two wavelengths: 586 nm (isosbestic point: the same absorption of oxy- anddeoxyhemoglobin) and 606 nm (the dominant absorption of deoxyhemoglobin).Figure 4.9 shows an image of the microvascular network in a mouse ear in pseudo-color from blue to red, corresponding to degrees of sO2. The amplitude of the PAsignal measured for the isosbestic point is shown in the form of pixel brightness.In this case, OR-PAM provides a map of the spatial distribution of sO2, includingbehavior revealing the degree of oxygenation during the transition from arteries toveins. Typically, sO2 monotonically decreases with the decreasing diameter of thevessel in the precapillary arterioles. For arterioles, denoted in Fig. 4.9 as a1–a3, sO2

values are 0.97 ± 0.01, 0.92 ± 0.01, and 0.91 ± 0.01, respectively, for vessels withdiameters of >20, 10–20, and <10μm. sO2 then continues to decrease with theincreasing diameter of the vessel in the postcapillary venules. For venules, denotedin Fig. 4.9 as v3–v1, sO2 values are 0.85 ± 0.01, 0.82 ± 0.01, and 0.73 ± 0.02 forvessels with diameters of <10, 30–40, and >50 μm, respectively. These measuredvalues of sO2 are slightly higher than normal because the experimental animalswere under systemic hyperoxia.

Thus, multispectral optoacoustic tomography (MSOAT) allows one to receiveimages of tissues that provide information about the functional state of the tissueat the molecular level. MSOAT images received for multiple excitation wave-lengths are processed based on specific spectral information to determine thebiodistribution of various endogenous molecules.

Another example of MSOAT application is exogenous dye contrasting.922,

923, 940–942 Often, the need for additional contrasting by the exogenous dyes isfundamentally important; for example, in the diagnosis of disease, when theabsorption of endogenous chromophores is inadequate, absorption occurs awayfrom the window of tissue transparency, or absorption lines of many chromophoresare strongly overlapping. From a technical point of view, for the successful



Figure 4.10 ICG entering the kidneys of a mouse. OA slice image through the kidneys (a):(1) vena cava, (2) portal vein, (3) kidneys, (4) spine. Corresponding cryosection photographshowing the same structures (b). Selected images from single laser pulses at 800 nm duringICG injection showing increased contrast from the agent (c). Overlay of differential contrasthighlighting the ICG enhancement (d). Overlay showing the distribution of ICG in the sameanimal by spectral unmixing after imaging at multiple wavelengths (750, 770, 790, 810, 830,850, 870, 890, and 910 nm) (e) (see Refs. 924 and 955). (See color plates.)

implementation of MSOAT, narrow band contrasting agents with high absorptionin the NIR should be used. In addition, the speed of dye diffusion in the body andcharacteristic time it remains in certain tissues and organs are of great importance.These parameters all determine the quality of the images, the dynamic nature ofdiagnostics, and toxicity issues. The ideal dye to satisfy these requirements is theICG.954 Figure 4.10 shows dynamic in vivo MSOAT images of ICG transportedinto mouse kidney.924, 955 The OA cut of the kidney clearly demonstrates the visi-ble tissue structures, such as hollow cavities, portal veins, the two kidneys, and thespine, corresponding to images of cryogenic tissue cuts. Selected images of OAsections, obtained for single laser shots at a wavelength of 800 nm, close to theabsorption maximum of ICG, clearly show an evident increase of image contrastupon arrival of the dye [Fig. 4.10(c)]. Presentation of these images in the formof differential contrast further highlights the ICG contrasting effect [Fig. 4.10(d)].The total map representing the distribution of ICG in the same animal, obtained byspectral separation after capturing images at several wavelengths (750, 770, 790,810, 830, 850, 870, 890, and 910 nm) [Fig. 4.10(e)], accurately fits the areas ofhigh contrast for images in Fig. 4.10(d).924, 955

4.6 Optothermal Radiometry

Pulse laser heating of a tissue causes temperature perturbations and correspondingmodulations of its thermal (IR) radiation. This is the basis for pulse optothermalradiometry (OTR/PTR).153, 826–828, 864–874, 886, 956–959 The maximum intensity of thethermal radiation of living objects falls at a wavelength range close to 10 μm.A detailed analysis of OTR/PTR signal formation requires knowledge of the inter-nal temperature distribution within the tissue sample, the tissue thermal diffusivity,


156 Chapter 4

and its absorption coefficients at the excitation, μa, and emission, μ′a (10μm),

wavelengths. At the same time, knowledge of some of these parameters allowsone to use the measured OTR/PTR signal to reconstruct, for example, the depthdistribution of μa.864, 870

The characteristic thermal time response of a specimen is defined by its dimen-sion, R0 (radius of a cylinder form), and the thermal diffusivity of its material, aT

[see Eqs. (4.10) and (4.13)]:

τT ∼ (R0)2/aT. (4.33)

Experimental values for the aT of certain human tissues are presented in Table 4.1.For many soft tissues, these values lie within the rather narrow range defined by thethermal diffusivity of tissue components: Type I hydrated collagen (50% water),1.03 × 10−7 m2/s; and pure water, 1.46 × 10−7 m2/s.867, 868 Therefore, the char-acteristic thermal time responses for various organs are primarily defined by theirdimensions and can be estimated as 10−3 s for a cell, 3 × 10−2 s for a small bloodvessel, 102 s for a finger, and more than 104 s for a whole arm.

For a laser pulse duration much shorter than the thermal relaxation time of thesample, τT, the OTR/PTR signal normalized to incident radiant exposure and initialtemperature (normalized surface temperature) induced in homogeneous absorbing-only and turbid samples is defined by the following expressions, derived on thebasis of Beer’s law and diffusion approximation, respectively:870

Sr(t) = δ

1 − δ2[exp (δ2αt) erfc(δ

√αt) − δ exp(αt)erfc(

√αt)], (4.34)

Sr(t) = δ

{A

1−δ2d

[exp ( δ2d αt) erfc(δd

√αt) − δd exp(αt)erfc(

√αt)] +

+ B1−δ2

t[exp ( δ2

t αt) erfc(δt√αt) − δt exp(αt)erfc(

√αt)]

}. (4.35)

Table 4.1 Experimental values for thermal diffusivity, aT, of human tissues (see Ref. 2).

Tissue aT, 10−7 m2/s Remarks

Muscle, underarm 0.601.001.30

In vivo, 0.45 mmIn vivo, 0.90 mmIn vivo, 0.90 mm

Muscle, thigh 0.5450.963

In vivo, 0, . . . , 1 mmIn vivo, 1, . . . , 2 mm

Skin 0.4. . . 1.60.82. . . 1.2

In vivoIn vitro, room to body temperature

Kidney 1.32 In vitro, 5◦C, 84% waterHeart 1.48 In vitro, 5◦C, 81% waterSpleen 1.38 In vitro, 5◦C, 80% waterLiver 1.50 In vitro, 5◦C, 77% waterBrain 0.44. . . 1.4 In vitro, room to body temperatureBrain, white matter 1.35 In vitro, 5◦C, 71% waterBrain, gray matter 1.43 In vitro, 5◦C, 83% waterBrain, whole 1.37 In vitro, 5◦C, 78% waterBlood, hemolyzedBlood, plasma

1.191.21

Power measurement, use of thermal model

Teeth 4.09 —



Here, δ=μa/μ′a,α = (μ′

a)2aT, δd = μd/μ

′a, δt = (μa + μ′

s)/μ′a, erfc(x) = (2/

√π)∫ x

0 e−ξ2dξ is the complementary error function, and A and B are defined in diffusion

theory. The corresponding temperature distributions inside the homogeneous andlayered samples are presented in Ref. 870.

The surface radiometric signal, Sr(t), at any time t is the sum of the contribu-tions from all depths in the tissue at time t. The radiation from deeper depths isattenuated by the infrared absorption of the sample before reaching the detector.Because the initial surface temperature is known, the temperature distribution intothe sample depth can be extracted by measuring Sr(t). An inverse OT method toconvert surface temperatures as a function of time into internal temperatures as afunction of depth is described in Ref. 870.

Figure 4.11 shows the results of pulse OTR/PTR experiments conducted onskin using a 577-nm, 1-μs pulsed dye laser.870 Radiometric signals were collectedfrom visibly healthy areas of the wrist and also from a port wine stain on the wristof a Caucasian volunteer. The laser energy was maintained at 100 mJ over an areaof approximately 20 mm2. The infrared thermal signal from the irradiated area wasmonitored by using a 1-mm2 HgCdTe photoconductive detector with a wavelengthdetection range of 8 to 12 μm. The detector signal was conditioned by using adc to 1.5 MHz amplifier impedance matching the detector. The signal was thenrecorded on a digital oscilloscope. The sampling rate was 10 to 50 μs per point,and 10,000 data points were collected after the laser pulse. The detector responsewas approximately 50 mV/◦C. Twenty pulses were averaged to reduce the noise.

Figure 4.11 OTP depth profiling for skin (see Ref. 870). The graph shows the temperaturedistribution for a healthy area of the skin (a) and for a port wine stain (b). A temperaturepeak is evident at approximately 80 μm, indicating the presence of a subsurface absorber.


158 Chapter 4

The calculated internal temperature distributions for a healthy area on the wristand for a port wine stain are presented in Figs. 4.11(a) and 4.11(b). There is anoticeable peak in the temperature profile at approximately 80 μm, indicating asubsurface absorber. The limitations of this technique are that absorption profilescan only be made to a depth of 500 μm before the signal decays too extensively.Fortunately, the most interesting structures in the skin are found between 0 and 600μm from the surface of skin.

Uncertainty in the location of the internal temperature layers increases withthe depth of the layer.870 However, the single-wavelength pulsed OTR/PTR tech-nique is applicable for the accurate determination of port wine stain depth if bloodvessels are deeper than 100 μm.871 When blood vessels are close or partially over-lap the epidermal melanin layer, a two-wavelength (585 and 600 nm) technique isa superior method to determine lesion depth. It was demonstrated both theoreti-cally and experimentally in in vivo measurements that a two-wavelength method isappropriate for a wider range of port wine stain patients with various blood volumefractions, blood vessel size, and depth distribution.871, 872 This is attributable to theuse of the direct difference approach, in which vessel depth is determined froma weighted difference of temperature profiles reconstructed independently fromtwo-wavelength measurements.

It was also demonstrated both theoretically and experimentally that morpho-logical information can be extracted from a simplified 2D model of a blood vesselif pulsed OTR/PTR imaging is performed and multidimensional analysis of thedata is conducted.886

The pulse OTR/PTR method displays excellent potential for the study of theoptical and thermal properties of tissues in vitro and in vivo.863–870 Certain datareceived for the optical parameters are given in Table 7.1. Sequences (pairs) ofinfrared emission images recorded following pulsed laser irradiation were used todetermine the thermal diffusivity of the biomaterial with high precision.868 Themean thermal diffusivity of an in vitro Type I hydrated (50% water) collagen filmstructure (a model skin phantom) at room temperature (22◦C) deduced from 60recorded infrared emission image pairs is equal to aT = (1.03 ± 0.07) × 10−7 m2/s(see Table 4.1). Application of the method to in vivo tissue study was discussed.

Time-resolved OTR/PTR was used to determine the absorption coefficients ofdental enamel and dentin at 2.79, 2.94, 9.6, and 10.6 μm.827 These data are alsopresented in Table 7.1 and are potentially important for the application of erbium[Er-YSGG (2.79 μm) and Er-YAG (2.94 μm)], or CO2 (9.6 and 10.6 μm) lasers forthe ablation of hard dental tissue. On the other hand, the OTR/PTR technique mayserve for online monitoring of tooth ablation or hard tissue depth profilometry forthe inspection of dental defects.

The frequency-domain OTR/PTR technique uses an intensity-modulated laserradiation for inducing modulation frequency–dependent infrared optothermalradiometric (FD-OTR/PTR) signals from tissue lesions or defects873, 874, 956–959

(Figs. 4.12 and 4.13). The significance of this technique to dentistry is caused by itspotential for monitoring dental lesions at the early stages of carious decay, whichmay require lateral and subsurface spatial resolution on the order of crack sizes and



Figure 4.12 Schematic of the FD-PTR-LUM method (a), lT is the thermal length; and dia-gram of experimental setup for combined OTR and LUM monitoring of a tooth (b) (seeRef. 956).

small holes, and subsurface depth probing of 100–300 μm. FD-OTR/PTR exhibitsa much higher signal-to-noise ratio than its pulsed counterpart and a fixed probedepth with the use of a single modulation frequency. For an image to be formed,either the source or the detector must be localized. Photothermal imaging generallyfalls into the category of scanned microscopy with a localized source. The temper-ature modulation allows for thermal energy to diffusively reach the surface from adepth approximately equal to a thermal length, described by Eq. (4.15). Scattererslocated within a fraction of a thermal length from the source dominate the con-trast of radiometric images. In this way, when the thermal length is varied, e.g.,by changing the laser-beam modulation frequency, the region of the specimen thatcontributes to the image is also varied.

In dental practice, it is often desirable to obtain detailed local information aboutpotential lesions, and inside pits and fissures with high spatial resolution, such asthat achieved with a focused laser source. To meet these objectives, a combinationof FD-OTR/PTR and FD-luminescence (LUM) was recently used as a fast dentaldiagnostic tool to quantify sound enamel or dentin as well as subsurface cracks in


160 Chapter 4

Figure 4.13 PTR-LUM amplitude and phase curves on modulation frequency for 5- or 10-day demineralized samples (see Ref. 956). Error bars, when not visible, are the sizes of thesymbols. The densitometric tracing (top right) and microradiographic image (bottom right)of the lesion are presented in the adjacent figures. From TMR analyses: mineral loss = 1310vol. % μm; surface layer thickness = 3.6 μm and lesion width = 85.0 μm.

human teeth.873, 874, 956–959 Under laser excitation and modulation frequencies in therange from 10 Hz to 10 kHz, it was found that OTR/PTR images are complemen-tary to LUM images as a direct result of the complementary nature of nonradiative(thermal) and radiative (fluorescence) de-excitation processes, which are respon-sible for OTR/PTR and LUM signal generation, respectively. Measurements wereperformed at the wavelengths of 488, 659, and 830 nm.

The FD-PTR-LUM method is schematically shown in Fig. 4.12(a). When theintensity-modulated laser radiation meets the surface of the tooth, the light is con-verted into heat (temperature change <1◦C), which then travels into the interiorof the tissue in a wave of heat and generates a PTR signal. The same light excitesthe fluorophores to produce modulated fluorescence (luminescence). This waveof LUM intensity originates from near-surface tooth structures and is defined bythe optical properties of the tissue. Changes in the microstructure of the tooth,such as those caused by caries, lead to corresponding changes in the optical andthermal properties of tooth structure and, consequently, the frequency-dependentPTR-LUM response. The amplitude and phase of these responses are differentbetween healthy, demineralized, and carious enamel.

Figure 4.12(b) presents the experimental setup that implements the FD-PTR-LUM technique.956 A diode laser with wavelength of 659 nm, output power of130 mW, and beam size of ∼5.6 mm is used as the light source. Modulation oflaser intensity is provided by modulating its electrical power supply by the signalfrom the internal oscillator of the lock-in amplifier used in the detection circuit.The intensity of the laser is modulated harmonically. The variable infrared PTR



signal originating from the tooth is collected by a parabolic rhodium-plated mirrorand transferred to the HgCdTe detector with the spectral range at cooling by liquidnitrogen of 2–12 μm and with peak detection ability of ∼5 × 1010 cm·Hz1/2·W−1.The active area of the detector is 1 mm2. The PTR signal is preamplified, then fedto the lock-in amplifier and then to the computer. The intensity-modulated fluores-cence (luminescence) signal from the tooth passes through an optical filter (with acutoff at 715 nm) to a silicon photodiode. A colored glass filter blocks laser radia-tion reflected and scattered from the tooth. To control the modulated luminescencesignal, a second lock-in amplifier is used. Both lock-in amplifiers are controlled bycomputer.

In Ref. 956, the effectiveness of the FD-PTR-LUM technique for monitoringand quantification of dental caries was studied by using the described instrumen-tation. Artificial caries were created in the extracted human molars (n = 15) byusing an acidified gel (pH 4.5), which was applied for 10 or 40 days. PTR-LUMsignals before and during tissue demineralization were measured by scanning themodulation frequency in the range from 1 Hz to 1 kHz. As the “gold standard”for determining the degree of tooth demineralization, transverse microradiographic(TMR) analysis was used. TMR allows for reliable information about the loss ofthe mineral component of tissue and the depth of artificially demineralized lesions.To process PTR experimental data for obtaining the time-dependent changes inthermal properties over the course of tissue demineralization, the correspondingtheoretical model was used. The growth of demineralization was accompanied byan increase in the scattering properties and deterioration in thermal conductivity.The increase in the scattering of light appears to reduce the luminescence signaldue to the increased scattering of both incident and converted radiation. The depen-dences of amplitude and phase of the PTR and LUM signals on the modulationfrequency for a sample of the tooth before and after a 5- or 10-day demineralizationare presented in Fig. 4.13. This figure also gives the results of the correspondingdensitometry of a TMR image of the tooth enamel, which enables one to visual-ize the affected area and to quantify the loss of the mineral component of tissue.Thus, a sufficiently sensitive FD-PTR-LUM technique to changes in the degree oftooth mineralization was demonstrated. The high sensitivity is attributable to cor-responding changes in optical and thermal properties of tissue. This increases thepossibility of effective early detection of caries.958, 959

4.7 Optothermal Spectroscopy and Imaging

A probe beam deflection technique was described for detecting the thermallyinduced refractive index gradient inside the sample [see Eq. (4.7)].875 From theHe-Ne laser probe beam deflection measurements and refractive index gradientestimates, it was found that a diode laser (1480 nm) beam produces superheatedwater at ∼200◦C. The temperature profile in the diode laser beam and vicinity ispredicted as a function of laser pulse duration and power. An optimal (safe) regimeto dissect the zona pellucida (shell) of pre-embryos by a focused laser beam (1480nm) was defined as pulse duration of ≤5 ms and laser power of ∼100 mW.


162 Chapter 4

As in conventional absorption spectroscopy, the basic information providedby laser photothermal (PT) spectroscopy is the absorption coefficient wavelengthdependence, μa(λ). However, instead of a path-dependent result as the product,μa(λ) × l, where l is the length of the sample, in PT spectroscopy, the measuredsignal is as directly proportional to absorption coefficient as in PA spectroscopy[see Eqs. (4.2), (4.6)–(4.8)]. For example, in conventional absorption spectroscopy,to measure absorption in a 300-nm-long optical path (the typical diameter ofan elongated mitochondrion) with accuracy of ∼0.5 % in measuring light varia-tion, a minimum detectable coefficient of absorption, (μa)min ≈ 1.5 × 102 cm−1.25

This sensitivity is insufficient to study cellular structures that typically have lowercoefficients of absorption and size.

PT spectroscopy with visible and NIR tunable laser sources provides at leastfour to five orders of magnitude higher sensitivity to absorption than that withconventional absorption spectroscopy, along with the capability of measuring sub-cellular localized absorption spectra with a spectral width of 0.1–1 nm.5, 6, 25, 826–828

PT spectral identification of just three primary cellular components, such ascytochrome c (Cyt-c), P450, and cytochrome-c-oxidase (Cyt-c-oxidase), with dis-tinguishable absorption bands near 450, 550, and 700–900 nm, respectively,960

may provide many potential applications of PT spectroscopy in cell biochemistry,because these components are involved in such important cellular processes asapoptosis, drug kinetics, and cellular energy transform, respectively. Identificationof cellular components is also possible, including Cyt-a (605 nm) and Cyt-c-oxidase with copper A center (CuA) in reduced (620 nm) and oxidized (820 nm)states, and with copper B center (CuB) in oxidized (680 nm) and reduced (760 nm)states.

Measurement of PT responses from different forms of hemoglobin may makeit possible to estimate the biochemical processes of blood in flow at the singleerythrocyte level. As in conventional spectroscopy, it is possible to use specificabsorption bands for red blood cells (RBCs): Soret band at 415 nm (oxy) and 425nm (deoxy), Q-bands at 542 nm (oxy), 578 nm (oxy) and 554 (deoxy), and band at760 nm (deoxy); almost maximal difference in absorption between oxy and deoxyhemoglobin is at 675 nm, almost minimum is at 760 nm. At hemoglobin isosbesticwavelength equal to 805 nm, blood absorption is independent of oxygenation, butinstead only depends on the number of RBCs and white blood cells (WBCs) in thevolume. WBCs absorb light on the wavelengths 525–565 and 750–830 nm, deter-mined by the absorption of Cyt-c and Cyt-c-oxidase. For example, in in vivo flowcytometry, these spectral differences allow for identification the rare RBCs amongWBCs in lymph flow.961 To identify abnormal cells (e.g., cancer cells among nor-mal WBCs) that do not differ significantly in absorption, the specific PT responserelated to cell shape and its structural parameters is used.

The technical platform for PT imaging (PTI) of cells is a well-developed con-ventional microscopy, which simplifies cell manipulation and allows one greatflexibility in choosing the signal acquisition algorithms. However, to create images,most described techniques require time-consuming scanning of a focused laserbeam across the cells. For example, with the PT thermal lens technique, cell



imaging with a high resolution of ∼1 μm was achieved by laser scanning of one cellfor ∼1 h.962 Thus, scanning technology is suitable only for high-resolution imag-ing of nonmoving living cells. To avoid time-consuming scanning and to allowdynamic cell studies, a wide-field PTI963, 964 for in vivo flow cytometry961 can beused. In this scheme, the PTI of one cell is obtained in 0.1 s after just one lasershot with an 8-ns pulse width and sufficiently broad beam diameter (15–25 μm) tocover an entire cell.

By recording laser-induced temperature-dependent variations of the refractiveindex around absorbing micro- or nano-inclusions within a cell, high-resolutionand high-sensitive PTI can be provided (see Fig. 4.14). For example, PTI of in vivoflow cytometry systems uses irradiation of absorbing nano-targets, flowing alone oras components of cells, with a focused short laser pump pulse and recording of ther-mal effects with various PT techniques, such as phase-contrast (Fig. 4.15),961, 963, 965

thermal-lens,877, 966 and confocal thermal-lens967 imaging of a second collinearlaser pulse that probes the heated cells.

The interaction of laser radiation with absorbing micro- and nano-structures ofcells or tissues (small-scale variations of hemoglobin and melanin concentrations,correspondingly, in RBC or melanoma cells, or/and exogenous nanoparticle mark-ers) is accompanied by a variety of OT (PT) phenomena (see Fig. 4.14).966 Theyinclude: heating (temperature elevation, �T), secondary IR radiation (OTR/PTRmethod; see Section 4.6); photomechanical stress (�F); thermal expansion (�L);acoustic and shock waves (�p; see Sections 4.4 and 4.5); evaporation, bubble cre-ation, and cavitation (at high pulse energy); and index of refraction change (�n). Ingeneral, these phenomena can all be used for the detection of absorbing inclusionsof cells and tissues.

Two optothermal methods are the most suitable for cell analysis: the previouslydescribed PA technique (see Sections 4.1–4.5) and the PTI method, which can berealized by a thermal lens technique or different modifications. The basic principleof PT phase-contrast microscopy for the detection of micro- and/or nano-scaled

Figure 4.14 Laser-induced PT and related phenomena around an absorbing micro- or nan-otarget (endogenous or exogenous inclusions) of diameter 2R ≤ λ in a cell or tissue (seeRef. 966).


164 Chapter 4

Figure 4.15 Principle of laser-based dual (pump-probe) PT phase-contrast microscopy ofmicro- or nanoscaled absorbing cell or tissue inclusions on the basis of two laser beams:from the pumping beam, which selectively heats this inclusion, and from the probing beam,which reads information about changes of the spatial distribution of the index of refractionof the surrounding medium (see Ref. 877).

Figure 4.16 Temporal dynamics of thermal fields formed around a nano-object of radiusR at a short laser pulse absorption: temperature profiles along x-axis (solid lines) (a), RTis the increase in the thermal-spot size (blurring effects) for time t2 elapsed since lasershot time t1, RT becomes larger than target size R and diffraction limited optical image(puncture curve), the diffraction limit RD ∼ 0.61λ/NA; margins of temperature distributionsfor a cylindrical nano-target at times elapsed since laser shot, t3 > t2 > t1 (b) (see Ref. 877).

absorbing inclusions of cells or tissue follows from Fig. 4.15. It uses two laserbeams, one from a pumping laser, which selectively heats inclusion, and anotherfrom a probing laser, which records information about variations in the refrac-tive index of the medium surrounding the absorbing target.877 Correspondingly,Fig. 4.16 illustrates the temporal dynamics of thermal fields created around a cylin-drical nanotarget upon absorption of a short laser pulse for three time intervals afterlaser shot, t3 > t2 > t1.877

According to Abbe’s principle, light cannot create an adequate image ofan object whose structural details are smaller than the diffraction limit, RD ∼0.61λ/NA, in the far field.226 However, image creation that is not based on theinteraction of light with an object itself, but on a laser-induced thermal field aroundthe object (Fig. 4.16), may overcome Abbe’s law.877 This happens because thethermal field holds information about target size and shape, even during expansionas a result of heat diffusion. Therefore, optical analysis of the spatial structure ofa thermal field when it has grown sufficiently to satisfy Abbe’s criterion makes



it possible to provide the PTI of a nano-scaled inclusion and to reconstruct itssize and shape. Thus, PTI transforms absorbing nanoscaled targets that are invis-ible with far-field optics to microscaled dimensions that are visible with opticaltechniques.877

If the laser pulse width, τL, is significantly shorter than the thermal relaxationtime of the nanoscaled target, τT (i.e., τL � τT), the initial margin of laser-inducedtemperature distribution, �T(r, t), will coincide with the target’s geometry. Forexample, targets with three basic geometries: a sphere with radius R � λ, a cylin-der with radius Rc � λ and length l (l � Rc), and a planar circlar plate with radiusRp and thickness (d � λ, Rp) − τT may be estimated as follows877 [see also Eqs.(4.10) and (4.11)]:

Sphere : τT = R2/6.75aT (4.36)

Cylinder : τT = (Rc)2/4aT (4.37)

Circular plate : τT = d2/8aT, (4.38)

respectively.For known heat diffusion coefficients aT and τT, determined from the mea-

surement of a target’s thermal dynamics, it is possible to use Eqs. (4.36)–(4.38)to obtain information about a target whose size is smaller than the wavelength.For example, for spherical targets with R = 50 nm, 500 nm, and 5 μm, estima-tions of τT [aT = 1.44 × 10−3 cm2/s for water parameters, see Eq. (4.11)] areapproximately 4 ns, 0.4 μs, and 40 μs, respectively. The theoretical limit forthis method is characterized by the transfer time of absorbed light energy intoheat (i.e., at τT = τNR, where τNR is the nonradiative relaxation time), which, fortypical parameters, corresponds to a minimal size of ∼0.1–1-nm. The acousticrelaxation time, τoa [Eq. (4.9)], is always shorter than the thermal relaxation time,τT [see Eqs. (4.10), (4.11), (4.36)–(4.38)], except for very small targets with sizesdetermined from Eqs. (4.36)–(4.38) at τoa = τT. Thus, for an approximately 0.1 to1-nm target, when both times are equal, this range seems to be the principal limitfor different PT methods.

Because a thermal field keeps the memory of the target’s spatial shape, analy-sis of the shape of the thermal field can reveal the target’s shape [see Fig. 4.6(b)].This approach may be valuable in the near-field zone of relatively large objectswith R > RD/5(>50 nm). In particular, if the cylinder length, l, or the radius ofthe planar structure, Rp, exceeds λ, such objects can be partly visible through adiffraction-limited microscope. Measuring the cooling time by using Eqs. (4.37)and (4.38) may yield additional information on nanoscaled parameters, such ascylinder diameter or thickness of the planar structure. In particular, this informa-tion may be important for the study of platelets, nuclear chromatin, cell or musclefilament diameter, or ellipsoidal mitochondria, especially for monitoring processessuch as the growth or modification of spatial structures under different externalimpacts (e.g., radiation, drugs).

The laser-induced thermal effects around a nanotarget can be evaluated bymonitoring temperature-dependent changes in the refractive index, �n, of thesurrounding medium by wide-field phase-contrast imaging of a second coaxial


166 Chapter 4

probe laser pulse (see Fig. 4.5). Upon passage of the heated area by the probebeam with pathway dp, phase shift is obtained876, 965 [see basic Eq. (4.8)] as

�ψ = 2πdp(r)�n(r, t)/λp = 2π(dn/dT)dp(r)�T(r, t)/λp. (4.39)

The first pumping beam, after passing the object, is cut off by a Zernike rejec-tion filter with a circular shape that is more suitable for laser measurement (seeFig. 4.15). After filtering, interference between the unperturbed and perturbedcomponents of the probe beam transforms phase changes into images of spatial-intensity distribution that correlate with the thermal fields in the object plane. Thisimage, captured by a CCD camera and designated as a PT image, can be obtainedwithout laser scanning using just one laser shot with a relatively broad beam diam-eter.963, 966 A similar scheme may also realize multiplex thermal-lens imaging witha CMOS camera, in which each spatially confined pixel is equivalent to a singlephotodetector with a pinhole.877, 964

With a low NA of the microscope objective, the probe beam is diffracted (atR ∼ λ) or spatially redistributed (at R � λ) by a nanotarget in broad angles that aregreater than the NA angle of the objective, and only part of the diffracted energyenters the objective. At PTI during pumping laser pulse, temperature distributioncoincides with the absorbing target’s geometry. Then, heat diffusion leads to anincrease in the thermal-spot size, RT (blurring effects), which becomes larger thanthe target size, R. The maximum PTI sensitivity is expected at RT = RD, whenmost diffracted energy enters the objective. Target size can be estimated with Eqs.(4.36)–(4.38) by measuring the temperature evolution outside the diffraction spotfor at least two different moments of time at the same spatial point or at differentspatial points at the same time. At RT � RD, loss of diffracted light energy may beoffset by the increased energy of the probe beam. Immersed objectives with highNA make it possible to collect diffracted (redistributed) energy at a nearly optimalangle aperture,877 and hence, to monitor the initially high temperature level aroundan object immediately after the pumping laser pulse.

The time shape of the PT signal represents a high initial peak owing to fastheating of the target, and a much lower exponential tail, corresponding to thecooling time of the heated target (Fig. 4.17). The temperature rises practicallyinstantaneously, and in the first moment, repeats the spatial distribution of absorbedenergy, depending on the spatial distribution of the pumping laser beam and thetarget’s coefficient of absorption.

Figure 4.17 Typical time shape of the PT-pulsed response (see Ref. 966).



For example, this full-field nonscanning PTI technique was successfully usedto realize PT flow cytometry (PTFC).961, 966, 968 In PTFC, moving single cells ofinterest are irradiated with a pumping laser pulse, typically from a tunable opticalparametric oscillator (OPO) (wavelength range, 410–2300 nm; pulse width, 8 ns;pulse energy, 0.1–1000 μJ; pulse rate, 10 Hz; pumped by an Nd-YAG laser). Laser-induced temperature-dependent variations in the refractive index of a cell are trans-lated into images by a second, collinear probe laser pulse, typically from a Ramanshifter (wavelength, 639 nm; pulse width, 13 ns; pulse energy, 10 nJ) and with aCCD camera having the following typical parameters: pixel size, 20 μm; area, 512× 512 pixels; maximum frame rate, 12 frames per second (fps), and digitization,14 bits at 1.3 MHz. The spatial intensity profiles of the pump- and probe-beamsshould be sufficiently smooth, which is controlled by the CCD camera. For cytom-etry applications, the limits of laser beam diameter adjustment range from 10 to50 μm. Because the broadness of the laser beams typically covers an entire sin-gle cell, formation of a PT image requires just one pump pulse. Usually, the pumppulse is triggered by signals from a photodiode when individual cells in flow arecrossing the CW helium–neon (He-Ne) laser beam, thus changing its intensity.881

PT images are calculated, with the use of customized software, as the differ-ence between the two probe pulses, the first immediately before the pump pulseand the second together with the pump pulse.963, 966 Obtaining an image that repre-sents a normalization of the differences in the energy of each laser pulse typicallyrequired 0.1 s. In particular, in the phase contrast mode, a customized phase-contrast micro-objective (20×) and a Zernike coaxial quarter-wave filter can beused to image the probe laser beam.966 Regarding the problem under solution, thediameters of the pump and probe-beam spots may be varied in the range of 20–40 μm and 15–25 μm, respectively. In the presence of gaps between neighboringcells in lymph and blood flows, which is typical for small lymphatics and bloodcapillaries, circular laser-beam geometry (Fig. 4.18, left and middle) can be used.At shorter distances between cells, a linear beam shape is preferable (Fig. 4.18,right). In contrast to transmission digital microscopy (TDM), the PT technique is

Figure 4.18 Typical positions of probe (red) and pump (green) laser beams during PTimaging: circular beams in a blood capillary of rat mesentery (cell velocity, 0.5–2 mm/s;magnification,100×) (a); overlapping pump and probe pulses in an artery of rat mesentery(cell velocity, 2–5 mm/s; magnification, 10×) (b); a linear (or ellipsoidal) beam geometry in ablood vessel of rat mesentery (magnification, 10×) (c) (see Refs. 880 and 969). (See colorplates.)


168 Chapter 4

able to identify low-absorbing cells (e.g., normal and apoptotic WBCs or cancercells) in blood and lymph flows in vivo on the basis of their differences betweenintegral and local absorption associated with specific absorbing chromophores andpigments.876–881, 963, 966, 970, 971

PT image resolution (δPT) in flow mode depends on the optical resolution of themicroscope objective, δOPT = 0.61λ/NA, where λ is the wavelength and NA is thenumerical aperture; thermal resolution, δT ≡ lT = (4aTτL)1/2 [(see Eq. (4.15)];877

motion distortion, δF = VFτL owing to cell displacement during the exposure or thetime between the two probe pulses;971 and the resolution of the recording system,particularly that of the CCD camera, δCCD = pix/M (where pix is the pixel size andM the optical magnification) in the plane of analysis:

δPT = {(δOPT)2 + (δT)2 + (δF)2 + (δCCD)2}1/2 ={(0.61λ/NA)2 + 4aTτL + (VFτL)2 + (δCCD)2}1/2, (4.40)

where aT is thermal diffusivity, τL is the laser pulse duration, and VF is the flowvelocity. For the typical parameters used in experiments: τL = 8 ns, λ ≈ 500 nm,aT = 1.44 × 10−3 cm2/s (water), NA = 0.4 (20× magnification), pix = 20 μm,M = 100, δOPT

∼= 760 nm, δCCD = 200 nm (i.e., δCCD < δOPT), δT∼= 69 nm, and

without the effect of flow (i.e., at VF = 0), the PT resolution is δPT∼= 763 nm (i.e.,

primarily depending on optical resolution). Even at the highest optical resolution,δOPT

∼= 250 nm (at NA = 1.25) and the effect of heat diffusion is still negligible,≤ 4% (δPT

∼= 259 nm) due to the very short laser pulses used.Maximum flow velocity, which does not distort PT resolution during laser

exposure, can be estimated from the component of the lowest resolution (i.e.,optical resolution, assuming δF ≤ δOPT and δT < δOPT):

(VF)max ≤ δOPT/τL. (4.41)

For the above parameters, (VF)max ≤ 95 m/s at a resolution of 763 nm and(VF)max ≤ 31 m/s at a resolution of 259 nm. Thus, the short exposure time mayallow high-speed, high-resolution imaging without reduced resolution at a highflow velocity. This is also valid for a one-probe imaging algorithm suitable for rel-atively strongly absorbing cells, such as RBCs or melanoma cells. However, theuse of the differential PT image algorithm with a significant time gap between thetwo probe pulses may decrease PT resolution in flow. To avoid this problem, a laserwith a high pulse repetition rate and a high-speed CCD camera operating at 100kHz and 104 fps, respectively, can be used.971

In the thermal-lens modification of PTFC, pump laser–induced refractive het-erogeneity around cells causes defocusing of a collinear intensity-stabilized CWlaser probe beam. The time-resolved integral PT response of a whole cell isrecorded via low-power beam defocusing, detected with a photodiode through asmall pinhole.966 This mode provides time-resolved (∼3 ns) monitoring of theintegral PT response, �T(t), from whole single cells, which can be approximatelydescribed as877, 966

�T(t) ≈ �Tmax[exp(−t/τT) − exp(−t/τRT)], (4.42)



where �Tmax is the maximum temperature elevation in the irradiated cell, τT isthe thermal relaxation time [for a spherical cell with radius R, τT is defined byEq. (4.36)] and τRT is the characteristic rise time.877 For small cells (e.g., small-animal RBCs) with radius R = 2.5 μm, τT is estimated to be 10 μs. The rise time(τRT) primarily depends on the longest time among the following: nonradiativerelaxation time (τNR), time to response of the photodetector (τPH), laser pulse width(τL), and temperature-averaging time within the whole cell (τTA) determined byheat diffusion from the initially heated local absorbing cellular structures.966 Forrelatively homogeneous cells (e.g., RBCs), τTA ≈ 0 as τNR ≈ 0.01 ns, τPH ≈ 3 ns,then τRT ≈ τL ≈ 8 ns; for heterogeneous cellular structures (e.g., WBCs), τTA ≈200−400 ns996 and hence, τRT ≈ τTA. Thus, in most cases, τRT < τT and the PTresponse demonstrates a high initial peak and a much slower exponential tail, cor-responding to the cooling time of the heated cell as a whole, with a time range ofτT ≈ 10−30 μs, depending on cell size (see Fig. 4.17). This result corresponds toa theoretical maximal rate of PT cell analysis, fcell ≈ 1/τT ≈ 104−105 cells/s. Toachieve this maximum, lasers with a high pulse-repetition rate are required. Thepresence of a long PT-response tail shape (e.g., for large cells, see Fig. 4.17) thatmay overlap the sequential PT response from other cells is not overly importantin PTFC because cells may flow away from the area of laser exposure after singleexposure. During in vivo measuring mode, cells may travel very quickly throughthe detected volume, thus, concurrent PTI and thermal-lens measurements, whichsupplement each other and provide additional information on cell types, are keypoints in PTFC. The combined mode involves splitting of the probe beams witheach portion of the beam directed separately to the CCD camera (PTI mode) orthe photodetector with a pinhole (PT thermal-lens mode) with the use of the beamsplitter and a spectral filter. The filter eliminates the interference of beams withdifferent wavelengths, particularly the influences of the CW He-Ne probe beam onthe CCD camera and of the pump laser pulse on the photodetector.

Figures 4.19(a) through 4.17(c), left, show typical PT-signal tracings fromcells as a function of the time interval required for the cell to flow through theirradiation area.880, 961 PT signals from RBCs in flow showing a purely positivecomponent [Fig. 4.19(a), left] indicate a linear PT response from the cells at alow laser-energy level. The amplitude difference indicates a difference in aver-age absorption and displays the natural heterogeneity of RBCs. Figure 4.19(b),left, demonstrates the possibility of detecting single, rare RBCs in lymph flow ata low laser-energy level that did not produce notable PT signals from the WBCsbecause of their low absorption. Laser-induced injury of a blood vessel close tothe lymph vessel leads to a fast-growing number of flowing RBCs in the lymphvessel [Fig. 4.19(c), left].880 The next PT signal traced in the same lymph vesselat higher laser energy shows damaged RBCs [Fig. 4.19(d), left]. The presence ofonly a negative PT signal indicates the development of strong, dominant nonlin-ear effects (e.g., microbubble formation around strongly absorbing cellular zones).The presence of both positive and negative components in PT signal amplitudetracing [Fig. 4.19(e), left] indicates noninvasive and invasive conditions for WBCsand RBCs, respectively, at the same energy level. The differences in the optical


170 Chapter 4

Figure 4.19 Typical tracings of PT signal from blood cells in blood and lymph flows ofrat mesentery in vivo (left panel) (see Refs. 880 and 961) and PT identification of K562cells labeled with 40-nm gold nanoparticles in artificial flow in vitro (see Ref. 970) (rightpanel). Left panel [λp = 525 nm, energy/amplitude/time scale/division: 0.3 μJ/50 mV/100ms/div (a), 0.5 μJ/20 mV/1 s/div (b), 0.6 μJ/100 mV/200 ms/div (c), 5 μJ/500 mV/4 s/div(d), and 145 μJ/100 mV/10 s/div (d)]: RBCs in blood capillary (Fig. 4.18 left) (a); rare RBCin lymph flow under normal conditions (b); growing number of RBCs in lymph flow duringlaser-induced hemorrhage (c); laser-induced damage of RBCs in lymph flow (d); WBCs andRBCs in lymph flow (e). Right panel: PT images (a) and (c); PT response amplitude tracings(arrows show responses of the particular cells) (time scale on horizontal axis, 200 ms/div);laser parameters: λp = 525 nm; pulse width, 8 ns; laser energy, 35 μJ (b).

properties of normal and cancerous cells, especially caused by differences in mito-chondrial distribution, which can be visualized with PTI, will allow one to usePTFC to distinguish these cells.

PT identification of cells with similar absorption properties and sizes, suchas subpopulations of WBCs, may pose a problem. The superior absorption sen-sitivity of the PT technique offers an opportunity to use gold nanoparticles asa new type of label absorbing in visible and NIR that is particularly importantfor PTFC.170, 878, 966, 970 These particles have unique properties for PT cell studybecause they are strong absorbers with adjustable spectral maximum, low toxicity,biocompatibility, and photostability, and can easily be conjugated with proteins andantibodies. PTFC mode may allow one to provide high-temporal/spatial resolutionPT monitoring of labeled cells in blood and lymph flows with the quantitation oftime-dependent numbers of circulating cells. In particular, the PT responses fromgold labeled cells typically show specific negative peaks associated with nano- andmicrobubble formation around overheated nanoparticles [Figs. 4.19(b) and 4.19(c),right]. Simultaneous monitoring of PT images from the same cells confirmed thisfinding: PT images of cells tagged with gold PT labels [Figs. 4.19(a), right andleft images; and 4.19(c), center image] revealed specific, highly localized imagecontrast, compared with cell PT images without labeling, showing the relativelysmooth contrast of endogenous absorbing structures [Figs. 4.19(a), center and right



images; and 4.19(c), left and right images]. This in vitro experiment demonstratesthe possibility of detecting cells with a rate of up to 10 cells/s, which is approxi-mately two orders of magnitude better than for conventional PT techniques.966 Inaddition to these two applications there are many others for characterizing and dif-ferentiating normal from abnormal blood cells as well as detecting cancer cells andpathogens in blood and lymph flows.899, 900

No notable change in the classic (heating–cooling phenomena) PT responseamplitude and shape at flow velocities up to 0.05 m/s was found.961, 970 With a fur-ther increase in the flow velocity to 0.1 m/s, a small fluctuation in the PT responsetail appeared, with more profound distortion developing at a flow rate of 2 m/s.However, no significant change in the maximal amplitude of PT response wasobserved, even at the high flow velocity of 10–20 m/s. PT images of RBCs ofinterest at high flow velocities (up to 2–10 m/s) without notable motion distortionwere also obtained.970

The general scheme of integrated multispectral in vivo PTFC, combin-ing the PT method, TDM, and fluorescence microscopy, is presented inFig. 4.20.880, 899, 900, 963, 969 Cell detection occurs in superficial microvessels in the

Figure 4.20 Optical scheme of the integrated multispectral flow cytometer for in vivo stud-ies, which combine photothermal, optical transmission, and fluorescence techniques; as ananimal model for in vivo cytometry, rat mesentery with blood and lymph vessels is shown[also see two insertions with lymph vessel transmittance image (a) and mesentery structure(b)]; lymph valve that works as a natural “nozzle” of a cytometer hydrodynamic cell is clearlyshown (a) (see Refs. 961 and 969). OPO is the optical parametric oscillator.


172 Chapter 4

skin, or in thin, relatively transparent living organs (e.g., animal ear or mesentery).To illuminate selected vessels, different optical sources can be used, ranging froma conventional lamp with filters to lasers in pulsed or CW modes. Light beams arefocused on a small area of the microvessels (the site for analysis). To detect allcells in the cross section of a vessel, the laser beam diameter must cover the wholevessel. To minimize simultaneous irradiation of several cells along the vessel axis,the beam may have a linear or elongated ellipsoidal shape-oriented perpendicularto the vessel axis (see Fig. 4.18, right).

Optical absorption by nonfluorescent cellular structures is measured withPT and PA methods. Specifically, a PT thermal-lens module is incorporated tomeasure integrated time-resolved PT responses from moving cells; a PTI mod-ule provides imaging of moving unlabeled cells or cells labeled with PT labels(e.g., gold nanoparticles).961, 969 A PT deflection module with a position-sensitivephotodetector can be added to measure flow velocity by using the principle oftime-of-flight PT velocimetry.971 Also, a PA transducer or transducer array allowsfor measurement of PA signals from single cells, either unlabeled or labeled bynanoparticles or strongly absorbing dyes, as well as measurement of PA signalsfrom cells accumulated at specific sites (vessel wall, surrounding tissue, or specificorgan) with a relatively broad laser beam using PA tomography schematics (seeSection 4.5).832, 839, 843, 848, 850, 854–857, 890, 891, 893–898, 904–915, 918–952, 955

The photothermal microscopy (PTM) technique has demonstrated its capa-bility to image absorbing cellular structures of living cells in vitro withoutlabeling,876–879 as well as moving cells in vivo in real time, in studies of circulatingRBCs and WBCs in blood capillaries and lymphatic microvessels of rat mesen-tery.880, 881 Imaging of single cells in vessels in vivo is potentially important forearly disease diagnostics (e.g., cancer and diabetes) or for studies of the impactsof various factors (e.g., drugs, smoking, or ionizing radiations) on living cellsin situ.

The PTFC setup described in Ref. 881 is based on a nonscanning PTM sys-tem, which requires high rates of data acquisition and analysis even for a relativelyslow capillary blood flow, because of the short time needed for a cell to cross thedetection area, 0.1–0.01 s. Such a system was built on the basis of a pulsed pump-ing tunable OPO (wavelength range, 420–570 nm; pulse width, 8 ns; pulse energy,0.1–400 μJ; Lotis Ltd.). Laser-induced temperature-dependent variations of therefractive index in the cell were detected by using a phase-contrast imaging tech-nique (Olympus BX51 microscope with a CCD camera; AE-260E, Apogee Inc.) atillumination from a low-intensity pulsed probe light beam from the Raman shifter(wavelength, 639 nm; pulse width, 13 ns; and pulse energy, 2 nJ). The diameters ofthe pump- and probe-beam spots, with stable and smooth intensity profiles, rangedfrom 20 to 50 μm and 15 to 50 μm, respectively, and thus covered entire singlecells and even whole microvessels. A spatial resolution of ∼0.7μm was provided.The entire PT image acquisition procedure includes illumination of the cell withthree pulses: an initial probe pulse, followed by the pump pulse, then a secondprobe pulse with a tunable time delay of 0–5000 ns to the pump pulse. The PTimage, calculated as the difference between the two probe-pulse images, depends



only on absorption contrast transformed by the pump laser pulse into refractivecontrast, but not on the possible phase distortion of the probe beam itself or naturalrefractive cellular heterogeneities.881

To experimentally proof the concept of in vivo PTFC, a rat mesentery modelwas chosen among various animal models (e.g., ears and lips) because of its uniqueanatomic structure consisting of thin, transparent, duplex connective tissue with asingle layer of blood and lymph microvessels. Using TDM, RBCs and lympho-cytes traveling through blood and/or lymph vessels, lymphatic valves and othermesenteric structures were imaged (Fig. 4.21).880, 881, 969 It was found that in mostintact lymph vessels (diameter of 50–150 μm), lymphocytes in flow had an averagevelocity of ∼211± 11 μm/s. In comparison, the velocity of RBCs was significantlyhigher, up to 2 mm/s in blood vessels with a diameter of 20–30 μm and from 100 to500 μm/s for capillaries with a diameter less than 10 μm. The high spatial resolu-tion of TDM (300 nm at 100×, NA 1.25 with immersion) allowed rough estimationof cell size and even shape (Fig. 4.22, left).

However, because of its low sensitivity to absorption owing to small light path-ways in a cell, TDM is not applicable to the imaging of cell intrinsic absorbingstructures. In contrast, the PTFC mode (navigated by TDM) allowed for obtain-ing images of moving lymphocytes and RBCs (Fig. 4.22, right) that showedstructures specific to PT images and associated with the spatial distribution ofabsorbing cellular chromophores (e.g., hemoglobin in RBCs, or cytochromes in

Figure 4.21 Typical optical image of a lymph microvessel of rat mesentery with bloodmicrovessels along the lymphatic walls (bottom), RBCs in a capillary (top left), and singlecells in lymph flow (top right) (see Ref. 881).


174 Chapter 4

Figure 4.22 Optical transmission (left column) and PT (right column) images in vivo of asingle, moving lymphocyte (top row) and RBC (bottom row) in lymph flow in rat mesentery(vessel diameter 105 μm, velocity ∼120μm/s). Pump pulse parameters: wavelength, 525nm; pulse width, 8 ns; and pulse energy, 30 and 0.5 μJ (right column, top and bottom,respectively); time delay between pump and probe pulses, 10 ns (see Ref. 881).

lymphocytes). The PTFC rate of cell analysis is limited by the pulse repetition rateof the pumping laser and typically equal to ∼10 cell/s at a pulse repetition rate of10 Hz.

Potential applications of in vivo PTFC may include: (1) identification of cellswith differences in natural absorptive properties (e.g., the counting of white cellsin blood flow or of rare RBCs among lymphocytes in microlymphatic vessels); (2)monitoring of the circulation and distribution of absorbing nanoparticles used forPT probing or photosensitizing; (3) study of laser–cell interactions; and (4) studyof the influence of different environmental factors on cells.

4.8 Acousto-Optical Interactions

Acousto-optical tomography (AOT), or ultrasound-modulated optical tomography,is based on the acoustic [ultrasound (US)] modulation of coherent laser light trav-eling in tissue.196, 204, 890, 974–981 An acoustic wave (AW) is focused into tissue andlaser light irradiates the same volume within the tissue; for instance, as shownin Fig. 4.23. Any light that is encoded by US, including both singly and multi-ply scattered photons, contributes to the imaging signal. Axial resolution along theacoustic axis can be achieved with US frequency sweeping and subsequent applica-tion of the Fourier transformation,890, 976 whereas lateral resolution can be obtainedby focusing the AW. Three possible mechanisms have been identified for theacoustic modulation of light in scattering tissues890, 975, 979 (see Fig. 4.24). The firstmechanism is based on US-induced variations of the optical properties of a tissuecaused by spatially and temporally dependent tissue compression or rareficationupon propagation of the AW. These variations in tissue density cause correspond-ing oscillations of tissue optical properties, including absorption and scattering



Figure 4.23 Illustration of the principle of acoustic-modulated optical tomography (see Ref.975).

Figure 4.24 List of possible mechanisms of acoustic modulation of light in tissues (see Ref.975).

coefficients, and refractive index. Accordingly, the detected intensity of light varieswith the AW. However, US modulation of incoherent light has been too weak to beobserved experimentally.

The second mechanism is based on variations in the optical properties inresponse to US-induced displacement of scatterers. The displacements of scat-terers, assumed to follow AW amplitudes, modulate the physical path lengthsof light traveling through the acoustic field. Multiply scattered light accumulatesmodulated physical path lengths along its path. Consequently, the intensity of thespeckles formed by the multiply scattered light fluctuates with the AW. The mod-ulated component of the speckle pattern carries spatial information determined bythe US and can be utilized for tomographic imaging.

The third mechanism is caused by photon–phonon interactions, where light isconsidered as an ensemble of photons and AW as an ensemble of phonons. The


176 Chapter 4

photon–phonon interactions cause a Doppler shift, in the classical sense, to thefrequency of the photons by the acoustic frequency and its harmonics. An opticaldetector functions as a heterodyning device between the Doppler-shifted light andunshifted light and produces an intensity signal at the acoustic frequency and itsharmonics.

Both the second and third mechanisms require the use of coherent light, andboth may be associated with the speckle effect. The modulation of speckles inthe second mechanism is caused by the acoustic modulation of scatterer displace-ments, whereas the modulation of speckles in the third mechanism is caused bythe acoustic modulation of the refractive index of the tissue. The acoustic modu-lation of the refractive index also appears in both the first and third mechanisms.However, in the first mechanism, the variation of refractive index causes light thatmay or may not be coherent to fluctuate in intensity, whereas in the second, thevariation of refractive index causes fluctuation in phase of coherent light, which isconverted to fluctuation in intensity by a square-law detector. Thus, as a resultof acoustic modulation of the refractive index, the optical phase between twoconsecutive scattering events is modulated, multiply scattered light accumulatesmodulated phases along its path, and the modulated phase causes the intensity ofthe speckles formed by the multiply scattered light to vary with the AW.

The intensity modulation depth, M, is defined as the ratio between the intensityat the fundamental frequency, I1, and the unmodulated intensity, I0:

M = I1/I0. (4.43)

The spectral intensity, I1, at the fundamental acoustic frequency, ωa, is calculatedfrom890

In = (1/Tac)∫ Tac

0cos(nωacτ)G1(τ)dτ (4.44)

at n = 1; here, Tac is the acoustic period. In Eq. (4.44), the autocorrelation functionof the scalar electric field, E(t), of the scattered light calculated in the approx-imation of weak scattering (the optical MFP is much longer than the opticalwavelength) and weak modulation (the acoustic amplitude is much less than theoptical wavelength) has the view890

G1(τ) = 1 − (1/6)(L/ltr)ε[1 − cos(ωacτ)], (4.45)

where

ε = 6(δn + δd)(n0k0A)2,

δn = (αn1 + αn2)η2,

αn1 = (1/2)kacltr · arctg(kacltr),

αn2 = αn1/{(kacltr)/[arctg(kacltr)] − 1},δd = 1/6,

L is the tissue slab thickness, n0 is the background refractive index, k0 is the opticalwave vector in vacuum, A is the acoustic amplitude, kac is the acoustic wave vector,



and ltr is the photon TMFP. Parameter η is related to the adiabatic piezo-opticalcoefficient of the tissue, ∂n/∂p, the density, ρ, and the acoustic velocity, υac : η =(∂n/∂p)ρ(υac)2. The parameters δn and δd are related to the average contributionsper photon free path (or per scattering event) due to the ultrasonic modulation oflight intensity through index of refraction (δn) and displacement (δd), respectively.

The contribution from δn increases with kacltr because a longer photon free pathrelative to the acoustic wavelength accumulates a greater phase modulation. Bycontrast, the contribution from δd stays constant at 1/6, independent of kac and ltr.The contribution from the index of refraction above a critical point at kacltr = 0.559,where contributions from refractive index and displacement are equal, increaseswith kacltr and significantly outmatches the contribution from displacement. Thepossible correlation between the two modulation mechanisms is neglected here forsimplicity.

Accounting for Eq. (4.45), the modulation depth of intensity fluctuations canbe presented as

M = (1/12)(L/ltr)2ε ∝ A2, (4.46)

This equation shows a quadratic relationship between intensity modulation depth,M, and acoustic amplitude, A. Only the nonlinear terms of phase accumulationcontribute to the acoustic modulation of coherent light at multiple scattering. Thelinear term vanishes as a result of optical random walk in scattering media. Inthe ballistic (nonscattering) regime, M is proportional to A owing to nonaveragedcontributions from the linear term of phase accumulation. In the quasi-ballistic(minimal scattering) regime, M may show mixed behavior with A.

The quadratic relationship described by Eq. (4.46) can be experimentallyobserved if a spectrometer, such as a Fabry-Perot interferometer, is used as a detec-tor. In many cases, the measured modulation depth, M′, is defined as the ratiobetween the observed ac and dc signals, where the ac signal originates from thebeats between the electric field at the fundamental frequency of the modulatedlight (ω0 ±ωac) and that at the intrinsic unmodulated optical frequency (ω0). Asa result, the measured modulation depth will be approximately described by

M′ ∝ (I1/I0)1/2 = M1/2 ∝ A, (4.47)

indicating that measured modulation depth is proportional to the acoustic ampli-tude.

A frequency-swept (chirped) AW is used to encode a laser beam that crossesthe acoustic axis of the US transducer with various frequencies.890 Decoding ofthe transmitted light in the frequency domain allows one to image objects buriedinside the scattering media. This image will be resolved along the acoustic axis.This encoding scheme is analogous to that of MRI.

A parallel AOT uses a CCD camera for pixel by pixel detection of a US-modulated signal.890 A schematic of the experimental arrangement is shown inFig. 4.25(a). The z-axis is on the acoustic axis pointing from the US transducerto the sample, the y-axis is along the optical axis pointing to the diode laser, and


178 Chapter 4

Figure 4.25 Parallel AOT (see Ref. 890). Schematic of the experimental setup (a): DL,diode laser; C, CCD camera; U, ultrasonic transducer; FG-1, FG-2, and FG-3, functiongenerators; DG, delay generator; PA, power amplifier; T, tissue sample. Experimental 2Dimage of 1.2-cm-thick chicken breast tissue containing a buried object (b); the horizontal andvertical axes are along the x- and z-axes, respectively. Demonstration of the virtual source ofultrasound-modulated light (c); left frame, the entire virtual source; following frames, virtualsources corresponding to various values of z obtained by adjusting the frequency fh.

the x-axis is perpendicular to both the acoustic and optical axes. The AOT system,described in Ref. 890, had the following parameters: a focused US transducer witha 2.54-cm focal length in water; a 1-MHz central response frequency; and peakfocal pressure of ∼2 × 105 Pa (or less, below the damage threshold for tissue);a diode laser with 690-nm wavelength; average power of 12 mW; and coherencelength of ∼7 cm. The laser beam was expanded to 1.6 × 0.3 cm and projected ontothe tissue sample. A high-speed 12-bit digital CCD camera was used. The tissuesample was partially immersed in water to provide acceptable acoustic coupling.The light transmitted through the sample produced a speckle pattern, which wasdetected by the CCD camera. Three function generators, FG-1, FG-2, and FG-3,shared the same time base to ensure synchronization. FG-1 and FG-2 generatedchirp functions to modulate the laser and to excite the US transducer, respectively.A delay generator (DG) controlled the time delay between the trigger signals toFG-1 and FG-2.



If no amplitude modulation is provided by FG-3, the frequency of theheterodyne signal received from location z along the US axis is defined by

fh(z, τ) = b

(τ− z

υac

), (4.48)

where b is the rate of frequency sweep and τ is the time delay between the twochirps from FG-2 and FG-1. By producing a reference sinusoidal wave with afrequency equal to fh(z, τ), which modulates the amplitude of the chirp, FG-3implements the source-synchronized lock-in measurement. The signal in a singleCCD pixel can be represented as

Ii(φi) ∝ Ib + Im cos(φs + φr), (4.49)

where Ib is the background intensity, Im is the signal intensity related to theultrasound-modulated component, φi is the randomly distributed initial phase ofthe speckle that does not provide useful information in this imaging system, andφr is the initial phase of the reference sinusoidal wave from FG-3. The modulationdepth, M′ = Im/Ib, which reflects the local optical and acoustic properties, can becalculated from four consequent frames of CCD taken at φr equal to 0, 90, 180,and 270 deg, using the following expression:890

M′ = 1

2Ib

√[Ii(90◦) − Ii(270◦)]2 + [Ii(0◦) − Ii(180◦)]2. (4.50)

To recover M′, calculations should be performed for each pixel and a total of N×N-pixel data points should be averaged to produce a single data point for the image.

For fixed reference (lock-in) frequency, fr, from FG-3, the US-modulated lightfrom a specific spatial location, z0, corresponding to heterodyne fr and the timedelay, τ, can be detected, where z0 is derived from Eq. (4.48) as

z0 = υac

(τ− fr

b

). (4.51)

The US-modulated light from the other locations will have different frequencies,and hence, will be rejected by the CCD camera. One-dimensional images alongthe US axis are obtained by electronically scanning the time delay, τ, as well as2D tomographic images by additionally mechanically scanning the US transduceralong the x-axis.

Figure 4.25(b) illustrates a 2D image of the object buried inside a chickenbreast tissue sample. The buried object, which has little acoustic absorption, isclearly visible in the background. The image resolution along the x-axis is ∼2 mm,which is determined by the 2-mm focal diameter of the US transducer. The spatialresolution along the US axis (z-axis) �z is determined by the frequency span, �f ,of the chirp function and the US velocity, υac, as follows:

�z ≈ υac/�f , (4.52)

where υac ≈ 1500 m/s; for �f = 800 kHz, �z is ∼2 mm.


180 Chapter 4

The special measurements with the laser beam illuminating the sampleobliquely at 10 deg to the z-axis has shown that images were the same as thosemeasured in the case of normal incidence.890 Hence, AOT depends primarily onscattered photons, and ballistic photons are not the major contributors to the signal.

Figure 4.25(c) shows a series of images of the virtual light sources definedby US. As it follows from Eq. (4.48), the frequency of the heterodyned sig-nal is related to the source location, z; thus, these images correspond to variousvalues of z obtained by adjusting the frequency, fh. When the virtual source prop-agates through a scattering medium, a direct view of the virtual source is blurred.However, if the virtual source is detected immediately without further propagation,a clear view of the virtual source can be acquired. This demonstration clearly illus-trates the importance of US tagging of light that enhances the spatial resolution ofimaging.

4.9 Thermal Effects

Thermal imaging is based on sensing the IR radiation that is emitted by allobjects at any temperature above absolute zero temperature.982 This emission isattributable to molecular transitions from a high-energy to a low-energy state;for condensed media, its energy distribution between different wavelengths isdescribed by the Planck curve. At the normal temperature of the human body, thepeak of the Planck curve occurs in mid-IR between wavelengths of 9 and 10 μm.

The Planck function is exponentially nonlinear in temperature; it followsfrom this function that lower-temperature objects emit orders of magnitude lessenergy than higher-temperature objects. The human body belongs to these low-temperature objects; therefore, accurate detection of IR radiation from the body isnot simple. Moreover, a human body and its surroundings usually emit compara-ble amounts of IR energy, which leads to additional difficulties in measurement.Often, the SNR is low and correction instrumentation, lock-in signal process-ing techniques, and careful analysis of the resulting data are required to detecta signal specialized background.982 The technologies of IR array detectors, asso-ciated electronics, image processing, and noise reduction have been significantlyimproved over the last 10 years. IR cameras suitable for medical thermal imagingare reviewed in Ref. 982. At present, the accuracy with which temperature andtemperature changes can be measured has reached 10−3 K.

The steady-state form of the bioheat equation originated from the energybalance and describes the change in tissue temperature, T(r), at point r in thetissue:2, 3, 42, 982–987

∇[kT∇T(r)] + S(r) + ρbcbqb[Ta − T(r)] = 0, (4.53)

where kT is the thermal conductivity of the tissue (W/K); S is the heat source term(W/m3), defined by the metabolic heat generation rate at point r; ρb is the blooddensity (kg/m3); cb is the blood specific heat (J/kgK); qb is the blood perfusionrate (1/s), defined as the volume of blood flowing through a unit volume of tis-sue in one second; Ta is the arterial blood temperature (K); and T(r) is the localtemperature of the tissue, all at points r in the tissue. The first term describes



any heat conduction (typically away from point r), the source term accounts forheat generation attributable to metabolic processes, and the last term describes theheat transfer caused by blood perfusion. The temperature of the arterial blood isapproximated to be the core temperature of the body.

In many practical cases, it may often be assumed that only the heat transferprocess normal to the surface needs to be taken into account as a one-dimensionalproblem:987

1

rn

∂

∂r

(kTrn ∂T

∂r

)+ S + ρbcbqb(Ta − T) = 0, (4.54)

where n = 0, 1, and 2 are for slab, cylinder, and sphere, respectively.To solve this equation, the boundary conditions must be considered. The

boundary conditions depend on tissue and environmental states. The tissueexchanges energy (and mass) with the environment through a combination ofconvection, radiation, evaporation, and conduction. The driving forces for theseexchanges are the differences in temperature and water vapor partial pressurebetween the tissue and its surroundings. The boundary conditions for heat transferat the tissue surface can be considered in the general form:987

−kT∂T

∂r

∣∣∣∣s = h(Ts − Te), (4.55)

where h is the apparent energy transfer coefficient, which may be dependent ontemperature, pressure, relative humidity, and tissue insulation; Ts and Te are thetemperature of the tissue surface and environment, respectively. Assuming a con-stant temperature at a depth R0 that equals the core body temperature (or arterialblood temperature, Ta), the deep boundary condition is expressed as

T∣∣R0 = Ta. (4.56)

The bioheat equation of the general form [see Eqs. (4.53) and (4.54)] can be appliedto each tissue and surrounding material layer to establish a partial differential equa-tion group, coupled by conditions that ensure the continuity of temperature and heatfluxes at any interface between adjacent layers. Methods of solving of the bioheatequation can be found in Refs. 2, 3, 42, 323–325, and 982–987.

The metabolic heat generation rate may be significantly different for normaland tumorous tissues. For example, S(r) was estimated at 450 and 29,000 W/m3

for normal breast tissue and a tumor, respectively, and the corresponding bloodperfusion rate, qb, as 0.00018 s−1 and 0.00900 s−1 for normal tissue and patholog-ical tissues, respectively.982 Theoretical modeling, conducted using these data andEq. (4.53) for a normal breast and breast with a tumor as a spherical inclusion ofradius 1.1 cm with its center located at 2.1 cm beneath the skin surface, showeda temperature rise of the skin surface caused by the tumor of approximately 2◦C,from ∼32◦C for the normal breast to ∼34◦C for the breast with the tumor. Thisis a most significant result, because the tumor introduces a local temperature riseon the breast surface that is accurately detectable by modern IR cameras. Further,inverse bioheat transfer calculations may provide a method of locating the tumorusing the surface thermograms.982


182 Chapter 4

For different normal tissues, blood perfusion rate, qb, is evaluated as the highestfor choroids/kidney, 0.05–0.10 s−1; at midlevel for brain cortex, 0.007–0.02 s−1,skin, 0.002–0.007 s−1, and muscle, 0.0003–0.002 s−1, and lowest for fat, 0.0001–0.0003 s−1.983

A simplified 3D bioheat equation describing the effect of blood flow on blood–tissue heat transfer was proposed in Ref. 986. This equation contains a remarkablysimple expression for the tensor conductivity of tissue as a function of the localvascular geometry and flow velocity in the thermally significant countercurrentvessels, which was derived by using the concept of anisotropic heat transfer. Theconcept is based on the statement that the primary mechanism for blood–tissueenergy exchange is an incomplete countercurrent exchange in thermally significantmicrovessels.

Many applications of IR thermal imaging have been reported, some of whichare reviewed in Ref. 982. The basic measurements involve tissue temperature distri-butions resulting from a variety of internal and external conditions affecting bloodmicrocirculation and metabolic processes. Thermal imaging was used for detectingbreast cancer, monitoring an inflammatory state of human gingiva, identifying thehealth status of the thyroid gland, indicating ectodermal dysplasia, measuring thedepth of burns, managing pain, monitoring surgical tendon repair, measuring brainactivity, imaging atherosclerotic plaque, and detecting anxiety, among other uses.The temperature increase of thermally insulated skin measured by IR radiometryprovides useful information about its blood flow and blood temperature.987, 988

The primary disadvantages of thermal imaging for monitoring of any diseasestate, including breast cancer, is its nonspecific nature connected with tissue bloodperfusion response and tissue metabolic activity, and its ability to make only sur-face temperature measurements. Therefore, this technique must be used as anadjunct to other diagnostic techniques and in conjunction with newly designedinstrumentation, analytical, and numerical computational tools.982

4.10 Sonoluminescence

A sonoluminescence (SL) signal generated internally in the media with a 1-MHzcontinuous-wave US can be used to produce 2D images of objects imbedded inturbid media.989, 990 This technique is based on the light emission phenomenonconnected with driving small bubbles by US collapse. The bubbles start out with aradius of several microns and expand to ∼50 μm, owing to a decrease in acousticpressure in the negative half of a sinusoidal period; after the AW reaches the posi-tive half of the period, the resulting pressure difference leads to a rapid collapse ofthe bubbles, accompanied by a broadband emission of SL light. This emission hasa short duration (in tens of picoseconds), repeatable with each cycle of sound, andhas a spectrum containing molecular emission bands (with peaks near 300–500 nm)associated with the liquid, mostly water, in which the SL occurs.

SL tomography (SLT) is described in Refs. 989 and 990 as a new approach foroptical imaging of dense turbid media (biological tissues). The major advantagesof SLT include: (1) high signal-to-noise ratio due to the internally generated probe



optical signal; (2) high contrast of imaging; (3) satisfactory spatial resolution,which is limited by the US focal size; and (4) low cost of equipment. It has beenshown experimentally that there is a threshold of SL generation at applied USpressure, when the peak US pressure at the US focus was ∼2 bars (∼100 V, seeFig. 4.26). The rapid increase of SL intensity with acoustic pressure above thethreshold indicates that the SL signal may be a sensitive measure of local acous-tic pressure. Additionally, Fig. 4.26 shows that generation of SL is not affected bythe addition of Intralipid or trypan blue, but is significantly affected by the addi-tion of polystyrene spheres. Because SL is a broadband emission, the scatteringand absorption spectra of tissues and immersion liquids should be considered inimaging algorithms.990 On the basis of the calculated diffuse transmittance of thepolystyrene phantom near 400 nm, the SL power at the source was estimated tobe greater than 1 pW. The turbid media (tissue) functions as a filter that modifiesthe spectrum of the SL signal. For a cubic object made from rubber buried in theIntralipid phantom, the spatial resolution of the edges was estimated to be 2–3 mm,and an excellent imaging contrast was observed.990

SLT is based on several contrast mechanisms:990 (1) for objects with UScontrast relative to the background, the SL signal originating from the object willdiffer from that originating from the background medium, and SL generation isaffected by the local US intensity (see Fig. 4.26); (2) for objects with contrast inoptical properties, the SL signal from the object is attenuated differently becausethe SL light must propagate through the object; (3) for objects with the ability togenerate SL, the SL from the object is different, even if the local US pressure isthe same.

The peak pressure at the US focus is typically less than ∼2 bars (1.3 W/cm2 inspatial peak–temporal peak power), which is one order in magnitude lower thanthe safety limit set by the U.S. FDA (23 bars) and two orders lower than thethreshold for tissue damage (400 and 900 W/cm2 at 1 MHz for brain and muscle,respectively).990

Figure 4.26 SL intensity versus the driving voltage on the US transducer (see Ref. 990).


184 Chapter 4

4.11 Prospective Applications and Measuring Techniques

4.11.1 Vascular imaging

It was shown some time ago that OA/PA imaging allows one to achieve high-resolution 3D images of artificial blood vessels in a tissue phantom with ∼20-μmdepth resolution and ∼200-μm resolution in a lateral direction.850 The designedmeasuring technique and reconstruction algorithm were applied to image a vascu-lar tree from a Wistar rat in vitro853 and human wrist skin blood vessels in vivo.854

In Ref. 854, a double-ring OA sensor, together with measurements of a cross-correlation between the signals detected by the two rings, were used to providea narrow angular aperture of the system. The depth position of the observed ves-sels of the human wrist was approximately 1.5 to 2 mm beneath the skin surface.It was also demonstrated that in addition to skin and superficial blood vessels, theunderlying bone was identified at a depth of approximately 3 mm beneath the skinsurface. The total data acquisition time for acquiring a 2D image with 101 mea-surement positions (A-scans) was approximately 5 min for a laser with a pulserepetition rate of 10 Hz. The maximum depth at which vessels can be detected isdependent on parameters such as the illuminating light intensity, the wavelength inuse, and the sensitivity of the OA sensor.

Application of a PA setup with a US Fabry-Perot sensor based on polymer filmfor in vivo imaging of the subsurface vascular network is described in Refs. 920 and921. Studies for human skin and mouse cancer models showed that this system canproduce 3D images of vascular structures with high spatial resolution at a depthof 5 mm. This technique can be used for the clinical assessment of changes inthe vascular system associated with the development of skin tumors or superficialtissue lesions (burns, wounds, or ulcers), and for monitoring the healing process inresponse to therapy. Another interferometry OA/PA system capable of angstrom-level measurements of displacement with a nanosecond temporal resolution wasapplied to detect OA/PA signals from subsurface blood vessels within a humanforearm in vivo.486, 487

Further development of OA/PA vascular imaging includes bright-field OR-PAM (see Figs. 4.8 and 4.9)897 and multiwavelength OA/PA angiography usingdyes (see Fig. 4.10).924, 955

4.11.2 Glucose monitoring

In monitoring and determining chemical traces, the time-resolved OA/PA tech-nique and other optothermal techniques may prospectively be used in noninva-sive monitoring of glucose.887, 991–1003 In the low-scattering mode when aqueousglucose solutions were irradiated by NIR laser pulses at wavelengths that corre-sponded to NIR absorption of glucose (1.0–1.8 μm), OA signal generation wasassumed to be attributable to initial light absorption by the glucose molecules.993

A linear relationship between the OA signal and glucose concentration was found.It was also shown that the OA signal tracks changes in glucose concentrations



in human measurements. No specific advantages of OA spectroscopy over NIRmeasurement of glucose are expected in this case.991

Another approach for OA glucose detection is based on glucose’s ability tochange the scattering properties of tissue.238, 467–469, 887, 991, 1006–1008 As it followsfrom Eq. (4.22), the OA signal from the tissue depth is defined by optical atten-uation coefficient, μeff, which is related to changes in the refractive index of themedium induced by changes in glucose concentration. Decreasing the scatteringincreases the energy density in the OA sound source and induces higher OA in-depth signals.998 OA temporal profiles induced by 355-nm laser pulses in in vivorabbit sclera upon intravenous glucose administration demonstrated that a 1-mMincrease in glucose concentration resulted in up to a 5% decrease in μeff.994 The UVlight used in this experiment allowed one to increase the absolute value of the OAsignal and its sensitivity to scattering changes owing to the much higher absorptionand scattering of tissues in UV than in visible and NIR [see Eq. (4.22)].

However, in the NIR range, the effect of glucose on the scattering propertiesof tissue phantoms is also detectable by using the OA technique.997, 998 At 905 nm,a 1% (1 g·dl−1) change in glucose concentration increased the OA signal by 2.0%in distilled water, 5.4% in 3% milk, and 2.5% in bloodless tissue; at 1064 nm, asimilar change in glucose concentration increased the OA signal by 2.7% in 1%Intralipid. It was also found that the glucose-induced change in the OA signal waslarger in blood than in Intralipid, amounting to 6.0%/0.5 g·dl−1 of added glucoseat 532 nm and 11.4%/0.5g·dl−1 of added glucose at 1064 nm.997 Glucose-inducedchanges in the 1% Intralipid can be explained by the matching of refractive indicesof phospholipid micelles and water with added glucose, whereas the observedchanges in blood may additionally be influenced by changes in the size and shapeof RBCs owing to changes of blood plasma osmolarity.48, 995, 997, 1009, 1010

In addition to the increase in the peak-to-peak value of the OA signal as a func-tion of glucose concentration, a corresponding shift was found in the position ofthe OA signal maximum toward earlier times at higher glucose concentrations, pro-duced by changes in the sound velocity of the sample at glucose addition.997, 1000

The other two parameters in Eq. (4.22), the thermal expansion coefficient, β, andthe specific heat, cT, of tissue or blood, may also be changed with a change inglucose concentration. Estimations conducted in Ref. 998 showed that variationsin these two parameters are not overly high and do not seriously influence the OAsignal in the limits of physiological glucose concentrations. Regarding the depen-dence of sound velocity on glucose concentration, it may be excluded from themeasurements of the OA temporal profile, but on the other hand, it may provideadditional information about glucose concentration.

One of the drawbacks of the OA technique is that the measurement of soundpropagation in tissue is dependent on mechanical coupling between the tissue andthe measuring probe and on the pressure of the probe on the tissue surface. Thiseffect is quite similar to US propagation in tissue, in which coupling gels are usedto decrease sound reflections.

Further work is needed to understand origination and propagation of theOA/PA signal in tissue and its use for glucose sensing. At present, the OA/PA


186 Chapter 4

technique based on scattering measurements does not offer any noticeableadvantage over other scattering methods.991 However, a few groups and compa-nies are developing new and different approaches to OA/PA glucose sensing,999

including techniques based on combining US and OA/PA spectroscopy.991

Thermal gradient spectroscopy (TGS) is based on measuring the fundamentalabsorption bands of glucose at 9.1–10.5 μm by using the body’s naturally emit-ted IR radiation as an internal source of radiation.991, 1001–1003 The cooling-inducedskin transparency allows for the monitoring of IR emissions from the interstitialfluid and cutaneous layers.1001, 1002 A linear response between in vivo TGS detectedglucose and reference blood glucose values has been reported in clinical studiesfor several individuals with Type 1 diabetes.1001 Different modifications to thismethod and corresponding instrumentation for more precise quantifying of glucosein a human body are described in the literature.991, 1002, 1003 The simplicity of thismethod makes it quite appealing; however, the overlap between the effect of glu-cose on the signal and variations attributable to circadian periodicity, as well astemperature and blood flow responses to glucose change, should be eliminated orconsidered.991

4.11.3 Quantification of total hemoglobin and blood oxygenation

OA/PA is a promising method for the determination of total hemoglobin inthe blood and the degree of blood oxygenation.889, 897, 901, 939, 1004, 1005, 1011–1018 Thein vivo quantification of blood and tissue oxygenation is critical for monitoring thedevelopment and effectiveness of treatment of many diseases, including cancer.Equations (4.31) and (4.32) present the basic relations of the method. An exam-ple of in vivo imaging of the microvascular network and the distribution of bloodoxygen saturation, sO2, in the ear of an athymic hairless mouse is shown in Fig. 4.9.

An OA laser system was also designed for noninvasive monitoring of cere-bral venous oxygenation in the superior sagittal sinus based on a Q-switchednanosecond Nd-YAG laser (wavelength 1064 nm, pulse repetition rate 1 Hz).889

The authors demonstrated that the amplitude and temporal profile of OA waves arelinearly dependent on blood oxygenation in its wide range of magnitude from 24%to 92%. The designed system was capable of real-time, continuous measurementsof blood oxygenation, despite optical and acoustic attenuation by thick bone.

The use of an OA technique for noninvasive and real-time continuous monitor-ing of total hemoglobin concentration (THb) was proposed.1004, 1005 It was shownthat the OA technique may provide accurate measurements of THb through thedetection and analysis of OA signal temporal profiles induced by short opticalpulses in blood circulating in arteries or veins. A portable OA system based ona 10-ns Nd-YAG laser (1064 nm) was designed for monitoring THb in the radialartery. Results of in vitro and in vivo studies demonstrated that (1) the slope of OAwaves induced in blood in the transmission mode is linearly dependent on THb inthe range from 6.2 to 12.4 g/dl; (2) OA signals can be detected despite optical atten-uation in turbid tissue phantoms with a thickness of 1 cm; and (3) the OA systemdetects signals induced in blood circulating in the radial artery. Clinical studies for



healthy volunteers, described in Ref. 1005, showed that the amplitude of OA signalgenerated in the radial artery closely followed the changes in THb. In this study,THb was changed rapidly upon the infusion of intravenous saline and measureddirectly in concurrently collected blood samples.

The OA/PA method is used for the characterization of layered tissue structuresin the near and far fields,844 which is important for providing in-depth measure-ments of port wine stains of human skin.847 It can be also used to perform in vivotomographic images of small animals. The 2D OA images,848 as well as slices ofa 3D image,849 of sacrificed mice were reported. A system capable of performingOA structural and functional imaging in rat brain was developed.856, 857

Research and development are conducted toward noninvasive monitoring ofvenous oxygenation.1015, 1016 The authors of these papers have designed and builta novel OA monitor of cerebral venous oxygenation, as measured in the superiorsagittal sinus (SSS), the large midline cerebral vein. The experimental setup allowsfor detecting SSS signals in vivo at 700, 800, and 1064 nm through a thick (5–6mm) sheep skull containing circulating blood with high (submillimeter) in-depthresolution. These results demonstrate that OA/PA monitoring of cerebral venousblood oxygenation may be noninvasively and accurately performed in humansthrough the intact scalp.

A theoretical model describing the dependence of the OA/PA signal onhemoglobin saturation with oxygen (sO2) is presented in Ref. 1017. The full OAsignal generated by many RBCs was calculated by summing the OA signals (fields)from each RBC, represented as a spherical drop of fluid. To generate a 2D spatialdistribution of RBCs, the MC simulation method was used. It was assumed thatall RBCs have the same level of sO2 for a particular distribution. The fraction ofoxygenated hemoglobin in every RBC determines the degree of oxygenation ofthe cell, and thus, the blood. Satisfactory qualitative agreement has been foundbetween the calculated and published experimental data.1017

For reliable quantification of blood oxygenation, different combined methodsmay be useful, such as the combination of OA detection of absorption with exoge-nous dyes, whose lifetime in the intermediate triplet state is sensitive to oxygenconcentration.1018 This method is intended to excite the dye molecules on the pumpwavelength at the maximum of their absorption, which, for example, is 630 nmfor G2-dye, and then probing by the beam with a longer wavelength (950 nm forG2-dye) for OA detection of time-varying absorption in the excited triplet state.By tuning the time delay between the pump and probe beams, an exponentiallydecaying curve for OA signal amplitude can be obtained, which is determined bythe concentration of oxygen in the tissue. Because this is a temporal method, it isonly slightly dependent on the optical properties of tissue heterogeneity and thedistribution of light energy within tissue.

4.11.4 Temperature measurement and monitoringof temperature effects

Laser OA/PA techniques were suggested for real-time noninvasive monitoring ofin-depth temperature distribution and thermal damage in tissues.888, 1019–1022 The


188 Chapter 4

possibility of temperature measurement is based on the fundamental phenomenonthat the Grüneisen parameter, expressed by Eq. (4.23), is temperature dependent.The linear dependence of the OA pressure amplitude on temperature in tissues hasbeen demonstrated;888 thus, it can be expressed by an empirical equation:

� = A + BT , (4.57)

where A and B are constants and T is the temperature. One can rewrite Eq. (4.22)in the case of an absorbing medium as

δp(z) = [A + BT(z)]μaE0exp(−μaz), (4.58)

and in the case of strongly scattering media in deep (not subsurface) areas as

δp(z) = [A + BT(z)]μabsE0exp(−μeffz), (4.59)

where T(z) is the temperature distribution in tissue; bs is the parameter resultingfrom multiple scattering in tissue, which is dependent on the absorption and scat-tering coefficients; and μeff is the effective attenuation coefficient [see Eq. (1.18)].Rearranging Eq. (4.59), one can obtain

T(z) = C + Dδp(z)

δp(z)T=T0

, (4.60)

where δp(z)T=T0 is the OA pressure profile recorded at the initial temperature,T0; C and D are parameters that are dependent on tissue properties. Therefore,by recording and analyzing the temporal OA pressure profile, one can recon-struct the temperature distribution during hyperthermia if optical properties areunchangeable.

In Ref. 888, real-time detection of thermally induced changes in opticalproperties was performed with sensitive wideband acoustic transducers throughmeasurement and analysis of amplitude and temporal characteristics of OA/PAsignals and through diffuse reflectance measurements. Part of the experimentalsetup is presented in Fig. 4.27. Coagulation of liver, myocardium, and prostatewas induced by interstitial CW Nd-YAG laser irradiation of the samples or byconductive heating. It was found that the optical properties remained constantuntil reaching the temperature of coagulation (approximately 53◦C) and that OAresponse was sharply increased during heating from this temperature up to 70◦C(see Figs. 4.28 and 4.29), which is associated with changes in the absorption andscattering coefficients of coagulated tissue [C and D parameters in Eq. (4.60)].Real-time monitoring of the expansion of the interstitial coagulation front withinfreshly excised canine tissues demonstrated satisfactory spatial resolution at ∼600μm. The results of this study suggest that the OA/PA technique can potentiallybe used for real-time, precisely controlled thermotherapy of malignant and benignlesions at depths on the order of centimeters.

The feasibility of guiding cancer photothermal therapy by using OA/PA imag-ing to detect light absorbers and to monitor temperature elevation was shown



Figure 4.27 Experimental setup for OA/PA measurements of temperature in tissue andtissue phantoms.888

Figure 4.28 Amplitude of OA pressure induced in canine liver (a) and canine myocardium(b) versus temperature. The vertical and horizontal lines in (a) mark the temperature rangethat is normally used in tumor hyperthermia (see Ref. 888).


190 Chapter 4

Figure 4.29 OA pressure amplitude versus temperature for canine myocardium samplesduring conductive heating (see Ref. 888).

in Ref. 1019. Photothermal therapy was conducted by utilizing a CW laser andmetal nanocomposites broadly absorbing in NIR. A linear array-based US imagingsystem was interfaced with a nanosecond pulsed laser to image tissue phan-toms and ex vivo animal tissue before and during photothermal therapy. Thermalmaps computed by monitoring temperature-induced changes in the photoacous-tic signal during the therapeutic procedure and comparing with US temperatureimaging allowed the authors to conclude that the combined use of these two imag-ing technologies will be beneficial to guide nanoparticle-enhanced photothermaltherapy.

A temperature sensitivity of 0.15◦C was obtained at a temporal resolution asshort as 2 s, using the average of 20 signals, by using combined thermoacoustic andphotoacoustic measurements.1020 The deep-tissue imaging capability of this com-bined technique can potentially lead to in vivo temperature monitoring in thermalor cryogenic applications.

As discussed previously, temperature distribution in tissues can be recon-structed on the basis of registering OA/PA signals by a matrix of OA/PA detectorsand subsequently solving the inverse problem, if the calibration dependence of μa�[see Eqs. (4.57)–(4.59)] on the temperature of the tissue type under investigation isknown.1021, 1022 When using a narrow laser beam and a finite duration of the laserpulse, amplitude of the OA/PA signal is proportional to the absorption coefficientand does not practically depend on the reduced scattering coefficient, μ′

s [see Eqs.(1.36) and (1.37)].

For OA signal excitation, the authors of Refs. 1021 and 1022 used the funda-mental harmonic 1064 nm Q-switch Nd-YAG laser with pulse width and repetitionrate of 12 ns and 50 Hz, respectively (Fig. 4.30). The pulse energy at the surfaceof the tissue was 2–3 mJ with a beam diameter of 2.5 mm. Heating of the mediumwith a single laser pulse does not exceed one hundredth of a degree, and the entirecycle of measurements, when averaged over 128 realizations, equals one degree.



Figure 4.30 Experimental setup for OA/PA temperature control at heating of biologicaltissues (see Ref. 1022).

Measures have been undertaken to minimize the pyroelectric signals generated inthe piezoelectric transducer, and changes in their sensitivity with temperature. Atransducer with a smooth transient response in the frequency range of 0.05–12MHz and low-frequency sensitivity of 845 μV/Pa (with 50-fold gain) was madefrom 110-μm-thick PVDF (polyvinylidene fluoride) film. The registered transducersignal was recorded by a digital oscilloscope (sampling rate of 1 GHz and ana-log frequency of 100 MHz). The system was synchronized by using a photodiodeplaced behind a low transparent laser mirror. After degassing, the tissue sampleswere fixed in a holder, which was then placed in a thermostat with distilled water.To provide uniform temperature distribution, heating of the samples was fairly slow(approximately 2◦C for 5–10 min) and controlled by a thermocouple.

Measured dependencies of the OA signal amplitude on temperature for pigliver, chicken muscle, and pig fat are shown in Fig. 4.31. During the cooling ofmuscle tissue samples [Fig. 4.31(a)] from a temperature greater than 45◦C, theamplitude of the OA signal does not return to its original value, showing thatirreversible changes occur in the structure of the tissue. The difference for the tem-perature dependence of pig fat [Fig. 4.31(b)] is that the amplitude of the OA signaldecreases when temperature increases from 25◦C to 80◦C. In the case of samplecooling from a temperature above ∼36◦C, the slope of the dependence is less steepthan that observed during heating. This may indicate a modification of adiposetissue at any temperature above the temperature of a living organism and can beassociated with the temperature-induced lipolysis of fat cells.1023 Similarly to thecase of muscle tissue, upon cooling liver tissue samples from a temperature of45◦C [Fig. 4.31(c)], the characters of the cooling and heating curves are identicalin reverse. Upon cooling from a temperature above 45◦C, the dependence of theOA signal on temperature is linear, with a lower slope than at heating.


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Figure 4.31 Examples of a temperature dependence of the OA signal amplitude for tissuesamples: chicken muscle (breast) (a), pig fat (b), and liver (c). Open symbols correspondto heating and solid symbols correspond to cooling modes that start from different initialtemperatures. The heating mode data were fitted by the least-squares method in the form ofone or two linear functions in the following temperature ranges: (a) 25–45◦C and 46–63◦C;(b) 25–65◦C and (c) 25–42◦C (solid line) and 42–62◦C (dashed line) (see Ref. 1022).

The laser OA/PA method is also used to monitor the cooling and freezing oftissue.1024 This is important, for example, to obtain reproducible measurementsof the optical properties of tissue in a certain sample preparation technology (seeChapter 7), or in some therapeutic procedures, such as reduction of body fat.

One more important application of the time-resolved OA/PA method is mon-itoring tissue mechanical response, coagulation, and ablation.861, 862, 884, 1025 Thefeasibility of using the OA/PA method for the monitoring of glaucoma treatmentby application of a laser cyclophotocoagulation technique has been proven.861

According to the described results, the laser OA/PA method seems to be a promis-ing tool for localization of the ciliary body and monitoring of the coagulatingprocess. To optimize fundus laser treatments of the eye, an online, noninvasiveOA technique was designed for monitoring of fundus temperature.862 It was foundthat the OA method can be used to noninvasively determine retinal temperaturesduring pulsed laser treatment of the eye. This technique can also be adapted toCW photocoagulation, photodynamic therapy, and transpupillary thermotherapy,or other fields of laser-heated tissue.



4.11.5 In vivo cytometry and imaging of sentinel lymph nodes

The OA/PA techniques using endogenous chromophores (e.g., melanin orhemoglobin) or synthetic nanoparticles as OA/PA contrast agents have demon-strated exclusive potential for imaging tumors in vivo with higher resolution indeeper tissues (up to 3–5 cm) than existing optical modalities.897, 898, 904, 968, 1026–1047

In addition, carbon nanotubes (CNTs),1029 quantum dots (QDs),1030 and goldencarbon nanotubes (GNTs)1031 and their clusters with red shift effects971 weresuccessfully applied for in vivo flow cytometry on the basis of the OA/PA method.

The capability of the OA/PA method for assessment of sentinel lymph nodes(SLNs),968, 1029, 1031, 1033–1035 multicolor PA detection of disseminated tumor cells(DTCs) in lymphatics,968 and counting of metastatic cells transported by lymphto SLNs1033 has been demonstrated by using tumor-bearing animal models. Itwas shown that PA detection of metastasis in SLNs can be integrated with PTpurging by using a fiber-based multimodal diagnostic–therapeutic platform withtime-resolved multicolor PA lymphography, PA lymph flow cytometry, and PTtherapy.1033 A microscopic PA imaging technique was successfully applied formapping lymph nodes with depths up to ∼3 cm in animal models using blue dyesand nanoparticles as contrast agents.936, 1034, 1035

An OA/PA experimental setup is typically built on the basis of an uprightmicroscope, such as an Olympus BX51 microscope (Olympus America, Inc.,USA), with incorporated PA fiber-based, PT, fluorescent, and TDM mod-ules.961, 968, 1026, 1031, 1033 Tunable pulse OPOs with a wavelength range of 420–2300nm, pulse width of ∼8 ns and repetition rate of 10–50 Hz, beam diameter of 10–100 μm, and fluence range of 10−3−10 J/cm2 are often used as a light source.Diode lasers are also used for particular measurements; for example, a diode laserwith wavelength of 905 nm, pulse width of 15 ns and repetition rate of 10 kHz,and fluence rate of 0.01–0.7 J/cm2 was used for the detection of melanoma cells.PA waves are detected by US transducers [e.g., model 6528101 (Imasonic Inc.,Besançon, France) with 3.5 MHz frequency and 5.5 mm diameter], then amplifiedand recorded with a Boxcar and digital oscilloscope (e.g., Tektronix TDS 3032B).US gel or warm water is typically used to provide acoustic and optical couplingbetween tissue and transducer.

In Ref. 968, two-color mapping of lymphatics and identification of nanoparti-cles was realized with two laser pulses at wavelengths of 850 nm (OPO) and 639nm (Raman shifter) with 10 μs delay, followed by time-resolved detection of cor-responding PA waves. Delivery of laser radiation to samples was performed eitherwith a microscope schematic or with a 400-μm-diameter fiber with focusing tipfixed in a customized folder (see Fig. 4.32). To extend the experimental possibil-ities, the PA microscope was integrated with a PT module.961 In PT thermal-lensmode, defocusing of a collinear He-Ne laser probe beam was measured using apinhole. A fluorescence module with color CCD camera (e.g., Nikon DXM1200)was added to verify the PA/PT data. Navigation of the laser beams and anatomicmicrostructure of the SLNs was controlled with high-resolution (300 nm) TDM.PA mapping was achieved in vivo and ex vivo by spatial scanning of focused


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Figure 4.32 Principle of PA detection of single absorbing targets in blood flow in vivo (seeRef. 1029).

beam or fiber across samples using a computer-controlled microscopic stage andVisual Basic software with a total scanning time of 1–10 min, depending on thesample size.

Magnetic nanoparticles (MNPs), as well as recognized lymphographic tracerand novel GNTs,1031 were used as PA contrast agents.1033 The 30-nm sphericalpolyethylene glycol (PEG) coated MNPs with a Fe2O3 core (Ocean NanoTech;Springdale, AR, USA) and customized hollow single-walled CNTs surrounded bythin gold layers with average dimensions of 12.8 × 91.7 nm were used in theseexperiments. The CNTs exhibit high water solubility and biocompatibility, lowcytotoxicity due to the protective layer of inert gold around the particle, and highplasmon absorption in the NIR range of 850 nm.1031 The GNTs often conjugatedwith folate; therefore, they are highly expressed in selected human breast tumorsand not expressed in normal endothelial cells in lymphatics.

Melanoma tumors were created in mouse ear by inoculating 106 B16F10melanoma cells in 50 μL of PBS with a 30-gauge needle.1033 The progressionto metastatic disease was estimated by measurements of primary tumor size andsubsequently verified with PA evaluation and histology. Also, breast cancer cellswere injected with a microsyringe directly into the lymph nodes to mimic metas-tasis. In vivo and ex vivo PA mapping and microscopic and H&E (hematoxylin &eosin) pathological examination of lymph nodes were performed at 1 and 2 weeksafter melanoma tumor cell inoculation (see Figs. 4.33 and 4.34).1033 In vivo assess-ment of SLNs and lymphatic vessels was performed noninvasively through intactskin and intraoperatively through a small skin incision overlying the SLN anddirect attachment of the folder with a fiber to skin and lymph node, respectively.For ex vivo study, lymph nodes were excised without fat and surrounding tis-sues from the mouse. To decrease beam blurring due to light scattering in lymphnodes, the nodes were embedded for 5 min in 40% glucose, 100% DMSO, and80% glycerol as hyperosmotic optical clearing agents (OCAs), which reduce tissuescattering6, 162, 163, 200 (see Chapter 9).

The combination of PA mapping of SLN metastases with high resolutionTDM mode (up to 300 nm) allows one to assess the exact distribution and



Figure 4.33 PA detection and counting of melanoma metastasis during tumor develop-ment. Top row: photo of tumor with visualization of the lymph vessel (using Evans Blue dye)collecting lymph from primary tumor area (top, callout) and in vivo two-wavelength PA detec-tion (bottom oscillogram) of melanoma metastasis with tumor progression in the SLN at first(left) and second (right) week. Middle row: ex vivo PA mapping of the SLN with melanomametastasis at single cell level at 1 (left) and 2 (right) week(s) of primary tumor development.The data are presented as 2D high-resolution (bottom) and 3D low-resolution (top, callout)simulation. Each single spot on bottom is associated with single metastatic cells shown onthe right panel (top, left callout). Red pseudo-color peaks indicate the photoacoustic sig-nals with maximum amplitudes (bottom row). Histological images of the investigated SLNsdemonstrating no histological changes at week 1 (left) and the detectable metastases, con-toured by a green line, at week 2 after tumor inoculation (right) (see Ref. 1033). (See colorplates.)

number of melanoma metastases and laser-induced damage area.1033 To evalu-ate two lymphatic basins, MNPs and GNTs (each ∼1011 NPs/mL in 5 μL ofPBS) were intradermally injected in the tip of the left and right ears of intact,healthy mice (n = 4). The prior measurement of PA spectra of NPs revealed that639 nm is the optimal wavelength, providing the best PA contrast of MNPs intissues and minimal interference with GNTs that have a maximum absorption at


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Figure 4.34 Melanoma in mouse ear with micrometastasis in the SLN at week 2 aftertumor inoculation (a). Laser-induced localized damage of the SLN containing melanomamicrometastasis at different laser energy (b). Laser parameters: wavelength, 639 nm; 10laser pulses with overlapping beams with diameter on skin of 1 mm; laser fluence, 200mJ.cm2 (b, left) and 750 mJ.cm2 (b, right). PA signals from the SLN using a low fluencelaser pulse (c), 50 mJ.cm2 (left); at high fluence laser pulse, 400 mJ.cm2 (middle); and atlow fluence laser pulse again, 50 mJ.cm2 after high fluence laser pulse (right). Amplitude(vertical axis), time scale (horizontal axis): 100 mV/div, 2 μs/div (left); 50 mV/div, 2 μs/div(middle); 20 mV/div, 4 μs/div (right) (see Ref. 1033).

850 nm.1031 Dual-color PA mapping using two laser pulses at 639 nm and 850nm was performed immediately after injection and then periodically every 10 minfor 5 hrs. Then, co-injection of GNTs with Evans Blue (EB) dye (5 μL) providedadditional imaging of lymphatic vessels and SLNs. This dye, with absorption inthe visible region (below 660 nm), was chosen to avoid interference from GNTswith maximum absorption in the NIR region. This study revealed that nanoparti-cles quickly entered lymphatics and migrated in less than 3–5 min to the left andright cervical lymph nodes at a depth of 1–3 mm. This aligns with rapid uptakes ofsmall NPs by lymphatics.

The PA signal amplitude at 850 nm on the site over SLNs before and afterinjection of GNTs increased from 1.5 ± 0.2 to 30.1 ± 3.2 a.u. (10 min after injec-tion, p = 0.05). The PA signal amplitude at 639 nm on the site over SLNs beforeand after injection of MNPs increased from 2.2 ± 0.3 to 8.7 ± 0.9 a.u. (p = 0.01).This led to increases in PA contrast (as the ratio of signals before and after injectionat the skin site overlying SLNs) of ∼20 for GNTs and ∼4 for MNPs at 850 and639 nm, respectively.

The feasibility of this integrated PA platform for the assessment of lymphaticdisseminated tumor cells (DTCs) and SLN status was first tested in a melanoma



tumor model.1033 Melanoma is a malignancy that can quickly progress to incur-able metastasis. Conventional diagnostic tools have high false-negativity (∼25%)in detecting positive SLNs. From a clinical perspective, melanin is a very promisingendogenous PA contrast agent; it provides PA signals from individual pigmentedmelanoma cells above blood background in NIR range.968, 1026 Monitoring of thePT signals from individual B16F10 cells (total of 300) in suspension demonstrateda high level of heterogeneity: 5–10 % of cells with increased pigmentation pro-duced PT signals with amplitudes much greater than PT signal amplitudes fromcells with less pigmentation.1026 Approximately 82 ±3.8% of tumor cells weredetectable with the PT/PA technique.

EB injection was also used to visually differentiate an afferent lymph vesselthat was exclusively collecting lymph from the tumor [Fig. 4.33(a), top callout].Many (20–50) diode laser-induced PA signals from the same flowing melanomacells were acquired by using the Boxcar system and transformed into signals withwidth determined by the transit time of the cells through the laser beam. Real-timePA monitoring of prenodal lymph vessels and the SLN revealed the number ofmetastatic cells producing rare flash PA signals, which increased from 0.26 ± 0.05to 2.13 ± 0.30 cells/min at 1 and 2 weeks after melanoma inoculation, respectively.At 1 week postinoculation, the primary tumor size was 1.0 ± 0.2 mm2 (Fig. 4.33top row, left); 493 PA signals associated with individual melanoma cells (singlespots covering 6% of the examined area) and three SLN micrometastases wereidentified with PA contrast of 10.6 ± 1.2 (Fig. 4.33 middle row, left). At twoweeks, the primary tumor size was increased to 3.6 ± 0.5 mm2 (Fig. 4.33, toprow, right) and much larger numbers of PA signals (3,188 spots covering 39% ofthe examined area) with mean contrast of 22.5 ± 0.9 were detected, including 7–10high-amplitude signals, which were indicative of metastases (Fig. 4.33, middle row,right). The histology of these nodes showed an absence of metastases at 1 week(Fig. 4.33, bottom row, left), but single metastases were present on histology at2 weeks postinoculation (Fig. 4.33, bottom row, right). This result is consistentwith the ability of the PA technique to detect single cell metastases with improvedsensitivity over conventional histology.968, 1026, 1033

Targeted laser purging of SLN metastasis is possible at optical monitoringwith TDM imaging of laser ablated breast cancer cells labeled by GNT-folate con-jugates and detection of linear/nonlinear PT responses from live/damaged cells,and by PT signal elimination after cell disintegration by a high-energy laserpulse.1033 Figure 4.34 illustrates laser-induced localized damage of the SLN con-taining melanoma micrometastasis at different laser energies controlled by PAsignal generation.

4.11.6 OA/PA sensors and systems

Measurement of the pressure transient or displacement at the tissue surface ismost commonly provided by the use of piezoelectric sensors.831, 832, 854 Althoughpiezoelectric sensors have the advantage that broadband sensors are easy to con-struct and their sensitivity is rather high, optical methods may occasionally be


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preferable in in vivo studies due to their ability to provide noncontact measurements(see Fig. 4.1).846, 858–860 A minimally invasive noncontact interferometric techniqueto accurately measure the effective optical attenuation depth of a sample isdescribed.859, 860 This technique measures time-resolved tissue surface displace-ment resulting from the absorption of a short laser pulse. The surface motionis caused by thermoelastic stress relaxation, whose time constant is proportionalto the optical attenuation depth of the sample. The magnitude of expansion isa function of the incident radiant exposure and thermophysical properties of thesample. This technique is complementary to interferometric photothermal spec-troscopy, a method that determines the effective optical attenuation depth throughtime-resolved measurements of surface displacement resulting from the ther-mal diffusion that follows the thermoelastic stress relaxation process.882, 883 Theinterferometric system, described in Refs. 859 and 860, utilizes a time-resolvedhigh-resolution interferometer capable of angstrom-level displacement resolutionand nanosecond temporal resolution to detect subsurface blood vessels within ahuman forearm in vivo.

High resolution and minimal artifacts of the images are characteristic forcircular-scanning OA computed tomography with a full 360-deg scan aboutan object with elevated geometry, such as brain or breast.856, 857, 890, 891 Planarreflection-mode techniques831, 832, 838, 850 are not limited by the shape of the sam-ple, but may suffer from the strong OA waves emitted from optical absorbers nearthe surface, such as hair follicles and melanin granules in the skin, whose acous-tic reverberations can potentially overshadow the much weaker OA signals fromstructures deep in the tissue. A reflection-mode microscopic OA imaging techniquethat uses dark-field illumination prevents the occurrence of such artifacts.891 Highimage resolution and high sensitivity were achieved by utilizing a high-frequency,large-NA spherically focused ultrasonic transducer that is coaxial and confocalwith the optical illumination. Both wide bandwidth and large NA provide the highresolution of the acoustic detector; however, the increasing of frequency is limitedbecause of a corresponding decrease in the acoustic wave penetration depth (atten-uation in a tissue is of 0.7–3 dB/cm/MHz). Therefore, an OA sensor with a largeNA (=0.44) and frequency range from 32.5 to 67.5 MHz was used by the authorsof Ref. 891 in in vitro and in vivo studies of rat skin. These parameters of theOA sensor provide lateral resolution of 45–120 μm (defined by the NA) and axialresolution of ∼15 μm (defined by the frequency range). The system is capable ofimaging optical-absorption contrast as deep as 3 mm in tissue.

The primary technical difficulty of the time-resolved measurements of OAprofiles is associated with correct detection of acoustic signals, which simulta-neously requires high temporal resolution, equal to or higher than laser pulseduration, and wideband frequency detection extending into low-frequency ultra-sound.831 Wideband piezoelectric transducers with short- or open-circuit operatingmodes, as low noise detectors, have proved to be eminently suitable for this pur-pose. The transducer operating in the short circuit has substantial thickness thatis larger than the spatial width of the detected ultrasonic transient. The transducer



thickness limits the lower limit of detected ultrasonic frequencies and duration ofthe detection window. An excessively thick piezoelement would (1) lead to a moreprominent acoustic diffraction at lower ultrasonic frequencies in the detected signaland (2) reduce the electric capacity to a value below that of the electronic circuitry.It is difficult to design acoustic transducers operating in short-circuit mode fordetection of OA profiles longer than 1–2 μs. However, these transducers would bemost optimal for the detection of submicrosecond and nanosecond OA signals. Theupper limit of ultrasonic frequency is defined by the discharge time of the trans-ducer capacity. The US detection band can reach several hundred megahertz. Thistype of transducer does not require backing material to reduce resonant vibrations.

In the case of an acoustic transducer operating in the open-circuit mode, itis necessary for the thickness of the piezoelectric element to be smaller than theacoustic wavelength detected in its upper ultrasonic frequency limit.831 The lowerlimit of detectable ultrasonic frequencies is defined by the discharge time of thetransducer electric capacity through the input resistor of the electronic preampli-fier. To design acoustic transducers operating in the open-circuit mode with verywide ultrasonic detection band (≥100 MHz), it is necessary to employ piezoelectricelements that are a few microns thick. The choice of appropriate backing material iscrucial for widening the frequency band. Design of a backing layer that acousticallymatches the piezoelectric material for effective damping of transducer resonancesis a critical technical problem. The sensitivity of open-circuit transducers is greaterthan that of short-circuit transducers due to its longer sustainment of electric chargeat the piezoelement.

Another technical difficulty in providing high temporal resolution in the detec-tion of OA profiles is the need for precise adjustment of the detector face withrespect to the wavefront of the arriving optoacoustic signal.831 Obviously, the timedifference between the instances of laser-induced pressure transient (LIPT) arrivalto the opposite edges of the piezoelectric element should be shorter than the tem-poral resolution of this transducer. Therefore, the angle between the direction ofLIPT wavefront propagation and that normal to the piezoelectric detector must beas small as possible. For example, to achieve temporal resolution of � τ ∼ 10 ns,LIPT has to be incident with angle less than ∼3 min relative to the sensitive areaaperture of ∼3 mm.

The highest possible piezoelectric efficiency for wideband piezoelectric detec-tion can be achieved with piezoceramics, such as PZT-5H.831 A lower sensitivitymay be obtained with polyvinylidene fluoride (PVDF) or PVDF copolymers.Quartz and lithium niobate have significantly lower sensitivity for wideband USdetection.

Low acoustic impedance, which is similar to biological tissues, makes PVDFsuitable for applications in medical and biological sensing.831 Design of effectivebacking for PVDF transducers does not represent a significant problem and makesdetected OA signals clear from reverberations within the piezoelement.

Many designs of wideband acoustic and OA transducers may be employed fora variety of applications in biomedicine (see Fig. 4.3).831, 840, 891 Two-dimensional


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OA images can be provided either by using a stationary array of acoustictransducers or by scanning a single transducer along the tissue surface.832 Anarc-shaped array containing 32 ultra-wideband piezoelectric transducers with1×12.5-mm size and distance of 3.85 mm between the elements is described.832

A 110-μm-thick piezoelectric polymer PVDF was used to operate in a wide USfrequency band. The transducers were mounted on the arc surface with a radius of60 mm; this geometry provided optimal resolution in the entire 60 × 60-mm fieldof view within the image plane. The shape and length of individual piezoelementsdetermine spatial resolution of this array in the plane perpendicular to the imageplane. The flat elements in use provided a resolution equal to the linear size ofthe element. This 32-element array was used for the acquisition of 2D OA imagesof breast tumors.832 Two images at two different laser wavelengths of 1064 and757 nm were acquired in succession at irradiation with 16 100-ns pulses at eachwavelength over the course of 0.8 s. Image reconstruction required approximately1 s. Resolution of the image visualization was ∼1 mm along the depth axis and 1.5mm in the lateral direction, which is comparable to that of x-ray mammographyand US.

Three-dimensional OA imaging can be provided using the system designed byLaserSonix Technologies, Inc., which is based on a bifocal array of 64 piezoelec-tric transducers and 64 corresponding data acquisition channels.832 This systemhas close-to-real-time image acquisition and data processing, with a resolution ofapproximately 3 mm in the plane perpendicular to the image plane, so that thinfrontal slices of the breast can be visualized. Full-field-of-view 3D images canbe reconstructed by fusing 60 2D slices. A fast OA imaging system based on a320-transducer linear array was also recently developed and tested.914

A high-resolution confocal OA transducer providing subsurface imaging inthe scanning mode is applicable when super-high resolution on the cellular or sub-cellular level is needed.832 An ultra-wide band of ultrasonic detection realized infront-surface transducers yields an in-depth resolution close to 15 μm. In inci-dent optical beam focusing, a comparable lateral resolution is also achievable. Theconfocal OA transducer provides sharp focusing of the optical beam and a longnarrow waist of acoustic focus in the ultrasonic detection system. The distributionsof focused light and the caustic US detection define the measuring volume of theconfocal transducer.

Another modification of an OA sensor used in a dark-field reflection-modeimaging system, containing an optical fiber that is coaxially positioned with afocused US transducer and attached to a concave lens, is described in Ref. 891.

A small-animal whole-body imaging system designated ring-shaped confocalphotoacoustic computed tomography (RC-PACT), which is based on a confo-cal design of free-space ring-shaped light illumination and 512-element full-ringultrasonic array signal detection, is described in Ref. 1048. The free-space lightillumination maximizes the efficiency of light delivery, and the full-ring signaldetection ensures a full 2D view aperture for accurate image reconstruction. Usingcylindrically focused array elements, RC-PACT can image a thin cross section



with 0.10 to 0.25 mm in-plane resolutions and 1.6 s/frame acquisition time. Bytranslating a mouse along the elevational direction, RC-PACT provides a series ofcross-sectional images of the brain, liver, kidneys, and bladder.

Submicron-resolution PAM is typically provided in transmission mode,because of the technical difficulties of combining high-NA optical illuminationwith high-NA acoustic detection. The lateral resolution of reflection-mode PAMhas not reached <2 μm in the visible light range. However, the first reflection-modesubmicron-resolution PAM system with a new compact design was developed onthe basis of a parabolic mirror focusing and reflecting the PA waves.1049 Thus, suffi-ciently sensitive signals were collected without distorting the optical focusing, anda lateral resolution of ∼0.5 μm with an optical wavelength of 532 nm and opticalNA of 0.63 was achieved. The maximum penetration depth in optical-scatteringsoft tissue was measured as ∼0.42 mm and the axial resolution as ∼15 μm.Submicron-resolution PAM is suitable for in vivo high-resolution imaging, or evensubcellular imaging, of optical absorption.1049

An ultraviolet PAM system was developed to provide noninvasive cell nucleiin vivo imaging without staining.1050 This system was tested on the skin of mouseears at in vivo en face imaging. The optimal ultraviolet wavelength for PA imagingof cell nuclei was found to be 250 nm. However, with the application of a wave-length between 245 and 275 nm, images of cell nuclei with specific, positive, andhigh PA contrast can be produced.

A novel trimodality system for human breast imaging was designed byintegrating PA and thermoacoustic (TA) imaging techniques into a modified com-mercial US scanner.1051 In the system, light (for PA) was delivered with an opticalassembly placed within the microwave antenna (for TA). Laser and microwaveexcitation pulses were interleaved to enable PA and TA data acquisition in parallelat a rate of 10 frames per second. Using endogenous hemoglobin contrast in wholeblood, the authors demonstrated that the maximum penetration depth of PA tomog-raphy in chicken breast tissue was 6.6 cm, and that for exogenous dye MB solution,it was 8.4 cm for a 7-mm tube filled with 30 mM dye. The maximum penetrationdepth for TA tomography in porcine fat for a 13-mm tube filled with water was 4.4cm. The PA axial, lateral, and elevational resolutions were 640 μm, 720 μm, and3.5 mm, respectively. This system is prospective for clinical applications in breastcancer imaging.

An all-optical PA scanner for in vivo imaging of the development of tumorvasculature and its response to a therapeutic vasculature disrupting agent has beendescribed.1052 The scanner employs a Fabry–Perot polymer film ultrasound sen-sor for mapping the PA waves and an image reconstruction algorithm based uponattenuation–compensation acoustic time reversal. Label-free 3D in vivo images ofwhole tumors to depths of almost 10 mm with sub-100 micron spatial resolutionwere acquired in a longitudinal manner. This enabled the development of tumor-related vascular features to be visualized over time, including vessel tortuosity,feeding vessel recruitment, and necrosis.


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The development of OA/PA technology is moving toward endoscopy andintravascular imaging.947–951 In particular, Ref. 951 describes a coaxial systemwith a ring array of PA transducers. A variety of OA/PA probes suitable or alreadytested for OA/PA spectroscopy and imaging of tissues and blood are described inRefs. 885, 888, 889, 914–918, 921, 923, 925, 926, 929, 931, 932, 934, 997, 998,1004, and 1005.

4.12 Conclusion

OTR/PTR, OT/PT, and OA/PA transient techniques provide convenient means forin vitro, or even in vivo and in situ, monitoring of optical and thermal properties ofa variety of human tissues, including skin. In particular, water content and surfaceconcentration and diffusion of topically applied substances (drugs and sunscreens)can be measured.833, 863–865

The use of pulsed OA/PA and OTR/PTR techniques is more appropriate forin vivo and in situ experiments. The discussed optothermal and optothermoelas-tic responses of living tissue on pulse laser excitation are the basis for a novelapproach in medical tomography that combines achievements of optical, ther-mal, and acoustical probing of a tissue and is used for OA/PA tomography,831, 832,

837–839, 843, 846, 848–857, 890, 894–898, 906, 909–913, 918–944 microscopy,834,877, 897, 904–908, 938, 939,

944, 1049, 1050 and endoscopy.947–952

A variety of tissue-imaging techniques are suggested on the basis of US andlight beams interacting within an inhomogeneous medium, which occurs throughthe change in optical properties of the medium resulting from its compressionby the US.890, 974–981 These are so-called acousto-optical (AO) interactions andimaging technologies.

To OA/PA and AO, signals contribute scattered photons (singly and multiply);therefore, the imaging depth is extended compared with other ballistic or quasi-ballistic imaging modalities, such as OCT or confocal microscopy.

The OA/PA and AO tomographies (OAT/PAT and AOT) provide:890 (1) a com-bination of high optical contrast and high acoustic resolution; (2) the potential forsimultaneous functional imaging of blood oxygenation and blood volume; (3) ahigh ratio between imaging depth and resolution; (4) no speckle artifacts; (5) scal-able resolution and imaging depth by varying the US frequency; (6) the ability tosimultaneously acquire OAT/AOT images and pure US images from the same crosssections of the sample for added diagnostic value; and (7) nonionizing laser and USradiation within the safety limits for tissues.

As noted in Ref. 895, with PAT, one can create multiscale and multicon-trast images of living structures, from organelles to organs and even entiresmall animals. The generally achievable spatial resolution is 1/200 of a desireddepth of the image, which can reach up to 7 cm. PAT provides anatomical,functional, metabolic, molecular, and genetic contrast for monitoring of vascularhemodynamics, oxygen exchange, biomarkers, and gene expression.



The PA method is also prospective for ophthalmic diagnostics1053, 1054 andmonitoring of eye tissue ablation.1025 In particular, it can be used in diagnosticsfor label-free PA ophthalmic angiography1053 and PA ophthalmoscopy for in vivoretinal imaging.1054

A combined PA and US imaging approach shows strong potential to visualizeboth the seed and the surrounding anatomical environment of the prostate duringbrachytherapy seed placement procedures.1055

Reference 1056 describes an electrocardiogram-synchronized PAM system fornoninvasive quantification of the pulse wave velocity in the peripheral vessels ofliving mice. The authors have found a linear correlation between the pulse wavevelocity and the vessel diameter, which agrees with known physiology. Blood pulsewave velocity is an important physiological parameter that characterizes vascularstiffness.

In vivo PA flow cytometry for monitoring circulating cells and con-trast agents in blood and lymph vessels is now a well-established technol-ogy.899, 900, 968, 1026, 1027, 1029–1032 Descriptions of its principles and applications forreal-time detection and characterization of circulating single cells (velocity, mor-phology, and deformability), nanoparticles, pathogens, and contrast dyes in vivocan be found elsewhere (for example, Refs. 899, 900, 968, and 1029).

OA/PA techniques using endogenous chromophores (melanin or hemoglobin)or exogenous dyes and nanoparticles provide in vivo imaging of tumors with ahigh resolution at depths up to 3–5 cm.897, 898, 904, 968, 1026–1047 The potential capa-bilities of the OA/PA method for monitoring SLN quantification of the migrationof tumor cells in lymphatics has been demonstrated using tumor-bearing animalmodels.936, 968, 1029, 1031, 1033, 1033, 1035

Different types of nanoparticles are used as PA contrast agents in manybiomedical applications, such as in vivo cytometry, lymph node and tumor imaging,and cardiovascular dynamics.1027–1047 In particular, quantum dots1030 and GNTsare used as multimodal photoacoustic and photothermal high-contrast molecularagents.1031 Nanoparticles are also applied for in vivo magnetic enrichment andmultiplex PA detection of circulating tumor cells.1032

In vivo PA detection of metastasis targeted by nanoparticles in sentinel lymphnodes can be accompanied by photothermal cancer cell purging the single-celllevel.1033 NIR gold nanocages and nanorods were suggested as tracers for PAsentinel lymph node mapping.1034, 1035

Multiwavelength PA imaging at plasmon resonance coupling of gold nanopar-ticles is used for the selective detection of cancer.1028, 1037 Ultrahigh sensi-tivity of carbon nanotubes as PA molecular imaging agents in living ani-mals is proved in Refs. 1039 and 1040. For high-contrast PA imaging of thevasculature of a living mouse brain, hollow gold nanospheres were effectivelyemployed.1042 Bioconjugated gold nanocages were used for in vivo molecular PATof melanomas.1043 Multispectral PAT provides real-time imaging of cardiovasculardynamics and circulating gold nanorods.1046, 1047 Multifunctional nanoprobes areused to enhance the utility of OCT in combination with PA.1045


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However, OAT/PAT and AOT have some limitations, mostly related to theuse of ultrasonic technology. These include contact measurement, which is nec-essary for acoustic coupling, and strong wavefront aberrations of the ultrasonicwave induced by heterogeneous tissues and organs. In the case of high acoustichomogeneity, simultaneous US imaging may be useful to obtain information onthe acoustic properties of the medium, which is necessary for reconstruction of theimage in OAT/PAT and AOT.


Chapter 5

Fluorescence and InelasticLight Scattering

The physical bases for fluorescence and inelastic scattering of light are discussed,including multiphoton fluorescence, vibrational spectroscopy, and Raman spec-troscopy in applications to optical biopsy and imaging of biological tissuesand cells.

5.1 Fluorescence

One of the fundamental mechanisms of the interaction between light and biologicalobjects is luminescence, which is subdivided into fluorescence, corresponding toan allowed optical transition with a rather high quantum yield and a short (nanosec-ond) lifetime, and phosphorescence, corresponding to a “forbidden” transitionwith low quantum yield and long decay times in the microsecond–millisecondrange.1057–1059 In biomedical applications, fluorescence is a primary phenomenonused in optical biopsy for noninvasive diagnostics and monitoring of biological tis-sues and cells, providing diagnosis at the molecular level, and functional imagingof tissues and organs.1, 6, 31, 92, 98, 129, 130, 134, 135, 141, 253, 312, 347, 349, 350, 476, 481, 493, 783, 787,

789, 1057–1069

Absorption of light is connected with an electronic transition from a groundstate to an excited state of a molecule. Light passing through a layer of thickness,d, is thereby attenuated according to the equation1058

I(λ) = I0 exp(−μad) = I010−ελcabd, (5.1)

where I(λ) is the transmitted light intensity, I0 is the incident intensity, ελ is themolar extinction coefficient, and cab is the concentration of absorbing molecules.In scattering samples, the absorption coefficient, μa, and the scattering coefficient,μs [omitted from Eq. (5.1)] sum up, thus further reducing transmitted light, aspreviously described in detail.

205


206 Chapter 5

Fluorescence arises upon light absorption and is related to an electronic transi-tion from the excited state to the ground state of a molecule. Its intensity (quantumflux) corresponds to1058

IF(λ) = I0[1 − 10−ελcabd

]ηF�/4π, (5.2)

where ηF is the fluorescence quantum yield and � the angle of detection ofisotropic fluorescence radiation. In the case of thin samples, e.g., cell monolayersor biopsies a few micrometers in thickness, Eq. (5.2) can be approximated by

IF(λ) = I0 ln 10ελcabdηF�/4π. (5.3)

This implies that fluorescence intensity is proportional to the concentration andfluorescence quantum yield of the absorbing molecules. In scattering media, thepath lengths of scattered and unscattered photons within the sample are different,and Eqs. (5.2) and (5.3) have to be modified. However, in virtually homogenousthin samples, the linearity between IF, cab, and ηF is still fulfilled.

Energies of the electronic states of a molecule are complex functions of thenuclear distances of relevant atoms, usually forming potential wells, as shown inFig. 5.1 for the ground state (S0) and the first excited state (S1). Each well con-tains a larger number of vibrational levels, νi, that further split into numerousrotational levels (omitted from Fig. 5.1) of the molecule. Electronic transitionsoccur in the vertical direction because during their short duration, nuclear coor-dinates do not change (Franck-Condon principle). Electronic transitions usually

Figure 5.1 Potential diagram of electronic states (S0, S1) and vibrational levels (νi).Electronic wave functions and optical transitions are indicated (excitation: S0ν0 → S1νn;fluorescence: S1ν0 → S0νn) (see Ref. 1058).


Fluorescence and Inelastic Light Scattering 207

originate from vibronic ground states (excitation, S0 and ν0; fluorescence, S1 andν0). The probability of each transition corresponds to the square of the transitiondipole moment and is determined by an overlap of the corresponding electronicwave functions in the ground state and the excited state of the molecule. Therefore,absorption and fluorescence spectra originate from a superposition of several tran-sitions, often resulting in broad spectral bands. From Fig. 5.1, one can deduce thatthe so-called 0–0 transition between the lowest vibrational levels is only slightlypronounced, because the overlap between corresponding wave functions is verylow. Therefore, fluorescence spectra are usually shifted to lower energies, �W,corresponding to higher wavelengths, λ = �W/hc, than absorption or excitationspectra (h is Planck’s constant, c is the velocity of light). This phenomenon iscalled the Stokes shift.

If the potential curves are plotted without regard to the variable nuclear dis-tances, the different molecular states can be illustrated in a Jablonski diagram, asshown in Fig. 5.2. Excitation usually occurs from S0 to various vibronic levels ofthe excited singlet states, Sn, from where fast nonradiative transitions (internal con-version) occur within the femtosecond time range to the lowest excited state, S1.From S1, various transitions can be distinguished: fluorescence to S0 (includingits vibrational states) with rate kF, internal conversion to S0 (rate kIC), intersys-tem crossing from the singlet to triplet state T1 (rate kISC), and nonradiative energytransfer to adjacent molecules (rate kET). All of these rates sum up according to

k = kF + kIC + kISC + kET = 1/τ, (5.4)

where τ is the lifetime of S1. The ratio kF/k corresponds to the fluorescence quan-tum yield, ηF. Although only radiative transitions can be monitored by opticalspectroscopy, changes in kIC or kET are often deduced from fluorescence lifetime

Figure 5.2 Jablonski diagram of molecular energy levels and transition rates. Straight lines:radiative transitions; wavy lines: nonradiative transitions (see Ref. 1058).


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measurements. The radiative transition T1 → S0 is spin-forbidden, and only withina few specific molecules does this transition become prominent.

Transition dipole moments have defined orientations within a molecule. Uponexcitation with linear polarized light, one preferentially excites those molecules,whose transition dipoles are parallel to the electric field vector of incident light.This selective excitation of an oriented population of molecules results in par-tially polarized fluorescence, which is described by the degree of polarization[see Eq. (2.20)]:

PFL = (IF|| − IF⊥)/(IF|| + IF⊥) (5.5)

or by fluorescence anisotropy:1057

rF = (IF|| − IF⊥)/(IF|| + 2IF⊥) (5.6)

where IF|| and IF⊥ are the fluorescence intensities of light polarized parallel or per-pendicular to the exciting electric field vector, respectively. Usually, PFL and rF

depend on the time interval between excitation and fluorescence detection, becauseduring the lifetime of their excited states, many molecules change their orientationby rotation (rotational diffusion). From time-resolved measurements of fluores-cence anisotropy, a time constant, τr, of rotational diffusion can be determined,which is correlated with the volume, VM, of the molecule and the viscosity, η, ofits environment according to

τr = ηVM/kBT , (5.7)

where kB is the Boltzmann constant and T is the absolute temperature. Timeconstants of rotational diffusion of approximately 13 ns were correlated with amolecular weight of proteins around 50,000 daltons,1057 whereas a time constantof approximately 300 ps was attributed to an aggregated species of photosensitizingporphyrin (protoporphyrin) with a 1.6 nm diameter.1058

Upon excitation of biological objects by ultraviolet light (λ≤ 370 nm), fluores-cence of proteins and nucleic acids can be observed. This is autofluorescence (AF),or intrinsic fluorescence of biological material. Fluorescence quantum yields of allnucleic acid constituents, however, are approximately 10−4−10−5, correspondingto the lifetimes of excited states in the picosecond time range. The AF of proteinsis related to the amino acids, phenylalanine, tyrosine, and tryptophan with absorp-tion maxima at 257, 275, and 280 nm, respectively, and emission maxima between280 nm (phenylalanine) and 350 nm (tryptophan).1057–1059 The protein spectrum isusually dominated by tryptophan. Fluorescence from collagen or elastin is excitedbetween 300 and 400 nm and shows broad emission bands between 400 and 600 nmwith maxima around 400, 430, and 460 nm. In particular, the fluorescence of col-lagen and elastin can be used to distinguish various types of tissues, e.g., epithelialand connective tissue.31, 92, 98, 1058, 1059, 1064–1069

The reduced form of coenzyme nicotinamide adenine dinucleotide (NAD·H)is selectively excited in a wavelength range between 330 and 370 nm. NAD·His most concentrated within mitochondria, where it is oxidized in the respiratory



chain located within the inner mitochondrial membrane, and its fluorescence is anappropriate parameter for the detection of ischemic or neoplastic tissues.1058, 1069

Fluorescence of free and protein-bound NAD·H has been shown to be sensitiveto oxygen concentration. Flavin mononucleotide (FMN) and dinucleotide (FAD),with excitation maxima around 380 and 450 nm, have also been reported tocontribute to intrinsic cellular fluorescence.1058

Porphyrin molecules, e.g., protoporphyrin, coproporphyrin, uroporphyrin,or hematoporphyrin, occur within the pathway of biosynthesis of hemoglobin,myoglobin, and cytochromes. Abnormalities in heme synthesis, occurring in thecases of porphyrias and certain hemolytic diseases, may considerably enhance theporphyrin level within tissues. Several bacteria, e.g., Propionibacterium acnes,or bacteria within dental plaque (biofilm), such as Porphyromonas gingivalis,Prevotella intermedia, and Prevotella nigrescens, accumulate considerableamounts of endogenous protoporphyrin.1070, 1071 Therefore, diagnosis and moni-toring of acne,1070 other inflammatory skin pathologies,1072, 1073 or oral and toothlesion detection1071, 1074, 1075 based on measurements of intrinsic fluorescenceappears to be a promising method.

Many theoretical computer modeling and experimental studies of fluores-cence intensity distributions accounting for light scattering effects have beenperformed.350, 1076–1084 In particular, a diffusion theory model of spatially resolvedfluorescence from depth-dependent fluorophore concentration was described inRef. 1077. In Ref. 1078, 3D epithelial tissue phantoms suitable for fluorescencespectroscopy, collagen cross-linking studies, and cancer diagnosis were presented.Certain principal features of near-infrared fluorescence tomography, such as 3Dimage reconstruction from sparse and noisy data sets1079 and localization of fluo-rescent masses deeply embedded in tissue,1080 were discussed. A few experimentalapproaches have been developed for the recovery of scattering free fluorescencefrom measured fluorescence1081 and the validation of MC modeling of fluores-cence in tissues in the UV-visible spectrum.1082 MC simulations of some practicalcases were also performed, such as the effect of fiber-optic probe geometry ondepth-resolved fluorescence measurements from epithelial tissues1083 and spatialfluorescence distribution in the skin.350 A seven-layer skin model was considered,with individual fluorophores and optical characteristics for each layer.1084 In thiswork, a modified method of characteristics was used for solving the RTE. Thetechnology designed for simulating the intensity distributions for fluorescence,excitation, and reflection light should be useful in the development of laser medicaldevices for dermatology.

At present, various exogenous fluorescing dyes can be applied for probing cellanatomy and cell physiology.1058, 1085–1089 For instance, subcellular localization ofsulfonated tetraphenyl porphines in colon carcinoma cells was studied by spectrallyresolved fluorescence imaging.1085

In humans, such dyes as fluorescein and Indocyanine green are used forfluorescence angiography, blood volume determination, or maintenance of lasersurgery.954 Novel fluorescent contrast agents for optical imaging of in vivotumors based on a receptor-targeted dye–peptide conjugate1087 and fluorescent


210 Chapter 5

protein platforms fluorescing in green (GFP), yellow (zFP538), red (drFP583), orNIR (eqFP650 and eqFP670) regions of the spectrum1088, 1090–1093 were recentlydescribed. Reference 1091 shows the values of the extinction coefficient at themaximum of the absorption band of a large number of fluorescent proteins withvalues ranging from 0.05 × 10−4 to 16 × 10−4 M−1cm−1 in the wavelength rangefrom 380 to 600 nm, and corresponding fluorescence quantum yields ranging from0.01 to 0.9 in the wavelength range of fluorescence from 440 to 660 nm. Detailedanalysis of the structure and function of similar fluorescent proteins to GFP, andtheir numerous applications for in vivo imaging of cells and tissues, are given inRef. 1092.

Fluorescence properties of such dyes as albumin blue 633 and 670 in plasmaand whole blood were studied.1086 Exogenous specific fluorescence markers forin vivo quantitative 3D localization of tumors were studied in Ref. 1089. Dyesin the form of nanocrystals,1094 or plasmonic nanoparticles conjugated withdyes,1095, 1096 are being used as fluorescent agents.

For the development of innovative imaging of tissues and cells, reversiblephotoswitchable fluorophores1097, 1098 are of great interest. These fluorophorescan be proteins or organic molecules (dyes), and can be created in the form ofnanoparticles. Different approaches are used for the synthesis of photoswitchablefluorophores, including synthetic protein engineering, chemical synthesis, poly-merization, and self-assembly. The primary feature of these fluorophores is theirability to change luminescent intensity and wavelength (color), which allows forthe construction of two-color probes or sensors with on/off fluorescence. Suchprobes are used for high-resolution functional imaging.1098

Fluorescence spectra often provide detailed information on fluorescentmolecules, their conformation, binding sites, and interaction within cells and tis-sues. Fluorescence intensity can be measured as either a function of the emissionor excitation wavelength. The fluorescence emission spectrum, IF(λ), is specific forany fluorophore and is commonly used in fluorescence diagnostics.

For many biomedical applications, an optical multichannel analyzer (OMA)(a diode array or a CCD camera) is preferable as a detector of emission radia-tion because spectra can be recorded very rapidly and frequently with sequencesin the millisecond range. Fluorescence spectrometers for in vivo diagnostics arecommonly based on fiber-optic systems.133, 1058–1065, 1083 The excitation light of alamp or a laser is guided to the tissue (e.g., some specific organ) via fiber by usingappropriate optical filters. Fluorescence spectra are usually measured either via thesame fiber or via a second fiber or fiber bundle in close proximity to the excitationfiber.

Various comprehensive and powerful fluorescence spectroscopies and theircombinations are currently available, such as microspectrofluorimetry, polarizationanisotropy, time-resolved with pulse excitation and frequency domain, time gated,total internal reflection fluorescence spectroscopy and microscopy, fluorescenceresonant energy transfer, and confocal laser scanning microscopy.349, 350, 1057–1094,

1099–1101 These methods allow researchers to provide 3D-tissue topography and cellstructure imaging, high-resolution transmission microscopy, time-gated imaging



Figure 5.3 CW and time-gated fluorescence spectra of Saccharomyces cerevisiae afterexcitation at 365 nm (upper curve) or 355 nm (other curves) (see Ref. 1085).

of selected specific fluorescent molecules or molecular interaction, fluorescencelifetime and spectrally resolved imaging, and studies of fluorescence bleachingkinetics and the motion of cellular structures.

The potential of time-gated fluorescence spectroscopy is shown inFig. 5.3.1058, 1085 Shown fluorescence spectra of Saccharomyces cerevisiae are verysimilar to those of various cell cultures. An emission maximum at 460–465 nm,corresponding to free NAD·H, is clearly identified within a time gate of 0–5 ns,whereas emission maxima around 435 nm (bound NAD·H) and 515 nm (flavins)are resolved at later time gates. In contrast, CW spectra of AF are broad and exhibitlittle substructure.

Using time-resolved fluorescence detection, free and bound NAD·H can bestudied separately; time-gated fluorescence spectroscopy includes studies of thetumor-localizing porphyrins within tissues of strong AF; and the fluorescenceenergy transfer method can be used to selectively measure mitochondrial depolar-ization, which may precede mitochondrial autophagy, apoptosis, and necrotic celldeath.1058 Analytical models and solutions for time-resolved fluorescence lifetimequantitative spectroscopy and imaging in turbid media and tissue were recentlydeveloped.349, 1099–1102

Principles of optical clinical chemistry based on measuring changes of fluo-rescence intensity, wavelength, polarization anisotropy, and lifetime are describedin Ref. 1057. Various fluorescence techniques for selective oxygen sensing anddetection of blood glucose and blood gases are available.1057

A few examples should be discussed of fluorescence (AF) imaging andspectroscopy of normal and pathological tissues, such as normal and malig-nant mucosa in patients with head and neck cancer,1103 carotid atheroscleroticplaque,1104 cervical precancerous tissue,1105 normal and neoplastic human breast


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tissue,1106 and basal cell carcinomas in the skin.1107 A real-time calibrated AFtechnique for in vivo imaging of neoplastic growths was developed.1108 AF-basedmethods and instruments designed for ophthalmic diagnostics are reviewed inRef. 1109.

For complete information about the structure and nature of pathology in situ,the confocal reflectance/AF tomography system for in vivo studies of the skin siteshas been suggested.1110 The intensity of the reflected light is primarily charac-terized by structural alterations of tissue, such as changes in the density of cellsin areas of cancerous lesions, and AF–biochemical changes associated with thekinetics of NAD·H. Relying on these, the authors achieved the sensitive and spe-cific early diagnosis of cancer at 97.8%. A confocal laser endoscopic system forreceiving 3D fluorescence images of the surface and subsurface of cell and tissuestructures, used for studying the oral cavities of humans and animals, is describedin Ref. 1111.

To assess the possibility of multimodal confocal imaging to support brainsurgery in Ref. 1112, different types of benign and malignant primary andmetastatic brain tumors were investigated. Postoperative tissue samples wererapidly stained with aqueous methylene blue (MB) at a concentration of0.05 mg/ml. Reflection and fluorescence from the samples were excited at awavelength of 642 nm, and the fluorescence signal of the MB was recordedat wavelengths between 670 and 710 nm. Fluorescent images correlated wellwith histological images. In turn, the reflected and fluorescent images providedinformation about the morphology and vascularization of the samples. The opticalscheme of the confocal system and an example of the images of postoperativetissue samples are shown in Fig. 5.4.

The technology for obtaining in vivo images of the excretory function of theliver in rats by fluorescence microscopy is described in Ref. 1113. Two polyme-thine dyes were used: Indocyanine green (ICG), with excitation at a wavelengthnear 800 nm, and DY635, with a shorter wavelength excitation. ICG also has beensuccessfully used for the noninvasive detection of fluorescence in the adult brainby using a pulsed imaging system at picosecond resolution.1114 In this study, it wasshown that monitoring the ICG-bolus pulsed fluorescence system can provide ahigher signal-to-noise ratio than that of a pulse system based on measurements ofthe diffuse reflection.

A multifrequency (from 0 to 0.3 mm−1), multiwavelength (633, 680, 720, 800,and 820 nm) spatial-frequency imaging system was successfully used to determinethe absorbing, scattering, and fluorescence properties of glioblastoma spheroidsin vivo in a mouse model upon the induction of endogenous protoporphyrin IXby the administration of 5-aminolevulinic acid.1115 Principles of the system aredescribed in Section 1.4. The possibility of using the spatial-frequency imagingsystem to support resection of brain tumors has been also demonstrated.1115

Activatable fluorescent molecular probes generally do not fluoresce in theinactivated state because of intramolecular quenching, but they can significantlyincrease the yield of fluorescence in the enzyme-mediated hydrolysis of pep-tides.1116 Through the use of a cathepsin-activated infrared probe (PGC-800),



Figure 5.4 Multimodal confocal system: the optical scheme (a), images of a tissue sampletaken in the area of human glioblastoma, the size of the bar is 100 μm (b–d): (b) imagefor reflected light; (c) fluorescent image; (d) H&E histology. The solid arrows show the mat-ted mass of glial cells, dots indicate necrotic sites, and dashes indicate areas of vascularproliferation (see Ref. 1112).

it was shown that fluorescence lifetime is significantly increased in mousemyocardial tissue after a heart attack (0.67 ns) compared with healthy tissueinfarction (0.59 ns). This makes it possible to obtain in vivo information aboutthe molecular activity that alters the process of intramolecular quenching andto use the distribution of fluorescence lifetime as the image contrast for imag-ing of activated fluorophores in tissue. The fluorescence lifetime of activatedmolecular probes is an important parameter for the in vivo imaging of enzymeactivity.

Obtaining fluorescent images of objects with high spatial resolution in a highlyscattering medium, such as biological tissue, is a difficult task. However, as shownin Ref. 1117, the use of heat-sensitive ICG-filled nanocapsules based on micellarpolymer Pluronic can solve this problem. Capabilities of this method were demon-strated for the optical tomography system with modulated intensity at a frequencyof 100 MHz with local heating of embedded nanoparticles by focused ultrasound.


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In studies on tissue phantoms, it was possible to reliably visualize a 3-mmfluorescent object to a depth of 2 cm by using both contrasts: intensity and lifetime.

The method of fluorescent imaging can provide new insights into the molecularmechanisms of the origin and development of cancer in vivo.1063 For this purpose,for example, systems of genetic reporters are available, such as eGFP and DsRed,and highly sensitive fluorescence detection systems.

In practical terms, the combination of fluorescence imaging and local spec-trophotometry can increase the reliability of fluorescent diagnosis of early can-cer of the larynx and bronchi.1118 Intraoperative fluorescence diagnostics isused to accompany photodynamic therapy in patients with metastatic lesionsof the brain.1119 Diagnostics of pigmented skin tumors was successfully con-ducted by laser-induced AF and diffuse reflectance spectroscopy in a singleprocedure.1120

Currently, reflectance and fluorescence spectroscopies are the most developedamong all available optical methods for investigating skin in vivo. Reflectanceand fluorescence from skin carry information about the structure of the epider-mis and dermis, the quantity and density of blood vessels, the concentration andspatial distribution of chromophores and fluorophores in skin, and the nature ofskin metabolic processes. Typical applications include in vivo quantitative analysisof skin erythema and pigmentation, determination of cutaneous color variation,monitoring of dermatological treatment effects, determination of skin photoag-ing, diagnosis of skin tumors, and study of skin biophysics.57, 1059, 1061, 1062, 1066–1068,

1107, 1110, 1120

The absorption and scattering properties of the skin affect both the AF andreflectance spectra. Therefore, the combined use of fluorescence and reflectancemay provide additional information in the analysis of skin tissue. Reference1059 discusses the potential advantages and possible uses of the combined useof reflectance and fluorescence spectroscopy of skin for the evaluation of ery-thema and pigmentation indices, determination of hemoglobin oxygenation andconcentration, and investigation of the efficacy of topical sunscreens.

One of the goals of fluorescence spectroscopy is the identification of excita-tion wavelengths suitable for the differentiation of various pathological conditions.This is closely related to the identification of the chromophores responsible forthis differentiation. Most biological components, either related to the structure ofskin tissue or involved in metabolic and functional processes, generate fluorescenceemission in the UV-visible spectral region. As a result, different morphofunctionalconditions of the skin related to histological, biochemical, and physiochemicalalterations can be characterized, in principle, on the basis of information availablein the fluorescence excitation–emission maps (EEMs) (see Fig. 5.5).1059, 1065, 1067

The fluorescence maximum in the range 320–370 nm, with a peak at 340 nm, ariseswith excitation in the 250–290 nm range (peak at 280 nm). AF in the UVA rangeis dominated by the fluorescence bands of aromatic amino acids, namely tyrosineand tryptophan. There is only a slight variation in the UVA fluorescence of the skinbetween different skin sites. This may be attributed to the absence of AF attenua-tion by melanin, which is primarily deposited within the epidermis. Tyrosine and



Figure 5.5 Excitation-emission maps of the in vivo skin AF emission: see text and Ref.1067 (a); Normal skin phototype II. Measurements were carried out using FluoroLog 3 withfiberoptic adaptor - F-3000 (HORIBA Jobin Yvon S.A., France), supported by the NSF-Bulgaria under grant #DMU-03-46/2011, courtesy of Dr. Ekaterina Borisova, Institute ofElectronics, Bulgarian Academy of Sciences (b). (See color plates.)

tryptophan contents in epidermis are more than twice that of the whole skin, whichis why epidermis has high AF in the UVA range.

Among endogenous skin fluorophores are also different forms of NAD andkeratin located in the epidermis and dermal collagen. The reduced (NAD·H) andoxidized (NAD+) forms of NAD take part in cellular metabolism, and the inten-sity of their specific fluorescence (fluorescence maxima near 460 nm and 435 nm,respectively) is used not only for differential diagnostics of metabolic dysfunction,but also for quantitative NAD·H detection.1059

For collagen and elastin, which are located predominantly within the papil-lary and reticular layers of dermis, both excitation and emission light is attenuatedbecause of absorption by melanin; fluorescence intensity in the 400–480 nm rangeis subject to attenuation by other skin chromophores: hemoglobin, porphyrins, andcarotenoids. Both the total intensity and spectral features may be affected. The AFspectrum of human skin and fluorescence spectrum of collagen are essentially iden-tical, following optical filtering through the dermal blood plexus.1059, 1068 Figure 5.6presents the temporal dynamics of the AF skin spectra involved in the process ofthe UV-erythema formation. The primary change observed is a significant decreasein the AF intensity during the formation of erythema, caused by the optical filteringeffect of blood (early stage) and induced melanin (latter stage).

Simplicity and miniaturization of equipment for fluorescence studies of biolog-ical tissues and cells are important requirements for medical diagnostics. Recently,a wide-field fluorescence microscope for dark-field imaging was developed for amobile phone platform.1121 The microscope uses compact, lightweight, and inex-pensive optical components, which are mechanically attached to the mobile phonecamera. The possibility of using this device to receive images over a wide angleof view is critical for the study of relatively large sample sizes (>0.1 mL); forexample, samples of blood, urine, sputum, or water. As a demonstration of the


216 Chapter 5

Figure 5.6 3D plot of human skin AF after UV irradiation with four minimal erythema dose(MEDs) (see Refs. 1059 and 1068).

method from a set-top box to a mobile phone, fluorescent images of labeled whiteblood cells in whole blood samples were obtained.1121

To conclude this section, we present a simple and effective method that usesbioluminescent images of tissue samples.1122 Bioluminescence is the intrinsicemission of light by living organisms. It involves a process of oxidation of thesubstrate (luciferin) in the presence of the enzyme (luciferase). This reaction ischaracterized by the fact that the excess energy is released as light (not heat). Inthis method, a solution containing a mixture of bioluminescent enzymes, otherenzymes, and cofactors is applied to the surface of the tissue cryosection placedunder the microscope. For example, bacterial luciferase is introduced into a solu-tion of enzymes used for the determination of glucose, glycogen, and lactic andpyruvic acids. The solution reacts with the test metabolite in the cryosection. Asa result of this interaction, the number of emitted photons is proportional to theconcentration of the metabolite. The photons are detected by a microscope con-nected to a photosensitive camera for the detection of small light fluxes. In the finalimage, the light intensity distribution reflects the distribution of the metabolite con-centration in the sample. The signal is calibrated by using standard cryosectionswith a known concentration of metabolites. An important advantage of biolu-minescent imaging is its high spatial resolution, on the order of 50–100 μm.Bioluminescent imaging is a fundamentally ex vivo method, but the instantaneousfreezing of tissue samples reflects the situation in vivo. The authors of Ref. 1122used bioluminescent high-resolution imaging for studying the energy metabolismof two different vascular pathologies: ductus arteriosus and atherosclerosis.



5.2 Multiphoton Fluorescence

A new direction in laser spectroscopy and imaging of biological objects is associ-ated with multiphoton (two- and three-photon) fluorescence scanning microscopy,which makes it possible to image functional states of an object or, in combinationwith autocorrelation analysis of the fluorescence signal, determine intercellularmotility in small volumes.114, 122, 131, 137, 177, 609–618, 1123–1145 The two-photon tech-nique employs both ballistic and scattered photons at the wavelength of the secondharmonic of incident radiation entering a wide-aperture photodetector exactlyfrom the focal area of the excitation beam (see Fig. 5.7).1123 A unique advan-tage of two-photon microscopy is the possibility of investigating 3D distributionsof chromophores excited with ultraviolet radiation in thick samples. This type ofinvestigation is possible because chromophores can be excited (e.g., at the wave-length of 350 nm) with laser radiation whose wavelength falls within a range (700nm) in which tissue has high transparency. This radiation can reach deeply lyinglayers and produce less damage in tissues. In this case, fluorescent emission lies inthe visible range (>400 nm) and comparatively easily emerges from a tissue andreaches a photodetector, which only registers the legitimate signal from the focalvolume with no extraneous background.

In a two-photon excitation process, the rate of excitation is proportional tothe average squared photon density. This quadratic dependence follows from the

Figure 5.7 Confocal one-photon excitation imaging compared with two-photon imaging inscattering tissue (see Ref. 1123). Because of the longer wavelength, less excitation lightis lost to scattering when using two-photon excitation. Ballistic and diffusing fluorescencephotons can be used in the two-photon case, but only ballistic photons can be used in theconfocal case.


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Figure 5.8 Multiphoton fluorescence; Jablonski diagram of molecular energy levels show-ing the absorption and fluorescence processes for a molecule with one-photon absorption(a), two-photon absorption (b), and three-photon absorption (c). Solid and dashed hori-zontal lines represent, respectively, real and virtual molecular energy states; solid verticalarrows pointing up: photon absorption pathways; solid vertical arrows pointing down:radiation transitions (fluorescence); wavy lines: nonradiation transitions; λ1f is the wave-length necessary to excite the fluorescence at a single-photon absorption, λ2 ∼= 2λ1f andλ3 ∼= 3λ1f are wavelengths to excite fluorescence at two- and three-photon excitation,respectively.

requirement that the fluorophore must simultaneously absorb two photons perexcitation process. Multiphoton absorption processes are shown in Fig. 5.8. Todemonstrate that a multiphoton excitation process has occurred, it is necessary tomeasure the intensity of fluorescence as a function of the intensity of the excitedlight. A two-photon excitation process is characterized by a slope of 2 on a log-logplot of measured intensities; a three-photon excitation process is characterized bya slope of 3.

Two-photon-excited fluorescence (TPEF) of target molecules in a tissue is anonlinear process induced by the simultaneous absorption of two NIR photons iftheir total energy is sufficient to excite the electronic state of the molecular transi-tion. In general, one can use photons with wavelengths of λ1 and λ2, satisfying therelation

1

λ1f

∼= 1

λ1+ 1

λ2, (5.8)

where λ1f is the wavelength necessary to excite the fluorescence at single-photonabsorption. In practice, excitation by the same light source is preferred, i.e., λ1 =λ2, then λ2

∼= 2λ1f.Because the two-photon absorption cross section for biological molecules, σ2,

is typically very small (about 1 GM = 10−58 m4s·photon−1), it requires intensephoton fluxes on the order of 1030 photons per second per square meter (s−1m−2).This excitation can be achieved by using high-intensity, continuous (CW), orpulsed lasers with a short pulse duration (∼10−13 s). Pulsed excitation allows oneto reduce the heat load on the biological cell and selectively excite individual



electronic transitions. For two-photon processes, the time scale typically isin the range

τ2f = 10−16 − 10−17s, (5.9)

as it follows from the Heisenberg uncertainty principle:

τ2f∼= λ1f

4πc∼= 10−16s (5.10)

for the green line of the visible transition λ1f = 500 nm.The rate of two-photon excitation can be described analytically.114, 137, 1128,

1143, 1146 The TPEF intensity, I2f(t), is proportional to the square of the excita-tion intensity, I(t), two-photon absorption cross section of the relevant molecules,such as collagen or hemoglobin, σ2 = σ2(λexc), and fluorescence quantum yield,η = η(λem):

I2f(t) = σ2(λexc) · η(λem) · I2(t). (5.11)

Here, λexc and λem are the wavelengths of excitation and emission, respectively.In turn, the instantaneous rate of excitation is

I(t) = P(t)

A · hνexc= λexcP(t)

A · hc, (5.12)

where P(t) is the instantaneous power of the radiation within the illuminated area A,A ∼= π[λexc/(2NA)]2 (see Ref. 226), NA is the numerical aperture of the microscopeobjective, hνexc is the excitation photon energy, h is the Planck constant, and c isthe speed of light in vacuum.

The TPEF instant intensity collected by the optical system is given by

I2f(t) = κσ2ηI2(t) = κ(4/π)2σ2ηP2(t)

[(NA)2

hcλexc

]2

, (5.13)

where κ is the coefficient taking into account the collection efficiency of thefluorescent photons.

For CW laser excitation, time-averaged over any period of time, T, the TPEFintensity per single molecule is equal to

⟨I2f

⟩CW

= κ(4/π)2σ2ηP2ave

[(NA)2

hcλexc

]2

. (5.14)

For a pulse laser with pulse repetition rate fp = 1/T and duration of rectangularpulses τp, the average power, Pave, is related to peak power, Ppeak, by the equationPave = (τp · fp)Ppeak, then, for instant TPEF intensity, one can obtain

I2f(t) = κ(4/π)2σ2ηP2

ave

(τpfp)2

[(NA)2

hcλexc

]2

, (5.15)


220 Chapter 5

and for the time-averaged intensity of the TPEF, instead of Eq. 5.14, we have

⟨I2f

⟩p

= κ(4/π)2σ2ηP2

ave

τpfp

[(NA)2

hcλexc

]2

. (5.16)

The derivation of this equation assumes negligible saturation of the fluorophoreand that the paraxial approximation is valid.

It follows from these relations that the TPEF excitation efficiency at the sameaverage power in CW and pulsed modes, and independent of two-photon absorp-tion cross section on the pulse duration for CW radiation, is (τp · fp)1/2 timessmaller than for pulsed. For example, the excitation of fluorescence emissionby a 300-mW CW laser is approximately equivalent to excitation by a pulsedlaser with an average power of 1 mW at a repetition rate of 80 MHz and pulseduration of 100 fs. The emission of the 1-mW pulse laser with a wavelengthλ = 1000 nm, focused by the objective of a numerical aperture NA = 1.4 ontothe tissue with a typical cross section of two-photon absorption of biomoleculesσ2 = 10 GM = 10−57 m4s·photon−1 provides, in accordance with Eq. (5.16), a 105

Hz rate of fluorescence photon counting. However, the two-photon absorption crosssection for CW and picosecond radiation usually is on the order of more than afemtosecond. This allows for picosecond radiation to be used for tissues, althoughthermal effects can be significant.

The laser light in a two-photon excitation microscope is focused by the micro-scope objective to a focal volume. Only in this focused volume is there sufficientintensity to generate appreciable excitation. The low photon flux outside the focalvolume results in a negligible amount of fluorescence signal. The origin of theoptical sectioning capability of a two-photon excitation microscope is attributableto the nonlinear quadratic dependence of the excitation process and the strongfocusing capability of the microscope objective. Most specimens are relativelytransparent to NIR light. The focusing of the microscope objective results in two-photon excitation of UV-absorbing fluorophores in a small focal volume. It ispossible to move the focused volume through the thickness of the sample andachieve optical sectioning in three dimensions. Thus, the optical sectioning in atwo-photon excitation microscope occurs during the excitation process.

A significant advantage of multiphoton high-NA microscopy compared toconventional one-photon microscopy is the tiny subfemtoliter excitation volume.Absorption in out-of-focus regions is avoided because the probability of two-photon absorption decreases with nearly the distance, r, from the focal pointas r−4. Long-term studies have demonstrated that multiphoton microscopy canbe performed without photodamage under certain conditions. In particular, singlehamster ovarian cells have been femtosecond laser–exposed for hours with a high200 GWcm−2 peak intensity with no impact on cellular reproduction or vitality.1134

Investigations of tissues and cells by means of two-photon microscopy arecharacterized by the following typical parameters of laser systems: the wavelengthranges from 700 to 1200 nm, the pulse duration is on the order of 12–150 fs, thepulse repetition rate is 76–90 MHz, and the mean power is less than 10–40 mW.



These parameters can be achieved with mode-locked dye lasers pumped by aNd-YAG laser or with titanium sapphire lasers pumped by an argon laser. Diode-pumped solid-state lasers are also promising for the purposes of two-photonmicroscopy.1123 Virtually the same parameters of lasers are required for three-photon fluorescence microscopy of tissue, which possesses the same advantagesas two-photon microscopy but ensures a slightly higher spatial resolution andprovides an opportunity to excite chromophores with shorter wavelengths.1126

For example, the endogenous intracellular fluorophore NADP·H (reducedphosphate) can be imaged at the appropriate NIR excitation wavelength of a laserwith an average power less than 2 mW and a typical exposure time of 1 to 8 s perframe.1134

The first commercial multiphoton tomograph, DermaInspectTM (JenLabGmbH), is used in clinical practice for the diagnosis of melanoma and intradermalmonitoring of drugs in situ. It has been shown that the femtosecond laser system issafer than conventional UV light sources used in cosmetics.1134

A schematic diagram of the combined system for fluorescence spectroscopyand imaging is shown in Fig. 5.9.1145 A tunable femtosecond Ti-sapphire laser

Figure 5.9 Schematic diagram of the combined fluorescence spectroscopy and imagingsystem based on single-photon and two-photon measurements for tissue studies: a tunablefemtosecond Ti-sapphire laser and its SHG signal were used to excite two-photon signals(TPEF/SHG) and SPEF signals, respectively; M1, M2, M3 are removable mirrors; F1 is theshort pass optical filter to reject the NIR excitation of wavelength over 700 nm; F2 is thelong pass optical filter of cutoff wavelength approximately 30 nm longer than the excitationwavelength; DM is the dichroic mirror; BS is the beam splitter; BBO is the nonlinear crystal;SPC is the single photon counter (see Ref. 1145).


222 Chapter 5

was used to generate two-photon signals: TPEF and second harmonic generation(SHG). In turn, this laser radiation at the second harmonic was used for single-photon excitation fluorescence (SPEF). The choice of excitation for two- andsingle-photon measurements was provided with removable mirror M1. Two excit-ing beams, virtually united by a dichroic mirror, were directed at the tissue sampleafter focusing by the objective with water immersion (40×, NA = 1.15). Single-and two-photon signals were excited in the same location of the tissue sample.The excitation beams were scanned in a 100 × 100-μm sampling area by a pairof galvo-mirror scanners. A bifurcated fiber bundle with two single fibers (FibersI and II) was used to deliver the backscattered signals of SPEF and TPEF/SHG tothe spectrograph for spectral analysis. A cooled CCD camera was used to record thefluorescent and SHG signals. Another fiber (Fiber III) delivered an SPEF signal tothe PMT with a single photon-counting system for confocal fluorescence imagingof tissue in a certain small area at a specific depth. Small diameter core Fibers I andIII served as pinholes for collecting confocal SPEF signals, and large diameter coreFiber II was used for efficient collection of TPEF/SHG signals. Mirror M2 reflectedTPEF into the Fiber II for two-photon measurements and was removed for SPEFmeasurements. Mirror M3 reflected SPEF signals for confocal fluorescence imag-ing and was removed during SPEF confocal spectral analysis. Short-pass opticalfilter F1 was used for all TPEF measurements to reject infrared excitation radia-tion over 700 nm. Long-pass optical filter F2 of cutoff wavelength approximately30 nm longer than the excitation wavelength was always used to reject excitationlaser radiation in SPEF measurements. Axial and lateral resolutions were achievedof approximately 3.5 and 0.75 μm for the SPEF and 3 and 0.5 μm for the TPEF,respectively.

Figure 5.10 presents the SPEF signals excited at 355, 375, 395, and 415 nm,and the TPEF/SHG signals excited by NIR radiation at four correspondingwavelengths. The structure of the epithelial tissue under study consisted of top(keratinized epithelial layer), middle (noncornified epithelial layer), underlyingstromal layers. As shown in Figs. 5.10(c) and 5.10(d), noncornified epithelial tis-sue SPEF spectra excited at 355 and 415 nm, and the TPEF spectra excited atthe appropriate NIR wavelengths of 710 and 830 nm, are almost identical becausethe fluorescence excited at these wavelengths is largely attributable to endogenousfluorophores NAD·H and FAD, respectively. However, SPEF and TPEF spectraexcited at the other wavelengths are different because these signals represent amixture of the fluorescence signals of NAD·H and FAD, which feature differentexcitation efficiencies of SPEF and TPEF.

Control measurements of the fluorescence for individual solutions NAD·H,FAD, keratin, and collagen, which are the major fluorophores in the epitheliumand stromal layers, respectively, showed that SPEF and TPEF spectra of coenzymes(NAD·H, FAD) are identical.1145 However, TPEF spectra of keratin and collagen,structural proteins with much higher molecular weight than those of NAD·H andFAD, show a significant red shift and broadening of the spectrum compared withthe SPEF spectra. The mechanisms by which these differences occur are not clearand need to be studied.



Figure 5.10 Normalized spectra of single-photon (left) and two-photon (right) fluorescencefor different layers of tissue: topmost keratinized epithelial layer (a, b); nonkeratinized epithe-lial layer in the middle (c, d); and underlying stromal layer, clearly visible SHG peaks, whoseamplitude is reduced by a factor of 20 (e, f). Each pair of spectra of one- and two-photon fluo-rescence for different excitation wavelengths was obtained by averaging the measurementsfor samples from 12 experimental rabbits (see Ref. 1145).

The relationship between nonlinear optical signals from the collagen matrixin stroma and the progression of early epithelial carcinogenesis was studied byusing TPEF/SHG signals.1146 During precancer development in the epithelium,neoplastic cells remodel the underlying stroma, including the basement membrane,capillaries, fibroblasts, and extracellular matrix. In Ref. 1146, measurements wereconducted in vivo from the stroma of hamster oral cheek pouch. It was found thatthree features provide quantitative identification of epithelial precancer at differentpathologic stages: (1) the intensity ratio of TPEF/SHG, (2) the spatial frequencydistribution, and (3) the texture peculiarities of SHG images.

The authors of Refs. 1147–1149 have discovered that hemoglobin emits high-energy Soret fluorescence when two-photon excited by visible femtosecond lightsources. The unique spectral and temporal characteristics of hemoglobin fluores-cence were measured by using a time-resolved spectroscopic detection system.The high-energy Soret fluorescence of hemoglobin shows a spectral peak at 438nm with an extremely short lifetime of 230 ps. This discovery enables TPEFmicroscopy to become a potentially powerful tool for in vivo label-free imaging ofblood cells and vessels. The two-photon action cross section of hemoglobin dropsover two orders of magnitude in the wavelength range from 550 to 800 nm, whereasthe spectral and temporal characteristics of hemoglobin TPEF are insensitive to


224 Chapter 5

changes in the excitation wavelength.1149 However, hemoglobin fluorescence canbe excited with sufficient efficiency by using a conventional Ti-sapphire laser tunedto a wavelength close to 700 nm. With the employment of a time-resolved detec-tion method, the TPEF signals of hemoglobin can clearly be differentiated fromother nonlinear signals presented within the living biological tissues, indicatingthat a standard TPEF microscope can become a routine tool for in vivo label-freemicroangiography imaging.

Fluorescence is one of the primary methods of in vivo cytometry performeddirectly in tissues.179, 900, 972, 1150–1153 For example, for optimal recording of the flu-orescence signals from cancer cells circulating in blood vessels, a well-developedtechnique of confocal microscopy is often used. A line or slit illumination to excitefluorescence in the entire blood vessel allows for fast data acquisition. This is nec-essary for the analysis of cells moving through the vessels. Typically, such systemsare multiparametric and use several fluorescent probes and standard lasers, whichsignificantly increase the specificity of the assay. However, the SPEF-based in vivocytometry has several disadvantages.1152 The probing depth is limited by scatter-ing, absorption, and tissue AF. This limitation is <200 μm, corresponding to atypical sensing depth of confocal microscopes. However, for some animal mod-els, such as mouse ear, this depth is sufficient because a huge number of vessels isconcentrated in the tissue under the skin surface within a depth of 70–100 μm.

In general, TPEF-based in vivo cytometry has yielded an improved detectionrate and sensitivity over SPEF-based cytometry.1150–1155 Its major advantages are(1) higher probing depth up to 500–1000 μm; (2) naturally provided optical sec-tioning is without the use of pinholes on the path to the detector; (3) simultaneousexcitation of multiple fluorophores through the single laser source. The primarydrawbacks of TPEF-based cytometry are reduced to the high cost of equipment andexcessively small measuring volume, which necessitates a longer sampling time.

Nonlinear optical properties of nanoparticles are used to visualize them in theskin and other tissues, which is important for the study of migration routes ofnanoparticles in living organisms and to develop new, effective markers for imagingand monitoring of cells such as cancer cells.1157–1162 In the case of in vivo imagingof ZnO nanoparticles in human skin, the primary advantages are as follows: (1) thefluorescence of ZnO is at the wavelength of 385 nm, which is not overly affected bythe fluorescent spectral bands of endogenous skin fluorophores, such as NADP·Hand FAD; (2) and the cross section of two-photon absorption is high. For example,nanoparticles with a diameter of 18 nm have σ2

∼= 0.26 GM, which is approxi-mately 500 times higher than that suggested by the nonlinear susceptibility of thethird order for bulk ZnO material.1157 A commercially available ZnO nanoparticle(Zinclear) with an average diameter of 21 nm and a material bandgap wavelengthλbg = 370 nm, used in the study of transdermal transport, featured an absorptioncross section on ZnO crystal cell unit equal to σ2

∼= 32 ± 6 μGM at the excitationwavelength of 770 nm and 6.2 ± 0.8 μGM at 795 nm, and quantum efficiency of(0.9 ± 0.2)%.1159

It has been shown that TPEF, SHG, and hyper-Rayleigh scattering (HRS)microscopy can be used for imaging the penetration of TiO2 and ZnO nanoparticles



into tooth tissues.1161 On the background of tooth tissue AF, TiO2 nanoparticlescan accurately be detected by TPEF signal intensity, while ZnO nanoparticles canbe identified by SHG/HRS signal intensity, which significantly exceeds the toothbackground signal.

Two-photon fluorescence from gold nanoparticles (GNPs) shows consider-able potential in biological imaging of cells and tissues1162 and can be used in invivo cytometry as an additional channel for the recognition of NP-labeled cancercells. Additionally, fluorescence lifetime imaging microscopy (FLIM) with GNRsprovides images with better contrast and sensitivity than intensity imaging. Thecharacteristic fluorescence lifetime of GNRs with a longitudinal plasmon modecentered at approximately 750 nm, and a weak transverse plasmon mode at 550nm, was found to be less than 100 ps.1162 This characteristic lifetime may providesignificant selectivity and can be used to distinguish GNR-labeled cancer cells fromother fluorescent labels and endogenous fluorophores in lifetime imaging.

The use of FLIM is also possible to monitor transport ZnO nanoparticles inhuman skin.1158 The characteristic two-photon fluorescence lifetime measured inthis work for particles ∼30 nm is 289 ps.

5.3 Vibrational and Raman Spectroscopies

Middle and far IR and Raman spectroscopies use light-excited vibrational energystates in molecules to receive information about the molecular composition, struc-tures, and interactions in a sample.30, 99, 104, 105, 115, 123, 143, 218, 793, 1163–1190 In Fig. 5.11,the IR and Raman processes are depicted in a molecular energy level diagram.In IR spectroscopy, infrared light from a broadband source [usually in the wave-length range of 2.5–25 μm or in wavenumbers (1/λ) from 4000 to 400 cm−1] isdirectly absorbed to excite the molecules to higher vibrational states.1168 When theabsorbed energy, hν, matches the energy needed for an allowed infrared excitationof a molecular vibration, an absorption peak is observed in the IR spectrum.

In a Raman scattering event, light is inelastically scattered by a molecule whena small amount of energy is transferred from the photon to the molecule (or from

Figure 5.11 Illustration of an IR absorption process and a Raman scattering process in amolecular energy level diagram (see Ref. 1168).


226 Chapter 5

the molecule to the photon). This leads to an excitation of the molecule, usuallyfrom its lowest vibrational energy level in the electronic ground state, S0, to a highervibrational level of the same electronic state. The Raman spectrum displays theintensity of scattered light as a function of the difference in frequency between thescattered and incident lights. Because each molecular species has its own uniqueset of molecular vibrations, the Raman spectrum of a particular species will consistof a series of peaks or bands of scattered light, each shifted from the incident lightfrequency by one of the characteristic vibrational frequencies of that molecule. Theenergy (frequency) difference between incident (hν0) and scattered photon (hν) isexpressed as a wavenumber shift:1168

�k = 1

λ0− 1

λ. (5.17)

When the energy of the Raman-scattered photons is lower than the energy of theincident photons, the process is called Stokes–Raman scattering. When a photoninteracts with a molecule in a higher vibrational level, anti-Stokes–Raman scatter-ing can occur, in which the energy of the Raman-scattered photons is higher thanthat of the incident photons (see Fig. 5.11). The intensity ratio of the anti-Stokes(IAS) and Stokes (IS) Raman lines for a given vibrational state is given by1168

IAS

IS= (ν0 + νvib)

4

(ν0 − νvib)4 · exp

(−hνvib

kBT

), (5.18)

where �Evib = hνvib is the energy of the molecular vibrational state, kB is theBoltzmann constant, and T is the absolute temperature. It follows that at roomtemperature, the intensity of Stokes–Raman lines in the most informative spectralregion (>400 cm−1) is much higher than that of the anti-Stokes–Raman lines. Inturn, the intensity of Stokes–Raman scattered light is very low, typically 10−7 to10−15 times the intensity of the excitation light. The real-time detection of Ramanscattering spectra became practical because of the commercial development oflasers and subsequent advances in detector technology.

Different selection rules apply for the excitation of molecular vibrationalstates through absorption of an IR photon or Raman scattering of an incidentphoton.115, 123, 1164, 1168 Certain vibrations can be excited by both Raman and IRprocesses; others can only be excited by either Raman scattering or by IR absorp-tion. For symmetric molecules, the selection rules are mutually exclusive for allvibrations. Molecules exhibit IR activity when, during the vibration, a changeoccurs in the molecular dipole moment. Raman activity occurs when there is achange in polarizability. Therefore, the band intensity in IR and Raman spectra ofthe same molecular vibrational frequency can be quite different; symmetric vibra-tional modes are often strong in Raman, whereas antisymmetric vibrational modesare strong in IR. Depending on the polarization state of the incident and observedlight, information can be obtained regarding the symmetry of the molecules.

In most tissues, the fluorescence cross section, when excited by visible ornear UV wavelengths (within 300–700 nm), is approximately six orders of mag-nitude stronger than the Stokes-Raman cross section; moreover, the fluorescence



is a broadband signal within the same spectral range as the Stokes–Raman spec-trum.143, 1168 Fortunately, at different excitation wavelengths (UV, visible, andNIR), Raman scattering produces the same change in vibrational energy, whereasthe frequency of NIR light is too low to excite fluorescence, and UV-excited fluo-rescence has much lower frequency than the Stokes–Raman scattering frequency.Hence, the usage of NIR or UV excitation can reduce fluorescence backgroundin the Raman spectrum.1168, 1190 Particularly for tissue studies, NIR excitation ispreferable due to the high penetration depth.

IR and Raman spectroscopy techniques have been successfully applied in var-ious areas of clinical studies, such as examination of cancerous tissues;30, 1163, 1188

noninvasive diagnosis of skin lesions on benign or malignant cells;1163, 1169 mon-itoring of skin hydration under normal and pathological conditions;1166, 1168, 1185

skin treatments; topically applied substances (e.g., drugs, cosmetics, and moistur-izers);1184 antioxidants in the skin;1178–1183 studies of water metabolism in the eyelens;1176, 1177 diagnosis of cataract;793 monitoring of the mineralization process ofbone and teeth tissue;104 and glucose sensing in blood.105, 1187

Raman spectroscopy is widely used in biological studies, ranging from studiesof purified biological compounds to investigations on the level of single cells andother components of tissue.218, 1164, 1167, 1170, 1173 Currently, combinations of spectro-scopic techniques, such as IR and Raman with microscopic imaging techniques, arebeing explored to map molecular distributions at specific vibrational frequencies tolocally characterize tissues or cells.218, 1163, 1167, 1168, 1171, 1188 Spectral biochemicalimaging will become increasingly important for clinical diagnosis, particularly forthe differentiation between cancerous and noncancerous cells. Measured IR spectradepend on various aspects of sample preparation, i.e., the degree of hydration andhomogeneity, and on the physiological state of cells (exponential phase of growthor plateau); therefore, measurements accounting for named artifacts and cell statusshould be provided.218 As shown recently, the accurate measurement of vibrationalspectra of mammalian cells is possible for homogeneous aqueous cell suspensions;these IR spectra can be closely reproduced by using a linear combination of DNA,RNA, phospholipid, glycogen, and protein spectra.218

Because of the penetration depth of middle IR (MIR) light in tissue to only afew micrometers, the attenuated total reflectance Fourier transform infrared spec-troscopy (ATR-FTIR) method is suited to study changes in the outermost cell layersof the tissue.1168 As an example, ATR-FTIR spectra of sequential hydrated humanskin stratum corneum, measured during occlusion each minute for half an hour,are shown in Fig. 5.12. Hydration of the skin is obtained by keeping the forearmpressed against the ATR-FTIR crystal. During occlusion, water in the skin cannotevaporate and accumulates in the skin stratum corneum.

The Raman technique possesses certain characteristics that make it particularlysuitable for studying the skin, both in vitro and in vivo.1166, 1168 In vivo confocalRaman spectra of the skin show a considerable decrease in the absolute signalintensity if the distance is increased from the laser focus to the skin surface. This isprimarily attributable to diffuse light scattering, which is a much stronger effect inthe skin than light absorption. Therefore, confocal detection is particularly useful


228 Chapter 5

Figure 5.12 Sequential hydrated human skin stratum corneum MIR ATR-FTIR spectrameasured during occlusion each minute for half an hour (see Ref. 1168). The thick linerepresents the water spectrum (scaled twice). Spectral changes can clearly be identified:increased contribution of the water-bending mode at 1640 cm−1 and pronounced increaseof the OH stretches in a high wavenumber band around 3300 cm−1. Also, the water com-bination band around 2125 cm−1 is clearly visible in the hydrated spectra. A Nicolet-800Fourier Transform spectrometer with a “high-top” model ATR with a ZnSe (n = 2.42) crystalof rectangular shape (10 × 80 mm) with 45-deg entrance and exit facets is used to recordspectra. The ATR-FTIR spectrum is obtained by the Fourier transform of 64 and 128 inter-ferograms. The acquisition time for 64 scans at a resolution of 8 cm−1 is about 20 s. Spectrawere recorded on the volar part of the forearm by slight pressure on the ZnSe crystal.

in the study of outer skin layers, i.e., the stratum corneum and the viable epidermis.The in vivo Raman signal of the dermis is strongly reduced due to scattering in theepidermis; therefore, it requires considerably longer signal collection times thanfor the epidermis. However, because the dermis is much thicker than the epidermis(1–4 mm thick), it can easily be studied by using a nonconfocal detection schemewith a detection volume that is large compared to the thickness of the epidermis.In this case, the dermis will be the dominant source of the Raman signal, whichis illustrated by Fig. 5.13.1168 The figure shows confocal and nonconfocal spectrameasured by using a confocal spectrometer and a fiber-optic probe, respectively.Both spectra were scaled to equal intensity. It is clear that the spectrum obtainedwith the fiber-optic probe is almost entirely determined by the Raman signal ofthe dermis. For an equal signal collection time, the SNR of the dermis spectrumobtained with the fiber-optic probe is considerably higher than that of the spectrumthat was measured confocally.1168

Near-infrared Raman spectroscopy also features many advantages for in vivodetection of cervical tissue pathologies, particularly precancer predictions.30, 1169

Surface-enhanced Raman scattering (SERS) is based on a strong increase inRaman signals from molecules, if those molecules are attached to submicron metal-lic structures or nanoparticles.1163, 1173–1175 Two effects are believed to contribute



Figure 5.13 In vivo Raman spectra of the dermis, as obtained by confocal detection andby nonconfocal detection (fiber-optic probe). Experimental conditions for the confocal spec-trum and the nonconfocal spectrum: signal collection time 2 min, laser power 100 mW. Thespectra are scaled to equal intensity.1168

to SERS enhancement mechanisms: electromagnetic and chemical effects.1163, 1173

For a smooth metal surface, there is only a small (on the order of 10 times or less)enhancement of Raman intensity, compared with that in the absence of the surface;however, for a rough surface, due to excitation of electromagnetic resonances bythe incident radiation, a few orders of enhancement may be observed. These res-onances appear owing to the collective excitation of conduction electrons in thesmall metallic structures; they are also called surface plasmon resonances. Boththe excitation and Raman-scattered fields contribute to this enhancement; thus, theSERS signal is proportional to the fourth power of the field enhancement factor.1173

The surface-roughening effect can be achieved by isolated metal particles,gratings, assemblies of particles on surfaces, and randomly roughened sur-faces.1173–1175 All of these structures provide enhancement if the metal involved hasnarrow plasmon resonances at convenient frequencies for Raman measurements.The chemical mechanisms include enhancements that arise from interactionsbetween molecule and metal. The most commonly considered interaction thatrequires overlap between molecular and metal wave numbers occurs when thecharge transfer between the surface and molecule leads to the formation ofexcited states, which serve as resonant intermediates in Raman scattering.1163, 1173

Interactions that do not require overlap between molecular and metal wave num-bers arise from electromagnetic coupling between the vibrating molecule and themetal. These interactions can occur either at vibrational or optical frequencies. Thecombined enhancement factors can be as high as 1014, which is sufficient to observeSERS spectra from single molecules.


Chapter 6

Tissue Phantoms

This chapter describes the structure, manufacturing technology, and characteristicsof tissue phantoms used to test the methods and devices for optical diagnostics anddosimetry of laser and other optical radiation in a course of phototherapy.

6.1 Introduction

Phantoms that model the transport of visible and infrared light in tissue are neededto evaluate techniques, calibrate equipment, optimize diagnostic and therapeuticprocedures, and assure quality.31, 46, 47, 93–95, 197, 313, 314, 330, 333, 334, 389, 403, 410, 467–469, 545,

767, 840, 864, 867, 868, 870, 884, 889, 992, 993, 997, 998, 1191–1238 Optical medical devices for imag-ing, diagnosis, and therapy, as well as all other medical equipment and technolo-gies, should undergo a full cycle of research and development: from basic researchto practical application in clinical settings (Fig. 6.1).1209 The development of opti-cal medical technology at all stages, from designing the concept to obtainingthe necessary parameters, requires calibration and verification of designed toolsand techniques. Optical medical devices should be completed by tissue phantomsfor testing and optimization of device hardware and software, and a variety ofapplications; for training users to work on the equipment; and for providing com-parability of measurement data obtained with different hardware and in differentlaboratories.1219, 1220

Figure 6.1 Translational research map of medical devices from the basic research state topractical application in clinical settings (see Ref. 1209).

231


232 Chapter 6

6.2 Concepts of Phantom Construction

To describe the concepts of phantom construction, we will draw upon Refs. 1193–1195 and 1197. Phantoms consist of a scattering medium, an absorbing medium,a diluent, and in some cases, fluorophores.1193, 1194, 1197 Some common scatteringmedia are Intralipid, Nutralipid, or Liposyn. These intravenously administerednutrients are fat emulsions that contain soybean oil, egg phospholipids, and glyc-erol. Other common scatterers are milk or micron-sized latex (polystyrene) spheres.Polystyrene microspheres exhibit low fluorescence, and some of their optical prop-erties can be calculated from Mie theory. Absorbing media include black India inkor/and some biological dyes, such as trypan blue, EB, ICG, MB, and Photofrin II.The diluent is usually deionized water, although isotonic phosphate-buffered salinehas been used.

An optical phantom is developed by mixing the correct proportions of scat-tering and absorbing media in the diluent, so that the resulting suspension has thedesired intrinsic optical properties of the simulated tissue. These optical proper-ties include the absorption coefficient, μa, the scattering coefficient, μs, and theanisotropy factor, g. For soft tissues, typical optical properties are μa ≈ 0.5 to5.0 cm−1, μs ≈ 0.2 to 400 cm−1, and g = 0.9 for visible and NIR wavelengths(see Table 7.1).

A liquid phantom system is very easy to prepare; however, it cannot beused to make samples of realistic complexity. Solid phantom samples have beenmade by using either transparent hosts, like polymers, silicone, or gelatin; orinherently light-scattering materials, such as wax. Polymer-based phantoms havebeen reported to crack if they are too large, or to shrink during polymerization,which limit their applicability. Gels contain a solvent that evaporates, changing thedimensions and optical properties of the sample within a short period.

Steps toward realistic complex geometries have included layered samples,inserted inhomogeneities, and phantoms mimicking whole organs46, 47, 93–95, 330,

333, 334, 403, 410, 1193–1197 Certain phantom systems have realistic optical propertiesover a wide wavelength range.47, 94, 95, 333, 334 When the task is to model tissue, oreven a whole organ, with complex architecture, or to prepare the test object forevaluation of imaging techniques, the macroscopic geometry of the natural objectshould be reproduced in phantom. Some of the most commonly encountered fea-tures are layered tissue structures. Multilayered phantoms have been developed inthe past to mimic, for example, skin,870 human head,466, 1207 or cervix.1201–1203

A realistic tissue phantom should satisfy the following requirements:1193, 1194

(1) it should model the geometrical and optical parameters of the physiologicalstructures that are relevant for the transport of light; (2) all components must becompatible with each other regarding chemical stability and spectroscopic proper-ties; (3) the relevant parameters of radiation transport must be both reproducibleand predictable from the sample composition; (4) the physical parameters ofthe phantom sample should be temporally stable (evaporation, diffusion, aging)and independent of environmental influence; (5) the phantom should allow for


Tissue Phantoms 233

construction of inhomogeneous samples by stacking phantom slabs or by elabo-rating molding techniques; and (6) sample preparation should be simple, quick,and safe.

The strategy for systematic design of tissue phantom systems showing real-istic optical properties over a broad wavelength range is based on the discreteparticle model of tissue,1193, 1194 which corresponds to the fundamental conceptof describing the optical properties of tissues in the framework of a discrete model(see Chapter 3).

Light scattering and absorption of particles composing tissue (phantom) arecalculated by Mie theory. The relevant parameters are the size (radius a) and shapeof particles, their complex refractive index, ns(λ0), and the refractive index of thedielectric host (ground material), n0(λ0),

ns,0(λ0) = n′s,0(λ0) + in′′

s,0(λ0), (6.1)

or the relative refractive index of the scatterers and the ground materials, m =ns/n0; λ0 is the wavelength in vacuum. The imaginary part of the complexrefractive index of scatterer material is responsible for light losses attributable toabsorption. Mie theory yields the absorption and scattering efficiencies and thephase function from which the absorption and scattering coefficients, μs = ρσsca

and μa = ρσabs, and the scattering anisotropy factor, g, are calculated; ρ is the den-sity of scatterers (particles). In the framework of Mie theory, the expressions forscattering and absorption cross sections and scattering anisotropy are presented byEqs. (3.53)–(3.55).

The introduction of the specific scattering and absorption coefficients extrapo-lated to a volume fraction of 100% is useful for describing scattering and absorp-tion properties of the medium under construction.1193, 1194 In this case and whenthe particles are sufficiently diluted to prevent dependent scattering, the scat-tering, transport scattering, and absorption coefficients are proportional to thedimensionless volume fraction of scatterers, cs:

μs = csσsca,μ′s = csσsca[1 − g(λ0, a)],μa = csσabs, (6.2)

where the specific scattering and absorption coefficients, σsca and σabs, areexpressed in cm−1. The optical parameters of broad-banded particle size distri-butions are values averaged over the distribution weighted by the volume fractionsof particles with different diameters. The relative frequencies of the correspondingparticle size are determined from images made with an electron microscope. Theresulting specific optical coefficients are the averaged values and can be definedanalogously to Eqs. (3.24)–(3.27). The mean distance, ds, between the centers ofgravity of the particles is determined by their radius, a, and volume fraction, cs,

ds = 2a/ 3√

cs. (6.3)

Mie theory predicts that scattering introduced by spherical micrometer-sizedparticles is strongest if the particle radius and wavelength are of the same order


234 Chapter 6

Figure 6.2 Design of tissue phantom. Scattering properties of nonabsorbing particles ata wavelength of 633 nm are calculated by Mie theory.1193,1194 The transport scatteringcoefficient (a) strongly depends on both the particle size and relative refractive index. Thisgraph is approximately symmetric. The axis of symmetry is at n′

s/n0 = 1. Although thetransparent scattering coefficient equals zero at this point, the scattering anisotropy factoris maximal (b). In some parts of the range shown, the functions are not monotonous, butrapidly oscillating.

of magnitude. Mie theory is strictly only applicable to particles of particular reg-ular shapes, but the results are still useful if the shape is irregular. The oscillatorystructure of the scattering coefficient and anisotropy factor as a function of parti-cle size, which is observed with spherical particles (Fig. 6.2), is averaged out.214

The transport scattering coefficient, μ′s, increases strongly with the ratio n′

s/n0.In turn, the scattering anisotropy factor is maximal when this ratio approaches 1(Fig. 6.2). A tradeoff is necessary between maximizing the scattering (to pre-vent dependent scattering) and optimizing the scattering anisotropy factor whenconstructing certain phantoms.

For the matched refractive indices of scatterers and background material, thescattering coefficient goes to zero, which means that only absorption is responsiblefor the light beam extinction [see Eq. (1.1)]. However, it follows from Mie theorythat absorbing particles suspended in an index-matched medium causes stronglyforward-directed resonance scattering. Light absorption by such particles is smallerthan expected from their bulk absorption coefficient.1193, 1194 For 1-μm diameterparticles with ns = 1.6 and a bulk absorption coefficient of their material equal to104 cm−1 in an index-matched medium, μa = cs × 4120 cm−1.

The wavelength dependencies of scattering parameters are shown in Fig. 6.3.The spectral variation of the relative index has been neglected in calculations, butmay be relevant in practice. If particle size and ratio of refractive indices are fixed,the wavelength dependencies are caused by spectral variation of the ratio of particlesize and wavelength. For particles with a similar refractive index to that of thehost (see Fig. 6.3), the scattering coefficient of the particle system with a diameterof particles smaller than the wavelength decreases with wavelength, whereas that


Tissue Phantoms 235

Figure 6.3 Design of a tissue phantom. Wavelength dependencies of scattering by non-absorbing particles at n′

s/n0 = 1.07 are calculated by Mie theory (see Refs. 1193 and1194). Specific transport scattering coefficient (a) of particles smaller than the wavelengthincreases strongly toward shorter wavelengths. Particles with diameter larger than thewavelength have an almost constant specific transport scattering coefficient over the visiblespectral range. The scattering anisotropy factor (b) scarcely depends on the wavelength,but very much on the particle size.

of the system with a diameter of particles larger than the wavelength is almostconstant. The scattering anisotropy factor depends less on the wavelength. Thereare plateaus if the particles are much smaller (isotropic scattering) or larger (highlyanisotropic scattering) than the wavelength, with a steep increase between the two.

Biological tissue shows increased scattering toward shorter wavelengths andhigh scattering anisotropy. These cannot be realized by using monodisperse parti-cles. Therefore, a mixture of large particles contributing high scattering anisotropyand small particles with increased scattering toward a shorter wavelength shouldbe an accurate approximation for elaborating a tissue-like phantom.271, 1193, 1194

Phantoms can be designed not only on the basis of artificial ingredients, butwhen solving a number of specific problems, phantoms also serve as engineered tis-sues, ex vivo samples of tissues,1208 or in vivo animal tissues after a special surgerysimulating a particular pathology.1223

6.3 Examples of Designed Tissue Phantoms

Optical phantoms at 1064 nm on the basis of Intralipid and India ink mixtures havebeen developed by using the preliminary experimentally determined absorptioncoefficient, scattering coefficient, and anisotropy factor of the components.1195 Forevaluation of the optical parameters of phantom components and phantoms them-selves, the integrating sphere technique was used, together with collimated lighttransmission measurements and the inverse adding-doubling (IAD) algorithm. The


236 Chapter 6

Table 6.1 Average optical properties dependent on concentration of India ink, 10%Intralipid, and water at 1064 nm (see Ref. 1195).a

Scattering media μs/%, cm−1/% μa/%, cm−1/% g

India ink 4.64 ± 2.07 35.99 ± 4.28 0.30 ± 0.18Intralipid 1.30 ± 0.047 0.054 ± 0.02 0.50 ± 0.02Water − 0.0018 −aAbsorption results of Intralipid are corrected for water absorption.

Table 6.2 Predicted and measured optical properties of phantoms (see Ref. 1195).a

Phantoms μs, cm−1 μa, cm−1 g

Phantom 1 (Intralipid and India ink)Predicted 8.82 0.32 0.48Measured 9.69 ± 0.22 0.76 ± 0.01 0.56 ± 0.00Calculated 8.75 0.89 0.50

Phantom 2 (Intralipid only)Predicted 8.82 0.00 0.48Measured 8.84 ± 0.03 0.33 ± 0.01 0.51 ± 0.00Calculated 8.70 0.53 0.50

aPredicted values for phantoms 1 and 2 assume that Intralipid and water do not absorb and that ink does notscatter 1064-nm light. Calculated values were determined from the concentration values in Table 6.1.

Table 6.3 Predicted and measured optical properties of phantoms (804-nm diameterpolystyrene sphere and water suspensions) at 1064 nm (see Ref. 1195).a

Phantoms μs, cm−1 μa, cm−1 g

Phantom 1Predicted 2.23 − 0.807Measured 1.99 ± 0.12 0.28 ± 0.02 0.775 ± 0.04

Phantom 2Predicted 2.96 − 0.807Measured 3.15 ± 0.01 0.25 ± 0.01 0.811 ± 0.004

aPredicted values for phantoms 1 and 2 were calculated using Mie theory. Absorption coefficients were notcorrected for water absorption.

average optical properties from all data for the phantom components are listed inTable 6.1. A comparison of the predicted, measured, and calculated optical proper-ties of the two phantoms is listed in Table 6.2. Table 6.3 presents the predicted (Mietheory) and measured (IAD algorithm) data for two phantoms (804-nm diameterpolystyrene sphere and water suspensions).

These data all clearly show that liquid phantom systems allow the designof controlled tissue-like phantoms, and their optical properties on at least onewavelength are accurately predicted theoretically. In particular, by knowing thedependence of scattering and absorption of India ink and Intralipid, a phantomwith predicted optical properties can be constructed. However, the final optical


Tissue Phantoms 237

properties of the constructed phantom should be measured for an accurate deter-mination of its optical parameters. Unfortunately, the scattering properties ofdiluted Intralipid correspond to those of tissues that have a relatively low scat-tering anisotropy factor, g ∼= 0.56. A more realistic value of anisotropy factor canbe obtained by water suspensions of polystyrene spheres with a diameter similarto the wavelength. A comparison of the constructed phantom’s optical propertiesat 1064 nm with the corresponding optical parameters of human tissues, presentedin Table 7.1, shows that the absorption properties of these phantoms are accuratelymatched to many tissues, but the scattering properties are much lower than fortissues.

To verify the validity of analyzing the optical properties of human skin by usingin vivo reflectance measurements, liquid phantoms consisting of Intralipid-10% asa scatterer and EB as an absorber in phosphate-buffered saline were applied.767

Concentrations of Intralipid-10% in the range 10–50% and EB up to 0.01 g/Lwere used. In an ex vivo study of human skin in the NIR range, phantoms com-posed of aqueous solutions of 1.27-μm polystyrene microspheres and infrared dye(S109564 Zeneca) were used.333, 334 The accuracy and limitations of the exper-imental system for spatially resolved absolute diffuse reflectance measurementswere tested by using tissue-simulating phantoms that consisted of Liposyn-20%stock solution and trypan blue dye as the absorber.46, 93 For a 1% volume concen-tration of Liposyn (without trypan blue) at 633 nm μ′

s = 14.0 ± 0.5 cm−1, g = 0.8,and μa = 0.005 cm−1 were found.

Comparing the experimental results for absorption length, transport length,and anisotropy factor against wavelength obtained for a 2% Intralipid-10%stock solution with Mie theory, it was found that one can use the followingapproximations:31, 92

μ′s (λ) ≈ 1.6 · 103λ−1(cm−1),

g (λ) ≈ 1.1 − 0.58 · 10−3λ, (6.4)

for wavelengths from 400 to 1100 nm. To obtain a solution with μ′s = 76.9 cm−1

and μ′s = 10 cm−1 at 550 nm, the stock solution of Intralipid-10% was diluted to

1:2 and 1:15, respectively.31, 92

Sometimes, when constructing phantoms with precise optical properties in awide range of wavelengths, the dependencies of the refractive indices of thesephantoms’ components should be included. For example, for water-polystyrenesuspension phantoms, to include the wavelength dependence of the refractiveindices of water and polystyrene particles, the dispersion functions for water (w)and polystyrene (p) valid in the visible and NIR should be as follows:1191

nw (λ)=1.31848 + 6.662

λ[nm] − 129.2∼= 1.3199 + 6878

λ2− 1.132 · 109

λ4+ 1.11 · 1014

λ6,

(6.5)

np = 1.5626 + 11690/λ2 − 1.125 × 109/λ4 + 1.72 × 1014/λ6, (6.6)

where λ is in nanometers.


238 Chapter 6

To study laser-induced stress transients in a nonscattering, homogeneouslyabsorbing liquid, where a theoretical description of optoacoustic phenomenais straightforward, an aqueous solution of potassium chromate (K2CrO4) wasused.840, 884 This solution does not fluoresce; therefore, the total absorbed laserenergy is converted into heat; it is photochemically stable, and its optical prop-erties are not altered, even at high laser fluences. A solution of 35 mg of K2CrO4

per cubic centimeter yields an absorption coefficient of ∼1000 cm−1 at 355 nm.Dilution of the initial solution allows one to control the light penetration depth, andtherefore, the acoustic frequency of laser-induced stress waves.840

Laser-induced stress generation, propagation, and detection in tissues can beaccurately modeled with the help of turbid absorbing gels.840 A warm watersolution (90 cm3) was mixed with 10 g of gelatin powder to prepare gel phan-toms. These gels were colored with potassium chromate and made turbid withpolystyrene microspheres (0.9 μm in diameter). A 10% polystyrene sphere solu-tion has μs = 6090 cm−1 and g = 0.918 at 355 nm, yielding a reduced scatteringcoefficient, μ′

s = 499 cm−1; the absorption coefficient at 355 nm is defined bythe concentration of K2CrO4 and can very high, up to 1000 cm−1. However, thespectral range of importance for biomedical optics is from visible to NIR, inwhich diagnostics, imaging, and photodynamic therapy treatments are performed.Therefore, the polystyrene sphere concentration can be chosen as approximately2% in the experimental gels, which yields μ′

s = 99 cm−1. A typical μ′s/μa ratio

for tissues at 600–1000-nm wavelengths is from 70 to 100, which can easily berealized for such phantoms. Soft elastic collagen gel phantoms can be preparedby using milk as a scatterer and colored with hemoglobin or even whole blood.These allow for easy embedding of inclusions modeling various pathology states(for instance, an absorbing sphere simulating a tumor) or modeling the specificityof tissue structure (for instance, a vessel network).

Adding a small percentage of agarose to solidify the well-characterized andeasily available water solutions of Intralipid and India ink is a satisfactory alterna-tive for more complicated solid phantoms.410 Solutions of such phantoms consistof 1% agarose in distilled water, with Intralipid and black India ink added. Theagarose produces a gelatin that can easily be manufactured to create and embed aninclusion. In addition, gelatin (collagen) gel phantoms with different optical prop-erties can be stacked to yield a layered-tissue structure model.403, 1201–1203 TiO2

particles can be used as scatterers, and India ink can be used as an absorber inconstructing gelatin (collagen) gel phantoms.

TiO2 particles, 0.3 μm in diameter, and Pro-Jet 900NP dye (Zeneca) were usedas scatterers and absorber in solid phantoms composed of Araldite epoxy resin(Ciba Polymers).333, 334 These phantoms also allow optical properties to be com-bined by stacking slabs with different optical parameters. As a homogeneous solidscattering phantom for the calibration of a microspectrophotometric optical sys-tem, a composite consisting of highly dispersed SiO2 particles (diameter, <10 μm;volume-filling fraction, 43%) in an organic methacrylate matrix was used.389

Temporally stable samples were made from a phantom system based on poly-organosiloxane (POS, silicone) for a host, which has been described in detail


Tissue Phantoms 239

Table 6.4 Relative refractive indices of substances with negligibleabsorption in the visible spectral range (see Refs. 1193 and 1194).a

Substance In aqueous gel In POS

SiO2 1.10 1.04γ-Al2O3 1.20 1.14BaSO4 1.23 1.17MgO 1.31 1.24α-Al2O3 1.33 1.26TiO2 1.95 1.86

aRelative refractive index is given for aqueous gel (n0 = 1.33) and POS (n0 = 1.40 at589 nm) for a host. The particles are assumed to be massive.

elsewhere.1193, 1194 Highly hydrophobic POS is supplied in monomeric form as atwo-component system. It is especially suited to the modeling of fine structures.When a crosslinking component is added, POS starts to polymerize in an addi-tional reaction; it typically takes less than 30 min at 80◦C in a drying oven. Thereis no shrinking or cracking. Particles as small as 40 nm in diameter are immobilizedin the rubber meshwork. The resulting rubber is mechanically stable and transpar-ent in the visible range. Its refractive index equals 1.40 at 589 nm. This methodof phantom preparation allows one to construct multilayer phantoms with stepwisevarying optical properties with no gap between homogeneous layers, and to includefine tissue details like structured surfaces and tiny holes, tissue surfaces, and bloodvessels. Various types of particles can be used to induce scattering. Some, withnegligible absorption in the visible spectral region, are presented in Table 6.4. Thistable illustrates the range of values for the relative refractive indices that can beprovided in two phantom systems under consideration.

To achieve homogeneous dispersion, particles should be dispersed in a hostmedia by an ultra-centrifuge. The authors of Refs. 1193 and 1194 used spheri-cal porous aluminum oxide, iron, and modified amino resin (MAR) particles toobtain appropriate scattering. Certain data are presented in Table 6.5 that allowcomparison between the optical properties predicted by Mie theory, taking intoaccount the optical properties of isolated particles and their size distributions, andthe optical properties of POS phantoms measured by using the integrating spheretechnique. These phantoms were designed for modeling the fluorescence of tissuecomponents, particularly protoporphyrin IX fluorescence.

Tissue phantoms have been used in all fields of optical diagnostics, particularlyfor testing instruments for time-, frequency- and spatial-domain tomographyand spectroscopy,410, 545, 1216, 1218–1220, 1230 spatially resolved reflectance measure-ments,46, 93, 1198, 1199, 1215, 1219, 1237 and hyperspectral imaging,1222, 1223 includingusage of multicolor phantoms;1224 for evaluating the fluorescence spectroscopictechnique;1193, 1194, 1197, 1201–1203 and for experimentally testing theoretical predic-tions.47, 94, 95, 313, 314, 1195, 1197, 1211, 1212 Tissue models have been developed for tissuenoninvasive glucose monitoring,467–469, 992, 993, 997–999, 1191, 1192, 1196, 1235 oxygena-tion monitoring and oxymetry,889, 1204, 1219 optoacoustics,840, 884, 887, 889, 992, 993, 997, 998

pulsed photothermal measurements,864, 868, 870 measuring of polarization degree


240 Chapter 6

Table 6.5 Comparison of the results of integrating sphere measurements and Mie calcula-tion based on isolated characterization (see Refs. 1193 and 1194).a

Wavelength, nm Method Porous aluminum oxide particles Iron particles

σsca, cm−1 σabs, cm−1 σsca, cm−1 σabs, cm−1

546 Mie theory 210 (50)b − 3000 (600)d 4500 (900)d

546 Measured 200 (10)c <0.7 3500 (900)b 3800 (200)b

633 Mie theory 210 (50)b − 3000 (600)d 4500 (900)d

633 Measured 190 (10)c <0.7 2800 (800)b 3900 (200)b

aThe assumption was that the pores of the particles are completely filled with POS and the average refractiveindex of particles was estimated. Spherical porous aluminum oxide particles have a symmetrical size distribution,with mean value of 5.3 ± 1.0 μm, and spherical iron particles have an asymmetrical size distribution: 16% of thevolume fraction is contributed by particles of diameter up to 2.0 μm, 50% by particles up to 3.0 μm, and 84% byparticles up to 3.6 μm.Errors are given in parentheses in units of the last digit(s) and are:bUpper limit error caused by uncertain refractive index (particle composition).cSum of error of measurement, limited reproducibility of sample production, error of sample thickness, andsystematic error of diffusion theory.dVariations of reported values.

decay,586, 1205 and calibration of reflective confocal microscope1225 and opticalcoherence tomography systems.1226–1229, 1234, 1235 The effectiveness of optical clear-ing agents can be verified with liquid phantoms.1231, 1232 A special class ofphantoms, designated dynamic phantoms, generally combines a complex struc-ture, representing the vascular system of tissue, and the possibility of pumpingof a liquid simulating blood or whole blood through this artificial capillary net-work.1233–1236 Dynamic phantoms are often built on the basis of microfluidic devicetechnology1233, 1236 and used for the calibration of instruments for blood flow veloc-ity measurement and imaging including speckle and Doppler systems.1233–1236

Another type of dynamic phantom accounts for differences in the absorption ofhemoglobin in the superficial and deep layers of tissue, and can simulate the activ-ity of the brain and other systemic changes.1237 Available phantoms have beendeveloped to calibrate the Raman signals from different types of tissues.1189, 1235

Tissue-like phantoms have also been used in areas of research connected withtherapeutic implementation of optical radiation, including light dosimetry,1206 laserablation,884 and photodynamic therapy (PDT).1200, 1206

A complete review on tissue phantom studies conducted prior to 2006 is givenin Ref. 1208. In this overview, tissue-like phantom composition and properties areoutlined, and different materials for matrix, scattering provision, and absorbingproperties are presented with discussion of the benefits and weaknesses in eachcategory. Matrix materials are typically water, gelatin, agar, polyester or epoxy andpolyurethane resin, room-temperature vulcanizing (RTV) silicone, or polyvinylalcohol gels. The water and hydrogel materials provide a soft medium that is bio-logically and biochemically compatible with the addition of organic molecules,and are optimal for scientific laboratory studies. Polyester, polyurethane, and sil-icone phantoms are essentially permanent matrix compositions that are suitable


Tissue Phantoms 241

for routine calibration and testing of established systems. The most commonmaterials providing scattering were presented as: (1) lipid-based emulsions, (2)titanium or aluminum oxide powders, and (3) polymer microspheres. Thesedescribed absorbers varied widely from biological, such as hemoglobin or pig-mented cells, to more stable absorbers, such as molecular dyes and India ink.In this review, one can find the optimal recipes of phantoms for the specificapplications.

In Ref. 1225, the testing procedure for a laser scanning confocal microscopeoperating in reflection mode at 488 nm is described in detail. This procedureincluded the three types of optical phantoms: (1) polystyrene microspheres of 100nm in diameter in gel with 2% volume fraction of the particles, (2) solid phan-toms based on polyurethane (INO Biomimic), and (3) the well-known standardsof reflection (Spectralon). By measuring exponentially decaying reflectance as onemoves the focus (zf) deep into phantom material, the scattering coefficient, μs, andscattering anisotropy factor, g, of phantoms were determined. The results show thatchanges in μs and g-factor were in the limits of 58, 8−24, and 130−200 cm−1

and 0.112, 0.53−0.67, and 0.003−0.26 for the phantoms of types 1, 2, and 3,respectively.

An overview of research on the development of phantoms for OCT, simulatingthe optical, mechanical, and structural properties of a number of tissues, is givenin Ref. 1226. These phantoms are an important element in the further developmentand application of OCT. The authors focused on the analysis of phantoms based onsilicone, fibrin, and cryogels of polyvinyl alcohol (PVA-C) as the most promisingmaterials for solid phantoms, with possibly the most accurate reproduction of theproperties of biological tissues.

In Ref. 1227, the design and characteristics of optical phantoms based on sil-icone elastomer are described. Appropriate absorption was achieved by addinggreen dye and scattering by the addition of TiO2 or SiO2. In the absence ofabsorbers, OCT measurements demonstrate a linear dependence of the attenuationcoefficient on the concentration of scatterers. In the absence of scatterers, opticaltransmission spectroscopy also shows linear dependence of the absorption coef-ficient on the dye concentration. Both types of phantom samples were stable for6 months. Phantom studies using confocal microscopy showed a uniform distri-bution of scatterers in the samples, although with some clustering. The use of thin(50 μm) layers of phantom material allowed the authors to construct complex phan-toms with flow channels, wavy interfaces (model of papillary layer of the skin),and layered and curved phantoms simulating the human retina. The authors alsodemonstrated the possibility of inclusion of gold nanoparticles in the phantoms,which is important, for example, to calibrate optical devices and techniques fordiagnosis of precancer conditions.

Optical properties of quantum dots (QDs) in the form of individual particlesand clusters in the application to the development of new types of optical molec-ular imaging phantoms, including the calibration of the luminescence lifetime, aredescribed in detail in Ref. 1238.


242 Chapter 6

6.4 Examples of Whole Organ Models

Models of whole organs are described in the literature.466, 1197, 1207 For example,human skin was modeled by a film (50 to 150 μm) of hydrated type I colla-gen.867, 868 This film contained variable amounts of subsurface absorbers positionedat a given depth and simulated discrete chromophores buried in multilayered com-posite human skin. The chromophores were constructed by staining a film withtriphenylmethane dye, which absorbs optimally at 585 nm. Discrete chromophoreswere prepared by cutting a stained collagen film (125 μm thick) with known opti-cal absorption (μa = 400 cm−1) into several thin strips (100 to 300 μm width).A model skin phantom was constructed by positioning variably spaced (50 to700 μm) absorbing thin strips underneath nonabsorbing collagen film with knownthickness (110 μm). The absorbing thin strips and nonabsorbing films were posi-tioned on a 10-mm thick collagen sponge to simulate an infinite half-space as inliving skin.

Another example of whole organ modeling consists of models of the adulthead.330, 466, 1207 The models330 consists of three- or four-layered slabs, the lat-ter incorporating a clear cerebrospinal fluid (CSF) layer. The most sophisticatedmodel also incorporates slots that imitate sulci on the brain surface. Using thesemodels, it was shown that light propagation in the adult head is highly affected bythe presence of the clear CSF layer, and that both the optical path length and thespatial sensitivity profile of the models with a CSF layer are quite different fromthose without the CSF layer. However, the geometry of the sulci and the bound-ary between the gray and the white matter have little effect on the detected lightdistribution.

A phantom with embedded nanoparticles, which has been built into a commer-cially available artificial model of the eye to characterize the image point spreadfunction of the retina in three dimensions under real conditions using OCT imagingdevices was designed, manufactured, and tested.1229 A phantom was constructedby using a transparent cured epoxy resin with dispersed therein rare silica-goldnanoshells with a strong backscattering.

6.5 Summary

Tissue phantoms are beneficial for testing theoretical predictions and hardware ofdifferent optical methods, including time-, frequency- and spatial-domain diffusetissue tomography and spectroscopy, spatially resolved reflectance measurements,hyperspectral imaging, and fluorescence spectroscopy/imaging.

Phantom-based testing procedures are also developed for laser scanning con-focal microscopy and OCT. Some phantoms are multifunctional by simulatingthe optical, mechanical, and structural properties of tissues. The multifunction-ality of phantoms is a key feature for the further development and applicationof OCT, confocal microscopy, photoacoustic, and photothermal techniques, andpolarization-sensitive and other optical methods.


Tissue Phantoms 243

Tissue phantom composition, technology for production, living time, and manyproperties and their stability are of great importance for particular biomedicalapplications and cost. Phantom matrix materials are water, gelatin, agar, polyvinylalcohol gels, fibrin, polyester, epoxy, polyurethane, and silicone. Water and hydro-gel materials provide a soft biocompatible phantom medium that is optimal forresearch. Polyester, epoxy, polyurethane, and silicone phantoms are essentiallylong-lived stable compositions that are suitable for routine calibration and test-ing of optical systems. The most common materials used to provide scatteringare lipid-based emulsions, TiO2, SiO2, or aluminum oxide nano/micropowders,and polymer microspheres. To achieve appropriate absorption, different biologicalmaterials (hemoglobin and pigmented cells, for example) to more stable moleculardyes and India ink are used.

Some dynamic phantoms combine a complex structure, presenting tissueground matter, the vascular system, and liquid simulating blood or whole bloodpumped through the artificial capillary network. These phantoms can be used forthe calibration of instruments measuring/imaging blood flow velocity, and for sim-ulation of brain activity and other systemic changes associated with blood flow andblood oxygenation alterations. The effectiveness of optical clearing agents can beverified with liquid and solid pore phantoms.

One prospective direction of phantom designing is the development of phan-toms to calibrate Raman and fluorescence signals, including nonlinear phenomena,such as coherent anti-Stokes Raman scattering (CARS), two-photon fluorescence,and second harmonic generation (SHG). Rapidly developing terahertz diagnostictechnologies also require adequate tissue phantoms.

Optical molecular imaging phantoms based on QDs, allowing for calibration ofthe luminescence lifetime and other properties of QD luminescence in tissue-likeenvironments, are of great importance.

The inclusion of plasmonic gold nanoparticles, or other metal and oxidenanoparticles in tissue phantoms, is useful to calibrate optical devices and tech-niques for diagnosis of precancer and laser theranostic technologies.

In general, therapeutic implementation of optical radiation, including lightdosimetry, laser ablation, and photothermal and photodynamic therapy, should bebeneficial when using high-quality tissue phantoms.


Chapter 7

Methods and Algorithms forMeasurement of the OpticalParameters of Tissues

Methods and algorithms for solving the inverse problem of finding tissue and bloodoptical parameters, such as absorption and scattering coefficients, anisotropy factor,and refractive index, are presented. Advantages and drawbacks of these methodsare analyzed. Widespread measuring techniques are reviewed, including integrat-ing sphere; spatially, time, and angularly resolved; and OCT; as well as inversemethods, such as Kubelka–Munk, multiflux, adding-doubling, and inverse MonteCarlo. Exhaustive data are presented on optical properties of human tissue andblood measured in vitro, ex vivo, and in vivo.

7.1 Basic Principles

Methods for determining the optical parameters of tissues can be dividedinto two large groups: direct and indirect methods.1–4, 9–16, 29, 32, 33, 37, 38, 40, 46,

48, 49, 56, 72, 87–90, 98, 129, 130, 197, 230, 271, 274, 306, 315, 316, 320–322, 328–330, 333–335, 345, 383, 389, 495, 581,

767–769, 1239–1322 Direct methods include those based on certain fundamental con-cepts and rules, such as the Bouguer–Beer–Lambert law [see Eq. (1.1)], thesingle-scattering phase function [see Eqs. (1.13) and (1.15)] for thin samples,or the effective light penetration depth for slabs. The measured parameters arethe collimated light transmission, Tc, and the scattering indicatrix, I(θ) (angulardependence of the scattered light intensity, W/cm2sr), for thin samples or thefluence rate inside a slab. The normalized scattering indicatrix is equal to thescattering phase function I(θ)/I(0) ≡ p(θ), 1/sr. These methods are advantageousin that they use very simple analytic expressions for data processing. Their disad-vantages are related to the necessity of strictly fulfilling experimental conditionsdictated by the selected model (single scattering in thin samples, or exclusion ofthe effects of light polarization and refraction at cuvette edges); in the case of slabswith multiple scattering, the recording detector (usually a fiber light guide with an

245


246 Chapter 7

isotropically scattering ball at the tip end) must be placed far from both the lightsource and the medium boundaries.

Indirect methods obtain the solution of the inverse scattering problem by usinga theoretical model of light propagation in a medium. These, in turn, are dividedinto iterative and noniterative models. The former use equations in which theoptical properties are defined through parameters directly related to the quantitiesbeing evaluated. The latter are based on the two-flux Kubelka–Munk model andmultiflux models.40, 46, 56, 93, 275, 284, 306, 383, 1251, 1264 In indirect iterative methods,the optical properties are implicitly defined through measured parameters.Quantities determining the optical properties of a scattering medium are enumer-ated until the estimated and measured values for reflectance and transmittancecoincide with the desired accuracy. These methods are cumbersome, but theoptical models currently in use may be even more complicated than those under-lying noniterative methods (examples include the diffusion theory,40, 275, 290–295

IAD,372, 392, 393, 1206, 1242, 1257, 1265–1267, 1316–1318 and IMC306, 320, 333–335, 339, 341, 344, 370,

372, 383, 389, 390, 581, 723, 1240, 1245, 1246, 1252, 1255, 1268, 1274, 1277, 1278, 1308, 1309, 1316–1318

methods).The optical parameters of tissue samples (μa, μs, and g) are measured by

different methods. In vitro evaluation is most often achieved by the double inte-grating sphere method combined with collimated transmittance measurements (seeFig. 7.1 and Table 7.1). This approach implies either sequential or simultaneousdetermination of three parameters: collimated transmittance, Tc = I(d)/I(0) [seeEq. (1.1)], total transmittance, Tt = Tc + Td (Td being diffuse transmittance), anddiffuse reflectance, Rd. The optical parameters of the tissue are deduced from these

Figure 7.1 Measurement of collimated (a) and total transmittance (b), and diffusereflectance using an integrating sphere. The integrating surface of the sphere is coatedwith BaSO4, MgO, or Spectralon, which have nearly 100% diffuse remittance over the entireoptical spectrum, including NIR (see Ref. 6 and 57).


Methods and Algorithms for Measurement of the Optical Parameters of Tissues 247

Tab

le7.

1O

ptic

alpr

oper

ties

ofhu

man

tissu

esm

easu

red

invi

tro,

exvi

vo,

and

invi

vo(r

ms

valu

esar

egi

ven

inpa

rent

hese

s;n

isth

enu

mbe

rof

sam

ples

).

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Invi

tro

mea

sure

men

tsA

orta

:N

orm

alN

orm

alco

agul

ated

Fibr

ous

plaq

ueFi

brou

spl

aque

coag

ulat

ed

308

308

308

308

33 44 24 34

− − − −

77 270

81 272

− − − −

Post

mor

tem

(6h)

,ex

cise

d,in

4◦C

salin

e,sl

ab,

wat

erba

th(8

5◦C

),in

tegr

atin

gsp

here

(IS)

tech

niqu

e,in

vers

ead

ding

doub

ling

(IA

D)

met

hod,

data

from

Ref

.40.

Nor

mal

Coa

gula

ted

1064

1064

0.53

(0.0

9)0.

46(0

.18)

239

(45)

293

(73)

23.9

29.3

0.9

0.9

Post

mor

tem

,sla

b,70

◦ Cw

ater

bath

,10

min

,IS,

inve

rse

Mon

teC

arlo

(IM

C)

met

hod,

goni

opho

tom

etri

cm

easu

rem

ents

(GPM

),da

tafr

omR

ef.4

0.

Fibr

o-fa

tty35

553

210

64

17.7

3.6

0.09

− − −

64.9

24.8

7.7

− − −

Post

mor

tem

,re

sect

ed,

slab

(24

h),

phot

oaco

ustic

(PA

),da

tafr

omR

ef.4

0.

Nor

mal

633∗

1064

∗∗10

64∗

1320

∗∗13

20∗

0.52

0.5

0.7

2.2

4.3

316

239

− 233

−

41 23.9

22.4

23.3

17.8

0.87

0.9 − 0.9 −

Post

mor

tem

,sl

ab,

IS,

GPM

,∗ d

iffu

sion

theo

ry(D

T),

∗∗IM

C,

data

from

Ref

.40.

Nor

mal

(n=

9)47

047

648

851

4.5

580

600

633

1064

5.3

(0.9

)5.

1(0

.9)

4.5

(0.9

)3.

7(0

.9)

2.8

(0.9

)2.

6(0

.9)

2.6

(0.9

)2.

7(0

.5)

− − − − − − − −

42.6

(6.0

)41

.9(5

.9)

39.9

(5.6

)36

.9(5

.4)

31.1

(4.9

)29

.6(4

.7)

27.4

(4.4

)15

.5(2

.8)

− − − − − − − −

IS,D

T,δ

-Edd

ingt

onph

ase

func

tion;

thin

sect

ions

(250

μm

,int

ima

and

med

ia),

kept

insa

line.

764

Cor

rect

edda

ta(s

eeR

ef.

3,p.

379)

.In

the

spec

tral

rang

e30

0–18

00nm

:μ′ s

=2.

78×

105λ−1

.443

,[λ

]in

nm;d

ata

from

grap

hsof

Ref

.764

.1318

(con

tinue

d)


248 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Adv

entit

ia47

658

060

063

3

18.1

11.3

6.1

5.8

267

217

211

195

69.4

49.9

46.4

37.1

0.74

0.77

0.78

0.81

Froz

ense

ctio

ns,I

S,D

T,R

ef.3

12.

1064

2.0

484

−0.

97D

oubl

eIS

(DIS

),D

T,da

tafr

omR

ef.1

281.

Intim

a47

658

060

063

3

14.8

8.9

4.0

3.6

237

183

178

171

45.0

34.8

33.8

25.7

0.81

0.81

0.81

0.85

Froz

ense

ctio

ns,I

S,D

T,R

ef.3

12.

1064

2.3

165

−0.

97D

IS,D

T,da

tafr

omR

ef.1

281.

Med

ia47

658

060

063

3

7.3

4.8

2.5

2.3

410

331

323

310

45.1

33.1

35.5

31.0

0.89

0.90

0.89

0.90

Froz

ense

ctio

ns,I

S,D

T,R

ef.3

12.

1064

1.0

634

−0.

96D

IS,D

T,da

tafr

omR

ef.1

281.

Bla

dder

:In

tegr

al63

31.

4088

.03.

520.

96E

xcis

ed,k

epti

nsa

line,

Ref

.40.

Inte

gral

633

1.40

29.3

2.64

0.91

DIS

,DT,

data

from

Ref

s.2

and

1281

.M

ucou

s10

640.

77.

5−

0.85

Wal

l10

640.

954

.3−

0.85

Inte

gral

1064

0.4

116

−0.

90

Blo

odH

bO2

(Hct

=0.

41)

HbO

2(H

ct=

0.41

)H

bO2

(Hct

=0.

41)

HbO

2(H

ct=

0.4)

HbO

2(H

ct=

0.4)

Hb

(Hct

=0.

41)

Hb

(Hct

=0.

4)H

b(H

ct=

0.4)

665

685

960

810

1064 96

081

010

64

1.30

2.65

2.84

4.5

3.0

16.8

4.5

0.3

1246

1413 50

5− − 66

8− −

6.11

14.1

33.

846.

63.

45.

083.

96.

6

0.99

50.

990

0.99

2− −

0.99

2− −

Who

lebl

ood;

abso

rban

ce,r

adia

lrefl

ecta

nce,

and/

orG

PM;

Mie

theo

ry,

tran

spor

tth

eory

,or

IMC

;da

tafr

omR

efs.

40an

d12

81.



Hct

=0.

47(p

artia

llyox

ygen

ated

)45

048

851

457

763

076

0

381

133

116

301

14.3

15.5

2940

3190

3320

3140

3660

2820

8.3

4.0

4.1

7.3

8.9

7.9

0.99

720.

9987

0.99

880.

9977

0.99

760.

9972

Who

lebl

ood;

IAD

and

Bee

r’s

law

;da

taby

Jacq

ues

(199

3)fr

omR

ef.4

0.

(Hct

=0.

45–0

.46,

oxyg

enat

ion

>98

%)

633

710

765

810

865

910

965

1010

1065

1110

1165

1210

15.5

4(0

.8)

5.3

(0.6

)6.

5(0

.5)

7.2

(0.3

)8.

9(0

.4)

9.3

(0.6

)8.

3(0

.4)

5.6

(0.3

)4.

2(0

.3)

4.1

(0.7

)5.

5(0

.5)

644.

773

7(7

5)72

5(7

5)69

0(8

0)64

9(2

5)64

9(2

5)65

0(2

5)64

5(2

5)64

5(2

5)63

0(2

0)65

5(1

5)65

4(2

0)

– – – – – – – – – – – –

0.98

20.

986

(0.0

06)

0.99

1(0

.002

)0.

989

(0.0

02)

0.99

0(0

.001

)0.

992

(0.0

02)

0.99

1(0

.001

)0.

992

(0.0

01)

0.99

2(0

.001

)0.

993

(0.0

01)

0.99

3(0

.001

)0.

995

(0.0

01)

DIS

,Hen

yey–

Gre

enst

ein

phas

efu

nctio

n(H

GPF

),IM

C,12

55,1

256

data

from

grap

hsof

Ref

s.23

0,34

5;w

hole

bloo

d.

(Hct

=0.

421,

oxyg

enat

ion

>99

%)

260

350

375

415

450

490

520

540

555

575

585

620

630

670

700

750

780

375.

5(9

.0)

368.

133

8.6

(4.2

)78

2.5

(62.

9)26

3.0

106.

812

0.4

(6.9

)23

2.3

178.

923

1.6

160.

2(1

0.3)

4.14

2.51

(0.0

9)1.

221.

251.

992.

85

631.

5(5

7.6)

559.

554

2.8

(66.

5)39

0.3

(61.

2)68

2.6

793.

876

6.2

(42.

4)65

5.6

709.

365

8.0

751.

7(4

6.1)

905.

389

4.6

(28.

6)89

2.3

879.

384

0.8

821.

5

136.

4(2

8.0)

82.5

69.5

(12.

7)12

9.5

(17.

0)52

.530

.424

.9(7

.6)

35.8

33.0

31.7

33.5

(9.7

)23

.322

.3(3

.3)

21.5

21.1

20.6

20.5

0.78

4(0

.030

)0.

852

0.87

2(0

.007

)0.

668

(0.0

08)

0.92

30.

962

0.96

7(0

.009

)0.

945

0.95

30.

952

0.95

5(0

.007

)0.

974

0.97

5(0

.004

)0.

976

0.97

60.

975

0.97

5

IS,f

resh

eryt

hroc

ytes

from

ahe

alth

ybl

ood

dono

rdi

lute

din

PBS,

pH7.

4,he

mog

lobi

nco

ncen

trat

ion

129

g/l,

tem

pera

ture

kept

con-

stan

tat

20◦ C

,tu

rbul

ence

-fre

ecu

vette

with

ala

min

arflo

wan

da

sam

ple

thic

knes

sof

116μ

m,c

onst

antw

alls

hare

rate

of60

0s−

1;

inw

avel

engt

hre

gion

arou

nd41

5nm

,acu

vette

of40

μm

inth

ick-

ness

was

used

;R

eyno

lds–

McC

orm

ick

phas

efu

nctio

n(α

=1.

7),

IMC

,dat

apr

esen

ted

byth

eau

thor

sof

Ref

.134

7.

(con

tinue

d)


250 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

800

830

850

870

900

950

980

1000

1050

1100

3.27

(0.1

2)4.

904.

655.

105.

436.

15(0

.35)

6.79

6.51

4.91

(0.1

2)3.

74

809.

9(6

6.4)

798.

779

9.5

784.

475

1.4

712.

0(6

9.8)

685.

968

0.8

661.

3(1

2.8)

639.

5

20.2

(5.4

)20

.120

.120

.119

.920

.8(2

.7)

20.8

20.5

19.9

1(0

.67)

18.8

5

0.97

5(0

.003

)0.

975

0.97

50.

974

0.97

30.

971

(0.0

02)

0.97

00.

970

0.96

99(0

.000

6)0.

970

Bra

in:

Ast

rocy

tom

a(g

rade

III

WH

O,n

=7,

diff

eren

tsp

ots

onth

esa

mpl

e)

400

633

700

800

10∗

6.3

(1.6

)4∗ 3∗

84∗

67(8

)50

∗50

∗

– – – –

0.9∗

0.88

3(0

.011

)0.

88∗

0.88

∗

Mic

rosp

ectr

opho

tom

etry

,IM

C,s

lab

600μ

m,26

3∗ d

ata

from

grap

hs.

Glio

ma

(mal

e,65

yr,

4h

post

mor

tem

)41

548

863

080

0–11

00

16.6

12.5

3.0 ≈1

.0

– – – –

6 3 3 >1–

2

– – – –

Ref

.39,

data

from

grap

hs.

Gra

ym

atte

r(m

ale,

71yr

,24

hpo

stm

orte

m)

514

585

630

800–

1100

19.5

14.5

4.3 ≈1

.0

– – – –

85 63 52 45–2

0

– – – –

Mel

anom

a(m

ale

71yr

,24

hpo

stm

orte

m)

585

630

800

900

1100

2 20.0

8.0

4.0

2.0

– – – – –

158

75 40 30 25

– – – – –W

hite

mat

ter

(fem

ale,

32yr

,24

hpo

stm

orte

m)

415

488

630

800–

1100

2.1

1.0

0.2

0.2–

0.3

– – – –

24 60 32 40–2

0

– – – –



Whi

tem

atte

r(f

emal

e,63

yr,3

0h

post

mor

tem

)

488

630

800–

1100

2.7

0.9

1.0–

1.5

– – –

25 22 20–1

0

– – –

Gra

ym

atte

r63

310

642.

7(2

)5.

0(5

)35

4(3

7)13

4(1

4)20

.6(2

)11

.8(9

)0.

94(0

.004

)0.

90(0

.007

)Fr

eshl

yre

sect

ed,s

labs

;dat

afr

omR

ef.4

0.

Whi

tem

atte

r63

310

642.

2(2

)3.

2(4

)53

2(4

1)46

9(3

4)91

(5)

60.3

(2.5

)0.

82(0

.01)

0.87

(0.0

07)

Gra

ym

atte

rW

hite

mat

ter

800

800

0.25

0.05

– –25 60

– –R

ef.3

30.

Gra

ym

atte

r(n

=7)

360

640

1060

3.33

(2.1

9)0.

17(0

.26)

0.56

(0.7

)

141.

3(4

2.6)

90.1

(32.

5)56

.8(1

8.0)

– – –

0.81

8(0

.093

)0.

89(0

.04)

0.90

(0.0

5)

DIS

,IM

C.12

55,1

256

Gra

ym

atte

r,co

agul

ated

(n=

7)36

074

011

00

9.39

(1.7

0)0.

45(0

.27)

1.0

(0.4

5)

426

(122

)– 17

9.8

(32.

6)

– – –

0.86

8(0

.031

)– 0.

954

(0.0

01)

DIS

,IM

C;2

h,80

◦ C.12

55,1

256

Gra

ym

atte

r45

651

463

067

510

64

9 11.7

1.4

0.6

1.9

686

578

473

364

267

34.3

17.3

433

.11

32.7

610

.7

0.95

0.97

0.93

0.91

0.96

IS,δ

-Edd

ingt

onap

prox

imat

ion;

1287

data

from

Ref

.390

.

Whi

tem

atte

r45

651

463

067

510

64

8.1

5.0

1.5

0.7

1.6

923

1045

386

436

513

73.8

473

.15

54.0

456

.68

25.6

5

0.92

0.93

0.86

0.87

0.95

Whi

tem

atte

r(n

=7)

360

640

860

1060

2.53

(0.5

5)0.

8(0

.2)

0.97

(0.4

)1.

08(0

.51)

402.

0(9

1.8)

408.

2(8

8.5)

353.

1(6

8.1)

299.

5(7

0.1)

– – –

0.70

2(0

.093

)0.

84(0

.05)

0.87

1(0

.028

)0.

889

(0.0

10)

DIS

,IM

C12

55,1

256

Whi

tem

atte

r,co

agul

ated

(n=

7)36

086

010

60

8.3

(3.6

5)1.

7(1

.3)

2.15

(1.3

4)

604.

2(1

31.5

)41

7.0

(272

.5)

363.

3(2

26.8

)

– – –

0.80

0(0

.089

)0.

922

(0.0

25)

0.93

0(0

.015

)

DIS

,IM

C;2

h,80

◦ C.12

55,1

256 (c

ontin

ued)


252 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Whi

tem

atte

r80

010

640.

8(0

.16)

0.4

(0.0

8)14

0(1

4)11

0(1

1)– –

0.95

(0.0

2)0.

95(0

.02)

DIS

,IM

C;s

ampl

es0.

5–3

hpo

stm

orte

m,f

astf

roze

nan

dho

mog

-en

ized

;coa

gula

tion

ina

bath

at75

◦ C.12

52

Whi

tem

atte

r,co

agul

ated

800

1064

0.9

(0.1

8)0.

5(0

.1)

170

(17)

130

(13)

10.2 9.1

0.94

(0.0

2)0.

93(0

.02)

Gra

ym

atte

r(n

=7)

450

510

630

670

1064

0.7

0.4

0.2

0.2

0.5

117

106

90 84 57

14.0

412

.72

9.9

8.4

5.7

0.88

0.88

0.89

0.90

0.90

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

ns(<

48h

post

mor

tem

):gr

aym

atte

r,10

0–20

0μ

m;

whi

tem

atte

r,80

–150

μm

;co

agul

atio

n:sa

line

bath

80◦ C

coag

ulat

ion:

salin

eba

th80

◦ C,2

h;da

tafr

omta

bles

ofR

ef.3

90.

Whi

tem

atte

r(n

=7)

450

510

630

670

850

1064

1.4

1.0

0.8

0.7

1.0

1.0

420

426

409

401

342

296

92.4

80.9

465

.44

60.1

541 32

.56

0.78

0.81

0.84

0.85

0.88

0.89

Whi

tem

atte

r,co

agul

ated

(n=

7)85

010

640.

90.

130

027

036

.029

.70.

880.

89

Ast

rocy

tom

a(g

rade

IIW

HO

,n=

4)40

049

060

070

080

090

010

0011

00

18.8

(11.

3)2.

5(0

.9)

1.2

(0.7

)0.

5(0

.3)

0.7

(0.2

)0.

3(0

.2)

0.5

(0.3

)0.

6(0

.2)

198.

4(5

5.6)

158.

5(5

3.7)

132.

4(4

9.0)

113.

2(4

1.8)

96.7

(41.

8)86

.4(3

4.6)

79.0

(34.

2)73

.8(2

9.6)

– – – – – – – –

0.93

(0.0

3)0.

96(0

.02)

0.96

(0.0

2)0.

96(0

.02)

0.96

(0.0

1)0.

96(0

.01)

0.96

(0.0

1)0.

96(0

.01)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

tum

ors

≈300

μm

inth

ickn

ess

exci

sed

from

patie

nts

(<48

hpo

stm

orte

m);

data

from

grap

hsof

Ref

.39

0,ta

ken

from

Ref

.12

85w

ithco

rrec

tions

;in

this

spec

tral

rang

e:μ

s=

9.25

4×

104λ−1

.025

;g

=0.

903

+0.

06[1

–exp

(–(λ

–410

.5)/

33.7

)],[λ

]in

nm.13

18

Cer

ebel

lum

(n=

7)40

050

060

070

080

090

010

0011

00

4.7

(0.8

)1.

4(0

.2)

0.8

(0.2

)0.

6(0

.1)

0.6

(0.1

)0.

7(0

.1)

0.8

(0.1

)0.

7(0

.1)

276.

7(1

9.1)

277.

5(3

2.6)

272.

1(1

2.3)

266.

8(1

2.1)

250.

3(1

7.2)

229.

6(1

5.8)

215.

4(1

4.7)

202.

1(1

3.9)

– – – – – – – –

0.80

(0.0

3)0.

85(0

.02)

0.87

(0.0

2)0.

89(0

.01)

0.90

(0.0

1)0.

90(0

.01)

0.90

(0.0

1)0.

90(0

.01)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200μ

m(<

48h

post

mor

tem

);da

tafr

omgr

aphs

ofR

ef.

390,

take

nfr

omR

ef.

1285

with

corr

ec-

tions

;in

this

spec

tral

rang

e:g

=0.

836

+0.

067

[1–e

xp(–

(λ–

459)

/160

.5)]

,[λ

]in

nm.13

18



Cer

ebel

lum

,coa

gula

ted

(n=

7)40

050

060

070

080

090

010

0011

00

19.3

(7.7

)5.

1(1

.7)

2.9

(1.4

)1.

7(0

.4)

1.1

(0.2

)1.

1(0

.3)

1.0

(0.4

)1.

1(0

.5)

560.

0(2

5.5)

512.

2(4

7.8)

458.

2(6

5.6)

489.

9(7

0.1)

458.

2(5

4.0)

458.

2(6

5.6)

419.

1(4

9.4)

428.

5(4

0.0)

– – – – – – – –

0.61

(0.0

1)0.

77(0

.02)

0.78

(0.0

1)0.

85(0

.01)

0.87

(0.0

2)0.

89(0

.02)

0.90

(0.0

3)0.

91(0

.03)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200

μm

(<48

hpo

stm

orte

m);

salin

eba

th80

◦ C,

2h;

data

from

grap

hsof

Ref

.39

0,ta

ken

from

Ref

.12

85w

ithco

rrec

tions

;in

this

spec

tral

rang

e:g

=0.

743

+0.

184

[1–e

xp(–

(λ–5

19.7

)/21

7)],

[λ]

innm

.1318

Gra

ym

atte

r(n

=7)

400

500

600

700

800

900

1000

1100

2.6

(0.6

)0.

5(0

.2)

0.3

(0.1

)0.

2(0

.1)

0.2

(0.1

)0.

3(0

.2)

0.6

(0.3

)0.

5(0

.3)

128.

5(1

8.4)

109.

9(1

3.0)

94.1

(13.

5)84

.1(1

2.0)

77.0

(11.

0)67

.3(9

.6)

61.6

(5.7

)55

.1(6

.5)

– – – – – – – –

0.87

(0.0

2)0.

88(0

.01)

0.89

(0.0

2)0.

90(0

.02)

0.90

(0.0

2)0.

90(0

.02)

0.90

(0.0

2)0.

90(0

.02)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200μ

m(<

48h

post

mor

tem

);da

tafr

omgr

aphs

ofR

ef.3

90,t

aken

from

Ref

.128

5w

ithco

rrec

tions

;in

this

spec

tral

rang

e:μ

s=

2.08

×10

4λ−0

.85;g

=0.

883

+0.

019

[1–e

xp(–

(λ–4

82.8

)/10

5.6)

],[λ

]in

nm.13

18

Gra

ym

atte

r,co

agul

ated

(n=

7)40

050

060

070

080

090

010

0011

00

7.5

(0.4

)1.

8(0

.2)

0.7

(0.1

)0.

7(0

.1)

0.8

(0.1

)0.

9(0

.1)

1.4

(0.2

)1.

5(0

.2)

258.

6(1

8.8)

326.

5(7

.7)

319.

0(1

5.2)

319.

0(7

.5)

252.

7(1

8.3)

214.

6(1

0.3)

191.

0(1

8.7)

186.

6(1

3.5)

– – – – – – – –

0.78

(0.0

4)0.

85(0

.03)

0.87

(0.0

3)0.

88(0

.03)

0.87

(0.0

2)0.

87(0

.02)

0.88

(0.0

3)0.

88(0

.03)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200

μm

(<48

hpo

stm

orte

m);

salin

eba

th80

◦ C,

2h;

data

from

grap

hsof

Ref

.39

0,ta

ken

from

Ref

.12

85w

ithco

rrec

tions

;in

this

spec

tral

rang

e:g

=0.

833

+0.

046

[1–e

xp(–

(λ–4

59.4

)/90

.9)]

,[λ

]in

nm.13

18

Men

ingi

oma

(n=

6)41

049

059

069

079

091

099

011

00

4.1

(0.5

)1.

3(0

.2)

0.7

(0.2

)0.

3(0

.1)

0.2

(0.1

)0.

2(0

.1)

0.4

(0.2

)0.

6(0

.2)

197.

4(1

9.8)

188.

2(1

8.8)

171.

1(1

2.7)

155.

5(1

5.6)

141.

3(1

4.2)

116.

8(8

.6)

163.

5(1

5.3)

133.

7(1

9.2)

– – – – – – – –

0.88

(0.0

2)0.

93(0

.01)

0.95

(0.0

1)0.

95(0

.01)

0.96

(0.0

1)0.

95(0

.01)

0.96

(0.0

1)0.

97(0

.01)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

tum

ors

exci

sed

from

patie

nts

of≈3

00μ

min

thic

knes

s(<

48h

post

mor

tem

);da

tafr

omgr

aphs

ofR

ef.3

90,

take

nfr

omR

ef.

1285

with

corr

ectio

ns;

inth

esp

ectr

alra

nge

500–

1100

nm:μ

s=

1.69

×10

4λ−0

.718

;in

the

spec

tral

rang

e36

0–11

00nm

:g=

0.88

9+

0.07

[1–e

xp(–

(λ–4

18.6

)/78

.6)]

,[λ

]in

nm.13

18

(con

tinue

d)


254 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Pons

(n=

7)40

050

060

070

080

090

010

0011

00

3.1

(0.7

)0.

9(0

.3)

0.6

(0.2

)0.

5(0

.2)

0.6

(0.3

)0.

7(0

.3)

1.0

(0.4

)0.

9(0

.4)

163.

5(1

5.3)

133.

7(1

9.2)

109.

4(1

8.5)

93.5

(20.

9)83

.6(2

1.0)

74.8

(18.

7)69

.9(1

7.5)

64.0

(17.

8)

– – – – – – – –

0.89

(0.0

2)0.

91(0

.01)

0.91

(0.0

1)0.

91(0

.01)

0.91

(0.0

1)0.

92(0

.01)

0.91

(0.0

1)0.

92(0

.01)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200μ

m(<

48h

post

mor

tem

);da

tafr

omgr

aphs

ofR

ef.

390,

take

nfr

omR

ef.

1285

with

corr

ectio

ns;

inth

issp

ectr

alra

nge:

μs

=4.

332

×10

4λ−0

.934

;g

=0.

908

+0.

012(

1–ex

p(–

(λ–4

84.8

)/15

3.7)

),[λ

]in

nm13

18

Pons

,coa

gula

ted

(n=

7)41

051

061

071

081

091

010

1011

00

17.2

(1.6

)8.

5(0

.8)

7.7

(0.5

)6.

9(0

.6)

6.5

(0.6

)5.

9(1

.0)

5.7

(1.0

)6.

5(0

.9)

685.

7(6

3.7)

627.

5(7

3.6)

510.

5(7

0.5)

402.

5(6

7.7)

329.

7(5

5.4)

276.

0(4

6.4)

241.

6(3

4.4)

221.

1(3

1.5)

– – – – – – – –

0.85

(0.0

2)0.

89(0

.01)

0.89

(0.0

1)0.

89(0

.01)

0.89

(0.0

1)0.

88(0

.01)

0.88

(0.0

1)0.

88(0

.01)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200μ

m(<

48h

post

mor

tem

);sa

line

bath

80◦ C

,2h;

data

from

grap

hsof

Ref

.390

,tak

enfr

omR

ef.1

285

with

corr

ectio

ns;i

nth

issp

ectr

alra

nge:μ

s=

9.77

9×

105λ−1

.2;g

=0.

86+

0.02

7[1

–exp

(–(λ

–425

.1)/

56.4

)],[λ

]in

nm.13

18

Tha

lam

us(n

=7)

410

510

610

710

810

910

1010

1100

3.2

(1.0

)0.

9(0

.3)

0.6

(0.2

)0.

5(0

.3)

0.7

(0.3

)0.

7(0

.3)

0.8

(0.3

)0.

8(0

.3)

146.

7(4

9.4)

188.

7(3

1.9)

176.

3(3

4.5)

169.

0(2

8.7)

158.

5(3

5.3)

155.

4(2

2.3)

139.

3(3

4.9)

146.

0(3

6.6)

– – – – – – – –

0.86

(0.0

3)0.

87(0

.03)

0.88

(0.0

2)0.

89(0

.03)

0.89

(0.0

2)0.

90(0

.02)

0.90

(0.0

2)0.

91(0

.02)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200μ

m(<

48h

post

mor

tem

);da

tafr

omgr

aphs

ofR

ef.

390,

take

nfr

omR

ef.

1285

with

corr

ectio

ns;

inth

esp

ectr

alra

nge

500–

1100

nm:μ

s=

1.79

3×

103λ−0

.363

;in

the

spec

tral

rang

e36

0–11

00nm

:g

=0.

865

+0.

04[1

–exp

(–(λ

–48

6.9)

/239

.9)]

,[λ

]in

nm.13

18

Tha

lam

us,c

oagu

late

d(n

=7)

400

500

600

700

800

15.0

(3.3

)4.

2(0

.9)

1.6

(0.6

)1.

4(0

.3)

1.1

(0.3

)1.

1(0

.3)

391.

1(5

6.1)

399.

9(6

7.7)

365.

7(4

3.2)

327.

0(3

0.6)

286.

0(3

3.8)

267.

4(3

1.6)

– – – – – –

0.83

(0.0

4)0.

90(0

.01)

0.92

(0.0

1)0.

92(0

.01)

0.93

(0.0

1)0.

93(0

.01)

IS,I

MC

,qua

si-N

ewto

nin

vers

eal

gori

thm

,HG

PF;h

emog

lobi

n-fr

eecr

yose

ctio

nsof

100–

200μ

m(<

48h

post

mor

tem

);sa

line

bath

80◦ C

,2

h;da

tafr

omgr

aphs

ofR

ef.

390,

take

nfr

omR

ef.

1285

with

corr

ectio

ns;

inth

esp

ectr

alra

nge

500–

1100

nm:μ

s=

5.57

8×

104λ−0

.792

;in

the

spec

tral

rang

e36

0–11

00nm

:g

=0.

864

+0.

068

[1–e

xp(–

(λ–4

31.3

)/11

5.6)

],[λ

]in

nm.13

18



900

1000

1100

1.4

(0.4

)1.

5(0

.4)

233.

8(3

9.7)

223.

6(3

2.1)

– –0.

93(0

.01)

0.94

(0.0

1)

Whi

tem

atte

r(n

=7)

400

500

600

700

800

900

1000

1100

3.1

(0.2

)0.

9(0

.1)

0.8

(0.1

)0.

8(0

.1)

0.9

(0.1

)1.

0(0

.1)

1.2

(0.2

)1.

0(0

.2)

413.

5(2

1.4)

413.

5(4

3.9)

413.

5(2

1.4)

393.

1(3

0.9)

364.

5(2

8.6)

329.

5(3

5.0)

305.

4(1

5.9)

283.

2(2

2.2)

– – – – – – – –

0.75

(0.0

3)0.

80(0

.02)

0.83

(0.0

2)0.

85(0

.02)

0.87

(0.0

1)0.

88(0

.01)

0.88

(0.0

1)0.

88(0

.01)

IS,

IMC

,qu

asi-

New

ton

inve

rse

algo

rith

m,

HG

PF;

hem

oglo

bin-

free

cryo

sect

ions

of80

–150

μm

(<48

hpo

stm

orte

m);

data

from

grap

hsof

Ref

.39

0,ta

ken

from

Ref

.128

5w

ithco

rrec

tions

;in

the

spec

tral

rang

e70

0–11

00:

μs

=1.

67×

106λ−1

.375

+70

2.8λ

−0.1

92,i

nth

esp

ectr

alra

nge

360–

1100

:g

=0.

8+

0.09

9[1

–exp

(–(λ

–484

.7)/

216.

18)]

,[λ

]in

nm.13

18

Whi

tem

atte

r,co

agul

ated

(n=

7)41

051

061

071

081

091

010

1011

00

8.7

(1.7

)2.

9(0

.6)

1.7

(0.4

)1.

4(0

.5)

1.5

(0.5

)1.

7(0

.6)

1.9

(0.6

)2.

4(0

.5)

568.

7(1

11.9

)51

3.2

(116

.9)

500.

2(1

29.9

)47

5.2

(108

.3)

440.

0(1

14.3

)40

7.4

(92.

8)36

7.7

(95.

5)35

8.4

(81.

6)

– – – – – – – –

0.83

(0.0

3)0.

87(0

.02)

0.90

(0.0

2)0.

91(0

.01)

0.92

(0.0

1)0.

93(0

.01)

0.93

(0.0

1)0.

93(0

.01)

IS,

IMC

,qu

asi-

New

ton

inve

rse

algo

rith

m,

HG

PF;

hem

oglo

bin-

free

cryo

sect

ions

of80

–150

μm

(<48

hpo

stm

orte

m);

salin

eba

th80

◦ C,

2h;

data

from

grap

hsof

Ref

.390

,tak

enfr

omR

ef.1

285

with

corr

ectio

ns;i

nth

esp

ectr

alra

nge

600–

1100

:μs

=1.

92×

106λ−1

.434

+84

6.94

λ−0

.168

,in

the

spec

tral

rang

e36

0–11

00:

g=

0.85

9+

0.08

2[1

–exp

(–(λ

–468

.2)/

200.

3)],

[λ]

innm

.1318

Gra

ym

atte

r(n

=25

)40

041

842

845

048

850

055

060

0

9.77

814

.873

16.7

225.

161

2.27

22.

206

2.95

51.

460

– – – – – – – –

25.8

7826

.593

26.7

0919

.389

15.9

5715

.283

13.3

1511

.367

– – – – – – – –

IS,

IAD

,fix

edan

isot

ropy

fact

org

=0.

85an

dre

frac

tive

inde

xn

=1.

40w

ere

assu

med

fore

very

wav

elen

gth

and

fore

very

sam

ple;

brai

ntis

sue

sam

-pl

esw

ere

acqu

ired

duri

ngop

encr

anio

tom

yfo

rtum

orre

sect

ion

orte

mpo

ral

lobe

ctom

y;he

mog

lobi

n-fr

eecr

yose

ctio

nsw

ithth

ickn

ess

from

0.22

to1.

25m

mw

ere

stud

ied,

mea

sure

men

tsw

ere

done

at25

◦ C,

pH7.

4;da

taw

ere

pres

ente

dby

the

auth

ors

ofR

ef.1

419.

For

data

from

grap

hsof

Ref

.141

9:μ

′ s=

9.21

×10

7λ−2

.564

+99

.4λ−0

.473

,[λ

]in

nm.13

18

(con

tinue

d)


256 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

632

670

700

750

800

830

850

870

900

950

1000

1064

1100

1150

1200

1250

1300

0.92

50.

809

0.73

30.

599

0.50

70.

485

0.47

20.

479

0.50

30.

521

0.58

50.

502

0.50

20.

815

1.01

00.

865

0.89

4

– – – – – – – – – – – – – – – – –

10.3

709.

480

8.90

78.

481

7.88

67.

707

7.55

57.

351

7.05

56.

868

6.05

95.

333

5.19

75.

070

4.88

24.

669

4.56

0

– – – – – – – – – – – – – – – – –W

hite

mat

ter

(n=

19)

400

418

428

450

488

500

550

600

632

670

700

750

800

830

850

870

9.13

413

.603

15.4

173.

958

1.86

91.

834

2.58

41.

175

0.80

10.

711

0.67

40.

649

0.62

20.

626

0.64

30.

666

– – – – – – – – – – – – – – – –

88.6

1183

.304

80.9

0577

.053

70.1

1268

.318

62.3

8356

.759

53.1

7950

.067

47.6

2645

.061

41.8

7840

.634

39.6

5838

.785

– – – – – – – – – – – – – – – –

IS,

IAD

,fix

edan

isot

ropy

fact

org

=0.

85an

dre

frac

tive

inde

xn

=1.

40w

ere

assu

med

fore

very

wav

elen

gth

and

fore

very

sam

ple;

brai

ntis

sue

sam

-pl

esw

ere

acqu

ired

duri

ngop

encr

anio

tom

yfo

rtum

orre

sect

ion

orte

mpo

ral

lobe

ctom

y;he

mog

lobi

n-fr

eecr

yose

ctio

nsw

ithth

ickn

ess

from

0.22

to1.

25m

mw

ere

stud

ied,

mea

sure

men

tsw

ere

done

at25

◦ C,

pH7.

4;da

taw

ere

pres

ente

dby

the

auth

ors

ofR

ef.1

419.

For

data

from

grap

hsof

Ref

.141

9:μ

′ s=

2.67

×10

7λ−2

.188

+39

9.6λ

−0.3

96,[λ

]in

nm.13

18



900

950

1000

1064

1100

1150

1200

1250

1300

0.68

40.

785

0.88

30.

752

0.76

21.

135

1.42

01.

268

1.27

4

– – – – – – – – –

37.6

0735

.851

32.6

0330

.161

29.2

1927

.951

26.6

4625

.310

24.2

50

– – – – – – – – –

Glio

ma

(n=

39)

400

418

428

450

488

500

550

600

632

670

700

750

800

830

850

870

900

950

1000

1064

1100

1150

1200

1250

1300

12.3

9317

.496

16.1

244.

891

2.59

22.

352

2.76

81.

149

0.84

60.

741

0.70

90.

679

0.65

60.

662

0.67

00.

685

0.70

70.

768

0.93

80.

822

0.83

11.

231

1.51

81.

379

1.41

2

– – – – – – – – – – – – – – – – – – – – – – – – –

39.0

0937

.867

37.0

7632

.340

28.9

3328

.057

25.3

0022

.514

21.0

6819

.608

18.5

4317

.343

15.9

6915

.481

15.1

3314

.749

14.1

3813

.646

11.5

8810

.344

10.0

059.

654

9.28

28.

813

8.52

3

– – – – – – – – – – – – – – – – – – – – – – – – –

IS,

IAD

,fix

edan

isot

ropy

fact

org

=0.

85an

dre

frac

tive

inde

xn

=1.

40w

ere

assu

med

fore

very

wav

elen

gth

and

fore

very

sam

ple;

brai

ntis

sue

sam

-pl

esw

ere

acqu

ired

duri

ngop

encr

anio

tom

yfo

rtum

orre

sect

ion

orte

mpo

ral

lobe

ctom

y;he

mog

lobi

n-fr

eecr

yose

ctio

nsw

ithth

ickn

ess

from

0.22

to1.

25m

mw

ere

stud

ied,

mea

sure

men

tsw

ere

done

at25

◦ C,

pH7.

4;da

taw

ere

pres

ente

dby

the

auth

ors

ofR

ef.1

419.

For

data

from

grap

hsof

Ref

.141

9:μ

′ s=

2.25

×10

7λ−2

.279

+26

6.6λ

−0.4

95,[λ

]in

nm.13

18

(con

tinue

d)


258 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Bre

ast(

fem

ale)

:Fa

ttyno

rmal

(n=

23)

749

789

836

0.18

(0.1

6)0.

08(0

.10)

0.11

(0.1

0)

8.48

(3.4

3)7.

67(2

.57)

7.27

(2.4

0)

– – –

– – –

Exc

ised

,kep

tin

salin

e,37

◦ C,R

ef.3

29.

Fibr

ous

norm

al(n

=35

)74

978

983

6

0.13

(0.1

9)0.

06(0

.12)

0.05

(0.0

8)

9.75

(2.2

7)8.

94(2

.45)

8.10

(2.2

1)

– – –

– – –In

filtr

atin

gca

rcin

oma

(n=

48)

749

789

836

0.15

(0.1

4)0.

04(0

.08)

0.10

(0.1

9)

10.9

1(5.

59)

10.1

2(5

.05)

9.10

(4.5

4)

– – –

– – –M

ucin

ous

carc

inom

a(n

=3)

749

789

836

0.26

(0.2

0)0.

016

(0.0

72)

0.02

3(0

.108

)

– – –

6.15

(2.4

4)5.

09(2

.42)

4.78

(3.6

7)

– – –D

ucta

lcar

cino

ma

insi

tu(n

=5)

749

789

836

0.07

6(0

.068

)0.

023

(0.0

34)

0.03

9(0

.068

)

– – –

13.1

0(2

.85)

12.2

1(2

.45)

10.4

6(2

.65)

– – –

Gla

ndul

artis

sue

(n=

3)54

070

090

0

3.58

(1.5

6)0.

47(0

.11)

0.62

(0.0

5)

– – –

24.4

(5.8

)14

.2(3

.0)

9.9

(2.0

)

– – –

IS,I

MC

;hom

ogen

ized

tissu

e,R

ef.1

250.

Fatty

tissu

e(n

=7)

540

700

900

2.27

(0.5

7)0.

70(0

.08)

0.75

(0.0

8)

– – –

10.3

(1.9

)8.

6(1

.3)

7.9

(1.1

)

– – –Fi

broc

ystic

(n=

8)54

070

090

0

1.64

(0.6

6)0.

22(0

.09)

0.27

(0.1

1)

– – –

21.7

(3.3

)13

.4(1

.9)

9.5

(1.7

)

– – –Fi

broa

deno

ma

(n=

6)54

070

090

0

4.38

(3.1

4)0.

52(0

.47)

0.72

(0.5

3)

– – –

11.1

(3.0

)7.

2(1

.7)

5.3

(1.4

)

– – –C

arci

nom

a(n

=9)

540

700

900

3.07

(0.9

9)0.

45(0

.12)

0.50

(0.1

5)

– – –

19.0

(5.1

)11

.8(3

.1)

8.9

(2.6

)

– – –



Car

cino

ma

580

850

1300

4.5

(0.8

)0.

4(0

.5)

0.5

(0.8

)

– – –

– – –

– – –

Tis

sue

slic

esof

thic

knes

s5–

5.3

mm

,Ref

.317

.

Adj

acen

thea

lthy

tissu

e58

085

013

00

2.6

(1.1

)0.

3(0

.2)

0.8

(0.6

)

– – –

– – –

– – –Fa

ttytis

sue

700

––

13(5

)0.

95(0

.02)

Fibr

ogla

ndul

artis

sue

700

––

12(5

)0.

92(0

.03)

Car

cino

ma

(cen

tral

part

)70

0–

–18

(5)

0.88

(0.0

3)

Fatty

tissu

eB

enig

ntu

mor

625

625

0.06

(0.0

2)0.

33(0

.06)

– –14

.3(2

.1)

3.8

(0.3

)– –

Ref

.31.

Inva

sive

duct

alca

rcin

oma

(n=

10;

9in

age

grou

p55

–65

yran

d1

35yr

)

450

460

470

480

490

500

510

520

530

540

550

560

570

580

590

600

610

620

630

640

650

2.55

(0.3

0)2.

62(0

.34)

2.44

(0.2

5)2.

32(0

.26)

2.23

(0.2

5)2.

22(0

.22)

2.16

(0.2

4)2.

12(0

.22)

2.07

(0.2

2)1.

99(0

.21)

2.13

(0.2

3)2.

09(0

.21)

2.09

(0.2

5)2.

07(0

.21)

2.01

(0.2

2)1.

90(0

.19)

1.82

(0.1

8)1.

71(0

.18)

1.64

(0.1

7)1.

55(0

.17)

1.48

(0.1

5)

– – – – – – – – – – – – – – – – – – – – –

31.5

(2.5

)31

.0(2

.4)

30.7

(2.2

)30

.3(2

.4)

29.9

(2.4

)29

.5(2

.2)

29.1

(2.3

)29

.0(2

.3)

28.7

(2.0

)28

.0(2

.1)

28.4

(2.0

)27

.7(2

.0)

27.5

(1.9

)27

.3(2

.0)

27.1

(1.7

)26

.8(1

.8)

26.8

(1.6

)26

.4(1

.8)

26.2

(1.5

)25

.9(1

.4)

25.7

(1.3

)

– – – – – – – – – – – – – – – – – – – – –

Spat

ially

reso

lved

refle

ctan

ce(S

RR

);D

T;so

urce

–det

ecto

rse

para

tion,

r sd

>1.

2m

m;fi

bers

with

core

diam

eter

400μ

m;

tissu

esl

ices

ofth

ickn

ess∼0

mm

.1288

(con

tinue

d)


260 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

633

––

–0.

96(0

.01)

GPM

,tis

sue

slic

esof

20μ

m;

HG

PF;θ

=10

–165

deg;

radi

usof

Mie

scat

tere

r:a M

=0.

64(0

.06)

μm

.1288

633

––

–0.

86(0

.02)

GPM

,tis

sue

slic

esof

20μ

m;d

oubl

eH

GPF

[g=

f(1

–g 1

)+

(1–

f)g 2

];θ

=52

–165

deg;

a M=

0.28

(0.0

2)μ

m.12

88

Adj

acen

the

alth

ytis

sue

(n=

10;

9in

the

age

grou

p55

–65

yran

d1

35yr

)

450

460

470

480

490

500

510

520

530

540

550

560

570

580

590

600

610

620

630

640

650

1.45

(0.2

2)1.

48(0

.21)

1.42

(0.2

1)1.

35(0

.19)

1.26

(0.2

1)1.

24(0

.21)

1.23

(0.1

9)1.

19(0

.18)

1.14

(0.1

7)1.

19(0

.22)

1.16

(0.2

6)1.

14(0

.17)

1.13

(0.1

6)1.

17(0

.17)

1.07

(0.1

7)1.

00(0

.12)

0.95

(0.1

2)0.

89(0

.11)

0.82

(0.0

7)0.

79(0

.08)

0.74

(0.0

8)

– – – – – – – – – – – – – – – – – – – – –

21.7

(2.1

)21

.3(2

.2)

20.8

(1.9

)20

.3(1

.8)

19.9

(2.0

)20

.1(1

.8)

19.1

(1.9

)18

.7(1

.8)

18.4

(1.8

)18

.0(1

.8)

18.2

(1.6

)17

.4(1

.5)

17.2

(1.5

)16

.9(1

.3)

16.6

(1.4

)16

.4(1

.5)

16.2

(1.5

)15

.9(1

.3)

15.7

(1.3

)15

.5(1

.2)

15.3

(1.2

)

– – – – – – – – – – – – – – – – – – – – –

SRR

;DT;

r sd

>1.

2m

m;fi

bers

with

core

diam

eter

400μ

m;t

issu

esl

ices

ofth

ickn

ess∼1

0m

m.12

88

633

––

–0.

88(0

.01)

GPM

,tis

sue

slic

esof

20μ

m;

HG

PF;θ

=10

–165

deg;

a M=

0.32

(0.0

2)μ

m.12

88

633

––

–0.

76(0

.01)

GPM

,tis

sue

slic

esof

20μ

m;

doub

leH

GPF

[g=

f(1

−g 1

)+

(1−

f)g 2

];θ

=52

−165

deg;

a M=

0.19

(0.0

2)μ

m.12

88



Col

on:

Mus

cle

1064

3.3

238

–0.

93D

ata

from

Ref

.128

1.Su

bmuc

ous

1064

2.3

117

–0.

91M

ucou

s10

642.

739

–0.

91In

tegr

al10

640.

426

1–

0.94

Nor

mal

muc

osa/

subm

ucos

a(n

=13

)47

6.5

488.

049

6.5

514.

553

2.0

2.32

(0.0

9)3.

27(0

.13)

2.58

(0.1

0)3.

12(0

.12)

3.33

(0.1

4)

214

(5.3

5)22

8(5

.69)

212

(5.2

7)21

6(5

.38)

208

(5.1

6)

– – – – –

0.88

5(0

.019

)0.

891

(0.0

21)

0.89

7(0

.024

)0.

902

(0.0

26)

0.90

8(0

.029

)

IS,I

AD

;dat

afr

omgr

aphs

ofW

eiet

al.(

2005

).13

18

Ade

nom

atou

sm

ucos

a/su

bmuc

osa

(n=

13)

476.

548

8.0

496.

551

4.5

532.

0

5.27

(0.2

1)5.

34(0

.22)

4.87

(0.1

9)4.

37(0

.17)

5.16

(0.2

0)

233

(5.7

2)23

8(5

.84)

228

(5.6

7)23

1(5

.69)

223

(5.6

3)

– – – – –

0.89

7(0

.023

)0.

903

(0.0

27)

0.90

7(0

.028

)0.

917

(0.0

33)

0.91

3(0

.031

)

IS,I

AD

;dat

afr

omgr

aphs

ofW

eiet

al.(

2005

).13

18

Nor

mal

mus

cle

laye

r/ch

orio

n(n

=13

)47

6.5

488.

049

6.5

514.

553

2.0

1.31

(0.0

5)1.

73(0

.07)

1.27

(0.0

5)1.

14(0

.04)

1.53

(0.0

6)

221

(5.6

1)21

5(5

.33)

200

(5.0

8)18

9(5

.03)

193

(5.0

5)

– – – – –

0.92

3(0

.037

)0.

932

(0.0

44)

0.92

7(0

.041

)0.

933

(0.0

45)

0.94

1(0

.048

)

IS,I

AD

;dat

afr

omgr

aphs

ofW

eiet

al.(

2005

).13

18

Ade

nom

atou

sm

uscl

ela

yer/

chor

ion

(n=

13)

476.

548

8.0

496.

551

4.5

532.

0

3.17

(0.1

2)3.

51(0

.14)

2.90

(0.1

1)2.

57(0

.09)

2.75

(0.1

0)

233

(5.7

1)22

3(5

.62)

216

(5.3

6)19

8(5

.07)

208

(5.1

4)

– – – – –

0.92

7(0

.042

)0.

935

(0.0

46)

0.93

3(0

.044

)0.

936

(0.0

47)

0.94

5(0

.049

)

IS,I

AD

;dat

afr

omgr

aphs

ofW

eiet

al.(

2005

).13

18

Eso

phag

us63

30.

4–

12–

2.5-

mm

slab

,Ref

.40.

Eso

phag

us(m

ucou

s)10

641.

183

–0.

86D

ata

from

Ref

.128

1.

Fat: A

bdom

inal

1064

3.0

37–

0.91

Dat

afr

omR

ef.1

281.

Subc

utan

eous

1064

2.6

29–

0.91

(con

tinue

d)


262 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Gal

lbla

dder

:B

ile(n

=5)

350

450

550

650

750

850

950

1050

1150

1250

1350

1450

1550

1650

1750

1850

1950

2050

2150

2250

2350

2450

32.9

875

.81

2.58

1.81

0.53

0.39

0.41

0.92

1.89

2.30

3.99

25.1

39.

985.

827.

5413

.18

71.6

338

.09

19.3

119

.48

31.8

453

.18

– – – – – – – – – – – – – – – – – – – – – –

16.3

926

.01

2.48

1.74

1.67

1.91

1.97

1.74

1.97

2.21

2.94

9.01

3.98

3.05

3.44

5.52

20.7

79.

165.

844.

459.

1815

.22

– – – – – – – – – – – – – – – – – – – – – –

IS,

diff

usio

nap

prox

imat

ion;

data

from

grap

hsof

Mai

tland

etal

.(1

993)

.1318

Tis

sue

(n=

6)35

045

055

065

075

085

095

010

5011

5012

50

37.6

223

.17

13.6

35.

164.

844.

434.

534.

505.

275.

29

– – – – – – – – – –

29.3

416

.66

10.7

68.

196.

675.

925.

444.

754.

504.

39

– – – – – – – – – –

IS,d

iffu

sion

appr

oxim

atio

n;in

spec

tral

rang

e35

0–18

50nm

:μ′ s

=1.

761

×10

8λ−2

.692

+5.

95λ−0

.061

,[λ

]in

nm;

data

from

grap

hsof

Mai

tland

etal

.(19

93).

1318



1350

1450

1550

1650

1750

1850

1950

2050

2150

2250

2350

2450

6.95

24.4

311

.36

8.07

9.24

14.0

378

.15

36.1

120

.20

20.3

530

.86

49.5

7

– – – – – – – – – – – –

4.56

5.92

4.62

4.15

4.45

5.25

10.9

46.

384.

994.

335.

8010

.76

– – – – – – – – – – – –G

alls

tone

s:Po

rcin

e35

148

858

063

010

60

102

(16)

179

(28)

125

(29)

85(1

1)12

1(1

2)

– – – – –

– – – – –

– – – – –

Deh

ydra

ted,

embe

dded

inpl

astic

,an

dsl

iced

in1-

mm

slab

,pu

lsed

phot

othe

rmal

radi

omet

ryte

chni

que,

data

from

Ref

.40.

Cho

lest

erol

351

488

580

630

1060

88(7

)62

(15)

36(7

)44

(10)

60(9

)

– – – – –

– – – – –

– – – – –H

ead

(adu

lt):

Dur

am

ater

(n=

8)40

045

050

055

060

065

070

0

3.08

(0.1

5)1.

51(0

.08)

1.09

(0.0

5)1.

10(0

.05)

0.80

(0.0

4)0.

70(0

.04)

0.74

(0.0

4)

– – – – – – –

22.3

5(0

.89)

22.8

9(0

.92)

21.6

0(0

.86)

18.4

8(0

.74)

17.1

1(0

.68)

15.5

1(0

.62)

13.9

9(0

.56)

– – – – – – –

IS,I

AD

;pos

tmor

tem

,<24

hex

cise

dtis

sue

slab

s,st

ored

at−1

2◦C

;m

easu

rem

ents

atro

omte

mpe

ratu

re;i

nsp

ectr

alra

nges

480–

550

and

600–

700

nm:μ

′ s=

2.88

7×

104λ

1.16

4,[λ

]in

nm.12

93

(con

tinue

d)


264 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Scal

pan

dsk

ull

Cer

ebra

lspi

nalfl

uid

800

800

0.4

0.01

– –20 0.

1– –

Ref

.330

Scal

p(n

=3)

805

900

950

1000

1100

1200

1300

1400

1430

1500

1600

1700

1800

1900

1930

2000

0.52

(0.0

4)0.

40(0

.02)

0.39

(0.0

3)0.

33(0

.03)

0.19

(0.0

4)0.

65(0

.04)

0.50

(0.0

7)1.

98(0

.31)

2.19

(0.2

9)2.

04(0

.35)

1.43

(0.2

2)1.

87(0

.28)

1.73

(0.2

2)2.

57(0

.28)

2.52

(0.2

5)2.

09(0

.29)

– – – – – – – – – – – – – – – –

14.0

9(1

.74)

15.6

6(2

.06)

16.4

4(2

.63)

16.8

3(2

.77)

17.1

0(2

.69)

16.7

0(2

.89)

14.7

0(2

.59)

14.2

8(3

.69)

– – – – – – – – – – – – – – – –

Adu

ltsc

alp

post

mor

tem

(<12

h),e

xcis

ed,s

lab,

IS,I

AD

;da

taav

er-

aged

fort

hree

tissu

esa

mpl

esw

ithth

ickn

esse

sof

6±

0.5,

3.5

±0.

15,

and

3.5

±0.

12m

m.13

42,1

343

Skul

lbon

e(n

=10

)80

10.

11(0

.02)

–19

.48

(1.5

2)–

Adu

lthe

adpo

stm

orte

m(2

4h)

,ex

cise

d,sl

abfr

omth

eoc

cipi

-ta

lpa

rt,

IS,

IAD

;in

spec

tral

rang

e80

0–13

00nm

:μ

′ s=

1.53

3×

103λ−0

.65,[λ

]=

nm.13

18,1

342,

1343

900

0.15

(0.0

2)–

18.0

3(1

.19)

–98

00.

23(0

.03)

–17

.38

(1.0

1)–

1000

0.22

(0.0

3)–

17.1

0(0

.91)

–11

000.

16(0

.03)

–15

.92

(0.7

6)–

1180

0.67

(0.0

7)–

16.5

3(0

.83)

–12

000.

67(0

.07)

–16

.77

(0.8

5)–

1300

0.54

(0.0

5)–

14.7

8(0

.80)

–14

002.

43(0

.24)

–17

.22

(1.7

3)–

1465

3.33

(0.3

1)–

16.8

4(1

.88)

–15

003.

13(0

.26)

–15

.96

(1.3

7)–

1600

2.47

(0.4

0)–

15.8

4(3

.05)

–17

002.

77(0

.46)

–16

.12

(3.7

2)–



1740

2.98

(0.5

4)–

15.8

2(3

.79)

–18

002.

97(0

.62)

–15

.42

(3.9

8)–

1900

4.39

(1.3

3)–

11.3

7(2

.76)

–19

304.

97(1

.52)

–10

.92

(2.1

7)–

2000

4.47

(1.1

8)–

11.4

8(2

.01)

–H

eart

:E

ndoc

ard

1060

0.07

136

–0.

97E

xcis

ed,k

epti

nsa

line,

Ref

.40.

Epi

card

1060

0.35

167

–0.

98D

ata

from

Ref

.128

1.M

yoca

rd10

600.

317

7.5

–0.

96E

pica

rd10

600.

2112

7.1

–0.

93A

neur

ysm

1060

0.4

137

–0.

98T

rabe

cula

1064

1.4

424

–0.

97M

yoca

rd10

641.

432

4–

0.96

Ref

.581

.M

yoca

rd10

600.

52–

4.48

–K

idne

y:Pa

rsco

nv.

1064

2.4

72–

0.86

Dat

afr

omR

ef.1

281.

Med

ulla

ren.

1064

2.1

77–

0.87

Liv

er51

518

.9(1

.7)

285

(20)

––

Froz

ense

ctio

ns.12

47

635

2.3

(1.0

)31

3(1

36)

100

0.68

1064

0.7

356

–0.

9563

03.

241

4–

0.95

Ref

.581

.L

iver

,nat

ive

(n=

10)

850

1.0

(0.2

)20

4(3

6)0.

955

(0.0

1)–

DIS

,IM

C,G

erm

eret

al.(

1998

).13

18

980

0.8

(0.1

)18

2(3

3)0.

955

(0.0

1)–

1064

0.5

(0.1

)16

9(3

3)0.

952

(0.0

1)–

Liv

er,c

oagu

late

d(n

=10

)85

00.

7(0.

2)23

6(4

7)0.

887

(0.0

2)–

DIS

,IM

C,G

erm

eret

al.(

1998

).13

18

980

0.5

(0.1

)21

0(2

7)0.

896

(0.0

2)–

1064

0.2

(0.1

)20

0(2

6.8)

0.90

4(0

.01)

–L

ung

515

25.5

(3.0

)35

6(3

9)–

–Fr

ozen

sect

ions

,1247

635

8.1

(2.8

)32

4(4

6)81

0.75

data

from

Ref

.128

1.10

642.

839

–0.

91

(con

tinue

d)


266 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Lun

g:E

pith

eliu

m(n

=9)

400

3.41

355.

8–

0.93

8IS

,IA

D;d

ata

from

grap

hsof

Qu

etal

.(19

94).

1318

Inth

issp

ec-

tral

rang

e:μ

s=

1.21

9×

106λ−1

.347

;g=

0.94

6+

0.04

7[1

–exp

(–(λ

–500

.9)/

556.

3)],

[λ]

innm

500

2.03

286.

2–

0.94

560

01.

2921

1.8

–0.

954

700

1.10

189.

5–

0.96

7Su

bmuc

osa

(n=

15)

400

38.8

263.

1–

0.91

1IS

,IA

D;

data

from

grap

hsof

Qu

etal

.(1

994)

.1318

Inth

issp

ectr

alra

nge:

μs

=6.

036

×10

3λ−0

.52;

g=

0.92

2+

0.08

4[1

–exp

(–(λ

–488

.2)/

599.

4)],

[λ]

innm

500

4.03

241

–0.

923

600

2.21

212.

4–

0.93

570

01.

4920

5–

0.94

6C

artil

age

(n=

12)

400

15.1

300.

9–

0.90

2IS

,IA

D;

data

from

grap

hsof

Qu

etal

.(1

994)

.1318

Inth

issp

ectr

alra

nge:

μs

=3.

524

×10

3λ−0

.409

;g

=0.

929

+0.

072

[1-e

xp(–

(λ–4

99.7

)/30

9.1)

],[λ

]in

nm50

02.

5327

5.1

–0.

929

600

1.13

255

–0.

948

700

0.87

246.

3–

0.96

5M

uscl

e51

511

.2(1

.8)

530

(44)

––

Froz

ense

ctio

ns,12

47

1064

221

5–

0.96

data

from

Ref

.128

1.M

enis

cus

360

13–

108

–Fr

ozen

,tha

wed

,sla

b,40

04.

6–

67–

data

from

Ref

.40.

488

1–

30–

514

0.73

–26

–63

00.

36–

11–

800

0.52

–5.

1–

1064

0.34

–2.

6–

Pros

tate

:N

orm

al85

00.

6(0

.2)

100

(20)

–0.

94(0

.02)

Shoc

kfr

ozen

sect

ions

of60

–500

μm

,0.

5–3

hpo

stm

orte

m,

Ref

.128

1.98

00.

4(0

.2)

90(2

0)–

0.95

(0.0

2)10

640.

3(0

.2)

80(2

0)–

0.95

(0.0

2)C

oagu

late

d85

07.

0(0.

2)23

0(3

0)–

0.94

(0.0

2)Se

ctio

nsof

60–5

00m

m,0

.5–3

hpo

stm

orte

m,w

ater

bath

(75◦

C,

10m

in),

Ref

.128

1.98

05.

0(0

.2)

190

(30)

–0.

95(0

.02)

1064

4.0

(0.2

)18

0(3

0)–

0.95

(0.0

2)N

orm

al10

641.

5(0

.2)

47(1

3)0.

640.

862

Fres

hly

exci

sed,

slab

,wat

erba

th(7

0◦C

,10

min

),R

ef.4

0.C

oagu

late

d10

640.

8(0

.2)

80(1

2)1.

120.

861



Nor

mal

(n=

3)69

50.

833

0(3

0)0.

95P3

appr

oxim

atio

n;th

ick

slab

s;<

36h

post

mor

tem

;fibe

rpr

obe.

304

Scle

ra65

00.

08–

25–

Ref

.441

.Sc

lera

(n=

5)40

45.

00(0

.50)

–81

.40

(8.1

4)–

IS,I

AD

;exc

ised

tissu

esl

abs,

<24

hpo

stm

orte

m,s

tore

din

salin

eat

4◦C

;m

easu

rem

ents

atro

omte

mpe

ratu

re;μ

′ s=

8.95

×10

4λ−1

.16,

[λ]

=nm

;Ref

.129

2.44

93.

99(0

.40)

–73

.34

(7.3

3)–

499

2.96

(0.3

0)–

65.1

7(6

.52)

–54

92.

26(0

.23)

–58

.00

(5.8

0)–

599

1.95

(0.1

9)–

53.1

6(5

.32)

–64

91.

74(0

.17)

–48

.21

(4.8

2)–

699

1.67

(0.1

7)–

44.1

5(4

.42)

–74

91.

65(0

.17)

–40

.10

(4.0

1)–

799

1.58

(0.1

6)–

37.6

4(3

.76)

–Sc

lera

(n=

10)

400

4.25

(0.2

5)–

78.6

3(9

.35)

–IS

,IA

D;

stor

edat

20◦ C

insa

line;

mea

sure

men

tsat

room

tem

pera

-tu

re;i

nsp

ectr

alra

nge

370–

1800

nm:μ

′ s=

2.41

1×

105λ−1

.325

,[λ

]in

nm;R

ef.1

317.

500

1.84

(0.2

1)–

61.4

9(5

.56)

–60

00.

85(0

.21)

–51

.95

(4.9

4)–

700

0.59

(0.2

1)–

43.6

2(4

.91)

–80

00.

48(0

.21)

–36

.68

(4.9

2)–

900

0.52

(0.2

1)–

31.4

7(4

.51)

–10

000.

77(0

.25)

–26

.30

(3.7

8)–

1100

0.57

(0.2

2)–

21.5

7(3

.12)

–12

001.

56(0

.34)

–19

.09

(2.8

9)–

1300

1.58

(0.3

3)–

16.4

7(2

.44)

–14

009.

50(1

.19)

–21

.23

(3.3

9)–

1500

14.1

(1.9

1)–

23.2

6(4

.19)

–16

006.

05(1

.13)

–15

.23

(2.3

2)–

1700

5.33

(1.0

2)–

13.3

9(2

.00)

–18

006.

94(1

.27)

–13

.84

(2.0

7)–

1900

28.8

(3.9

8)–

28.8

5(6

.11)

–20

0038

.4(6

.25)

–36

.07

(8.5

4)–

2100

20.1

(2.5

6)–

22.3

2(4

.18)

–22

0015

.97

(1.8

9)–

18.5

0(2

.97)

–23

0019

.4(2

.23)

–21

.56

(3.1

4)–

2400

28.7

(3.4

6)–

28.5

7(5

.07)

–25

0049

.16

(5.7

2)–

39.3

1(8

.88)

–

(con

tinue

d)


268 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Skin

:St

ratu

mco

rneu

m19

360

00−

−–

Froz

ense

ctio

ns.40

Dat

afr

omgr

aphs

ofR

ef.

37;μ

′ sis

calc

ulat

edus

ing

Eq.

(1.2

1)fo

rg

=0.

9.25

011

5026

0026

00.

930

860

024

0024

00.

933

733

023

0023

00.

935

130

022

0022

00.

940

023

020

0020

00.

9E

pide

rmis

250

1000

2000

616

0.69

Dat

afr

omgr

aphs

ofR

ef.3

7;μ

′ san

dg

are

calc

ulat

edus

ing

308

300

1400

407

0.71

Eqs

.(1.

21)

and

(7.2

6).

337

120

1200

338

0.72

351

100

1100

306

0.72

415

6680

020

60.

7448

850

600

143

0.76

514

4460

013

90.

7758

536

470

990.

7963

335

450

880.

880

040

420

620.

85D

erm

is25

035

833

257

0.69

Dat

afr

omgr

aphs

ofR

ef.3

7;va

lues

are

tran

sfor

med

inac

cord

ance

with

data

forλ

=63

3nm

1248

(blo

odle

sstis

sue,

hydr

atio

n:85

%),μ

′ san

dg

are

calc

ulat

edus

ing

Eqs

.(1.

21)

and

(7.2

6).

308

1258

317

00.

7133

78.

250

014

10.

7235

17

458

127

0.72

415

4.7

320

820.

7448

83.

525

060

0.76

514

325

058

0.77

585

319

641

0.79

633

2.7

187.

537

0.8

800

2.3

175

300.

85E

pide

rmis

(n=

10)

400

26.3

6−

31.7

3–

IS,

DT,

10sa

mpl

esfr

omC

auca

sian

skin

;μ

′ s=

1.17

5×

103λ−0

.6,

[λ]

innm

;dat

afr

omgr

aphs

ofM

arch

esin

ieta

l.(1

992)

.372,

1318

450

13.8

4−

30.1

1–

500

7.79

−28

.27

–



550

5.73

–26

.82

–60

03.

01–

25.2

9–

650

1.58

–24

.14

–70

00.

89–

22.9

7–

750

0.49

–22

.09

–80

00.

35–

21.2

7–

Stra

tum

corn

eum

350

25.9

250

048

.99

0.90

2D

ata

from

grap

hsof

Patw

ardh

anet

al.

(200

5)(w

ithre

fere

nces

toR

efs.

37,1

248)

.372,

1318

Insp

ectr

alra

nge

400–

700

nm:g

=0.

918

+0.

304

[1–e

xp(–

(λ–5

07.4

)/24

04)]

.40

017

.28

500

48.4

40.

903

450

11.6

350

045

.24

0.91

050

010

.47

500

41.9

30.

916

550

9.83

500

38.6

90.

923

600

8.67

500

35.0

20.

930

650

8.21

500

32.2

10.

936

700

8.15

500

28.9

30.

942

Epi

derm

is(l

ight

lypi

gmen

ted/

mod

erat

ely

pigm

ente

d/hi

ghly

pigm

ente

d)

350

9.99

/30.

16/6

9.82

210.

4–

0.70

2D

ata

from

grap

hsof

Patw

ardh

anet

al.

(200

5)(w

ithre

fere

nces

toR

efs.

37,

1248

).37

2,13

18In

spec

tral

rang

e35

0–70

0nm

:μ

s=

1.75

2×

108λ−2

.33

+13

4.67

λ−0

.494

,[λ

]in

nm;

g=

0.74

5+

0.54

6[1

–exp

(–(λ

–500

)/18

06)]

.

400

6.77

/20.

21/4

6.67

156.

3–

0.71

245

04.

41/1

3.51

/31.

5212

1.6

–0.

728

500

2.58

/9.7

7/21

.82

93.0

1–

0.74

555

01.

63/6

.85/

16.1

374

.70

–0.

759

600

1.47

/5.2

2/12

.35

63.7

6–

0.77

465

01.

2/3.

68/9

.15

55.4

8–

0.78

770

01.

06/3

.07/

7.11

54.6

6–

0.80

4D

erm

is35

020

.74

212.

7–

0.71

5D

ata

from

grap

hsof

Patw

ardh

anet

al.

(200

5)(w

ithre

fere

nces

toR

efs.

37,

1248

).37

2,13

18In

spec

tral

rang

e35

0–70

0nm

:μ

s=

1.75

2×

108λ−2

.33

+13

4.67

λ−0

.494

,[λ

]in

nm;

g=

0.71

5+

3.8

×10−

4[1

–exp

(–(λ

–542

)/11

29)]

.

400

13.8

215

9.9

–0.

715

450

9.31

124.

1–

0.71

550

08.

3792

.24

–0.

715

550

7.86

77.2

2–

0.71

560

06.

9463

.09

–0.

715

650

6.57

55.9

8–

0.71

570

06.

5253

.62

–0.

715

(con

tinue

d)


270 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Epi

derm

is51

719

480

–0.

787

Ave

rage

dus

ing

data

ofV

erkr

uyss

eet

al.

(199

3)an

dva

nG

emer

tet

al.(

1992

);ox

ygen

ated

bloo

d.38

7,38

858

519

470

–0.

790

590

1946

0–

0.80

059

519

460

–0.

800

600

1946

0–

0.80

0D

erm

is51

72.

221

0–

0.78

758

52.

220

5–

0.79

059

02.

220

0–

0.80

059

52.

220

0–

0.80

060

02.

220

0–

0.80

0B

lood

517

354

468

–0.

995

585

191

467

–0.

995

590

6946

6–

0.99

559

543

465

–0.

995

600

2546

4–

0.99

5D

erm

is(l

eg)

635

1.8

(0.2

)24

4(2

1)78

0.68

Froz

ense

ctio

ns.12

47

Der

mis

749

0.24

(0.1

9)–

23.1

(0.7

5)–

Froz

ense

ctio

ns.

789

0.75

(0.0

6)–

22.8

(1.2

9)–

DIS

.329

836

0.98

(0.1

5)–

15.9

(2.1

6)–

Der

mis

633

<10

–11

.64

0.97

Tre

wee

kan

dB

arbe

nel(

1996

).33

3

Der

mis

700

2.7

(1.0

)–

21.3

(3.7

)–

Ana

lysi

sof

data

from

Har

dyet

al.(

1956

).32

2

Der

mis

633

1.9

(0.6

)–

23.8

(3.3

)–

Ana

lysi

sof

data

from

Ref

.124

8.32

2

Der

mis

633

1.5

–50

.2–

Prah

l(19

88).

333

Cau

casi

ande

rmis

450

5.13

134.

9–

0.05

4IS

,IA

D;d

ata

from

grap

hof

Ref

.126

9;in

the

spec

tral

rang

e45

0–80

0nm

:μ

s=

2.97

×10

5λ−1

.257

,[λ

]in

nm;37

2,13

18in

spec

tral

rang

e50

0–80

0nm

:g

=0.

334

+0.

217

×[1

–exp

(–(λ

–567

)/90

.76)

],[λ

]in

nm.37

2,13

18

500

3.45

119.

9–

0.12

055

02.

2810

8.1

–0.

288

600

1.81

97.3

8–

0.41

065

01.

4487

.89

–0.

461

700

1.16

78.4

8–

0.50

075

01.

0372

.29

–0.

519

800

0.88

65.8

9–

0.53

1



Skin

and

unde

rlyi

ngtis

sues

incl

udin

gve

inw

all(

leg)

633

3.1

70.7

11.4

0.8

Tis

sue

sect

ions

.463

Cau

casi

anfe

mal

esk

in(n

=3)

400

13.4

8–

34.2

8–

IS,I

AD

;w

hole

skin

;in

spec

tral

rang

e40

0–18

00nm

:μ

′ s=

2.85

×10

7λ−2

.311

+20

9.31

λ−0

.518

,[λ

]in

nm;37

2,13

18da

tafr

omgr

aphs

ofR

ef.1

257.

500

6.19

–25

.05

–60

03.

77–

18.6

7–

700

2.41

–14

.82

–80

01.

94–

12.4

2–

900

1.76

–10

.57

–10

001.

55–

9.23

–11

001.

33–

7.91

–12

001.

76–

7.11

–13

001.

76–

6.6

–14

0010

.29

–6.

21–

1500

16.2

1–

5.47

–16

005.

44–

5.87

–17

004.

11–

5.59

–18

006.

05–

5.68

–C

auca

sian

mal

esk

in(n

=3)

500

5.1

–50

–IS

,IA

D;s

ampl

eth

ickn

ess:

0.40

,0.2

3,0.

25m

m.12

57

810

0.26

–15

.8–

Cau

casi

anm

ale

skin

500

15.3

–16

7.4

–IS

,IA

D,s

ampl

eth

ickn

ess:

0.15

,0.0

5,0.

13m

m.12

57

(n=

3),e

xter

nal

pres

sure

0.1

kg/c

m2

810

0.63

–52

.7–

Cau

casi

anm

ale

skin

500

13.6

–15

6.7

–IS

,IA

D;s

ampl

eth

ickn

ess:

0.12

,0.0

5,0.

13m

m.12

57

(n=

3),e

xter

nal

pres

sure

1kg

/cm

281

00.

57–

53.4

–

Cau

casi

anfe

mal

esk

in(n

=3)

500

5.2

–23

.9–

IS,I

AD

;sam

ple

thic

knes

s:0.

42,0

.50,

0.50

mm

.1257

810

0.97

–8.

2–

Cau

casi

anfe

mal

esk

in50

07.

4–

31.5

–IS

,IA

D;s

ampl

eth

ickn

ess:

0.30

,0.3

0,0.

34m

m.12

57

(n=

3),e

xter

nal

pres

sure

0.1

kg/c

m2

810

1.4

–11

.3–

(con

tinue

d)


272 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Cau

casi

anfe

mal

esk

in50

010

.0–

40.2

–IS

,IA

D;s

ampl

eth

ickn

ess:

0.27

,0.2

0,0.

23m

m.12

57

(n=

3),e

xter

nal

pres

sure

1kg

/cm

281

01.

7–

13.1

–

His

pani

cm

ale

skin

(n=

3)50

03.

8–

24.2

–IS

,IA

D;s

ampl

eth

ickn

ess:

0.70

,0.7

8,0.

63m

m.12

57

810

0.87

–7.

5–

His

pani

cm

ale

skin

500

5.1

–37

.6–

IS,I

AD

;sam

ple

thic

knes

s:0.

35,0

.62,

0.48

mm

.1257

(n=

3),e

xter

nal

pres

sure

0.1

kg/c

m2

810

0.93

–11

.4–

His

pani

cm

ale

skin

500

6.2

–40

.4–

IS,I

AD

;sam

ple

thic

knes

s:0.

28,0

.48,

0.33

mm

.1257

(n=

3),e

xter

nal

pres

sure

1kg/

cm2

810

0.87

–10

.2–

Cau

casi

ansk

in(n

=21

)40

03.

76(0

.35)

–71

.79

(9.4

2)–

IS,

IAD

;tis

sue

slab

s,1–

6m

m;

post

mor

tem

;<

24h

afte

rde

ath;

stor

edat

20◦ C

insa

line;

mea

sure

men

tsat

room

tem

pera

ture

;in

spec

tral

rang

e40

0–20

00nm

:μ

′ s=

1.1

×10

12λ−4

+73

.7λ−0

.22,

[λ]

=nm

;Ref

.131

2.

500

1.19

(0.1

6)–

32.4

6(4

.21)

–60

00.

69(0

.13)

–21

.78

(2.9

8)–

700

0.48

(0.1

1)–

16.6

9(2

.27)

–80

00.

43(0

.11)

–14

.02

(1.8

9)–

900

0.33

(0.0

2)–

15.6

6(2

.06)

–10

000.

27(0

.03)

–16

.83

(2.7

7)–

1100

0.16

(0.0

4)–

17.1

1(2

.69)

–12

000.

54(0

.04)

–16

.71

(2.8

9)–

1300

0.41

(0.0

7)–

14.6

9(2

.59)

–14

001.

64(0

.31)

–14

.28

(3.6

9)–

1500

1.69

(0.3

5)–

14.4

1(3

.75)

–16

001.

19(0

.22)

–14

.16

(3.4

1)–

1700

1.55

(0.2

8)–

14.7

1(3

.51)

–18

001.

44(0

.22)

–13

.36

(2.9

1)–

1900

2.14

(0.2

8)–

12.1

5(3

.05)

–20

001.

74(0

.29)

–12

.01

(2.9

1)–



Epi

derm

is(n

=7)

370

13.5

(1.6

)–

115.

6(1

2.5)

–IS

,IM

C,s

labs

,Ref

.142

0;g

=0.

8.In

spec

tral

rang

e37

0–14

00nm

:μ

′ s=

1.08

×10

8λ−2

.364

+13

5.7λ

−0.2

67,[λ

]in

nm.37

2,13

1842

012

.0(1

.2)

–98

.2(9

.9)

–47

08.

4(0

.6)

–79

.6(8

.2)

–48

87.

6(0

.7)

–74

.1(7

.4)

–51

46.

3(0

.7)

–66

.7(6

.6)

–52

06.

0(0

.7)

–65

.1(6

.4)

–57

03.

9(0

.8)

–55

.2(5

.5)

–62

02.

8(0

.7)

–49

.0(4

.7)

–63

32.

6(0

.7)

–47

.6(4

.5)

–67

02.

6(0

.8)

–44

.8(4

.3)

–72

02.

4(0

.7)

–41

.1(3

.9)

–77

01.

9(0

.6)

–37

.9(3

.7)

–82

01.

5(0

.6)

–36

.0(3

.5)

–83

01.

4(0

.6)

–35

.6(3

.5)

–87

01.

0(0

.5)

–34

.1(3

.4)

–92

00.

7(0

.4)

–33

.2(3

.4)

–97

00.

6(0

.3)

–31

.5(3

.4)

–10

200.

4(0

.3)

–30

.2(3

.3)

–10

640.

2(0

.2)

–29

.7(3

.2)

–10

700.

2(0

.2)

–29

.7(3

.2)

–11

200.

2(0

.2)

–28

.6(3

.2)

–11

700.

6(0

.4)

–27

.1(3

.1)

–12

200.

7(0

.4)

–26

.3(3

.1)

–12

700.

6(0

.4)

–26

.2(3

.1)

–13

201.

1(0

.5)

–25

.3(3

.0)

–13

705.

6(1

.4)

–25

.0(3

.1)

–14

2023

.6(3

.5)

–30

.1(4

.1)

–14

7029

.6(4

.2)

–30

.8(4

.5)

–15

2018

.9(2

.9)

–26

.6(3

.9)

–15

7010

.1(2

.0)

–23

.9(3

.4)

–

(con

tinue

d)


274 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Der

mis

(n=

8)37

09.

8(1

.4)

–87

.6(1

3.6)

–IS

,IM

C,s

labs

,Ref

.142

0;g

=0.

8.In

spec

tral

rang

e37

0–14

00nm

:μ

′ s=

1.19

×10

8λ−2

.427

+71

.476

λ−0

.258

,[λ

]in

nm.37

2,13

1842

08.

5(1

.1)

–68

.5(8

.9)

–47

04.

3(0

.6)

–53

.6(6

.0)

–48

83.

6(0

.5)

–49

.0(5

.1)

–51

43.

1(0

.4)

–43

.2(4

.1)

–52

03.

0(0

.4)

–42

.0(3

.9)

–57

02.

2(0

.3)

–35

.0(3

.1)

–62

01.

5(0

.2)

–30

.7(2

.8)

–63

31.

5(0

.2)

–29

.9(2

.7)

–67

01.

5(0

.2)

–27

.8(2

.6)

–72

01.

5(0

.2)

–25

.4(2

.4)

–77

01.

3(0

.2)

–23

.3(2

.4)

–82

01.

1(0

.2)

–21

.8(2

.3)

–83

01.

1(0

.2)

–21

.5(2

.3)

–87

00.

9(0

.2)

–20

.5(2

.2)

–92

00.

8(0

.2)

–19

.9(2

.3)

–97

00.

8(0

.2)

–19

.0(2

.2)

–10

200.

7(0

.2)

–18

.4(2

.2)

–10

640.

5(0

.2)

–18

.0(2

.1)

–10

700.

5(0

.2)

–17

.9(2

.1)

–11

200.

6(0

.2)

–17

.4(2

.1)

–11

701.

2(0

.2)

–16

.9(2

.0)

–12

201.

3(0

.2)

–16

.5(2

.0)

–12

701.

0(0

.2)

–16

.3(2

.0)

–13

201.

5(0

.3)

–16

.1(1

.9)

–13

704.

8(0

.4)

–16

.6(1

.9)

–14

2017

.6(1

.8)

–20

.3(2

.1)

–14

7021

.9(2

.0)

–21

.3(2

.1)

–15

2014

.1(1

.1)

–18

.7(2

.0)

–15

708.

5(0

.7)

–16

.5(1

.9)

–



Subc

utan

eous

fat(

n=

10)

370

11.8

(2.1

)–

52.7

(6.9

)–

IS,I

MC

,sla

bs,R

ef.1

420;

g=

0.8.

Insp

ectr

alra

nge

370–

1300

nm:

μ′ s

=1.

08×

108λ−2

.525

+15

7.49

4λ−0

.345

,[λ

]in

nm.37

2,13

1842

016

.5(3

.3)

–45

.9(5

.9)

–47

07.

5(0

.9)

–39

.2(5

.0)

–48

86.

3(0

.8)

–36

.9(4

.7)

–51

44.

7(0

.7)

–33

.7(4

.3)

–52

04.

4(0

.7)

–33

.1(4

.2)

–57

03.

1(0

.9)

–28

.9(3

.6)

–62

01.

5(0

.3)

–25

.9(3

.1)

–63

31.

4(0

.3)

–25

.4(3

.0)

–67

01.

3(0

.3)

–24

.0(2

.7)

–72

01.

2(0

.2)

–22

.2(2

.4)

–77

01.

1(0

.2)

–20

.7(2

.1)

–82

01.

0(0

.2)

–19

.8(2

.0)

–83

01.

0(0

.2)

–19

.6(2

.0)

–87

00.

9(0

.2)

–18

.9(1

.9)

–92

00.

9(0

.2)

–18

.1(1

.8)

–97

00.

9(0

.3)

–17

.6(1

.8)

–10

200.

8(0

.2)

–17

.2(1

.6)

–10

640.

7(0

.2)

–16

.9(1

.5)

–10

700.

7(0

.2)

–16

.8(1

.5)

–11

200.

8(0

.2)

–16

.5(1

.5)

–11

701.

4(0

.3)

–16

.3(1

.5)

–12

201.

5(0

.3)

–16

.1(1

.5)

–12

701.

0(0

.3)

–15

.9(1

.4)

–13

201.

2(0

.3)

–15

.8(1

.4)

–13

702.

7(0

.4)

–16

.0(1

.5)

–14

209.

3(1

.4)

–17

.7(1

.8)

–14

7010

.8(1

.8)

–18

.1(1

.9)

–15

207.

0(1

.2)

–17

.0(1

.7)

–15

704.

3(0

.7)

–16

.0(1

.6)

–

(con

tinue

d)


276 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Infil

trat

ive

basa

lcel

lca

rcin

oma

370

6.8

(0.8

)–

65.2

(9.2

)–

IS,I

MC

,sla

bs,R

ef.1

420;

g=

0.8.

420

6.7

(1.1

)–

58.9

(5.2

)–

470

3.3

(0.4

)–

48.8

(3.6

)–

488

2.9

(0.5

)–

45.0

(3.3

)–

514

2.6

(0.6

)–

40.4

(3.0

)–

520

2.5

(0.6

)–

39.5

(3.0

)–

570

2.0

(0.7

)–

33.3

(2.8

)–

620

1.5

(0.6

)–

29.0

(2.8

)–

633

1.5

(0.5

)–

28.1

(2.8

)–

670

1.4

(0.5

)–

25.9

(2.8

)–

720

1.3

(0.5

)–

23.5

(2.8

)–

770

1.1

(0.4

)–

21.2

(2.6

)–

820

0.9

(0.4

)–

19.6

(2.5

)–

830

0.9

(0.4

)–

19.2

(2.5

)–

870

0.7

(0.3

)–

18.0

(2.4

)–

920

0.6

(0.3

)–

16.6

(2.0

)–

970

0.8

(0.3

)–

15.0

(1.5

)–

1020

0.7

(0.3

)–

13.6

(1.1

)–

1064

0.8

(0.4

)–

12.6

(0.9

)–

1070

0.8

(0.4

)–

12.5

(0.9

)–

1120

1.0

(0.6

)–

11.9

(0.9

)–

1170

1.6

(0.7

)–

11.5

(0.9

)–

1220

1.7

(0.9

)–

10.9

(1.0

)–

1270

1.8

(1.2

)–

10.5

(1.1

)–

1320

2.7

(1.5

)–

10.4

(1.0

)–

1370

6.9

(2.7

)–

10.9

(1.0

)–

1420

22.1

(4.6

)–

15.4

(2.5

)–

1470

27.5

(5.4

)–

16.6

(3.2

)–

1520

19.0

(4.7

)–

13.3

(2.7

)–

1570

11.2

(3.1

)–

11.1

(1.6

)–



Nod

ular

basa

lcel

lca

rcin

oma

370

8.7(

2.9)

–46

.2(6

.1)

–IS

,IM

C,s

labs

,Ref

.142

0;g

=0.

8.42

07.

3(2

.0)

–43

.6(3

.8)

–47

04.

0(1

.2)

–38

.5(2

.2)

–48

83.

4(1

.2)

–36

.0(2

.0)

–51

42.

8(1

.1)

–32

.7(1

.8)

–52

02.

7(1

.1)

–32

.0(1

.8)

–57

01.

8(0

.9)

–27

.1(1

.6)

–62

01.

3(0

.6)

–23

.4(1

.3)

–63

31.

2(0

.6)

–22

.7(1

.2)

–67

00.

9(0

.5)

–20

.7(1

.1)

–72

00.

7(0

.4)

–18

.4(1

.0)

–77

00.

4(0

.3)

–16

.6(0

.9)

–82

00.

2(0

.2)

–15

.2(0

.7)

–83

00.

2(0

.1)

–14

.9(0

.7)

–87

00.

1(0

.1)

–14

.0(0

.7)

–92

00.

1(0

.0)

–13

.1(0

.6)

–97

00.

1(0

.1)

–12

.5(0

.6)

–10

200.

0(0

.0)

–12

.0(0

.6)

–10

640.

0(0

.0)

–11

.6(0

.6)

–10

700.

0(0

.0)

–11

.5(0

.6)

–11

200.

0(0

.0)

–10

.9(0

.5)

–11

700.

1(0

.1)

–10

.4(0

.4)

–12

200.

2(0

.1)

–10

.1(0

.4)

–12

700.

1(0

.1)

–10

.0(0

.4)

–13

200.

5(0

.1)

–9.

7(0

.4)

–13

703.

2(0

.3)

–10

.3(0

.6)

–14

2014

.6(2

.0)

–14

.4(1

.3)

–14

7018

.6(1

.6)

–15

.9(1

.5)

–15

2011

.9(0

.7)

–13

.1(1

.0)

–15

706.

7(0

.04)

–10

.6(0

.8)

–

(con

tinue

d)


278 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Squa

mou

sce

llca

rcin

oma

370

9.4(

2.0)

–43

.6(6

.1)

–IS

,IM

C,s

labs

,Ref

.142

0;g

=0.

8.42

012

.1(2

.3)

–42

.1(5

.0)

–47

04.

1(0

.6)

–33

.8(4

.7)

–48

83.

4(0

.5)

–31

.3(4

.3)

–51

43.

2(0

.4)

–28

.0(3

.9)

–52

03.

2(0

.4)

–27

.4(3

.8)

–57

02.

9(0

.4)

–23

.5(3

.2)

–62

01.

4(0

.2)

–19

.5(2

.6)

–63

31.

3(0

.2)

–18

.8(2

.5)

–67

01.

1(0

.2)

–17

.1(2

.3)

–72

00.

9(0

.2)

–15

.2(2

.0)

–77

00.

7(0

.2)

–13

.5(1

.8)

–82

00.

5(0

.2)

–12

.4(1

.6)

–83

00.

5(0

.2)

–12

.2(1

.5)

–87

00.

4(0

.1)

–11

.6(1

.4)

–92

00.

3(0

.1)

–10

.9(1

.3)

–97

00.

4(0

.2)

–10

.2(1

.2)

–10

200.

4(0

.2)

–9.

4(1

.2)

–10

640.

4(0

.2)

–8.

8(1

.2)

–10

700.

4(0

.2)

–8.

8(1

.2)

–11

200.

4(0

.2)

–8.

5(1

.2)

–11

701.

0(0

.3)

–8.

4(1

.1)

–12

201.

1(0

.3)

–8.

1(1

.1)

–12

701.

1(0

.3)

–7.

8(1

.1)

–13

201.

7(0

.4)

–7.

7(1

.1)

–13

704.

3(0

.5)

–8.

5(1

.1)

–14

2017

.0(1

.2)

–12

.9(1

.8)

–14

7023

.5(2

.1)

–14

.4(2

.3)

–15

2015

.0(1

.5)

–11

.6(1

.6)

–15

709.

2(1

.2)

–9.

2(1

.3)

–



Sple

en10

646.

013

7–

0.90

Dat

afr

omR

ef.1

281.

Stom

ach:

Mus

cle

1064

3.3

29.5

–0.

87D

ata

from

Ref

.128

1.M

ucou

s10

642.

873

2–

0.91

Inte

gral

1064

0.8

128

–0.

91M

ucou

s(n

=15

)40

013

.37

(2.0

9)53

.0(3

.23)

51.0

6(6

.85)

0.03

7(0

.107

)IS

,IM

C;

stor

edat

20◦ C

insa

line;

mea

sure

men

tsat

room

tem

pera

ture

;in

spec

tral

rang

e40

0–20

00nm

:μ′ s

=1.

027

×10

12λ−4

+16

4.3λ

−0.4

46;

g=

0.49

8+

0.31

9[1–

exp(

–(λ

–53

3.7)

/138

.7)]

,[λ

]in

nm;R

ef.1

316.

500

2.07

(0.2

5)44

.12

(2.4

7)24

.77

(2.2

4)0.

439

(0.1

08)

600

1.37

(0.2

2)46

.72

(1.6

9)17

.65

(1.5

4)0.

622

(0.1

09)

700

0.75

(0.1

5)48

.02

(1.1

9)13

.72

(1.0

9)0.

714

(0.0

86)

800

0.78

(0.1

7)46

.99

(0.8

9)11

.22

(0.8

1)0.

761

(0.1

08)

900

0.92

(0.2

0)44

.65

(0.8

3)9.

64(0

.76)

0.78

4(0

.108

)10

001.

18(0

.23)

42.1

7(0

.74)

8.73

(0.6

7)0.

793

(0.1

08)

1100

1.11

(0.2

4)42

.66

(0.6

6)7.

80(0

.60)

0.81

7(0

.108

)12

001.

76(0

.28)

40.8

3(0

.59)

7.38

(0.5

3)0.

819

(0.1

09)

1300

1.76

(0.2

7)39

.99

(0.5

1)6.

67(0

.47)

0.83

3(0

.109

)14

008.

70(1

.02)

25.7

2(0

.97)

9.34

(0.8

8)0.

637

(0.1

09)

1500

11.9

1(1

.85)

23.4

5(1

.56)

10.0

(1.4

2)0.

574

(0.0

97)

1600

5.0

(0.5

7)31

.25

(0.5

6)6.

56(0

.51)

0.79

0(0

.105

)17

004.

74(0

.56)

34.1

1(0

.47)

5.99

(0.4

3)0.

824

(0.1

05)

1800

6.05

(0.6

8)31

.15

(0.6

1)6.

43(0

.55)

0.79

4(0

.105

)19

0019

.48

(2.7

8)17

.34

(2.6

2)12

.25

(2.3

8)0.

294

(0.1

04)

2000

20.9

2(3

.53)

26.2

8(3

.80)

11.4

8(3

.45)

0.56

3(0

.105

)To

oth:

Den

tin54

34

180

––

IS,G

PM∗ ,

Ref

s.66

and

97,s

eeal

soR

ef.6

38.

633

413

0–

–E

nam

el63

36.

0∗12

00∗

672∗

0.44

∗54

3<

145

––

633

<1

25–

–D

entin

543

3–4

280

(84)

–0.

93(0

.02)

GPM

,do

uble

HG

PF,

frac

tions

ofis

otro

pic

scat

tere

rsar

e0–

2%fo

rde

ntin

and

60–3

5%fo

ren

amel

;po

lishe

dpl

ane-

para

llels

ectio

nsof

30–2

000

mm

.638

633

3–4

280

(84)

–0.

93(0

.02)

1053

3–4

260

(78)

–0.

93(0

.02)

Ena

mel

543

<1

105

(30)

–0.

96(0

.02)

633

<1

60(1

8)–

0.96

(0.0

2)10

53<

115

(5)

–0.

96(0

.02)

(con

tinue

d)


280 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Ena

mel

200

≈10

≈450

−–

Com

pile

dda

taof

afe

wpa

pers

,fro

mgr

aphs

ofR

ef.8

27.

300

≈5≈2

70−

–40

0≈1

≈150

−–

500

<1

≈73

−–

600

<1

≈64

−–

700

<1

≈50

−–

800

<1

≈33

−–

1000

<1

≈16

−–

Den

tin29

4022

00–

−–

Tim

e-re

solv

edra

diom

etry

,dat

afr

omgr

aphs

ofR

ef.8

27.

2790

1500

–−

–96

0065

00–

−–

10,6

0080

0–

−–

Ena

mel

2940

800

–−

–27

9040

0–

−–

9600

8000

–−

–10

,600

800

–−

–D

entin

2790

988

(111

)–

−–

Tra

nsm

issi

onm

easu

rem

ents

,Ref

.827

.10

,300

1198

(104

)–

−–

10,6

0081

3(6

3)–

−–

Ena

mel

2940

768

(27)

–−

–27

9045

1(2

9)–

−–

10,3

0011

68(4

9)–

−–

10,6

0081

9(6

2)–

−–

Tra

becu

lar

mes

hwor

kof

the

eye

(n=

10)

400

9.62

–21

.61

–IS

,K

ubel

ka–M

unk

mod

el,

the

K-M

coef

ficie

nts

wer

eca

lcul

ated

and

conv

erte

dto

linea

rtr

ansp

ort

coef

ficie

nts;

data

from

grap

hof

Farr

aret

al.

(199

9);

insp

ectr

alra

nge:

μ′ s

=7.

8×

107λ−2

.631

+11

7.4λ

−0.4

17,[λ

]in

nm.13

18

450

7.57

–17

.49

–50

05.

28–

14.6

1–

550

3.61

–12

.71

–60

02.

29–

11.4

7–

650

1.32

–10

.86

–70

00.

70–

10.3

4–

750

0.32

–9.

89–

800

0.16

–9.

56–



Ute

rus

635

0.35

(0.1

)39

4(9

1)12

20.

69Fr

ozen

sect

ions

.1247

Vei

n(f

emor

al)

1064

3.2

487

–0.

97D

ata

from

Ref

.128

1N

orm

al(n

=4)

1300

−15

0–36

0–

0.9–

1O

ptic

alco

here

nce

tom

ogra

phy

(OC

T);

1300

4h

auto

psy;

g eff

=co

sθrm

s,θ

rms:

rms

scat

teri

ngan

gle,

g eff≥

g.L

ipid

rich

(n=

4)13

00−

0–20

0–

0.6–

1Fi

brou

s(n

=3)

1300

−50

–400

–0.

6–1

Fibr

ocal

cific

(n=

3)13

00−

0–20

0–

0.8–

1Fa

t:A

bdom

inal

(n=

2)36

03.

12(0

.78)

–32

.59

(3.2

6)–

IS,

IAD

;tis

sue

slab

s,<

12h

afte

rsu

rger

y,st

ored

at4◦

Cin

salin

e;m

easu

rem

ents

atro

omte

mpe

ratu

re;i

nsp

ectr

alra

nge

600–

1600

nm:

μ′ s=1

.23

×10

3λ−0

.59,[λ

]=nm

;40

03.

97(0

.99)

–25

.62

(2.5

6)–

500

2.37

(0.5

9)–

28.2

3(2

.82)

–60

01.

90(0

.47)

–28

.58

(2.8

6)–

Ref

.129

4.70

01.

84(0

.46)

–26

.27

(2.6

3)–

800

1.87

(0.4

7)–

25.7

4(2

.57)

–90

01.

80(0

.45)

–21

.21

(2.1

2)–

1000

1.77

(0.4

4)–

20.1

4(2

.01)

–11

001.

68(0

.42)

–19

.05

(1.9

0)–

1200

1.79

(0.4

5)–

17.5

5(1

.76)

–13

001.

52(0

.38)

–17

.42

(1.7

4)–

1400

1.75

(0.4

4)–

17.1

5(1

.71)

–15

001.

63(0

.41)

–17

.08

(1.7

1)–

1600

1.47

(0.3

7)–

16.4

1(1

.64)

–17

002.

11(0

.53)

–17

.21

(1.7

2)–

1800

1.92

(0.4

8)–

17.4

0(1

.74)

–19

002.

48(0

.62)

–20

.38

(2.0

4)–

2000

2.12

(0.5

3)–

19.4

4(1

.94)

–21

001.

74(0

.43)

–18

.72

(1.8

7)–

2200

1.65

(0.4

1)–

18.9

5(1

.89)

–Su

bcut

aneo

us(n

=6)

400

2.26

(0.2

4)–

13.3

9(2

.78)

–IS

,IA

D;

tissu

esl

abs,

1–3

mm

;<

6h

afte

rsu

rger

y;st

ored

at20

◦ Cin

salin

e;m

easu

rem

ents

atro

omte

mpe

ratu

re;i

nsp

ectr

alra

nge

600–

1500

nm:μ

′ s=

1.05

×10

3λ−0

.68,[λ

]=

nm;R

efs.

1312

,129

5.50

01.

49(0

.06)

–13

.82

(4.0

0)–

600

1.18

(0.0

2)–

13.3

9(4

.65)

–70

01.

11(0

.05)

–12

.17

(4.4

1)–

800

1.07

(0.1

1)–

11.6

2(4

.63)

–90

01.

07(0

.07)

–9.

97(3

.42)

–

(con

tinue

d)


282 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

1000

1.06

(0.0

6)–

9.39

(3.3

2)–

1100

1.01

(0.0

5)–

8.74

(3.2

8)–

1200

1.06

(0.0

7)–

7.91

(3.1

7)–

1300

0.89

(0.0

7)–

7.81

(3.1

9)–

1400

1.08

(0.0

3)–

7.51

(3.3

1)–

1500

1.05

(0.0

2)–

7.36

(3.4

2)–

1600

0.89

(0.0

4)–

7.16

(3.2

1)–

1700

1.26

(0.0

7)–

7.53

(3.3

3)–

1800

1.21

(0.0

1)–

7.50

(3.4

8)–

1900

1.62

(0.0

6)–

8.72

(4.1

5)–

2000

1.43

(0.0

9)–

8.24

(4.0

3)–

Fore

arm

:Fa

t63

30.

026

–12

.00.

9�SR

R;(

�)

from

liter

atur

e.38

8

Mus

cle

633

0.96

–5.

30.

9�

Muc

ous

ofm

axill

ary

sinu

sat

antr

itis

(n=

10)

400

4.89

(0.9

2)–

36.0

1(6

.41)

–IS

,IA

D;

tissu

esl

abs,

1–2

mm

;<

6h

afte

rsu

rger

y;st

ored

at20

◦ Cin

salin

e;m

easu

rem

ents

atro

omte

mpe

ratu

re;i

nsp

ectr

alra

nge

600–

1300

nm:

500

1.13

(0.1

8)–

17.6

9(2

.84)

–60

00.

45(0

.23)

–13

.81

(2.4

3)–

700

0.16

(0.2

4)–

11.5

3(2

.02)

–μ

′ s=

4.43

7×

105λ−1

.62,[λ

]=

nm;R

efs.

1312

,129

5.80

00.

13(0

.16)

–9.

79(1

.68)

–90

00.

12(0

.09)

–7.

62(0

.92)

–10

000.

27(0

.21)

–6.

14(0

.74)

–11

000.

16(0

.14)

–5.

19(0

.58)

–12

000.

57(0

.31)

–4.

43(0

.43)

–13

000.

67(0

.35)

–3.

89(0

.38)

–14

004.

84(1

.79)

–5.

07(0

.71)

–15

006.

06(2

.38)

–4.

95(1

.21)

–16

002.

83(1

.01)

–3.

13(0

.55)

–17

002.

26(0

.79)

–2.

83(0

.51)

–18

003.

04(1

.15)

–3.

04(0

.57)

–19

009.

23(2

.69)

–7.

01(3

.57)

–20

009.

31(2

.28)

–6.

26(3

.56)

–



Ora

lmuc

osa:

Nor

mal

tissu

e85

5–

27(1

1)–

–O

ptic

alco

here

nce

mic

rosc

opy.

1421

Dys

plas

tictis

sue

855

–39

(6)

––

Squa

mou

sce

llca

rcin

oma

855

–60

(9)

––

Skin

:C

auca

sian

derm

is(n

=12

)63

30.

33(0

.09)

–27

.3(5

.4)

–Si

ngle

inte

grat

ing

sphe

reco

mpa

riso

nm

etho

d,IM

C;

sam

ples

from

abdo

min

alan

dbr

east

tissu

eob

tain

edfr

ompl

astic

surg

ery

orpo

stm

orte

mex

amin

atio

ns,

g=

0.9

issu

ppos

edva

lue

inca

lcul

atio

ns.33

3,33

4

700

0.19

(0.0

6)–

23.2

(4.1

)–

900

0.13

(0.0

7)–

16.3

(2.5

)–

Neg

roid

derm

is(n

=5)

633

2.41

(1.5

3)–

32.1

(20.

4)–

700

1.49

(0.8

8)–

26.8

(14.

1)–

900

0.45

(0.1

8)–

18.1

(0.4

)–

Subd

erm

is(p

rim

arily

glob

ular

fatc

ells

)(n

=12

)63

30.

13(0

.05)

–12

.6(3

.4)

–70

00.

09(0

.03)

–12

.1(3

.2)

–90

00.

12(0

.04)

–10

.8(2

.7)

–M

uscl

e(n

=1)

633

1.21

–8.

9–

700

0.46

–8.

3–

900

0.32

–5.

9–

Cau

casi

ande

rmis

(n=

12)

633

0.32

–26

.99

–IS

,IM

C;

sam

ples

from

abdo

min

alan

dbr

east

tissu

eob

tain

edfr

ompl

astic

surg

ery

orpo

stm

orte

mex

ami-

natio

ns;

data

from

grap

hsof

Ref

.33

3;μ

′ s=

1.66

×10

5λ−1

.356

,[λ

]in

nm.37

2,13

18

700

0.12

–23

.02

–75

00.

09–

20.6

2–

800

0.02

–18

.80

–85

00.

01–

17.4

1–

900

0.03

–16

.18

–95

00.

22–

15.1

0–

1000

0.39

–14

.68

–N

egro

idde

rmis

(n=

5)63

32.

45–

32.2

9–

IS,

IMC

;sa

mpl

esfr

omab

dom

inal

and

brea

sttis

sue

obta

ined

from

plas

ticsu

rger

yor

post

mor

tem

exam

i-na

tions

;da

tafr

omgr

aphs

ofR

ef.

333;

μ′ s

=3.

33×

105λ−1

.438

,[λ

]in

nm.37

2,13

18

700

1.51

–27

.24

–75

01.

12–

24.0

2–

800

0.80

–21

.26

–85

00.

61–

19.7

0–

900

0.46

–18

.55

–95

00.

49–

17.6

7–

1000

0.49

–16

.83

–

(con

tinue

d)


284 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Subd

erm

is(p

rim

arily

glob

ular

fatc

ells

)(n

=12

)63

30.

12–

12.5

8–

IS,

IMC

;sa

mpl

esfr

omab

dom

inal

and

brea

sttis

sue

obta

ined

from

plas

ticsu

rger

yor

post

mor

tem

exam

inat

ions

;dat

afr

omgr

aphs

ofR

ef.

333;

μ′ s

=13

9.24

λ−0

.373

,[λ

]in

nm.37

2,13

1870

00.

09–

12.1

0–

750

0.09

–11

.75

–80

00.

08–

11.4

0–

850

0.09

–11

.17

–90

00.

12–

10.9

5–

950

0.15

–10

.81

–10

000.

12–

10.7

1–

Mus

cle

(n=

1)63

31.

23–

8.94

–IS

,IM

C;

sam

ples

from

abdo

min

alan

dbr

east

tissu

eob

tain

edfr

ompl

astic

surg

ery

orpo

stm

orte

mex

amin

atio

ns;d

ata

from

grap

hsof

Ref

.33

3;μ

′ s=

7.67

×10

3λ−1

.045

,[λ

]in

nm.37

2,13

1870

00.

48–

8.18

–75

00.

41–

7.71

–80

00.

28–

7.04

–85

00.

30–

6.67

–90

00.

32–

6.21

–95

00.

46–

5.90

–10

000.

51–

5.73

–Sa

mpl

e/su

bjec

t:01

/01;

fem

ale

(F),

age

=51

yr;

back

ofkn

ee,l

eftl

eg;

mod

erat

ein

flam

mat

ion

inde

rmis

;SC

=40

–70μ

m;

E=

40–1

50μ

m;D

=30

0μ

m

1460

1600

2200

17.8

8(1

.12)

5.35

(0.2

4)7.

46(0

.56)

– – –

10.7

4(0

.49)

8.06

(0.2

9)7.

17(0

.26)

– – –

DIS

,IA

D;s

labs

cont

aini

ngst

ratu

mco

rneu

m(S

C),

epid

erm

is(E

),an

dde

rmis

(D),

take

nfr

om14

subj

ects

;mea

sure

dw

ithin

24h

ofex

cisi

on;

heat

edto

37◦ C

;th

ree

mea

sure

men

tson

each

side

ofth

esa

mpl

e;2.

5-cm

-dia

met

ersa

mpl

epo

rts

onth

ese

tup,

for

smal

lsam

ple

size

redu

ced

to1.

3cm

*;to

tal

data

for

52w

avel

engt

hsin

rang

e10

00–2

200

nmar

eav

aila

ble.

1267

02/0

1;F,

age

=51

yr;b

ack

1460

18.7

0(1.

13)

–11

.39(

0.65

)–

ofkn

ee,l

eftl

eg;m

oder

ate

1600

5.46

(0.2

7)–

8.62

(0.3

4)–

infla

mm

atio

nin

derm

is;

SC=

40–7

0μ

m;E

=40

–140

μm

;D=

300μ

m

2200

8.86

(0.4

6)–

8.15

(0.2

6)–

03/0

2;F,

age

=66

yr;l

ower

1460

16.0

1(0.

56)

–9.

83(0

.59)

–ba

ck,r

ight

side

;mild

sola

rda

mag

e;SC

=20

–50

μm

;E=

30μ

m;

D=

200μ

m

1600

4.91

(0.1

0)–

6.78

(0.4

5)–

2200

10.9

4(0.

23)

–9.

00(0

.54)

–



04/0

2;F,

age

=66

yr;l

ower

1460

12.6

5(0

.96)

–8.

61(0

.63)

–ba

ck,r

ight

side

;mild

sola

r16

003.

86(0

.28)

–6.

04(0

.29)

–da

mag

e;SC

=20

–50μ

m;

E=

30μ

m;D

=20

0μ

m22

008.

58(0

.55)

–7.

74(0

.23)

–

05/0

3;F,

age

=67

yr;s

hin,

1460

16.5

8(3

.26)

–11

.68

(1.4

1)–

righ

tleg

;mild

sola

rda

mag

e,16

005.

15(0

.60)

–8.

89(1

.11)

–ch

roni

cin

flam

mat

ion;

SC=

20–5

0μ

m;

E=

30–5

0μ

m;D

=20

0μ

m

2200

9.65

(1.1

7)–

10.3

1(0

.81)

–

06/0

3;F,

age

=67

yr;s

hin,

1460

18.0

7(0

.42)

–13

.13

(0.6

3)–

righ

tleg

;mild

sola

rda

mag

e,16

005.

60(0

.17)

–10

.34

(0.5

2)–

chro

nic

infla

mm

atio

n;SC

=20

–50μ

m;

E=

30–5

0μ

m;D

=20

0μ

m

2200

11.2

6(0

.16)

–12

.20

(0.8

8)–

07/0

4;M

,age

=64

yr;

1000

0.69

(0.0

1)–

10.4

5(0

.61)

–th

igh,

righ

tleg

;mild

chro

nic

1460

16.6

4(0

.95)

–10

.75

(0.8

1)–

derm

atiti

s;SC

=20

–30μ

m;

1600

4.96

(0.2

7)–

7.72

(0.4

0)–

E=

50–9

0μ

m;D

=30

0μ

m22

0013

.04

(2.3

6)–

9.42

(1.5

7)–

08/0

5;M

,age

=75

yr;

1000

0.83

(0.0

3)–

12.2

5(1

.20)

–lo

wer

thig

h,le

ftle

g;14

6019

.06

(1.2

2)–

11.4

6(1

.09)

–no

rmal

skin

;SC

=8–

12μ

m;

1600

5.75

(0.2

7)–

8.31

(0.7

6)–

E=

20–6

0μ

m;D

=20

0μ

m22

0011

.92

(0.4

1)–

10.3

4(0

.76)

–09

/05;

M,a

ge=

75yr

;lo

wer

thig

h,le

ftle

g;no

rmal

skin

;SC

=8–

12μ

m;

E=

20–6

0μ

m;D

=20

0μ

m

1000

0.85

(0.0

2)–

11.6

6(0

.96)

–14

6018

.03

(2.0

1)–

11.1

9(1

.51)

–16

005.

61(0

.56)

–7.

87(0

.81)

–22

0011

.85

(0.8

3)–

10.0

3(0

.90)

–10

/06;

F,ag

e=

42yr

;gr

oin,

left

side

;mild

chro

nic

infla

mm

atio

n;SC

=5μ

m;

E=

25–3

0μ

m;D

=20

0μ

m

1000

0.80

(0.0

1)–

14.1

7(0

.71)

–14

6020

.49

(0.8

9)–

13.6

4(1

.44)

–16

005.

85(0

.14)

–10

.05

(0.5

5)–

2200

12.4

6(0

.42)

–11

.79

(0.6

9)–

11/0

6;F,

age

=42

yr;

1000

0.77

(0.0

3)–

13.9

5(1

.12)

–gr

oin,

left

side

;mild

1460

20.2

4(1

.04)

–13

.18

(1.7

2)–

chro

nic

infla

mm

atio

n;16

005.

76(0

.28)

–9.

48(0

.91)

–SC

=5μ

m;E

=25

–30μ

m;

D=

200μ

m22

0012

.71

(0.5

8)–

10.8

9(1

.20)

–

(con

tinue

d)


286 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

12/0

7;M

,age

=33

yr;

1000

0.82

(0.0

2)–

14.3

5(0

.81)

–po

ster

ior

thig

h,ri

ghts

ide;

1460

19.0

1(1

.28)

–13

.30

(0.9

1)–

mild

chro

nic

derm

atiti

s;16

005.

81(0

.33)

–10

.14

(0.4

9)–

SC=

2–5μ

m;E

=5–

10μ

m;D

=30

0μ

m22

0011

.13(

1.21

)–

9.00

(0.3

3)–

13/0

8;F,

age

=52

yr;

1000

0.97

(0.0

8)–

13.7

0(0.

35)

–ax

illar

y,ri

ghts

ide;

mild

1460

21.3

9(1

.25)

–12

.54

(0.7

2)–

peri

vasc

ular

chro

nic

1600

6.17

(0.3

0)–

9.94

(0.7

8)–

infla

mm

atio

n;SC

=5–

7μ

m;

E=

25μ

m;D

=10

0μ

m22

0012

.53(

0.84

)–

9.45

(0.8

4)–

14/0

9;M

,age

=37

yr;b

ack

1000

0.82

(0.0

2)–

15.0

0(0

.49)

–of

thig

h,up

per

left

;mild

1460

23.3

1(0

.71)

–12

.32

(0.5

1)–

chro

nic

derm

atiti

s;16

006.

68(0

.11)

–10

.01

(0.3

7)–

SC=

3μ

m;E

=13

μm

;D

=30

0μ

m22

0015

.19

(1.3

7)–

8.54

(0.5

2)–

15/1

0;M

,age

=70

yr;

1000

1.04

(0.0

2)–

12.2

6(0

.44)

–sc

alp;

mild

chro

nic

1460

15.9

5(0

.99)

–10

.75

(1.2

0)–

derm

atiti

sw

/sol

arel

asto

sis;

1600

5.09

(0.2

3)–

8.83

(0.9

2)–

SC=

4–15

μm

;E=

8–10

μm

;D

=20

0μ

m22

0012

.65

(0.5

2)–

8.83

(1.9

4)–

16/1

1*;M

,age

=61

yr;

1000

0.79

(0.0

2)–

13.1

1(0

.61)

–sc

alp;

mild

chro

nic

derm

atiti

s14

6016

.47

(1.0

5)–

12.4

5(0

.56)

–w

/sol

arel

asto

sis;

SC=

2–4μ

m;

E=

6μ

m;D

=30

0μ

m16

005.

11(0

.24)

–10

.43

(0.5

7)–

2200

13.3

0(1

.48)

–9.

89(0

.79)

–17

/12*

;F,a

ge=

68yr

;10

001.

06(0

.03)

–8.

79(1

.18)

–sc

alp/

faci

altis

sue;

mild

sola

r14

6012

.81

(1.8

4)–

9.60

(0.5

7)–

dam

age,

chro

nic

infla

mm

atio

n;16

004.

26(0

.50)

–6.

93(0

.75)

–SC

=2μ

m;E

=8–

10μ

m;

D=

200μ

m22

0011

.32

(1.5

2)–

8.14

(0.8

1)–



18/1

2*;F

,age

=68

yr;

1000

1.32

(0.0

5)–

8.63

(1.9

1)–

scal

p/fa

cial

tissu

e;se

vere

1460

12.6

8(5

.07)

–8.

74(1

.26)

–so

lar

dam

age,

mild

chro

nic

1600

4.31

(1.3

4)–

6.60

(0.9

2)–

infla

mm

atio

n;SC

=2μ

m;

E=

8–10

μm

;D=

150μ

m22

0011

.33

(3.0

5)–

7.30

(0.2

4)–

19/1

3*;F

,age

=53

yr;

1000

1.55

(0.0

2)–

11.9

6(0.

65)

–sc

alp/

faci

altis

sue;

mild

1460

16.1

3(1

.38)

–11

.52(

0.64

)–

chro

nic

infla

mm

atio

n;16

005.

38(0

.31)

–8.

65(0

.54)

–SC

=4μ

m;E

=10

μm

;D

=20

0μ

m22

0013

.84

(1.0

2)–

9.67

(0.6

5)–

20/1

3;F,

age

=53

yr;

1000

1.53

(0.0

2)–

12.8

9(0.

77)

–sc

alp/

faci

altis

sue;

mild

1460

16.8

2(1

.13)

–12

.01(

0.81

)–

sola

rda

mag

e;SC

=4μ

m;

1600

5.57

(0.1

9)–

9.47

(0.6

0)–

E=

10μ

m;D

=20

0μ

m22

0013

.46

(0.5

8)–

10.4

1(0.

71)

–21

/14;

F,ag

e=

52yr

;10

000.

88(0

.03)

–14

.96(

1.28

)–

abdo

men

;mild

chro

nic

1460

18.2

1(2

.51)

–14

.20(

0.71

)–

infla

mm

atio

n;SC

=4–

5μ

m;

1600

5.74

(0.6

8)–

10.5

8(0.

44)

–E

=10

μm

;D=

200μ

m22

0011

.33

(0.7

6)–

10.4

0(0.

47)

–22

/14;

F,ag

e=

52yr

;10

000.

94(0

.02)

–15

.26(

0.63

)–

abdo

men

;mild

chro

nic

1460

18.4

6(1

.64)

–15

.10(

1.01

)–

infla

mm

atio

n;SC

=4–

5μ

m;

E=

10μ

m;D

=20

0μ

m16

005.

76(0

.31)

–11

.05(

0.39

)–

2200

13.7

2(0

.52)

–13

.72(

0.42

)–

Cau

casi

ansk

in(n

=22

)10

000.

98–

12.5

8–

DIS

,IA

D;w

hole

skin

,22

sam

ples

take

nfr

om14

subj

ects

;mea

sure

dw

ithin

24h

ofex

cisi

on;

data

from

grap

hsof

Ref

.126

7;in

spec

tral

rang

e10

00–1

250

nm:μ

′ s=

7.59

×10

7λ−2

.503

+16

5.86

λ−0

.402

,[λ

]in

nm.

1100

0.98

–11

.77

–12

001.

87–

11.0

8–

1300

1.77

–10

.69

–14

007.

94–

11.3

9–

1500

13.1

–11

.38

–16

005.

20–

10.1

0–

1700

4.85

–9.

96–

1800

6.5

–9.

96–

1900

13.0

–10

.63

–

(con

tinue

d)


288 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Ute

rus:

Post

men

opau

sal

630

0.51

5(0

.054

)–

9.1

(1.7

)–

Freq

uenc

y-do

mai

n(F

D);

inta

ctut

eri

wer

eob

tain

edby

hyst

erec

-to

my;

duri

ngm

easu

rem

entp

erio

d(3

–4h)

wet

gauz

ew

asap

plie

d,R

ef.4

46.

Prem

enop

ausa

l63

00.

193

(0.0

13)

–7.

3(0

.9)

–63

00.

314

(0.0

30)

–8.

9(1

.5)

–63

00.

213

(0.0

24)

–6.

0(0

.8)

–63

00.

197

(0.0

30)

–7.

3(1

.5)

–Fi

broi

d63

00.

0824

(0.0

075)

–7.

2(0

.9)

–M

yom

etri

um(n

=6)

610

0.45

–13

.3–

IS,I

MC

;in

the

spec

tral

rang

e:μ

′ s=

9.59

7×

105λ−1

.731

,[λ

]in

nm;d

ata

from

grap

hsof

Ref

.335

.1318

700

0.19

–11

.47

–80

00.

10–

9.08

–90

00.

10–

7.32

–10

000.

38–

6.09

–L

eiom

yom

a(fi

broi

d)(n

=6)

610

0.15

–10

.99

–IS

,IM

C;i

nth

esp

ectr

alra

nge:μ

′ s=

1.02

9×

106λ−1

.783

,[λ

]in

nm;d

ata

from

grap

hsof

Ref

.335

.1318

700

0.07

–8.

73–

800

0.03

–6.

75–

900

0.03

–5.

47–

1000

0.32

–4.

73–

Invi

vom

easu

rem

ents

Ade

noca

rcin

oma

(mul

tiple

subc

utan

eous

larg

e-ce

ll,m

ale

62yr

):

FD,r

sd=

2.2

cm.43

2,43

4

Abd

omin

al,n

orm

altis

sue

674

0.05

89(0

.003

6)–

8.94

(0.1

9)–

811

0.06

45(0

.003

2)–

8.82

(0.1

8)–

849

0.06

90(0

.002

5)–

8.77

(0.1

4)–

956

0.11

10(0

.015

)–

7.00

(0.6

2)–

Abd

omin

al,t

umor

674

0.16

9(0

.02)

–8.

48(0

.73)

–81

10.

190

(0.0

15)

–8.

30(0

.49)

–84

90.

276

(0.0

3)–

9.93

(0.8

7)–

956

––

––



Bac

k,no

rmal

tissu

e67

40.

0883

(0.0

06)

–10

.7(0

.4)

–81

10.

0892

(0.0

05)

–9.

99(0

.27)

–84

90.

0915

(0.0

030)

–9.

65(0

.15)

–95

60.

127

(0.0

3)–

6.3

(0.9

)–

Bac

k,tu

mor

674

0.17

4(0

.02)

–10

.4(0

.9)

–81

10.

177

(0.0

13)

–9.

23(0

.5)

–84

90.

190

(0.0

1)–

9.20

(0.3

3)–

956

0.18

6(0

.16)

–4.

7(2

.7)

–B

rain

:N

orm

alco

rtex

,tem

pora

lan

dfr

onta

llob

e67

4>

0.2

–10

(1)

0.92

SRR

;mea

sure

men

tsdu

ring

brai

nsu

rger

y.12

45

849

>0.

2–

9.2

(1)

0.92

956

>0.

2–

8.5

(1)

0.92

Nor

mal

optic

nerv

e67

40.

60(0

.25)

–18

(1)

0.92

849

0.75

(0.2

5)–

17(1

)0.

9295

60.

65(0

.25)

–16

(1)

0.92

Ast

rocy

tom

aof

optic

nerv

e67

41.

6(1

)–

14(1

)0.

9284

91.

1(1

)–

8.5

(1)

0.92

950

1.8

(1)

–8.

5(1

)0.

92N

orm

alco

rtex

,fro

ntal

lobe

674

<0.

2–

10(0

.5)

–SR

R;m

easu

rem

ents

duri

ngbr

ain

surg

ery;

1284

data

from

Ref

.128

5.81

1<

0.1

–9.

1(0

.5)

–84

9<

0.1

–9.

2(0

.5)

–95

60.

15(0

.1)

–8.

9(0

.5)

–N

orm

alco

rtex

,fro

ntal

lobe

674

0.2

(0.1

)–

10(0

.5)

–81

10.

2(0

.1)

–8.

2(0

.5)

–84

9<

0.1

–8.

2(0

.5)

–95

60.

25(0

.1)

–8.

2(0

.5)

–N

orm

alop

ticne

rve

674

0.6

(0.3

)–

17.5

(2)

–84

90.

8(0

.3)

–16

(2)

–95

60.

7(0

.3)

–15

.2(2

)–

(con

tinue

d)


290 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Ast

rocy

tom

aof

optic

nerv

e67

41.

4(0

.3)

–12

.5(1

)–

811

1.2

(0.3

)–

9.5

(1)

–84

90.

9(0

.3)

–7.

6(1

)–

956

1.5

(0.3

)–

7.3(

1)–

Nor

mal

whi

tem

atte

r67

42.

5(0

.5)

–13

.5(1

)–

849

0.95

(0.2

)–

8.5(

1)–

956

0.9

(0.2

)–

7.8(

1)–

Whi

tem

atte

rw

ithsc

ar67

4<

0.2

–6.

5(0.

5)–

849

<0.

2–

8(0

.5)

–M

edul

lobl

asto

ma

674

2.6

(0.5

)–

14(1

)–

849

1(0

.2)

–10

.7(1

)–

956

0.75

(0.2

)–

4(1)

–B

reas

t(fe

mal

e):

Nor

mal

(30

Japa

nese

wom

en,a

vera

ged

for

alla

ges)

753

0.04

6(0

.014

)–

8.9

(1.3

)–

Tim

edo

mai

n(T

D),

μa(

cm1)

≈0.

087

−8.

31×

10−4

x,μ

′ s(cm

−1)≈

13−

0.08

x,w

here

x=

age

(20-

80yr

).41

5

Nor

mal

(6w

omen

,26

–43

yr)

800

0.01

7–0.

045

–7.

2–13

.5–

TD

,μ′ s

(cm

−1)≈

16.7

–7.

9×

10−3

λ,λ

=50

0–10

60nm

,R

ef.4

14.

Nor

mal

(6w

omen

,tis

sue

thic

knes

s,33

–49

mm

atlig

htco

mpr

essi

on)

580

0.70

(0.1

2)–

––

Mea

sure

men

tsof

tran

smis

sion

,g≈

0.92

–0.9

5,μ

′ s=

12–1

3cm

−1,R

ef.3

17.

780

0.23

(0.0

2)–

––

850

0.27

(0.0

3)–

––

Bre

astc

ance

r(5

patie

nts)

630

0.30

5(0

.16)

–9.

41(7

.35)

–SR

R;r

elap

sed

canc

er,H

PD(7

2h)

.1249

Nor

mal

(56

yr)

674

0.04

–8.

5–

FD,r

sd=

2.2

cm.43

2,43

4

811

0.03

5–

7.4

–84

90.

035

–7.

0–

956

0.08

5–

6.5

–Fi

broa

deno

ma

with

duct

alhy

perp

lasi

a(5

6yr

)67

40.

055

–9

–81

10.

06–

8–

849

0.05

5–

7.6

–95

60.

12–

7.5

–



Nor

mal

(27

yr)

674

0.03

5–

11.1

–81

10.

03–

9.6

–84

90.

038

–9.

6–

956

0.09

–9.

7–

Flui

d-fil

led

cyst

(27

yr)

674

0.07

–7.

9–

811

0.07

–7.

0–

849

0.08

–7.

0–

956

0.16

–7.

0–

Papi

llary

canc

er(5

5yr

)69

00.

084

(0.0

14)

–15

.0(0

.3)

–FD

,dif

fusi

onap

prox

imat

ion.

1296

825

0.08

5(0

.017

)–

12.7

(0.3

)–

Nor

mal

(67

yr)

674

0.05

7–

9.5

–FD

,dif

fusi

onap

prox

imat

ion;

tum

or1.

8×

0.9

cm;s

egm

ente

dre

cons

truc

tion.

1303

782

0.05

0–

9.4

–80

30.

047

–9.

0–

849

0.05

4–

8.9

–D

ucta

lcar

cino

ma

insi

tu(6

7yr

)67

40.

17–

4.1

–

782

0.18

–3.

6–

803

0.15

–4.

2–

849

0.21

–3.

3–

Cal

f(1

1su

bjec

ts,

800

0.17

(0.0

5)–

9.4(

0.7)

–μ

′ s≈16

−8.

9×

10−3

λ,

14m

easu

rem

ents

)λ

=76

0−90

0nm

,Ref

.400

.C

ervi

cals

trom

altis

sue

849

0.34

61.1

–0.

9R

ef.1

289;

data

from

Ref

.339

.C

ervi

calt

issu

e:μ

bs=

μsp

b,w

here

p bis

the

prob

abili

tyof

back

scat

teri

ng.13

05–1

307

Epi

thel

ium

(n=

36)

1300

–10

–140

–0.

1–11

OC

T,tw

o-la

yere

dm

odel

,gen

etic

inve

rse

algo

rith

m.13

05

Stro

ma

(n=

36)

1300

–30

–290

–1.

5–12

Dys

plas

iaII

-III

1300

–40

–65

–1.

4–3.

6O

CT,

sing

le-l

ayer

edm

odel

,gen

etic

inve

rse

algo

rith

m.13

07

Leu

kopl

akia

1300

–16

–32

–1.

3–2.

0E

pith

eliu

m13

00–

80(2

5)–

0.28

(0.0

8)O

CT,

gene

ticin

vers

eal

gori

thm

Stro

ma

1300

–21

0(3

0)–

3.0

(2)

two-

laye

red

mod

elC

ance

r13

00–

300

(20)

–1.

2(0

.6)

sing

le-l

ayer

edm

odel

.1306

,130

7

(con

tinue

d)


292 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Gas

troi

ntes

tinal

trac

t:γ

=(1

−g2)/

(1−g

1)

Muc

osa

inth

ean

trum

500

2.5

(0.8

)–

16.8

(3.4

)1.

98(0

.20)

End

osco

pic

SRR

,r s

dfr

om0.

3to

1.35

mm

;IM

C,

two-

mom

ents

HG

PF[s

eeE

q.(7

.14)

];35

patie

nts

(21

fem

ales

and

14m

ales

,age

dfr

om23

to87

),fo

rea

chpa

tient

,fo

ursi

tes

wer

eus

ually

sele

cted

:tw

oin

antr

uman

dtw

oin

fund

us,

aver

age

data

for

norm

altis

sue

from

grap

hsof

Ref

.127

3.

550

3.6

(1.3

)–

13.8

(3.4

)1.

93(0

.15)

600

1.0

(0.6

)–

12.8

(2.1

)1.

90(0

.12)

650

0.5

(0.5

)–

11.7

(1.8

)1.

87(0

.12)

700

0.4

(0.4

)–

10.7

(1.6

)1.

86(0

.12)

750

0.45

(0.4

5)–

9.7

(1.6

)1.

85(0

.12)

800

0.5

(0.4

)–

9.0

(1.6

)1.

85(0

.12)

850

0.7

(0.5

)–

8.8

(1.6

)1.

85(0

.12)

900

0.8

(0.5

)–

8.3

(1.5

)1.

86(0

.12)

Muc

osa

inth

efu

ndus

500

3.3

(0.8

)–

21.7

(3.1

)2.

12(0

.26)

550

4.4

(1.5

)–

18.6

(3.1

)2.

04(0

.24)

600

1.8

(0.5

)–

16.5

(2.1

)2.

00(0

.19)

650

0.8

(0.4

)–

15.0

(2.1

)1.

97(0

.17)

700

0.7

(0.4

)–

13.8

(1.7

)1.

98(0

.15)

750

0.7

(0.5

)–

12.4

(1.6

)1.

98(0

.15)

800

0.7

(0.3

)–

11.7

(1.6

)1.

95(0

.12)

850

0.7

(0.3

)–

11.0

(1.4

)1.

92(0

.12)

900

0.8

(0.4

)–

10.3

(1.4

)1.

94(0

.12)

Hea

d(7

subj

ects

,80

00.

16(0

.01)

–9.

4(0

.7)

–μ

′ s(cm

−1)≈

14.5

−6.

5×

103λ

,λ=

760–

900

nm,R

ef.4

00.

10m

easu

rem

ents

)Fo

rear

m(5

subj

ects

,14

mea

sure

men

ts)

800

0.23

(0.0

4)–

6.8

(0.8

)–

TD

,μ′ s

(cm

−1)≈

11−5

.1×

10−3

λ,λ

=76

0–90

0nm

.329

Fore

arm

715

0.18

–3.

7–

FD;r

sd:a

few

cm;d

ata

from

Ref

.129

0.82

50.

24–

3.0

–Fo

rehe

ad71

50.

16–

7.3

–82

50.

16–

6.9

–Sk

in:

Der

mis

660

0.07

–0.2

–9−

14.5

–SR

R,I

MC

.322



Skin

633

0.62

–32

–D

ogni

tzan

dW

agni

eres

(199

8)(s

eeR

ef.7

67).

700

0.38

–28

.7–

Skin

(0–1

mm

)63

30.

67–

16.2

–R

ef.3

88.

Skin

(1–2

mm

)63

30.

026

–12

–Sk

in(>

2m

m)

633

0.96

–5.

3–

Fore

arm

:E

pide

rmis

633

8�–

17.5

0.9�

SRR

;(�

)fr

omlit

erat

ure.

388

Der

mis

633

0.15

–17

.50.

9�

Epi

derm

isan

dde

rmis

750

0.37

5–

15–

SRR

;dif

fusi

onap

prox

imat

ion12

91(f

rom

Ref

.495

).Su

bcut

aneo

usfa

t75

00.

03–

10–

Arm

633

0.17

(0.0

1)–

9.08

(0.0

5)–

SRR

,9

dete

ctin

g60

0-μ

mfib

ers;

mea

nse

para

tion

1.7

mm

;M

ieph

ase

func

tion.

767

660

0.12

8(0

.005

)–

8.68

(0.0

5)–

700

0.09

0(0

.002

)–

8.14

(0.0

5)–

Foot

sole

633

0.07

2(0

.002

)–

11.1

7(0

.09)

–66

00.

053

(0.0

03)

–10

.45

(0.0

9)–

700

0.03

7(0

.001

)–

9.52

(0.0

8)–

Fore

head

633

0.09

0(0

.009

)–

16.7

2(0

.09)

–66

00.

052

(0.0

03)

–16

.16

(0.0

8)–

700

0.02

40(0

.002

)–

15.3

8(0

.06)

–A

bdom

inal

skin

:C

hose

ndi

rect

ion

810

0.01

4–

20–

SRR

;C

CD

dete

ctor

,r s

d≤

10m

m;

diff

usio

nap

prox

ima-

tion.

495

Perp

endi

cula

rdi

rect

ion

(alo

ngco

llage

nfib

ers)

810

0.07

–10

–

Fore

arm

(lig

htsk

in,n

=7)

:Sk

inte

mpe

ratu

re:2

2◦C

590

2.37

2(0

.282

)–

9.19

1(0

.931

)–

SRR

;MC

-gen

erat

edgr

id.12

71

750

0.96

6(0

.110

)–

7.34

0(0

.901

)–

950

0.98

1(0

.073

)–

6.06

7(0

.847

)–

Skin

tem

pera

ture

:38◦

C59

02.

869

(0.2

89)

–9.

613

(0.8

94)

–75

01.

157

(0.1

06)

–7.

649

(0.9

71)

–95

01.

135

(0.1

23)

–6.

234

(0.9

28)

–

(con

tinue

d)


294 Chapter 7

Tab

le7.

1(c

ontin

ued)

Tis

sue

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

′ s,cm

−1g

Rem

arks

Der

mis

ofa

low

erar

m13

00–

47–

–O

CT.

13

Stra

tum

corn

eum

offin

ger

1300

–12

––

Vol

arsi

deof

low

erar

m:

OC

T.13

01

Epi

derm

is13

00–

15–2

0–

–U

pper

derm

is13

00–

80–1

00–

–Pa

lmof

hand

:St

ratu

mco

rneu

m13

00–

10–1

5–

–E

pide

rmis

:G

ranu

lar

laye

r13

00–

60–7

0–

–B

asal

laye

r13

00–

40–5

0–

–U

pper

derm

is13

00–

50–8

0–

–V

olar

side

oflo

wer

arm

(epi

derm

isan

dde

rmis

):O

CT;

1302

dept

hup

to35

0m

m;

skin

trea

ted

with

ade

terg

ent

solu

tion

(2%

ofan

ioni

cte

nsid

esin

wat

er).

Nor

mal

1300

–14

0–

–T

reat

ed13

00–

80–

–Sk

ull

674

<0.

2–

9(1

)–

SRR

;m

easu

rem

ents

duri

ngbr

ain

surg

ery;

1284

data

from

Ref

.128

5.84

9<

0.1

–9

(1)

–95

60.

15(0

.1)

–8.

5(1

)–



measurements by using different theoretical expressions or numerical methods(two-flux and multi-lux models; IMC or IAD methods) relating μa, μs, and g tothe parameters under investigation.

Any three measurements from the following five are sufficient for the evalua-tion of all three optical parameters:40

1. Total (or diffuse) transmittance for collimated or diffuse radiation,2. Total (or diffuse) reflectance for collimated or diffuse radiation,3. Absorption by a sample placed inside an integrating sphere,4. Collimated transmittance (of unscattered light), and5. Angular distribution of radiation scattered by the sample.

Iterative methods normally take into account discrepancies between refrac-tive indices at sample boundaries, as well as the multilayer nature of the sample.The following factors are responsible for errors in the estimated values of opticalcoefficients and need to be considered during a comparative analysis of opticalparameters obtained in different experiments:40

• Physiological conditions of tissues (degree of hydration, homogene-ity, species-specific variability, frozen/thawed or fixed/unfixed state,in vitro/in vivo measurements, smooth/rough surface),

• Geometry of irradiation,• Matching/mismatching interface refractive indices,• Orientation of detecting optical fibers inside the sample relative to the source

fibers,• Numerical aperture of the recording fibers,• Angular resolution of photodetectors,• Separation of radiation experiencing forward scattering from unscattered

radiation, and• Theory used to solve the inverse problem.

7.2 Integrating Sphere Technique

One indirect method to determine optical properties of tissues in vitro isthe integrating sphere technique.6, 48, 49, 57, 345, 372, 1239, 1240, 1242, 1246, 1251–1258, 1262, 1264,

1265, 1267, 1268, 1281, 1308, 1309, 1311, 1312, 1316–1318 Diffuse reflectance, Rd, total transmit-tance, Tt, and collimated transmittance, Tc, are measured. In general, absorptioncoefficient, μa, scattering coefficient, μs, and anisotropy factor, g, can be obtainedfrom these data by using an inverse method based on the radiative transfer the-ory. When the scattering phase function, p(θ), is available from goniophotometry,g can readily be calculated. In this case, for the determination of μa and μs

it is sufficient to measure Rd and Tt only. Sometimes in experiments with tis-sue and blood samples, a double-integrating sphere configuration is preferable,because in this case, both reflectance and transmittance can be measured simul-taneously, and less degradation of the sample is expected during measurements


296 Chapter 7

Figure 7.2 Double integrating sphere setup (see Ref. 1311).

(see Fig. 7.2). Nevertheless, in the case of a double-integrating sphere arrange-ment of the experiment, in addition to the single-integrating sphere corrections ofmeasured signals, multiple exchange of light between the spheres should be consid-ered.390, 1253, 1254 The collimated transmittance measurement is usually conductedas shown in Fig. 7.1(a).

The integrating sphere technique was used by a number of investigatorsto determine the absorption coefficient, scattering coefficient, anisotropy factor,and/or reduced scattering coefficient of tissues and blood.6, 48, 49, 57, 345, 372, 1239–1241,

1246, 1251–1258, 1262, 1264, 1265, 1267, 1268, 1281, 1308, 1309, 1311, 1312, 1316–1318 Barium-sulfate orSpectralon integrating spheres were used in these experiments. As monochromaticlight sources, a laser, a Xe-lamp, and/or a Hg-lamp combined with monochromatorwere used, while a photomultiplier or a Si-photodiode was employed as a detec-tor. Occasionally, a white light source was used as irradiator and CCD fiber-opticspectrometer as detector.1308

Certain tissues (for instance, those containing melanin) and blood have hightotal attenuation coefficients in the visible and NIR spectral ranges. Therefore, thecollimated transmittance measurement for such samples (for example, the undi-luted blood layer with a moderate thickness, ≈ 0.1 mm48) is a technically difficulttask. To solve this problem, a powerful light source combined with a sensitivedetector must be used.49 Alternatively, it is possible to collect the collimated lightalong with some forward-scattered light by using the third integrating sphere.1262

In this case, the collimated transmittance is separated from the scattered flux duringthe stage of the data processing by using, for example, an MC technique or a smallangle approximation.1255

7.3 Multiflux Models

To separate the light beam attenuation due to absorption from loss due to one-dimensional scattering, the two-flux Kubelka–Munk model (KMM) is the simplestapproach to solve the problem. This approach has been widely used to determinethe absorption and scattering coefficients of biological tissues, provided the scat-tering is significantly dominant over the absorption.1, 2, 36, 37, 40, 305, 1239, 1251, 1264, 1281

The KMM assumes that light incident on a slab of tissue because of interactionwith the scattering media can be modeled by two fluxes, counterpropagating inthe tissue slab. The optical flux, which propagates in the same direction as the



incident flux, is decreased by absorption and scattering processes, and increasedby backscattering of the counterpropagating flux in the same direction. Changes incounterpropagating flux are determined in an analogous manner. The fraction ofeach flux lost by absorption per unit path length is denoted as K, while the fractionlost due to scattering is called S. The primary assumptions of the KMM are as fol-lows: K and S parameters are assumed to be uniform throughout the tissue slab; alllight fluxes are diffuse; and the amount of light lost from the edges of the sampleduring reflectance measurements is negligible. Basic KMM does not account forreflections at boundaries at which index of refraction mismatches exist.

Following the KMM and diffusion approximation of the RTE, the KMMparameters were expressed in terms of light transport theory: the absorption andscattering coefficients and scattering anisotropy factor.37, 40 Thus, when scatteringsignificantly prevails on absorption, a simple experimental method using modifiedKMM expressions can be successfully employed as

S = 1

bd= ln

[1 − Rd(a − b)

Td

],

K = S(a − 1), a = 1 − T2d + R2

d

2Rd, b =

√a2 − 1, (7.1)

K = 2μa, S = 3

4μs(1 − g) − 1

4μa,

μt = μa + μs, μ′s = μs(1 − g) > μa,

where μt is determined based on Eq. (1.1) from measured values of collimatedtransmittance, Tc. Thus, all three parameters (μa, μs, and g) can be found from theexperimental data for total transmittance, Tt, diffuse reflectance, Rd, and collimatedtransmittance, Tc, of the sample.

Further modifications of the KMM were undertaken to account for reflectionsat the sample boundaries.306, 321, 1264 The use of one of the measuring modalitiesin question can be illustrated by determining the optical parameters of humanskin epidermis. Transmittance and reflectance spectra of thin epidermal slices(stripping samples, 20–50 μm thickness) measured in the wavelength range of240–400 nm on a spectrophotometer with an integrating sphere were used to cal-culate the absorption, μa(λ), and scattering, μs(λ), coefficients based on a four-fluxmodel, taking into consideration the collimated reflection at the sample bound-aries306, 321 (see Fig. 7.3). The differences between the absorption coefficients inthe considered wavelength range for normal human epidermis and samples con-taining psoriatic plaques are attributable to variations in skin metabolism (see UVabsorption spectra of major skin epidermal chromophores; Fig. 1.6). The epider-mis of psoriatic skin is characterized by a marked optical inhomogeneity causedby structural changes of the tissue in the psoriatic plaques and the appearance ofair-filled microspaces between parakeratotic scales, accounting for a 10–15% risein the diffuse reflection coefficient (for stripping samples of normal epidermis, thiscoefficient at 240–400 nm increases by 6–10% at most).


298 Chapter 7

Figure 7.3 Experimental spectra for total transmittance (a) and diffuse reflectance (b).Calculated spectra for the absorption (μa) and scattering (μs) coefficients derived fromexperimental transmittance and diffuse reflectance spectra of stripped human epidermisusing the four-flux model (c). Solid lines, normal skin; dotted lines, psoriatic skin (see Refs.306 and 321).

Often, such simple methods as the KMM48 or δ-Eddington approxima-tion345, 1255 are used as the first step in the inverse algorithm for estimation of theoptical properties of tissues and blood. The estimated values of the optical prop-erties are then used to calculate the reflected and transmitted signals, employingone of the more sophisticated models of light propagation in tissue or blood. Atthe next step, the calculated and measured values are compared. If the requiredaccuracy is not achieved, the current optical properties are altered by using one ofthe optimization algorithms. The procedures of altering the optical properties andcalculating the reflected and transmitted signals are repeated until the calculatedvalues match the measured values with the required accuracy.

7.4 Inverse Adding-Doubling Method

The IAD method provides a tool for the rapid and accurate solution of the inversescattering problem.372, 392, 393, 1242, 1256, 1257, 1265–1267, 1281, 1311, 1316–1318 It is based onthe general method for the solution of the transport equation for plane-parallel lay-ers suggested by van de Hulst274 and introduced to tissue optics by Prahl.1269, 1270

An important advantage of the IAD method when applied to tissue optics isthe possibility of rapidly obtaining iterative solutions with the aid of up-to-datemicrocomputers; moreover, it is sufficiently flexible to account for anisotropy ofscattering and the internal reflection from the sample boundaries. The methodincludes the following steps:

1. Choice of optical parameters to be measured,2. Counting reflections and transmissions,3. Comparison of calculated and measured reflectance and transmittance, and4. Repetition of the procedure until the estimated and measured values coincide

with the desired accuracy.



In principle, the method allows any intended accuracy to be achieved for allparameters being measured, provided the necessary computer time is available. Anerror of 3% or less is considered acceptable.1242 Additionally, the method may beused to directly correct experimental findings obtained with the aid of integratingspheres. The term “doubling” means that the reflection and transmission estimatesfor a layer at certain ingoing and outgoing light angles may be used to calculateboth the transmittance and reflectance for a twice as thick layer, by means of super-imposing one upon the other and summing the contributions of each layer to thetotal reflectance and transmittance. Reflection and transmission in a layer havingan arbitrary thickness are calculated in consecutive order, first for the thin layerwith the same optical characteristics (single scattering), then for any selected layerby consecutive doubling of the thickness. The term “adding” indicates that thedoubling procedure may be extended to heterogeneous layers for modeling multi-layer tissues or taking into account internal reflections related to abrupt changes inrefractive index.1242

The adding-doubling technique is a numerical method for solving the one-dimensional transport equation in slab geometry.372, 1242, 1269, 1270, 1311, 1312, 1318 It canbe used for media with an arbitrary phase function and arbitrary angular distri-bution of the spatially uniform incident radiation. Thus, finite beam size and sidelosses of light cannot be taken into account. The method is based on the observa-tion that for an arbitrary incident radiance angular distribution, Iin(ηc), where ηc

is the cosine of the polar angle, the angular distribution of the reflected radiance(normalized to an incident diffuse flux) is given by1242, 1269, 1270, 1311

Iref(ηc) =1∫

0

Iin(η′c)R(η′

c,ηc)2η′cdη

′c, (7.2)

where R(η′c,ηc) is the reflection redistribution function determined by the optical

properties of the slab.The distribution of the transmitted radiance can be expressed in a similar man-

ner, with obvious substitution of the transmission redistribution function, T(η′c,ηc).

If M quadrature points are selected to span over the interval (0,1), the respectivematrices can approximate the reflection and transmission redistribution functions:

R(η′ci,ηcj) → Rij; T(η′

ci,ηcj) → Tij. (7.3)

These matrices are designated as the reflection and transmission operators, respec-tively. If a slab with boundaries indexed as 0 and 2 is composed of two layers,(01) and (12), with internal interface of 1 between the layers, the reflection andtransmission operators for the whole slab (02) can be expressed as

T02 = T12(E − R10R12)−1T01,R20 = T12(E − R10R12)−1R10T21 + R21,T20 = T10(E − R12R10)−1T21,R02 = T10(E − R12R10)−1R12T01 + R01,

(7.4)


300 Chapter 7

where E is the identity matrix, defined in this case as:

Eij = 1

2ηciwiδij, (7.5)

where wi is the weight assigned to the ith quadrature point and δij is a Kronekerdelta symbol, δij = 1 if i = j, and δij = 0 if i �= j.

The definition of the matrix multiplication also slightly differs from thestandard. Specifically,

(AB)ik ≡M∑

j=1

Aij2ηcjwjBjk. (7.6)

Equation (7.4) allows one to calculate the reflection and transmission oper-ators of a slab when those of the comprising layers are known. The idea of themethod is to start with a thin layer for which the RTE can be simplified and solvedwith relative ease, producing the reflection and transmission operators for the thinlayer, then to proceed by doubling the thickness of the layer until the thickness ofthe whole slab is reached. Several techniques exist for layer initialization. Single-scattering equations for reflection and transmission for the Henyey–Greensteinfunction are given in Refs. 274 and 1269. The refractive index mismatch can betaken into account by adding effective boundary layers of zero thickness and deter-mining the reflection and transmission operators by Fresnel’s formulas. The totaltransmittance and reflectance of the slab are obtained by straightforward integra-tion of Eq. (7.2). Different methods of performing this integration are discussedin Ref. 1269. The IAD program provided by Prahl1270 allows one to obtain theabsorption and scattering coefficients from the measured diffuse reflectance, Rd,and diffuse transmittance, Td, of the tissue slab. This program is the numericalsolution to the steady-state RTE [see Eq. (1.9)] realizing an iterative process, whichestimates the reflectance and transmittance from a set of optical parameters untilthe calculated reflectance and transmittance match the measured values. Valuesfor the anisotropy factor, g, and the refractive index, n, must be provided to theprogram as input parameters.

When using only four quadrature points, the IAD method provides opticalparameters that are accurate to within 2–3%,1242 as was mentioned previously;higher accuracy, however, can be obtained by using more quadrature points, butthis would require increased computation time. Another valuable feature of theIAD method is its validity for the study of samples with comparable absorptionand scattering coefficients,1242, 1265, 1266 because other methods based on only dif-fusion approximation are inadequate. Furthermore, because both anisotropic phasefunction and Fresnel reflection at boundaries are accurately approximated, the IADtechnique is well-suited to optical measurements for biological tissues and bloodheld between two glass slides.49, 1242, 1265

The IAD method has been successfully applied to determine optical parame-ters of blood; human and animal dermis; ocular tissues such as retina, choroids,sclera, conjunctiva, and ciliary body; aorta; and other soft tissues in a wide rangeof wavelengths.49, 372, 392, 393, 593, 1257, 1266–1268, 1318



The adding-doubling method provides accurate results in cases when the sidelosses are not significant, but it is less flexible than the MC technique.

7.5 Inverse Monte Carlo Method

Both the real geometry of the experiment and the tissue structure may be com-plicated. Therefore, the MC method should be used if reliable estimates are tobe obtained. Many algorithms for using the IMC method are currently avail-able in the literature.2, 306, 311, 320, 322, 333–335, 339, 341, 344, 370, 372, 383, 389, 390, 581, 723, 1199,

1240, 1244–1246, 1252, 1268, 1271–1274, 1277, 1278, 1281, 1308, 1309, 1311, 1316–1318 Many studies usethe MC simulation program provided by Jacques.1274 Among the initially designedIMC algorithms, we will discuss two similar algorithms for determining all threeoptical parameters of the tissue (μa, μs, and g) based on the in vitro evaluationof the total transmittance, diffuse reflectance, and collimated transmittance usinga spectrophotometer with integrating spheres.306, 1240, 1246, 1252, 1281, 1308 The initialapproximation (to speed up the procedure) was achieved with the help of theKubelka–Munk theory, specifically its four-flux variant.306, 1246 Both algorithmstake into consideration the sideways loss of photons, which becomes essential insufficiently thick samples. Similar results were obtained by using the condensedIMC method.320, 322

The MC technique is employed as a method to solve the forward problemin the inverse algorithm for the determination of the optical properties of tissuesand blood. The MC method is based on the formalism of the RTT (see Chapters 1and 2), where the absorption coefficient is defined as a probability of a photon to beabsorbed per unit length, and the scattering coefficient is defined as the probabilityof a photon to be scattered per unit length. Using these probabilities, a randomsampling of photon trajectories is generated.

The basic algorithm for the generation of photon trajectories can be shortlydescribed as follows.1311 A photon, described by three spatial coordinates and twoangles (x, y, z, θ, and φ), is assigned weight W = W0 and placed in its initial posi-tion, depending on the source characteristics. The step size, l, of the photon isdetermined by using Eqs. (2.43)–(2.45). The direction of the photon’s next move-ment is determined by the scattering phase function, substituted as the probabilitydensity distribution.

Several approximations for the scattering phase function of tissue and bloodhave been used in MC simulations. These include the empirical phase functionswidely used to approximate the scattering phase function of tissue and blood,Henyey–Greenstein phase function (HGPF) [see Eq. (1.15)], the Gegenbauer ker-nel phase function (GKPF),1323 and the theoretical Mie phase function.214 TheHGPF has one parameter, g, that may be represented as an infinite series ofLegendre polynomials, P1

n(cosθ):

phg (θ) = 1

4π

∞∑n=0

(2n + 1) fnP1n (cosθ), (7.7)

where fn = gn is the nth order moment of the phase function.


302 Chapter 7

The GKPF has two variable parameters, α and g:

pgk (θ) = K[1 + g2 − 2g cosθ

]−(α+1), (7.8)

where

K = αgπ−1(1 − g2)2α[(1 + g)2α − (1 − g)2α]−1,α > −1/2, |g| ≤ 1.

The GKPF is a generalization of the HGPF and can be reduced to HGPF bysetting α = 0.5. The GKPF may be represented as an infinite series of Gegenbauerpolynomials, Cα

n :1323, 1324

pgk (θ) = 2K

(1 − g2)

∞∑n=0

(1 + n

α

)Cα

n (cosθ) gn. (7.9)

The HGPF and GKPF are widely employed in radiative transport calculationsfor description of the single-scattering process in whole blood because of theirmathematical simplicity.48, 346, 1325 However, it is clear that the HGPF and GKPFcannot be used for accurate calculations of the angular light distribution scatteredby a single erythrocyte. For some calculations, the theoretical Mie phase functionmay be useful:214

p (θ) = 1

k2r2

(|S1|2 + |S2|2), (7.10)

where S1 and S2 are functions of the polar scattering angle and can be obtainedfrom Mie theory in the form of Eq. (3.62).

As noted in Chapter 1, many MC algorithms309–311, 318, 327, 348, 356–358 do notallow us to describe the interaction of photons with RBCs or to reliably deter-mine the scattering anisotropy factor. The influence of the scattering phase functionform on the MC simulation is investigated in Refs. 360 and 361. An MC algorithm(pciMC), taking into account both the photon migration outside the cell and insidethe cell without the need for macroscopic scattering phase function and scatteringanisotropy factor, is presented in Ref. 368.

For the HGPF, the random scattering angle, θHGrnd , is given by311

θHGrnd = arccos

{1

2g

[1 + g2 −

(1 − g2

1 − g + 2gξ

)2]}

, (7.11)

where ξ is a random number uniformly distributed over the interval (0,1) [seeEq. (2.44)].

For the GKPF, the random scattering angle, θGKrnd , is determined as230

θGKrnd = arccos

[(1 + g2 − 1/ α

√ζrnd)/2g

], (7.12)

where ζrnd = 2αgξ/K + (1 + g)−2α, and α and K are defined in Eq. (7.8).



If the experimental scattering phase function is known for the discrete set ofscattering angles θi, f (θ) = f (θi), it can be determined in the total angular range byusing the spline-interpolation technique.1312 Then, the value of the function Fn =∫ θn

0 f (θ)dθ can be calculated numerically for any value of θn. It is clear that Fn is anondecreasing function that is mapping the interval (0,1). Therefore, when randomvalue γ is sampled, θexp

rnd is determined by setting Fn = ξ.The Mie phase function can be tabulated and treated in the same way as the

experimental phase function.230 In most cases, azimuthal symmetry is assumed.This leads to p(φ) = 1/2π and, consequently, φrnd = 2πξ. At each step, the pho-ton loses part of its weight due to absorption: Wn+1 = Wn(1 − �), where � is thealbedo of the medium.

When the photon reaches the boundary, part of its weight is transmitted accord-ing to the Fresnel equations. The amount transmitted through the boundary is addedto the reflectance or transmittance. Because the refraction angle is determined bySnell’s law, the angular distribution of the outgoing light can be calculated. Thephoton with the remaining part of the weight is specularly reflected and continuesits random walk.

When the photon’s weight becomes lower than a predetermined minimal value,the photon can be terminated using “the Russian roulette” procedure.311, 318 Thisprocedure saves time, because it does not make sense to continue the random walkof the photon, which will not essentially contribute to the measured signal. Onthe other hand, it ensures that the energy balance is maintained throughout thesimulation process.

The MC method has several advantages over other methods because it may takeinto account mismatched medium-glass and glass-air interfaces, losses of light atthe edges of the sample, any phase function of the medium, and the finite size andarbitrary angular distribution of the incident beam. If the collimated transmittanceis measured, then the contribution of scattered light into the measured collimatedsignal can be considered.1255 The only disadvantage of this method is the long timeneeded to ensure good statistical convergence, because it is a statistical approach.The standard deviation of a quantity (diffuse reflectance and transmittance) approx-imated by the MC technique decreases proportionally to 1/

√N, where N is the total

number of launched photons.Values of coefficients μa, μs, and g for the human brain, canine prostate, and

porcine liver at 800 and 1064 nm, as well as μa and μs spectra at 350–1050 nm forsome strongly scattering eye tissues (sclera, retina), obtained by the IMC methodfrom in vitro reflection and transmission measurements, have been reported in Refs.1240 and 1252 (some of these data for human tissues are presented in Table 7.1).Stable operation of the algorithm was maintained by generation of from 105 to5 × 105 photons per iteration. Two to five iterations were usually necessary toestimate the optical parameters with approximately 2% accuracy. The requiredcomputer time can be reduced not only by the condensed IMC method but alsoby means of graphical solutions of the inverse problem, following a preliminaryMC simulation.581, 1271–1273 In recent years, the parallel computing technology


304 Chapter 7

has widely been used, for example, an MCML algorithm has been adapted forGPU computing364 and a versatile MC algorithm CUDA NVIDIA GPU has beendeveloped.370

In general, in vivo μa and μ′s values for human skin proved to be significantly

smaller than those obtained in vitro (approximately 10 and 2 times, respec-tively).322, 333–335, 767 For μa, the discrepancy may be attributed to the low sensitivityof the double-integrating sphere, and goniometric techniques have been appliedfor in vitro measurements at weak absorption combined with strong scattering(μa � μs) and sample preparation methods. For μ′

s, the discrepancy may be relatedto the strong dependence of the method on variations in the relative refractiveindex of scatterers and the ground medium of the tissue m, μ′

s ∼ (m − 1)2, whichcan be quite different for living and sampled tissues.271, 1271 The ex vivo measure-ments using the single integrating sphere comparison technique, the correspondingIMC model, and very carefully prepared human skin samples allow for accurateevaluation of μa and μ′

s that are very similar to in vivo measurements333–335 (seeTable 7.1). This technique has the advantage over the conventional double-spheremethod in that no corrections are required for the sphere properties, so sufficientlyaccurate measurements to recover the absorption coefficient can be reliably made.

7.6 Spatially Resolved Techniques

For many tissues, in vivo measurements are possible only in the geometry of thebackscattering. The spatially resolved reflectance, R(rsd), is defined as the powerof the backscattered light per unit of area detected by a receiver at the surface ofthe tissue at a distance rsd from the source. R(rsd) depends on the optical propertiesof the sample, i.e., the absorption coefficient, μa, the scattering coefficient, μs, andthe phase function, p(θ), refractive index, and NA of the receiving system.1273, 1275

The corresponding relation for the backscattering intensity as a function of a sourceand detector positions and optical parameters can be written on the basis of a dif-fusion approximation. For a semi-infinite medium and source and detector probes(for instance, optical fibers) separated by distance rsd and normally oriented to thesample surface, the reflecting flux is given by1275

R (rsd) = z0A

2π

[μeff

r2sd + z2

0

+ 1(r2

sd + z20

)3/2

]exp

[−μeff

(r2

sd + z20

)1/2]

, (7.13)

where z0 = K/μ′s is the extrapolation length, K is a dimensionless constant with

a magnitude that depends on the anisotropy parameter of the scatterers and thereflection coefficient at the surface, A is the area of detector, and μeff is defined byEq. (1.18).

The measurement of the intensity of a backreflected light from a tissue fordifferent source–detector separations, rsd, is the basis of the spatially resolvedtechnique, which allows one to evaluate the absorption and the scattering coeffi-cients by using, for example, analytical Eq. (7.13), valid for highly scattering thicktissues.



When optical parameters of skin or mucosa are under investigation, smallsource–detector separations should be used, where the diffusion approximationis not valid owing to proximity to the tissue boundary.46, 47, 93, 94, 236, 272, 322, 372, 495,

767, 1163, 1244, 1271–1273, 1276, 1284, 1318, 1320, 1321, 1326–1330 In that case, more sophisticatedapproximations of the RTE solution should be employed; a numerical solutionof the inverse problem by the IMC method is also prospective. For example, theauthors of Ref. 1245 studied the parameters of spatial distribution of radiationtransmitted through a tissue (half-width), whereas the condensed IMC method wasemployed in Ref. 322 to process in vivo estimates of radiation reflected from a tis-sue, which were obtained with the aid of a special sensor consisting of two lightdiodes (660 and 940 nm) and three spaced photodetectors. Such a spatially resolvedreflectance technique can also be implemented by using multifiber probes with anumber of fixed source–detector separations767 or by using a CCD with a specialoptical system,46, 93 allowing for the depth profiling of tissue optical properties ifsufficient fibers or pixels are employed. For example, in Ref. 767, a fiber-opticalprobe with one signal and nine detecting 600-μm core diameter fibers with anaverage interfiber distance of 1.7 mm was used for the in vivo study of the opti-cal properties of human skin in the wide spectral range of 400–1050 nm. TheCCD system described in Refs. 46 and 93 provides absolute diffuse reflectancemeasurements when the reflectance images are referenced to images of the inci-dent beam by using a mirror. Such internal calibration leads to approximatelythree times less uncertainty in the determined absorption and reduced scatter-ing coefficients in comparison with the relative measurements that are usuallyused. This system also provides copolarized and cross-polarized measurementsof the backreflectance relative to the linear polarization of the incident light. Thelight-guiding effect for muscle tissue was determined on the basis of polarizationmeasurements.

The effective endoscopic fiber-optic system and the optimized algorithm forthe automatic spectral determination of tissue optical properties, both locallyand superficially, were described.1273 The optical probe was made of 11 opticalfibers, one for illumination and 10 for detection [see Fig. 7.4(e)]. The fibers hada numerical aperture of 0.22 and a core diameter of 0.2 mm. The 10 detectingfibers were placed at various distances (noted as ρi, i = 1−10, ρ ≡ rsd) from theillumination fiber, ranging approximately from 0.3 to 1.35 mm with a step ofapproximately 0.1 mm.

To provide absolute reflectance spectra recording, a two-step calibration pro-cedure was performed. First, the effect of the spectral responses of the light source,fibers, grating, and detector was corrected by performing a measurement on a spec-trally flat reflectance standard using an integrating sphere made of Spectralon.Second, the effective source intensity was obtained by performing a series ofmeasurements on a solid turbid siloxane phantom with known scattering andabsorption properties.

The model developed for the extraction of tissue optical parameters from the spa-tially resolved measurements takes into account the specific influence of the phasefunction and requires no assumption about the optical properties of the tissue, and can


306 Chapter 7

Figure 7.4 Diagram of the algorithm for the automatic spectral determination of tissue opti-cal properties. First, a set of reflectance curves simulated by the MC method is producedfor a wide range of discrete values for each optical coefficient [i.e., μa, μ′

s, and γ = (1 − g2)/(1 − g1)] (a). Second, the simulated curves are interpolated by cubic B-splines (b) to pro-vide a reflectance curve (c) for any value of μa, μ′

s, and γ. Finally for each wavelength of thespectrum, a fit (d) of the measured reflectance curve (e) is performed onto the interpolatedset of simulated curves, allowing for determination of μa, μ′

s, and γ. The fitting method usedis the Levenberg–Marquardt algorithm (see Ref. 1273).

accommodate more complex models that account for multilayer geometries.1273, 1277

The accuracy of the evaluated optical properties significantly depends on the phasefunction in use, when reflectance measurements close to the light source are pro-vided.1273, 1276 The phase function, p(θ), can be expanded into a series of Legendrepolynomials, P1

n( cos θ) [see Eq. (7.7)]. The received expression contains the dif-ferent order moments of the phase function as coefficients ranging from unity toinfinity, gn, where g1 is the conventional anisotropy factor, generally noted as g.

The diffusion approximation generally holds for μ′sρ > 5 and μ′

s > 100 μa.For shorter source–detector separations, typically when 0.5 < μ′

sρ < 5, the second

moment of the phase function, g2, must also be examined.1278 It can be shownthat, in addition to refractive index, only three parameters are needed to accuratelydescribe the light propagation at such small source–detector distances: μa, μ′

s,and γ, where



γ = 1 − g2

1 − g1(7.14)

and γ depends on the relative refractive index of the scatterer and on the ratiobetween the scattering size and the wavelength; γ varies between 0.9 (Rayleigh-type scattering) and values larger than 2 (large scatterers compared with wave-length). For an HGPF, g2 = (g1)2 and, therefore, g = g1 = γ − 1.1273 The authorsof Ref. 1273 showed that for fractal distribution, γ is related to the fractal powerof the size distribution of the scatterers.

Approximately 40 discrete values were chosen by the authors of Ref. 1273 forμa and μ′

s, ranging from 0.003 to 10 mm−1 and from 0.5 to 10 mm−1, respectively;20 values were chosen for γ, ranging from 1.0 to 2.9. This resulted in a four-dimensional matrix of simulated reflectance curves, noted as Rsim(ρi,μa,μ′

s,γ),each coefficient taking only discrete values [see Fig. 7.4(a)]. Using these param-eters, 32,000 reflectance curves have been computed, each for a specific tripletof optical coefficients (μa,μ′

s,γ). Because the path lengths and exit positions ofeach simulated photon were stored, a full MC simulation was required only foreach different value of γ (thus, only 20 simulations). Assuming that the tissueis homogeneous, scaling relationships allow one to derive any reflectance curve,Rsim(ρi,μa,μ′

s,γ), from a single simulation Rsim(ρi,μa = 0,μ′s = 1,γ), with γ kept

constant.1273

Clinical measurements performed endoscopically in vivo in the stomach ofhuman subjects were provided using the described technique and algorithm.1273

The absorption and scattering properties were found to be significantly differentin the antrum and fundus (see Table 7.1) and were correlated with histopathologicobservations.

In the six-detector fiber system made of the 0.4-mm core diameter opti-cal fiber that is described in Ref. 1271, typical source–detector distances were:rsd = 0.44, 0.78, 0.92, 1.22, 1.40, and 1.84 mm. The authors performed MC simula-tions using a program provided by Jacques.1274 In the course of their in vivo studies,temperature dependences of the absorption and reduced scattering coefficients ofhuman forearm skin were determined (see Table 7.1).

Another six-detector fiber system made of 0.2 mm-core diameter opticalfiber with the following range of source–detector separations: 0.23, 0.67, 1.12,1.57, 2.01, and 2.46 mm, and a corresponding algorithm based on the MCsimulation of light propagation and multivariate calibration models, using feed-forward artificial neural network or partial least-squares procedures, was appliedto the determination of optical properties in highly attenuating tissue.1272 Absoluteaccuracy of the determination of scattering and absorption coefficients, on thelevel of ±2 and ±3 cm−1, respectively (rms), was achieved. The method wasapplied to estimate the optical properties of ex vivo bovine liver samples. Theabsorption and scattering coefficients, determined as μa = 14.5 ± 3.5 cm−1 andμ′

s = 7.2 ± 3.7 cm−1 at 543 nm; μa = 4.7 ± 1.7 cm−1 and μ′s = 6.7 ± 3.4 cm−1

at 633 nm, are favorably compared with the limited and varied data in theliterature.


308 Chapter 7

One more example of the backreflectance method is tissue probing with anoblique laser beam. The following simple analytical formula for the linear shift ofthe center of maximum diffuse reflection from the point of beam incidence, �x, hasbeen suggested to facilitate the evaluation of the optical parameters of the mediumas808, 1260, 1261

�x = sinαi

n(μ′s + 0.35μa)

, (7.15)

where αi is the incidence angle of the beam, n is the relative mean refractive indexof the scattering medium, and μ′

s � μa. The relative index of refraction is unity fora matched boundary.

It was demonstrated that spectral dependencies of absorption and reduced scat-tering coefficients can easily be obtained with this method and with an accuracyof 10–17 % and 5–6%, respectively.1260 Oblique-incidence reflectometry has alsobeen implemented with optical fibers in the same way as the normal-incidencereflectometry described previously.1261 White light was delivered, and the diffuselyreflected light was collected with a fiber-optic probe made from black Delrin and600-μm core diameter, low-loss optical fiber. The source fiber was oriented at a45-deg angle of incidence, and the nine collection fibers, arranged in a linear array,collected the diffusely reflected light. This probe is sensitive for anisotropy in theabsorption and reduced-scattering coefficients, which is related to the structuralanisotropy in the tissue caused, for instance, by the alignment of muscle fibers.The lower absorption coefficient at 0-deg probe orientation (with respect to themuscle fibers) than that at 90 deg was probably caused by the light-guiding effectof the muscle fibers; these are less absorbing than the space between the musclefibers, which is occupied by blood capillaries of great absorption.808

Two precise optical systems, the fiber-optic spectrometer yielding spatiallyresolved backreflectance spectra and the single wavelength fiber-optic-CCD tissueimager, were used for in vivo measurements of anisotropy of scattering and absorp-tion coefficients of human skin at different body locations.495 The source–detectordistances between 0.33 and 10.0 mm for 18 detecting 200-μm core diameter fiberslinearly aligned with a central illuminating fiber provided 2D mapping of reflectedintensity by rotation of the detecting fiber system around the illuminating fiber. Avideo reflectometry system consisted of a photometric fiber-coupled CCD systemin direct contact with the skin, and a central optical illumination fiber delivering810-nm laser light from a laser diode into the tissue. The images acquired con-sisted of 10242 pixels sized 24 μm2. A 16-bit analog-to-digital converter was usedwith the CCD chip to provide the high dynamic range needed for reflectometry.The MC code accounting for a two-layered tissue model (skin itself and a semi-infinite subcutaneous fat layer) with two groups of scatterers, one of randomlydistributed scatterers and another of infinite dielectric cylinders (dermal collagenfibers) aligned along one of the principle Cartesian axes parallel to the skin surface,was designed to evaluate the distributions of scattering and absorption coefficients.In the skin layer, the scattering coefficient was recalculated before each interactionevent according to the current direction of photon propagation as495



μs = μs0[1 + f (0.5 −|cos �|)], (7.16)

where μs0 is a base scattering coefficient, f is the fraction of scatterers oriented inthe preferential direction, and � is the angle between the current photon directionand the cylinder axis.

7.7 Optical Coherence Tomography

OCT1, 3, 8, 13, 17, 18, 76, 77, 84, 102, 108–111, 116, 127, 129, 135, 139, 142 is a newly developed modal-ity that allows one to evaluate the scattering and absorption properties of tissuein vivo within the limits of an OCT penetration depth of 1–3 mm.13, 1300–1302,

1305–1307, 1309, 1310, 1331–1335 The principles and applications of OCT are describedin detail in Chapters 8 and 14. The use of OCT to measure the single-scattering coefficient of tissues, μs, was described by Schmitt et al. in 1993.13

More comprehensive algorithms accounting for the multiple scattering effectsand properties of a small-angle scattering phase function are available in theliterature.1300–1302, 1305–1307, 1332–1335

In general, the rms of the photodetector heterodyning signal of the OCTsystem, obtained from probing depth z, <i2(z)> is the product of two factors:the rms of the signal in the absence of light scattering, <i2>0, and hetero-dyne efficiency factor, �(z), which describes signal degradation attributable toscattering,1300, 1332–1335 i.e.,

<i2(z)> = <i2>0�(z), (7.17)

where factor <i2>0 is defined as

<i2>0 = β2PRPSσb/π(wH)2, (7.18)

and β is the factor that accounts for the conversion of optical power to the pho-todetector current; PR and PS are the powers of the reference and object beams ofthe OCT interferometer; σb is the effective backscattering cross section; and wH isthe radius of the beam at 1/e at a probing depth in the absence of scattering. Moreprecisely, the parameter wH is defined in Refs. 1300 and 1333.

The effectiveness of optical heterodyning, �(z), depends essentially on thenature of the scattering. It was shown that in the case of the contribution of singlescattering only,1300, 1333

�(z) ≈ exp{−2μsz}. (7.19)

Here, factor 2 accounts for exponential attenuation of the probing beam due toits double pass through the sample to probing depth z and back. In the absenceof absorption, μs can be determined from the measured slope of the OCT sig-nal through dependence on probing depth z. For media with absorption, but in asingle scattering regime, light propagates along ballistic trajectories, and Beer’slaw can be used to describe the attenuation of the OCT signal: μt = μs + μa.


310 Chapter 7

Accordingly, μs can be obtained by subtracting the absorption coefficient from thetotal attenuation coefficient, as measured by the slope of the OCT signal.

Thus, signal measured by the OCT is defined as1300, 1332–1335

(⟨i2(z)

⟩)1/2 ≈ (⟨i2

⟩0

)1/2 {exp(−2μt z)}1/2 . (7.20)

OCT measures the backscattering or reflection, R(z) ∝ (⟨i2(z)

⟩)1/2, from inho-

mogeneities in the tissue structure depending on their longitudinal position, ordepth, z:

R(z) ∝ exp(−μt z). (7.21)

The reflectivity depends on the optical properties of the tissue, namely, the totalattenuation, μt. The single-scattering approximation is implemented to an opticalthickness of less than 4,1331, 1336 so that the reflected optical power can be writtenas

R(z) = I0α(z) exp(−μt z). (7.22)

Here, I0 is the optical power introduced into the tissue and α(z) is the local tissuereflectivity at depth z.

In the simplest case, the measurement of an OCT signal for two depths, z1 andz2, allows one to evaluate μt, if the local reflectivity, α(z), does not depend on thedepth for a uniform tissue layer (z1 − z2):

R(z1)

R(z2)≈ exp {−μt [z1 − z2]} (7.23)

or

μt = 1

�zln

[R(z1)

R(z2)

], (7.24)

where �z = | z1 − z2 |.To describe the relationship between the OCT signal attenuation and probing

depth, such parameters as the OCT signal slope (OCTSS) are used.1337–1341 In thesingle-scattering approximation and weak dependence of the local reflectivity onthe depth,

OCTSS ≡ ln

[R(z)

I0

]= −μt z. (7.25)

Using OCT, the directional anisotropy of tissue can be studied. Thus, by using anOCT system working at 1300 nm, the authors of Ref. 1309, for cortical bone tissue,found changes in the scattering coefficient at approximately 40% for a light beamperpendicular (μs = 28 cm−1) and parallel (μs = 20 cm−1) to the main direction oftissue striations. This result is qualitatively described by Eq. (7.16).

The values of absorption and scattering coefficients and scattering anisotropyfactor for many of the human tissues measured in vitro, ex vivo, or in vivo andcalculated by using the previously discussed and other approaches are presented inTable 7.1.



7.8 Direct Measurement of the Scattering Phase Function

Direct measurement of the scattering phase function, p(θ), is important for thechoice of an adequate model for the tissue under examination.1, 58, 230, 345, 1191, 1311

The scattering phase function is usually determined from goniophotometric mea-surements in relatively thin tissue samples.1, 37, 56, 58, 87, 96, 315, 316, 321, 322, 329, 345, 383,

1191, 1247, 1248, 1255, 1256, 1259, 1308, 1311 A typical goniometer setup is depicted in Fig. 7.5.The scattering indicatrix measured with due regard for the geometry of the sampleand experimental datum is approximated either by the HGPF1, 31, 345, 383, 1311 [seeEq. (1.15)] or by a set of HGPFs, with each function characterizing the types ofscatterers and specific contributions to the indicatrix [see Eq. (7.7)].1247 In thelimiting case of a two-component model of a medium containing large and small(compared with the wavelength) scatterers, the indicatrix is represented in the formof anisotropic and isotropic components.56, 322, 1248 Other approximating functionsare equally useful, e.g., those obtained from the Rayleigh–Gans approximation,322

Mie theory,96, 1244, 1245 or a two-parameter GKPF [HGPF is a special, simpler caseof this phase function, as shown in Eq. (7.8)].1311 Some of these types of approxi-mations were used to determine the dependence of the scattering anisotropy factor,g, for dermis and epidermis on wavelengths in the range 300 to 1300 nm, whichproved to coincide fairly well with the empirical formula:37

ge ∼ gd ∼ 0.62 + λ × 0.29 × 10−3, (7.26)

on the assumption of a 10% contribution of isotropic scattering (at least in thespectral range of 300–630 nm). The wavelength, λ, is given in nanometers.

Analysis of scattering indicatrices measured for sequentially stripped humanskin epidermal slices has demonstrated that the g value averaged over five

Figure 7.5 Schematic diagram of a goniometer for measurement of light scattering as afunction of angle (scattering indicatrix measurement) (see Ref. 383).


312 Chapter 7

epidermal slices is g = 0.89 ± 0.02 at λ = 633 nm.383 The measurements havebeen performed by using the setup presented in Fig. 7.5. A single-mode He-Nelaser was used as a light source. The detector was a photon-counting system basedon the photomultiplier. The whole system was computer controlled. The epidermalsample was placed between a quartz slide and a hemisphere to avoid refraction ofboth incident and scattered lights. The measurements were performed in the rangeof 0–60 deg with one-degree steps. The experimental values of g, obtained usingdirect measurements of the scattering phase function for many types of humantissues, are presented in Table 7.1.

The correct prediction of light transport in tissues depends on the exact form ofthe phase function used for calculations.49, 1311 Simulations performed with differ-ent forms of p(θ) (HGPF, Mie, and GKPF) and the same value of <cos(θ)> ≡ gresult in the collection of significantly different fractions of the incident photons,particularly when small NA delivery and collection fibers (small source–detectionseparation) are employed.49, 1311 More photons are collected for a distribution thathas a higher probability of scattering events with θ>125 deg. For the clinicallyrelevant optical parameters employed in Ref. 49, the differences in light collectionwere greater than 60%.

Moreover, for media with high anisotropy factors, precise measurements of thescattering phase function in the total angle range from 0 to 180 deg is a difficulttechnical task, demanding an extremely large dynamic range of measuring equip-ment. Most of the scattered radiation lies in the range from 0 to 30 deg, countingfrom the direction of the incident beam. In addition, measurements at angles closeto 90 deg are strongly affected by scattering of higher orders, even for samples ofmoderate optical thickness.654

7.9 Estimates of the Optical Properties of Tissues

The previously discussed methods and techniques were successfully applied forthe estimation of optical properties of a wide range of tissues. Measurements con-ducted in vitro, ex vivo, and in vivo by different research groups are summarizedin Table 7.1. Evidently, many types of animal and human tissues may have verysimilar optical properties, but some specificity is expected. For example, normalbovine sclera is more pigmented and thicker, and its collagen structure makes itmore sensitive for swelling than human sclera. Another example is porcine skin,whose epidermis structure may be quite different from human skin, particularlyaged skin. Therefore, in Table 7.1, we present optical parameters of only humantissues. On the other hand, such tissues as muscle, vessel wall tissue, and livermay have very similar optical properties between human and animal tissues. Thus,another reason to present only human tissues is to not overburden the table. Earlypublished data on optical properties of both human and animal tissues are summa-rized in Refs. 40, 87, 1281, and 1285. More recent data can be found in Refs. 98,129, 130, 230, 333–335, 372, 389, 495, 767, 1245, 1246, 1262–1279, 1281–1286,1288–1297, 1318, 1320, and 1321.



Data presented in Table 7.1 accurately reflect the situation in the field of tis-sue optical parameters measurements. It is clear that major attention was paid toinvestigations into the optical properties of female breast and head/brain becauseof the great importance and perspectives of optical mammography and opticalmonitoring and treatment of mental diseases. Skin and underlying tissues are alsothoroughly studied. Nevertheless, in general, not many data for optical transportparameters are available in the literature. Moreover, these data are dependent onthe tissue preparation technique, sample storage procedure, applied measuringmethod and inverse problem-solving algorithm, measuring instrumentation noise,and systematic errors.

The most detailed in vitro investigations of normal and coagulated brain tissues(gray matter, white matter, cerebellum, pons, and thalamus), and of native tumortissues (astrocytoma WHO grade II and meningioma), using single-integrating-sphere spectral measurements in the spectral range from 360 to 1100 nm andIMC algorithm for data processing, are described in Ref. 390 (see Table 7.1).As listed in Table 7.1, all brain tissues under study shared qualitatively similardependencies of the optical properties on the wavelength. The scattering coeffi-cient decreased and the anisotropy factor increased with the wavelength, whichcan be explained by the decreasing contribution of Rayleigh scattering and increas-ing contribution of Mie scattering with the wavelength. The wavelength-dependentabsorption coefficient behavior of all brain tissues resembled a mixture of oxy- anddeoxy-hemoglobin absorption spectra. This means that in spite of careful prepara-tion of the samples, it was not possible to remove all blood residuals from the tissuesections.

At the same time, differences in the spectral characteristics of the brain tissueshave been observed. For example, the total attenuation coefficients (μt = μa + μs)of white matter are substantially higher than those of gray matter. The two brainstem tissues (pons and thalamus) also have different optical properties. The tumorsare generally macroscopically less homogeneous than any normal tissues; thus,their scattering coefficients and anisotropy factors are slightly higher than those ofnormal gray matter. The same tendency of scattering coefficients to grow is typicalfor breast tumors (carcinomas, see Table 7.1 and Refs. 1250 and 1288).

After coagulation, the values of absorption and scattering coefficientsincreased for all tissues. The extent of this increase, however, is different for eachtissue type, and is characterized by factors from 2 to 5. It was shown390 that a sig-nificant increase in both interaction coefficients is a result of substantial structurechanges, mostly caused by tissue shrinkage and condensation, as well as collagenswelling and homogenization of the vessel walls. Tissue shrinkage caused by losingwater at coagulation makes tissue more dense, which leads to increases in bothscattering and absorption coefficients in the spectral range where water absorptionis weak (up to 1100–1300 nm). The refractive index microscopic redistributionof a tissue due to denaturation and homogenization of cellular and fiber proteinsat thermal action also may have a strong inclusion in alteration of scattering andabsorption properties. Similar increases of both absorption (by a factor of 2–10)


314 Chapter 7

and scattering (by a factor of 2–4) coefficients in the wavelength range from 500 to1100 nm were found for coagulated human blood.

The reduced scattering coefficient of skull bone is considerably lower than thatof brain white matter and is comparable with that of gray matter, cerebellum, andbrain stem tissues (pons and thalamus). It is also comparable with scalp tissue val-ues. Upon coagulation of soft brain tissues, their reduced scattering coefficient mayconsiderably exceed that of skull bone for all tissues presented in Table 7.1. Thisimplies that in NIR spectroscopy on the adult head, the effect of light scatteringby the skull is of the same order of magnitude as that of surrounding scalp tis-sue and brain.1308 One possible reason for this is the high values of g attributableto the specific structure of bone. For example, the cortical bone consists of anunderlying matrix of collagen fibers, around which calcium-bearing hydroxyap-atite crystals are deposited. These crystals are the major scatterers of bone;1309 theyare large in size and have high refraction power, and therefore, may be respon-sible for the high values of g. Actually, the optical properties of bone samplestaken from pig skull and measured by using the goniophotometric technique ofthin bone slices over the wavelength range 650–950 nm gave values of anisotropyfactor in the range from g = 0.925 ± 0.014 at 650 nm to g = 0.945 ± 0.013 at950 nm, averaged for six samples.1308 The corresponding values of the absorptionand scattering coefficients measured on 18 samples using the integrating spheretechnique and IMC were: μa = 0.40 ± 0.02 cm−1 and μs = 350 ± 7 cm−1 at 650nm to μa = 0.50 ± 0.02 cm−1 and μs = 240 ± 6 cm−1 at 950 nm.

Analyzing data received by different groups for the same brain tissue, the influ-ence of the theoretical approach used or the sample preparation technique on resultscan be demonstrated. Because of a lack of experimental data for various brain tis-sues, at present, such a comparison can only be made for gray and white brainmatter (see Table 7.1). Authors of Ref. 390, by using an IMC method for dataprocessing of single-integrating sphere measurements, have obtained lower valuesfor the absorption and scattering coefficients than the author of Ref. 1287, whoused an inverse δ-Eddington method. This discrepancy may be explained by thelimitations of the δ-Eddington model, which is principally one-dimensional, andtherefore, could not account for losses of light at the side edges of the samples.This might have led to an overestimation of the extinction coefficients. On theother hand, in the framework of the application of identical theoretical approaches(IMC), the usage of shock freezing and homogenization for sample preparation,1287

in comparison with the usage of tissue cryosections,390 results in lower values ofscattering coefficients, at least for white brain matter. This same tendency was alsodemonstrated for liver samples1287 and breast tissue (compare data of Refs. 1250and 1288 in Table 7.1).

The 10-sphere discrete particle model of a soft tissue indicates that the scat-tering coefficient decreases with the wavelength approximately as μs ∼ λ2−Df for600 ≤ λ≤ 1400 nm, where Df is the limiting fractal dimension; 3 < Df < 4 fortypical soft tissues.222 In the model of spheres ranging from 5 to 30,000 nm,at an interval of 5 nm, μs ∼ λ3−Df for 600 ≤ λ ≤ 1500 nm and the range offractal dimension is 4 < Df < 5.107 Both models provide the same power law for



dependence of the scattering (or reduced scattering) coefficient on the wavelengthμs(μ′

s) = qλ−h, with h in the range from 1 to 2 [see Eqs. (3.29)–(3.32)]. As indi-cated by the data of Tables 3.2 and 7.1, most tissues such as aorta, skin, dura mater,sclera, and mucosa have parameters h = 1.16−1.62,764, 765, 1292, 1293, 1295 which sat-isfies the model’s predictions. The corresponding values of fitting parameter q arein the range from 8.9 × 104 to 4.7 × 105 cm−1. An in vitro study of rat skin in therange of 500 to 1200 nm gave h = 1.12.766 For soft tissues, Jacques modeled thereduced scattering coefficient by the same power law, with q ranging from 2 × 105

to 2 × 106 cm−1 and h = 1.5.1299 The experimental data for ex vivo skin samplesof Ref. 1267 in the spectral range from 1000 to 2200 nm (excluding the disper-sion of the strong water bands) are better modeled by using a q value equal to2 × 105 for h = 1.5. For the in vivo backscattering investigation of human skin andunderlying tissues in the wavelength range from 700 to 900 nm, constants q andh were determined as 550 ± 11 and 1.11 ± 0.08, respectively.767 The power con-stant, h, is related to an average size of the scatterers; thus, once h is determined, theMie-equivalent radius, aM, can be derived from Eqs. (3.31) and (3.32).767 If the rel-ative refractive index between spheres and surrounding medium is m = 1.037, themeasured constant h = 1.11 leads to an aM value of 0.30 μm. Diffuse reflectancemeasurements for female breast tissues produced aM values of 0.17 and 0.29 μmfor normal and malignant tissues (see Table 7.1).1288

In contrast to the above-discussed tissues, fat and bone tissue show very lowvalues of the power constant: h = 0.59 for abdominal1294 and h = 0.791294 orh = 0.681312 for subcutaneous fat, and h = 0.65 for bone.1342, 1343 One possiblereason is the specificity of fat and bone tissue structures. Fat consists mostly of fatcells; each fat cell contains a smooth drop of fat, which fills a whole cell. Cellsare spherically shaped and their diameters depend on fat content, and are in therange from 10 to 200 μm. For such large and rather homogeneous scatterers, aweak wavelength dependence of light scattering coefficients might be expected.This is similar for bone, where hydroxyapatite crystals, the major scatterers, arelarge and have high refraction power.1309 Another reason for the lower h is thepossible influence of dispersion of lipids and water bands (see Fig. 1.5), whichshould decrease inclination of the wavelength dependence in the range around1000–1300 nm.

A decrease in h was found from 1.12 to 0.52 for rat skin studied in vitro inthe range from 500 to 1200 nm induced by glycerol application.766 Because themajor action of glycerol on tissue is that its dehydration causes an increase oftissue density, this may be a third reason for such small values of h for fat andbone, being rather dense tissue and having the lowest hydration ability amongst avariety of tissues.

A low power dependence on the wavelength was also found for the scatteringcoefficient of leg bone of a horse (only cortical part of equine bone taken fromthe shaft of the third metacarpal of 2-mm thickness) measured using a single-integrating sphere and IMC techniques.1309 In the wavelength range from 520 to960 nm, values of the scattering coefficient were changed from 350 to 250 cm−1

for the constant value of g = 0.93 assumed in calculations.


316 Chapter 7

7.10 Determination of Optical Properties of Blood

Because knowledge about the optical properties of blood is very important for suc-cessful application of optical medical technologies, numerous works are devotedto the experimental studies of these properties and the development of appropri-ate algorithms of solving the inverse problem for reconstruction of blood opticalparameters.48, 49, 230, 275, 345, 346, 1279, 1280, 1311, 1325, 1344–1355 Fresh human blood placedin a calibrated thin cuvette (thickness from 0.01 to 0.5 mm, slab geometry) is usu-ally used for the determination of blood optical parameters. Prior to the opticalmeasurements, standard clinical tests are necessary to determine the concentrationof red and white blood cells, concentration of platelets, hematocrit, mean corpus-cular volume and hemoglobin, and the other parameters of interest. If blood sampleoxygenation level is of interest, it may be controlled by using a conventional bloodgas analyzer.230 In most cases, the experiments are performed with either com-pletely oxygenated or completely deoxygenated blood.48, 230, 345, 346, 1325 To obtaincomplete oxygen saturation, the sample is exposed to air or O2.48, 230 To com-pletely deoxygenate blood, sodium dithionite (Na2S2O4) is added.230 To be surethat neither the volume nor the surface area of the blood particles changes dur-ing the experiments, the pH of the samples should be maintained in the range ofphysiological values, at approximately 7.4.

In reality, blood is flowing through the blood vessels; therefore, it is preferableto study the optical properties of flowing blood. The RBCs in flow are subject todeformation and orientation. At lower shear rates, reversible aggregation occurs;under higher shear rates, erythrocytes are deformed into ellipsoids. Experimentswith flowing undiluted and diluted blood are reported in Refs. 48, 49, and 1279.Roggan et al.48 assembled sophisticated equipment to analyze the influence of dif-ferent hematocrit, flow velocity, osmolarity, hemolysis, and oxygen saturation onthe optical properties of RBC suspensions submerged in a saline solution. Nilssonet al.49 investigated the influence of slow heating on the optical properties ofwhole flowing blood; unfortunately, the oxygenation level was neither determinednor controlled. Influence of the shear stress on the optical properties of wholecompletely oxygenated blood was studied by Steenbergen et al.1279

Several authors reported the values of the optical parameters of blood deter-mined from single-scattering experiments (Table 7.2). Reynolds et al.1344 deter-mined the values of the absorption cross section, scattering cross section, andanisotropy factor of blood for several wavelengths in the visible and near infraredspectral ranges, and compared the experimental values with those calculated (Mietheory). In Mie calculations, they used the value of 2.79 μm for the RBC radius andthe value of 1.036 for the RBC refractive index (relative to blood plasma).275, 1344

Flock et al.1280 measured the total attenuation coefficient and the scatteringphase function of a diluted whole blood sample [phosphate buffered solution(PBS), hematocrit (Hct) of 1%, cuvette <100μm thick] at a wavelength of632.8 nm.

Steinke and Shepherd1345 determined the total attenuation coefficients, scat-tering cross sections, and anisotropy factors of RBCs suspended in blood plasma



Tab

le7.

2O

ptic

alpa

ram

eter

sof

bloo

dde

term

ined

and

app

roxi

ma

ted

from

the

sing

lesc

atte

ring

expe

rimen

ts(S

:oxy

gen

satu

ratio

n;H

ct:h

ema

tocr

it;a R

BC

:rad

ius

ofR

BC

;mR

BC

:rel

ativ

ein

dex

ofre

frac

tion

ofR

BC

;lcu

v:c

uvet

teth

ickn

ess)

(see

Ref

.131

1).

λ,

S,σ

a,σ

s,σ

t,nm

%μ

m2

μm

2μ

m2

μt,

cm−1

gP

hase

func

tion

Con

diti

onR

ef.

665

100

0.06

057

.20

–7.

470.

9951

Mie

Com

pari

son

with

Mie

theo

ry;a

RB

C=

2.79

mm

;mR

BC

=1.

036

1344

675

100

0.06

056

.14

–7.

440.

9950

685

100

0.05

955

.09

–7.

390.

9949

955

100

0.19

133

.47

–6.

660.

9925

960

100

0.18

733

.18

–6.

660.

9924

965

100

0.18

532

.90

–6.

650.

9924

665

00.

542

56.5

8–

7.38

0.99

5167

50

0.53

555

.53

–7.

350.

9950

685

00.

484

54.5

6–

7.31

0.99

4995

50

0.09

033

.54

–6.

680.

9925

960

00.

085

33.2

7–

6.67

0.99

2496

50

0.08

032

.98

–6.

660.

9924

Exp

erim

ent

630

100

0.09

956

.37

––

–66

010

00.

066

54.2

0–

––

685

100

0.06

353

.53

––

–80

010

00.

131

42.2

4–

––

632.

810

0–

––

290.

974

HG

PFH

ct=

1%;l

cuv<

100μ

m12

8063

2.8

100

–63

.82

–7.

090.

9853

Mie

l cuv

=14

4μ

man

d51

μm

1345

100

–66

.62

–7.

400.

9948

RB

Cin

plas

ma

100

–81

.24

–9.

030.

9818

RB

Cin

PBS

(0.9

%)

100

–79

.27

–8.

810.

9926

632.

810

0–

––

–0.

982

HG

PF34

510

0–

––

–0.

995

GK

PF(α

=1.

82)

632.

810

0–

––

–0.

971

HG

PFH

ct=

0.1%

;pH

=7.

4;l c

uv=

10μ

m23

010

0–

––

–0.

997

GK

PF(α

=3.

658)

100

––

––

0.99

6M

iea R

BC

=2.

995μ

m,m

RB

C=

1.04

577

100

––

≈95

–0.

966

HG

PFH

ct=

1%;p

H=

7.4;

l cuv

=10

0an

d10

μm

1325

100

––

––

0.99

7G

KPF

(α=

1.5)

100

––

––

0.99

7M

ie10

0–

––

–0.

9995

Ray

leig

h–G

ans


318 Chapter 7

and in PBS (0.9%) from the collimated transmittance and scattering phase func-tion measurements for a wavelength of 632.8 nm, and from calculations usingMie theory. For measurements of the collimated transmittance, cuvettes with athickness of 144 μm (slab geometry) were used. For the goniometrical measure-ments, an American Optical hemoglobinometer cuvette (path length of 51 μm) wasemployed.

Yaroslavsky et al.230, 345 measured the scattering phase functions of dilutedwhole blood samples; approximated the experimental scattering phase functionsusing Mie theory, HGPF, or GKPF [see Eqs. (1.15), (7.7), (7.8), and (7.10)]; anddetermined the anisotropy factors for each approximation at a wavelength of 633nm. For Mie calculations, the RBC radius and refractive index were assumed to beequal to 2.995 μm and 1.04 (relative to PBS), respectively. The scattering phasefunctions were measured in an angle range from 2 to 18 deg. For the experi-ments, fresh samples of whole blood were collected into heparinized containersand diluted with PBS (pH = 7.4) to Hct = 0.1%. The diluted blood samples wereplaced into the cuvettes (10-μm thick, slab geometry).

Reference 1325 presented a comprehensive study of RBC single-scatteringbehavior. The authors measured the collimated transmittance and scattering phasefunctions of RBC suspensions in isotonic PBS (pH = 7.4, Hct = 1%) for a num-ber of wavelengths in the visible spectral range from 458 to 660 nm. The scatteringphase functions were measured for 20 scattering angles in the range of 0.75 to 14.5deg. For the transmission measurements and scattering phase function, 100 and10 μm thick cuvettes were used, respectively (slab geometry).

The optical properties of the diluted and whole human blood, determined usingindirect techniques, were reported in Refs. 48, 49, 230, 345, and 1279. A sum-mary of the optical properties of diluted and whole blood determined using indirecttechniques is given in Table 7.3.

The optical parameters of completely oxygenated whole blood samples weredetermined on a selected wavelength of 633 nm230 and in the NIR spectralrange345 from double integrating sphere measurements using an IMC technique(see Table 7.3). The measured values included diffuse reflectance, total trans-mittance, and collimated transmittance. From the measured data, the absorptioncoefficient, scattering coefficient, and anisotropy factor (under the assumption ofthe HFPF) were derived. In Ref. 230, blood samples with Hct = 38% and oxygensaturation, S > 98%, were studied. In Ref. 345, the spectral range under investiga-tion extended from 700 to 1200 nm, and blood samples with Hct = 45.5 ± 0.5%placed into calibrated cuvettes (thicknesses of 0.1 and 0.5 mm, slab geometry) wereused. The spectral dependences of optical parameters of whole blood obtained inRefs. 345 and 1311 are presented in Fig. 7.6. In addition, the effect of the scatteringphase function approximation on the resulting estimates of the optical parameterswas analyzed.230, 345 The Henyey–Greenstein, Gegenbauer kernel, or Mie phasefunctions were considered [see Eqs. (1.15), (7.7), (7.8), and (7.10)]. The calculatedangular distributions of scattered light were compared with goniophotometric mea-surements performed at a wavelength of 633 nm. The scattering phase functionsof highly diluted blood samples (Hct = 0.1%, S > 98%) were also measured by



Tab

le7.

3O

verv

iew

ofth

eop

tical

prop

ertie

sof

bloo

d(*

data

take

nfr

omth

eg

raph

sof

the

resp

ectiv

ere

fere

nces

;H

ct:

hem

ato

crit,

S:

oxyg

ensa

tura

tion,

a RB

C:r

adiu

sof

RB

C,m

RB

C:r

ela

tive

inde

xof

refr

actio

nof

RB

C,t

b:b

lood

tem

pera

ture

,vsh

:she

arra

te,l

cuv:c

uvet

teth

ickn

ess)

(see

Ref

.13

11).

λ,n

mμ

a,cm

−1μ

s,cm

−1μ

t,cm

−1g

μ′ s,

cm−1

Pha

sefu

ncti

onC

ondi

tion

sR

ef.

633

15.5

645

–0.

982

11.6

HG

PFH

ct=

45%

,S>

98%

345

15.4

2239

−0.

995

11.2

GK

PFα

=1.

8263

315

.2±

0.6

400

±30

–0.

971

±0.

001

11.7

±1.

2H

GPF

Hct

=38

%,S

>98

%,7

sam

ples

230

16.1

±0.

641

30±

170

–0.

997

±0.

0001

12.4

±0.

9G

KPF

α=

3.65

816

.3±

0.5

2390

±16

0–

0.99

62±

0.00

01–

Mie

a RB

C=

2.99

5m

m;m

RB

C=

1.04

633

HG

PFH

ct=

44±

3%,S

=10

0%49

*3.

0–

––

18.5

t b=

25◦ C

3.5

––

–18

.2t b

=35

◦ C4.

0–

––

18.0

t b=

42◦ C

4.5

––

–21

.0t b

=48

◦ C6.

0–

––

17.0

t b=

54◦ C

633

GK

PFα

=1.

0;H

ct=

41%

48*

20–

––

20S

=25

%16

––

–20

S=

50%

12–

––

20S

=75

%7

––

–18

S=

100%

α>

0.99

,H

ct=

5%1.

2530

0–

––

S=

0%1.

130

0–

––

S=

100%

633

HG

PFH

ct=

50±

0.5%

;S=

100%

1279

*–

––

––

0.95

0–0.

963

v sh

=50

s−1

––

––

–0.

956–

0.96

5v s

h=

100

s−1

––

≈120

0–

–0.

960–

0.96

6v s

h=

150

s−1

––

≈120

0–

–0.

962–

0.96

7v s

h=

200

s−1

––

≈120

0–

–0.

963–

0.96

8v s

h=

300

s−1

––

≈120

0–

–0.

963–

0.97

0v s

h=

400

s−1

––

≈120

0–

–0.

964–

0.97

3v s

h=

500

s−1

488

102.

213

4.4

––

–0.

91IA

D,l

cuv

=90

μm

1354


320 Chapter 7

Figure 7.6 Optical properties of whole blood (see Refs. 345 and 1311). Hematocrit, Hct= 45.5 ± 0.5%; oxygen saturation, S > 98%. Average of six samples. Bars are standarderrors. Absorption coefficient (a), scattering coefficient (b), anisotropy factor (c).

using a goniophotometer. To evaluate the obtained data, the angular distributionsof scattered light for optically thick samples were calculated and the results werecompared with goniophotometric measurements. The presented data have shownthat the employed approximation of the scattering phase function can substantiallyimpact the derived values of μs and g, while μa and the reduced scattering coeffi-cient, μ′

s, are much less sensitive to the exact form of the scattering phase function.It was shown that both Rd and Tt are strongly affected by the form of the phasefunction, and that the magnitude of this influence depends on the thickness of theblood sample. The presented data prove that variations in the employed scatteringphase function approximation can cause large discrepancies in the derived opti-cal parameters. Therefore, exact knowledge about the scattering phase function isrequired for the precise determination of the blood optical constants.



Nilsson et al.49 studied the influence of slow heating on the optical propertiesof completely oxygenated whole blood at a wavelength of 633 nm (Table 7.3). Thediffuse reflectance, total transmittance, and collimated transmittance were mea-sured at different temperatures by using a double integrating sphere technique. Theabsorption coefficient, scattering coefficient, and anisotropy factor (assuming theHGPF) were determined by using an IAD method. For the measurements, wholeblood was collected into tubes that contained EDTA to prevent coagulation. Thehematocrit of the investigated samples was 44 ± 3%. During the measurements,the blood was pumped at a flow rate of 10.7 ml/min. The flow-cell (length =65 mm, height = 34 mm, total thickness = 2.5 mm) was placed between the inte-grating spheres. The blood sample thickness in the flow cell was 0.48 ± 0.02 mm.The blood was heated from approximately 25 to 55◦C at rates between 0.2 and1.1◦C/min. While the blood was heated, integrating sphere measurements werecontinuously taken. The authors found that changes in optical properties of bloodattributable to slow heating were reversible until a temperature of 44.6–46.6◦C.Coagulation of blood occurred at approximately 55◦C.

One of the most extensive studies of the macroscopic optical properties ofRBC suspension at different physiological and biochemical conditions (hemat-ocrit, oxygen saturation, flow velocity, osmolarity, and hemolysis) was conductedby Roggan et al. (Table 7.3).48 These authors measured the optical parametersof RBCs suspended in PBS under flow conditions by using a double integratingsphere technique and determined optical coefficients by using an IMC method.The absorption coefficient, scattering coefficient, and anisotropy factor (assumingGKPF with α = 1) were determined for the oxygenated and deoxygenated RBCsuspensions (Hct = 5%) under normal physiological conditions (see Fig. 7.7). Forthe experiments, erythrocytes were separated from blood plasma and white cellfraction, washed in PBS (300 mOsmol/L, pH = 7.4), and suspended in the PBS.The hematocrit was adjusted by diluting the erythrocytes with PBS. By using PBSswith different osmolarities, the osmolarity of the RBC suspension was varied.Hemolysis was induced by diluting the suspensions with distilled water. Bloodoxygenation and circulation were adjusted and controlled using an extracorporealcirculation unit. Blood temperature was kept constant at 20◦C. The thickness of theflow-through cuvette was 97 μm.

Roggan et al.48 have also come to the conclusion that an accurate approx-imation of the scattering phase function plays an important role in the correctdetermination of the optical properties of blood. They found that absorption andscattering increased linearly with hematocrit (for Hct < 50%). Absorption andscattering decreased slightly with an increase in shear rate. Among flow param-eters, axial migration was the primary factor that influenced optical properties.Deformation of the erythrocytes had no impact on optical properties if the volumeand hemoglobin content of the RBCs were kept constant. Hemoglobin solutionshad a smaller absorption than RBC suspensions with the same concentration ofhemoglobin. Obviously, the change in oxygenation of RBC suspensions inducedthe expected change in the absorption coefficient. The scattering coefficient wasnot affected by the change in the oxygenation of erythrocytes. The spectral


322 Chapter 7

Figure 7.7 Optical properties of RBCs suspended in PBS (Hct = 5%, osmolarity = 300mosmol/L, shear rate = 500 s−1) (see Ref. 48).

dependences of optical parameters of RBSs suspended in a PBS (Hct = 5%,shear rate = 500 s−1, osmolarity = 300 mOsmol/L) are given in Fig. 7.7. Furtherstudies of the optical properties of blood, made by this group, are presented in Refs.1347–1353 and analyzed in detail in the monograph.6

Steenbergen et al.1279 analyzed the effect of shear rate on the optical propertiesof completely oxygenated whole blood (Table 7.3). The collimated transmissionand angular distributions of light intensity were measured at 633 nm for variousshear rates (from 50 to 500 s−1) and blood layer thicknesses (from 20 to 100μm).For shear rates above 150 s−1, the total attenuation coefficient was directly deter-mined from the collimated transmission measurements. The anisotropy factorwas determined from the angular intensity distributions by using an IMC tech-nique and assuming the Henyey–Greenstein scattering phase function. The valueof the total attenuation coefficient (μt = 1200 cm−1) was determined from thecollimated transmittance measurements, and the values of the absorption coeffi-cient (μa = 7 cm−1 and 10 cm−1) were taken from the literature.48 In addition, theauthors measured the anisotropy g-factor for blood layers with different thicknesses



and determined the actual g-factor by extrapolating their results to the layer thick-ness of zero. The hematocrit of the investigated blood varied between 49.5 and50.5%. A continuous increase of the g-factor (from 0.950 to 0.973) with an increaseof shear rate was found.

The optical properties of blood-perfused tissues are significantly affected bytissue blood content. This is caused by two factors: first, the optical properties ofwhole blood itself are substantially different from those of soft tissues; second,whole blood is an extremely turbid medium with extraordinarily high scatteringanisotropy (see Tables 7.2 and 7.3). Thus, it has a very short optical mean freepath and a very long TMFP compared to the majority of bloodless tissues. Asa result, the presence of even a small amount of blood greatly changes the pro-cess of light propagation in tissues. This point is illustrated by Fig. 7.8, wherethe TMFP has been calculated for bloodless and blood-containing brain tissues attwo wavelengths.1256, 1311 Optical properties of other blood-containing tissues areaffected in a similar manner, in accordance with the total volume of blood con-tained and its spatial distribution.165, 168, 369, 372, 1058, 1061, 1316, 1318–1321 As a result, theoptical response of tissue depends strongly on the presence of blood and its relevantparameters, such as oxygen saturation and hematocrit. This allows wide possibili-ties for optical diagnostics, but also makes the dosimetry of light in tissues a moredifficult task. However, special techniques such as mechanical squeezing of bloodfrom the field of measurements can significantly simplify the analysis and allowfor detecting other important tissue chromophores.200, 1058, 1061, 1319 Methods for

Figure 7.8 Transport mean free path [ltr = (μa + μ′s)−1] at the wavelengths of 800 and 1100

nm for white brain matter (WM), gray brain matter (GM), oxygenated blood, deoxygenatedblood, perfused white matter, and perfused gray matter (see Ref. 1311). These are basedon the results of Refs. 48 and 1256. Blood hematocrit of 40% was assumed in computingdata for perfused tissues. CBV: cerebral blood volume.


324 Chapter 7

controlling the optical properties of blood and blood-perfused tissues are discussedin Chapter 9.

Laser photodynamic therapy19, 26, 29, 35, 1322 and laser-induced interstitial ther-mal therapy (LITT) of deep tumors2 are the most promising techniques amongthe least invasive therapies of cancer. In this case, in addition to knowledge of theoptical properties of tumor tissue and the surrounding substances, knowledge ofthe blood content and its optical properties is essential for therapy planning andfor exact dosimetry.1346 In addition, knowledge about the optical properties of tis-sues and blood allows one to determine the most effective treatment wavelength,where penetration depth of laser light is maximal. This emphasizes the need foran explicit account of the blood content in the modeling of laser-tissue interaction;for example, the planning of clinical procedures such as LITT, or photodynamic orphotochemical therapy.

7.11 Measurements of Tissue Penetration Depthand Light Dosimetry

In practice, direct measurements of the penetration depth of various tissues at dif-ferent or specific wavelengths are valuable. In particular, such data allow one toprovide a strategy of laser phototherapy. As shown earlier, a detailed calculation oflight distribution in tissues can be very complex and frequently requires numericalsolutions of the RTE, Eq. (1.9). However, if a specific experimental arrangement isprovided, i.e., a wide beam irradiation of semi-infinite samples, and light is scat-tered into a practically isotropic distribution very close to the irradiated surface,the one-dimensional diffusion model may be used, which provides the solutiondescribed by Eq. (1.36), valid for the depths z ≥ 2ld = 2/μeff, where μeff is definedby Eq. (1.18).

Using an analogue of Eq. (1.36) and providing measurements within thicktissue slabs at irradiation by a parallel laser beam 5 cm wide (at one of thesewavelengths: 633, 675, 780, or 835 nm) and light detecting by using a measur-ing needle with an optic fiber inserted into a tissue sample, values of penetrationdepth were estimated for a number of normal and pathological tissues.1282 Thesedata are summarized in Table 7.4. From the performed measurements, ld = 1/μeff

was determined. The detecting fiber tip captures an equal proportion of the fluencerate of light at every point from z ≥ 2ld to greater tissue depths. Logarithmizing thedetector response as a function of the position of the needle, z, and using the methodof least squares, a fitted straight line was obtained whose slope is the effectiveattenuation coefficient, μeff = 1/ld [see Eq. (1.36)].

The quantity usually measured in dosimetry is the irradiance, F(r) [seeEq. (1.11)], which is defined as the power per receiving area of a flat detector.1283

For such definition, light entering differently from perpendicular incidence con-tributes with reduced impact to F(r) and light from below does not contribute atall. Light-induced tissue heating or any photobiological effect in tissue or cellsdepends on light absorption. For isotropic media, absorption is not sensitive to theangle of irradiation; thus, an adequate light dosimetric quantity should be the total



Tab

le7.

4O

ptic

alpe

netr

atio

nde

pth

oftis

sues

,l d

,in

mm

,m

easu

red

exvi

vofo

ra

few

wav

elen

gths

.N

umbe

rof

sam

ples

from

diff

eren

tbo

dies

mea

sure

dfo

rea

chtis

sue

isgi

ven

inbr

acke

ts(s

eeR

ef.1

282)

.

Tis

sue

l d,m

ml d

,mm

l d,m

ml d

,mm

λ=

633

nmλ

=67

5nm

λ=

780

nmλ

=83

5nm

Blo

od0.

19±

0.01

a(1

0)0.

28±

0.01

a(1

0)0.

42±

0.02

a(1

0)0.

51±

0.02

a(1

0)Sa

rcom

as0.

2–4.

0(1

0)0.

4–4.

3(6

)0.

5–4.

6(6

)–

Liv

er(c

irrh

osis

)0.

43±

0.06

b(5

)0.

60±

0.02

(2)

1.04

±0.

02(2

)–

–0.

58±

0.01

0.99

±0.

02–

Sple

en0.

49±

0.07

b(5

)0.

87±

0.02

(2)

1.21

±0.

01(2

)–

–0.

94±

0.01

1.16

±0.

02–

Paro

tidgl

and

0.61

±0.

08b

(3)

––

–B

ronc

hial

gang

lion

met

asta

sis

1.05

±0.

01(2

)–

––

1.01

±0.

01–

––

Lun

g0.

81±

0.06

a(1

0)1.

09±

0.11

b(4

)1.

86±

0.12

b(4

)2.

47±

0.03

(1)

Bro

nchi

alcy

st1.

05±

0.02

(2)

––

–0.

97±

0.02

––

–C

loqu

etga

nglio

nm

etas

tasi

s1.

12±

0.01

(1)

––

–T

hyro

idgl

and

1.23

±0.

08a

(15)

1.42

±0.

15b

(5)

1.70

±0.

16b

(5)

3.04

±0.

05(1

)N

euri

lem

mom

a1.

23±

0.02

(1)

––

–Pe

lvic

gang

lion

1.39

±0.

11b

(6)

1.42

±0.

01(2

)1.

83±

0.02

(2)

2.32

±0.

03(1

)–

1.45

±0.

021.

78±

0.02

–A

ggre

ssiv

efib

rom

atos

is1.

41±

0.16

b(4

)1.

54±

0.03

(2)

1.87

±0.

02(2

)–

–1.

44±

0.03

1.77

±0.

03–

Hep

atic

met

asta

sis

1.53

±0.

15b

(5)

1.81

±0.

21b

(3)

2.48

±0.

30b

(3)

3.27

±0.

03(2

)–

––

3.81

±0.

03L

ung

carc

inom

a1.

68±

0.15

b(7

)2.

01±

0.27

b(3

)2.

82±

0.31

b(3

)3.

89±

0.03

(1)

(con

tinue

d)


326 Chapter 7

Tab

le7.

4(c

ontin

ued)

Prel

aryn

geal

stri

ated

mus

cle

1.72

±0.

20b

(3)

––

–M

amm

ary

fat

1.81

±0.

09a

(10)

2.03

±0.

18b

(6)

2.24

±0.

19b

(6)

2.79

±0.

28b

(3)

Mam

mar

ytis

sue

2.59

±0.

18a

(14)

2.87

±0.

30b

(5)

3.12

±0.

32b

(5)

3.54

±0.

40b

(3)

Mam

mar

ydy

spla

sia

2.21

±0.

20b

(9)

2.68

±0.

29b

(3)

3.03

±0.

33b

(3)

–M

amm

ary

carc

inom

a2.

87±

0.22

a(1

0)3.

14±

0.36

b(3

)3.

62±

0.41

b(3

)4.

23±

0.04

(1)

Ute

rine

myo

ma

2.74

±0.

22b

(6)

2.93

±0.

03(1

)3.

28±

0.03

(1)

–U

teru

s2.

14±

0.18

a(1

5)2.

40±

0.22

b(4

)2.

61±

0.25

b(4

)3.

31±

0.02

(1)

Subm

axill

ary

glan

d2.

49±

0.23

b(3

)–

––

Mal

igna

ntfib

rous

hist

iocy

tom

a2.

48±

0.03

(1)

––

–C

olon

2.48

±0.

21b

(7)

2.73

±0.

29b

(3)

2.91

±0.

31b

(3)

–L

ipom

a2.

83±

0.21

a(1

1)3.

03±

0.29

b(4

)3.

71±

0.33

b(4

)4.

19±

0.03

(1)

Mes

enqu

inom

a4.

01±

0.03

(1)

––

–A

xilla

rep

ider

moi

dca

rcin

oma

2.12

±0.

18b

(8)

2.51

±0.

22b

(4)

2.64

±0.

23b

(4)

3.24

±0.

03(1

)L

iver

(pos

tmor

tem

)1.

20±

0.13

a(1

0)1.

69±

0.16

a(1

0)2.

91±

0.30

a(1

0)3.

68±

0.35

a(1

0)B

rain

(pos

tmor

tem

)0.

92±

0.08

a(1

0)1.

38±

0.13

a(1

0)2.

17±

0.16

a(1

0)2.

52±

0.19

a(1

0)M

uscl

e(p

ostm

orte

m)

1.47

±0.

10a

(10)

1.63

±0.

10a

(10)

3.46

±0.

23a

(10)

3.72

±0.

29a

(10)

aSt

anda

rder

ror.

bA

bsol

ute

mea

nde

viat

ion,

pres

ente

dfo

rot

her

erro

rsob

tain

edby

the

leas

t-sq

uare

sm

etho

d.



Table 7.5 Optical properties and dosimetric correction factor, U/F, of skull bone for differentwavelengths (values are presented as mean ± SEM; to obtain the space irradiance, U, inan intact cochlea, transmitted irradiance measured for specimen slabs has to be multipliedby U/F) (see Ref. 1283).

λ, nm μa/μ′s Teff

c μa, cm−1 μ′s, cm−1 μeff, cm−1 U/F

593 0.0135 ± 0.0048 0.585 ± 0.054 0.561 ± 0.108 47.1 ± 8.3 8.70 ± 0.91 10.0 ± 1.5635 0.0072 ± 0.0018 0.501 ± 0.038 0.371 ± 0.022 55.7 ± 9.1 7.80 ± 0.44 12.9 ± 1.4690 0.0035 ± 0.0008 0.398 ± 0.026 0.169 ± 0.011 51.1 ± 7.3 5.04 ± 0.32 17.7 ± 1.7780 0.0028 ± 0.0005 0.367 ± 0.026 0.107 ± 0.009 40.0 ± 4.6 3.56 ± 0.18 19.5 ± 1.6830 0.0028 ± 0.0005 0.367 ± 0.027 0.104 ± 0.009 38.8 ± 4.4 3.45 ± 0.16 19.4 ± 1.6

radiant energy fluence rate, U(r) [see Eq. (1.12)], or the space irradiance, definedas the light power hitting a sphere, divided by the sphere’s cross section.1283 For anisotropic space distribution of light intensity, the space irradiance is four times theirradiance measured for the same point within tissue (r).

In Ref. 1283, experimental data for the diffuse reflectance, Rd, and collimatedtransmission, Tc, of an isolated bone specimen with defined thickness, d, were usedfor MC calculation of the transmitted irradiance, F(d), and its comparison with thespace irradiance at the same point, U(d), inside a specimen of infinite thickness.Finally, the dosimetric correction factor, U/F, was evaluated. The results of dosi-metric correction using in vitro experimental data and corresponding calculateddata for human skull bone are presented in Table 7.5. Calculations of μa and μ′

sfrom the measured Rd and Tc were performed by a simplified procedure valid ford of the bone with μeffd > 2. In this case, Tc = Teff

c exp(−μeffd). As shown in Ref.1283, in a good approximation, Teff

c , Rd, and U/F depend only on the ratio μa/μ′s.

The knowledge of Teffc allows one to evaluate μeff from the equation for Tc, and,

furthermore, μa and μ′s from Eq. (1.18) and the known ratio μa/μ

′s. All MC calcu-

lations were conducted for tissue mean index of refraction n = 1.35 and anisotropyfactor g = 0.8.

7.12 Refractive Index Measurements

The mean refractive index, n, of a tissue is defined by the refractive indices ofthe material in its scattering centers, ns, and ground (surrounding) matter, n0

[see Eqs. (3.1)–(3.5)]. The refractive index variation in tissues, quantified by theratio m = ns/n0, determines light scattering efficiency. For example, in a simplemonodisperse tissue model, such as dielectric spheres of equal diameter, 2a, thereduced scattering coefficient271

μ′s ≡ μs (1 − g) = 3.28πa2ρs

(2πa

λ

)0.37

× (m − 1)2.09 , (7.27)

where μs = σscaρs is the scattering coefficient, σsca is the scattering cross section,ρs is the volume density of the spheres, g is the scattering anisotropy factor, and


328 Chapter 7

λ is the light wavelength in the scattering medium. This equation is valid fornoninteracting Mie scatterers, g > 0.9; 5 < 2πa/λ < 50; 1 < m < 1.1.

For example, epithelial nuclei can be considered as spheroidal Mie scatterswith refractive index, nnc, which is higher than that of the surrounding cyto-plasm, ncp. Normal nuclei have a characteristic diameter d = 4−7μm. In contrast,dysplastic nuclei can be as large as 20 μm, occupying almost the entire cellvolume.1163 In the visible range, where the wavelength λ0�d, the van de Hulstapproximation can be used to describe the elastic scattering cross section of thenuclei as272, 273

σsca (λ, d) = 1

2πd2

[1 − 2 sin δ

δ+

(2 sin δ

δ

)2]

, (7.28)

with δ = 2πd(nnc − ncp)/λ0, λ0 is the wavelength of the light in vacuum. Thisexpression reveals a component of the scattering cross section, which varies peri-odically with inverse wavelength. This, in turn, generates a periodic component inthe tissue optical reflectance. Because the frequency of this variation (in inversewavelength space) is proportional to particle size, the nuclear size distribution canbe obtained from the Fourier transform of the periodic component.

Measuring refractive indices in tissues and their constituent components isan important focus of interest in tissue optics because the index of refractiondetermines light reflection and refraction at the interfaces between air and tis-sue, detecting fiber and tissue, and tissue layers; it also strongly influences lightpropagation and distribution within tissues, defines speed of light in tissue, andgoverns how photons migrate.31, 129, 130, 245, 248–270, 298, 1267, 1301, 1302, 1356–1391 Althoughthese studies have a rather long history,87 the mean values of refractive indicesfor many tissues are missing from the literature. According to Ref. 87, most haverefractive indices for visible light in the 1.335–1.620 range (e.g., 1.55 in the stratumcorneum, 1.620 in the tooth enamel, and 1.386 at the eye lens surface). In vitro andin vivo measures may differ significantly. For example, the refractive index in ratmesenteric tissue in vitro was found to be 1.52, compared with only 1.38 in vivo.87

This difference can be accounted for by the decreased refractivity of ground matter,n0, attributable to impaired hydration.

Actually, the optical properties of tissues, including refractive indices, areknown to depend on water content, which often determines spectral and disper-sive characteristics of tissues.87, 1382, 1392 The refractive indices of water over abroad wavelength range from 200 nm to 200 μm have been reported in Ref. 87.Specifically, nw = 1.396 for λ = 200 nm, 1.335 for λ = 500 nm, 1.142 for λ =2800 nm, 1.400 for λ = 3500 nm, 1.218 for λ = 10, 000 nm, and 2.130 forλ = 200μm. Equation (6.5) was shown to be valid for pure water in the visibleand NIR wavelength ranges, corresponding to the best light transmission throughtissues.1191

It is more adequate to model tissue by using a mixture of water and abio-organic compound of a tissue. For instance, the refractive index of humanskin can be approximated by a 70/30 mixture of water and protein.1267, 1386, 1392



Assuming that protein has a constant refractive index value of 1.5 over theentire wavelength range, the authors of Ref. 1267 have suggested the followingexpression for estimating the skin index of refraction:

nskin(λ) = 0.7(1.58 − 8.45 × 10−4λ + 1.10 × 10−6λ2 − 7.19 × 10−10λ3

+ 2.32 × 10−13λ4 − 2.98 × 10−17λ5) + 0.3·1.5, (7.29)

where wavelength λ is in nanometers.For different parts of a biological cell, values of refractive index in the

NIR range can be estimated as follows: extracellular fluid, n = 1.35−1.36; cyto-plasm, 1.360–1.375; cell membrane, 1.46; nucleus, 1.38–1.41; mitochondria andorganelles, 1.38–1.41; melanin, 1.6–1.7.58 Scattering arises from mismatches inthe refractive index of the components that make up the cell.1383 Organelles andsubcomponents of organelles having indices different from their surroundings areexpected to be the primary sources of cellular scattering. The cell itself may bea significant source of small-angle scatter in applications like flow cytometry, inwhich cells are studied separately.211, 215 In contrast, in tissues where cells aresurrounded by other cells or tissue structures of similar index, certain organellesbecome the important scatterers. For instance, the nucleus is a significant scattererbecause it is often the largest organelle in the cell and its size increases relativeto the rest of the cell throughout neoplastic progression.216–219, 229, 232, 236, 272, 1293

Mitochondria (0.5–1.5 μm in diameter), lysosomes (0.5 μm), and peroxisomes(0.5 μm) are very important scatterers whose size relative to the wavelength oflight suggests that they must make a significant contribution to backscattering.Granular melanin, traditionally deemed an absorber, must be considered an impor-tant scatterer because of its size and high refractive index.58 Structures consistingof membrane layers, such as the endoplasmic reticulum or Golgi apparatus, mayprove significant because they contain index fluctuations of high spatial frequencyand amplitude. In addition to cell components, fibrous tissue structures such ascollagen and elastin must be considered to be important scatterers.

Refractivity measurements in a number of strongly scattering tissues at 633 nmperformed with a fiber-optic refractometer are schematically shown in Fig. 7.9.248

This method is based on a simple concept: that the cone of light issuing from anoptical fiber is dependent on the indices of the cladding material, core material(quartz), and air into which the cone of light emerges. The cladding on a 1-mm corediameter optical fiber was stripped from the fiber, and the tissue for which the indexis to be measured was substituted for the cladding. With the indices for air (n0) andthe quartz fiber (nq) known, along with the emitted angular light distribution (θ)measured at the optical fiber’s output, the following equation for the determinationof tissue index of refraction (n) can be derived from the expression for the fibernumerical aperture:248

n ={

n2q − [n0 sin θ]2

}1/2. (7.30)


330 Chapter 7

Figure 7.9 Schematic of experimental setup for determining the index of refraction. A baresilica fiber is placed in a cladding of the substance to be measured. Angular light outputdistribution is measured, and the index is determined from Eq. (7.30) (see Ref. 248).

Using this simple and sensitive technique, it was found that fatty tissue hasthe largest refractive index (1.455), followed by kidney (1.418), muscular tis-sue (1.410), and then blood and spleen (1.400).248 The lowest refractive indiceswere found in lungs and liver (1.380 and 1.368, respectively).248 Also, it turnedout that tissue homogenization does not significantly affect the refractive indices(the change does not exceed a measurement error equal to 0.006), whereas coagu-lated tissues have higher refractive indices than native tissues (for example, for eggwhite, n changes from 1.321 to 1.388). Moreover, there is a tendency for refrac-tive indices to decrease with increasing light wavelength from 390 to 700 nm (forexample, for bovine muscle in the limits 1.42 to 1.39), which is characteristic ofthe majority of related abiological materials.

Experimental values of mean refractive index for some tissues measured forselected wavelengths are summarized in Table 7.6.

The principle of total internal reflection at laser beam irradiation is also usedfor tissue and blood refraction measurements.1357, 1358, 1375–1378 The scheme of alaser refractometer is shown in Fig. 7.10.1357 A thin tissue sample is sandwichedbetween two right-angle prisms that are made of ZF5 glass with a high refrac-tive index, n0 = 1.70827, and angle, α = 29◦55′41.4′′. For an incident laser beampolarized in the S-plane, the following equation for the determination of the meanrefractive index of tissues is valid:1357

n = sin it × cosα + sinα × [n2

0 − sin2 it]1/2

, (7.31)

where the incident angle of total reflectance, it, is a measurable parameter.Measurements for fresh animal tissues and human blood at room temperature

and four laser wavelengths of 488, 632.8, 1079.5, and 1341.4 nm were presentedin a form of Cauchy dispersion equation as1357

n = A + B · λ−2 + C · λ−4 (7.32)



Tab

le7.

6E

xper

imen

tal

mea

nva

lues

ofph

ase,

n,or

gro

up,

n g,

refr

activ

ein

dice

sof

tissu

es,

bloo

d,an

dth

eir

com

poun

dsm

easu

red

invi

tro

and

invi

vo*;

rms

valu

esar

egi

ven

inpa

rent

hese

s.

Tis

sue

λ,n

mn,

n gC

omm

ents

Hum

anao

rta:

Nor

mal

:In

tima

456–

1064

1.39

Ref

.128

1M

edia

456–

1064

1.38

Adv

entit

ia45

6–10

641.

36C

alci

fied:

Intim

a45

6–1

064

1.39

Med

ia45

6–10

641.

53H

uman

blad

der:

Muc

ous

456–

1064

1.37

Ref

.128

1W

all

456–

1064

1.4

Inte

gral

456–

1064

1.38

Hum

anbr

ain:

Gra

ym

atte

r45

6–10

641.

36R

ef.1

281

Whi

tem

atte

r45

6–10

641.

38W

hite

and

gray

456–

1064

1.37

Hum

anco

lon:

Mus

cle

456–

1064

1.36

Ref

.128

1Su

bmuc

ous

456–

1064

1.36

Muc

ous

456–

1064

1.38

Inte

gral

456–

1064

1.36

Fem

ale

brea

sttis

sue:

Nor

mal

800

1.40

3R

ef.3

1M

alig

nant

800

1.43

1

(con

tinue

d)


332 Chapter 7

Tab

le7.

6(c

ontin

ued)

Tis

sue

λ,n

mn,

n gC

omm

ents

Rat

brea

st(m

amm

ary)

tissu

e(8

anim

als,

32tu

mor

s):

OC

T,tit

aniu

m-s

apph

ire

lase

rso

urce

with

cent

ral

wav

elen

gth

of80

0nm

and

band

wid

thof

100

nm);

N-m

ethy

l-N

-nitr

osou

rea-

indu

ced

ratm

amm

ary

tum

ors

(sim

ilar

inpa

thol

ogy

tohu

man

duct

alca

rcin

oma)

,Ref

.136

4A

dipo

se75

0–85

01.

467

(0.0

26)

Fibr

ous

stro

ma

750–

850

1.38

8(0

.043

)T

umor

750–

850

1.39

0(0

.028

)H

uman

esop

hagu

s:M

ucou

s45

6–10

641.

37R

ef.1

281

Hum

anfa

t:Su

bcut

aneo

us45

6–10

641.

44R

ef.1

281

Abd

omin

al45

6–10

641.

46H

uman

mes

ente

ric

fat

1300

1.46

7(0

.008

)O

CT,

optic

alpa

thle

ngth

mea

sure

men

ts14

07

Bov

ine

fat

633

1.45

5(0

.006

)R

ef.2

48,fi

ber-

optic

refr

acto

met

er(F

OR

);ho

mog

eniz

edtis

sue

Porc

ine

fat

488

1.51

0(0

.002

)R

ef.1

357,

632.

81.

492

(0.0

03)

lase

rre

frac

tom

eter

(LR

)10

79.5

1.48

2(0

.002

)13

41.4

1.47

8(0

.004

)63

2.8

1.49

3(0

.005

)R

ef.1

358,

LR

Hum

anhe

art:

Tra

becu

la45

6–10

641.

4R

ef.1

281

Myo

card

456–

1064

1.38

Hum

anle

ftve

ntri

cula

rca

rdia

cm

uscl

e13

001.

382

(0.0

07)

OC

T,op

tical

path

leng

thm

easu

rem

ents

1407

Hum

anfe

mor

alve

in45

6–10

641.

39R

ef.1

281

Kid

ney:

Hum

an45

6–10

641.

37R

ef.1

281

Hum

an63

31.

417

(0.0

06)

Ref

.248

,FO

RC

anin

e63

31.

400

(0.0

06)

Porc

ine

633

1.39

0(0

.006

)B

ovin

e63

31.

390

(0.0

06)



Liv

er:

Hum

an45

6–10

641.

38R

ef.1

281

Hum

an63

31.

367

(0.0

06)

Ref

.248

,FO

R;h

omog

eniz

edtis

sue

Can

ine

633

1.38

0(0

.006

)Po

rcin

e63

31.

390

(0.0

06)

Bov

ine

633

1.39

0(0

.006

)L

ung: Hum

an45

6–10

641.

38R

ef.1

281

Can

ine

633

1.38

0(0

.006

)R

ef.2

48,F

OR

;hom

ogen

ized

tissu

ePo

rcin

e63

31.

380

(0.0

06)

Mus

cle:

Hum

an45

6–10

641.

37R

ef.1

281

Can

ine

633

1.40

0(0

.006

)R

ef.2

48,F

OR

;hom

ogen

ized

tissu

eB

ovin

e63

31.

412

(0.0

06)

Bov

ine

592

(560

–640

)1.

382

(0.0

04)

Ref

.136

3,flu

ores

cenc

eco

nfoc

alm

icro

scop

yO

vine

||48

81.

404

(0.0

03)

Ref

.135

7,L

R,t

issu

esa

mpl

esla

bele

das

||and

⊥ar

esa

me

sam

ple

with

tissu

efib

ers

orie

nted

para

llela

ndpe

rpen

dicu

lar

toin

terf

ace,

resp

ectiv

ely

632.

81.

389

(0.0

02)

1079

.51.

378

(0.0

04)

1341

.41.

375

(0.0

03)

Ovi

ne⊥

488

1.40

2(0

.002

)63

2.8

1.38

9(0

.002

)10

79.5

1.37

5(0

.003

)13

41.4

1.37

3(0

.003

)Po

rcin

e ||48

81.

402

(0.0

02)

632.

81.

381

(0.0

02)

1079

.51.

372

(0.0

03)

1341

.41.

370

(0.0

03)

Porc

ine ⊥

488

1.39

9(0

.002

)63

2.8

1.37

9(0

.002

)10

79.5

1.37

0(0

.002

)13

41.4

1.36

7(0

.003

)Po

rcin

e ||63

2.8

1.38

0(0

.007

)R

ef.1

358,

LR

Porc

ine ⊥

632.

81.

460

(0.0

08)

(con

tinue

d)


334 Chapter 7

Tab

le7.

6(C

ontin

ued)

Tis

sue

λ,n

mn,

n gC

omm

ents

Mus

cle

from

abdo

min

alw

allo

fth

era

t(s

peci

es:W

ista

rH

an)

589

1.39

80(m

=0.1

623

g)∗

Abb

ere

frac

tom

eter

,ref

ract

ive

inde

xan

dm

ass

(m)

mea

sure

men

tsin

aco

urse

ofa

dehy

drat

ion

proc

ess

recu

rrin

gto

sam

ple

heat

ing

with

hair

drye

r,∗ n

atur

altis

sue,

Ref

.138

658

91.

3995

(m=

0.14

55g)

589

1.41

05(m

=0.

1361

g)58

91.

4200

(m=

0.12

52g)

589

1.42

95(m

=0.

1144

g)58

91.

4410

(m=

0.10

53g)

589

1.45

25(m

=0.

0955

g)58

91.

4640

(m=

0.08

60g)

589

1.47

85(m

=0.

0747

g)58

91.

4910

(m=

0.06

54g)

589

1.50

35(m

=0.

0551

g)H

uman

skin

:St

ratu

mco

rneu

m(S

C)*

1300

n g=

1.51

(0.0

2)R

ef.1

407,

OC

T,re

fere

nce

mir

ror

and

focu

str

acki

ngE

pide

rmis

*13

00n g

=1.

34(0

.01)

Der

mis

1300

n g=

1.41

(0.0

3)D

erm

is13

00n g

=1.

400(

0.00

7)O

CT,

optic

alpa

thle

ngth

mea

sure

men

ts14

07

SC*

(pal

mof

hand

)13

00(n

n g)1/

2=

1.47

(0.0

1)R

ef.1

301,

OC

T,fo

cus

trac

king

bym

ovin

gof

fiber

tip/c

ollim

atin

gle

nsE

pide

rmis

*(p

alm

ofha

nd,g

ranu

lar

laye

r)13

00(n

n g)1/

2=1

.43(

0.02

)E

pide

rmis

*(p

alm

ofha

nd,b

asal

laye

r)13

00(n

n g)1/

2=1

.34(

0.02

)E

pide

rmis

*(v

olar

side

oflo

wer

arm

)13

00(n

n g)1/

2=1

.36(

0.01

)U

pper

derm

is*

(pal

mof

hand

)13

00(n

n g)1/

2=1

.41(

0.03

)U

pper

derm

is*

(vol

arsi

deof

low

erar

m)

1300

(nn g

)1/2=1

.43(

0.02

)SC

*(d

orsa

lsur

face

ofth

umb)

980

(nn g

)1/2

=1.

50(0

.02)

Bif

ocal

OC

Tre

frac

tom

eter

,Ref

.141

0A

ir/s

kin

inte

rfac

e*(v

olar

side

ofth

umb)

980

(nn g

)1/2=1

.56

Ref

.141

1SC

/epi

derm

isin

terf

ace*

(vol

arsi

deof

thum

b)98

0(n

n g)1/

2=1

.34

Hum

anst

ratu

mco

rneu

m40

0–70

01.

55R

ef.8

7



Hum

ansk

in(e

pide

rmis

)(1

2fe

mal

e,be

twee

n27

and

63yr

;10

are

Cau

casi

an*

and

2ar

eA

fric

anA

mer

ican

**)

325

(*)

1.48

9(S

)1.

486

(P)

Pris

mla

ser

refr

acto

met

erw

ithan

inci

dent

beam

ofS-

orP

-pol

ariz

atio

n,Fr

esne

l’seq

uatio

ns,

fres

htis

sue

sam

ples

exam

ined

atro

omte

mpe

ratu

rew

ithin

30h

afte

rab

dom

inop

last

ypr

oced

ure,

tota

lun

cert

aint

yin

nof

sam

ples

was

estim

ated

tobe

±0.0

06,R

ef.1

367

442

(*)

(**)

1.44

9(S

)1.

447

(P)

532

(*)

(**)

1.44

8(S

)1.

446

(P)

633

(*)

1.43

3(S

)1.

433

(P)

850

(*)

1.41

7(S

)1.

416

(P)

1064

(*)

1.43

2(S

)1.

428

(P)

1310

(*)

1.42

5(S

)1.

421

(P)

1557

(*)

1.40

4(S

)1.

400

(P)

Hum

ansk

in(d

erm

is)

(12

fem

ale,

betw

een

27an

d63

yr;1

0ar

eC

auca

sian

*an

d2

are

Afr

ican

Am

eric

an**

)

325

(*)

1.40

1(S

)1.

403

(P)

442

(*)

(**)

1.39

5(S

)1.

400

(P)

532

(*)

(**)

1.37

8(S

)1.

381

(P)

633

(*)

1.39

6(S

)1.

393

(P)

850

(*)

1.38

4(S

)1.

389

(P)

1064

(*)

1.37

5(S

)1.

385

(P)

1310

(*)

1.35

8(S

)1.

364

(P)

1557

(*)

1.36

3(S

)1.

367

(P)

Pigs

kin

1300

(nn g

)1/2

=1.

415

Ref

.130

2,O

CT,

focu

str

acki

ngPi

gski

n(t

reat

edby

ade

terg

ents

olut

ion)

1300

(nn g

)1/2

=1.

365

Rat

skin

456–

1064

1.42

Ref

.128

1M

ouse

skin

456–

1064

1.40

Porc

ine

skin

(der

mis

)32

51.

393

Pris

mla

ser

refr

acto

met

er,

Fres

nel’s

equa

tions

,fr

esh

tissu

esa

mpl

esof

thic

knes

sfr

om0.

31to

0.84

mm

,to

tal

unce

rtai

nty

inn

ofsa

mpl

esw

ases

timat

edto

be±0

.004

,Ref

s.13

65an

d13

6644

21.

376

532

1.35

963

31.

354

850

1.36

410

641.

3613

101.

357

1557

1.36

1Sp

leen

:H

uman

456–

1064

1.37

Ref

.128

1C

anin

e63

31.

400

(0.0

06)

Ref

.248

,FO

R;h

omog

eniz

edtis

sue

Porc

ine

633

1.40

0(0

.006

)

(con

tinue

d)


336 Chapter 7

Tab

le7.

6(C

ontin

ued)

Tis

sue

λ,n

mn,

n gC

omm

ents

Hum

anst

omac

h:M

uscl

e45

6–10

641.

39R

ef.1

281

Muc

ous

456–

1064

1.38

Inte

gral

456–

1064

1.38

Porc

ine

smal

lint

estin

e48

81.

391

(0.0

02)

Ref

.135

7,L

R63

2.8

1.37

3(0

.002

)10

79.5

1.36

1(0

.003

)13

41.4

1.35

9(0

.004

)H

uman

cere

bral

spin

alflu

id40

0–70

01.

335

Ref

.87

Rat

mes

ente

ry40

0–70

01.

52(0

.01)

Ref

.87

Rat

mes

ente

ry*

400–

700

1.38

(0.1

)R

atm

esen

tery

850

1.42

45(T

=25◦

C)

Ref

.13

61,

OC

T,se

vera

lpi

eces

ofra

tm

esen

teri

es,

mai

nly

com

pose

dof

phos

pho-

lipid

sbi

laye

rs;g

el-t

o-liq

uid

phas

etr

ansi

tion

inth

era

nge

from

38to

42◦ C

1.42

39(T

=30◦

C)

1.42

23(T

=35◦

C)

1.42

16(T

=38◦

C)

1.41

86(T

=40◦

C)

1.40

27(T

=42◦

C)

1.40

16(T

=44◦

C)

1.40

00(T

=46◦

C)

1.39

86(T

=48◦

C)

Hum

aney

e:A

queo

ushu

mor

400–

700

1.33

6R

ef.8

7C

orne

a:In

tegr

al40

0–70

01.

376

Fibr

ils40

0–70

01.

47G

roun

dsu

bsta

nce

400–

700

1.35

Len

s: Surf

ace

400–

700

1.38

6C

ente

r40

0–70

01.

406



Vitr

eous

hum

or40

0–70

01.

336

Tear

s40

0–70

01.

3361

–1.3

379

Scle

ra44

2–10

641.

47–1

.36

Ref

.128

1C

orne

a:A

bbe

refr

acto

met

erm

easu

rem

ents

and

calc

ulat

ions

onth

eba

sis

ofx-

ray

diff

ract

ion

data

,Ref

.771

Hum

an:

Fibr

ils58

91.

411

(0.0

04)

Ext

rafib

rilla

rm

ater

ial

589

1.36

5(0

.009

)O

x: Fibr

ils58

91.

413

(0.0

04)

Ext

rafib

rilla

rm

ater

ial

589

1.35

7(0

.009

)R

abbi

t:Fi

brils

589

1.41

6(0

.004

)E

xtra

fibri

llar

mat

eria

l58

91.

357

(0.0

10)

Tro

ut:

Fibr

ils58

91.

418

(0.0

04)

Ext

rafib

rilla

rm

ater

ial

589

1.36

4(0

.009

)B

ovin

e:D

ata

from

Ref

s.77

2an

d77

3St

rom

a58

91.

375

Hyd

rate

dfib

rils

589

1.41

3H

ydra

ted

extr

afibr

illar

mat

rix

589

1.35

9D

ryco

llage

n58

91.

547

Dry

extr

afibr

illar

mat

eria

l58

91.

485

Solv

ent(

salt

solu

tion)

589

1.33

5H

ydra

ted

stro

ma:

589

1.33

5+0.

04/(

0.22

+0.2

4H)

H=3

−8,H

=3.2

:phy

siol

ogic

alhy

drat

ion,

Ref

.772

Cal

fco

rnea

:N

orm

al82

0n g

=1.3

80(0

.001

)R

ef.1

413,

OC

T,re

fere

nce

mir

ror

met

hod;

Hyd

rate

d(H

=1.

5–5)

:82

0a

=1.

324

(0.0

02)

H=

5.3×

d-

0.67

,dis

corn

eals

trom

ath

ickn

ess

inm

mn g

(H)

=a

+b/

(H+

1)b

=0.

272

(0.0

09)

(con

tinue

d)


338 Chapter 7

Tab

le7.

6(C

ontin

ued)

Tis

sue

λ,n

mn,

n gC

omm

ents

Hum

anco

rnea

550

1.37

71O

bstf

eld

1982

,dat

umfr

omR

ef.1

415

589

1.38

0(0

.005

)Pa

tele

tal.,

1995

,dat

umfr

omR

ef.1

415

855

n g=

1.38

17(0

.002

1)R

ef.1

414,

OC

T12

70n g

=1.

389

(0.0

04)

Ref

.141

5,O

CT,

21′ C

,12

70n g

=1.

386

Ref

.141

5,ex

trap

olat

ion

ofda

tum

for

550

nm12

70n g

=1.

390

(0.0

05)

Ref

.141

5,ex

trap

olat

ion

ofda

tum

for

589

nm12

70n g

=1.

3838

(0.0

021)

Ref

.141

5,ex

trap

olat

ion

ofda

tum

for

855

nmH

uman

toot

h:E

nam

el22

01.

73R

ef.8

7E

nam

el40

0–70

01.

62A

patit

e40

0–70

0>

1.62

3D

entin

mat

rix

Vis

ible

1.55

3(0

.001

)R

ef.1

403,

optic

alim

mer

sion

met

hod

Ena

mel

856

n g=

1.62

(0.0

2)R

ef.6

35,O

CT,

refe

renc

em

irro

rm

etho

dD

entin

856

n g=

1.50

(0.0

2)E

nam

el85

0n g

=1.

65R

ef.1

408,

OC

TD

entin

850

n g=

1.54

Hum

anna

il*85

0n g

=1.

51R

ef.1

408,

OC

TH

uman

hair

shaf

t:B

lack

850

n g=

1.59

(0.0

8)R

ef.1

406,

OC

TB

row

n85

0n g

=1.

58(0

.06)

Red

850

n g=

1.56

(0.0

1)B

lond

850

n g=

1.57

(0.0

1)G

ray

850

n g=

1.58

(0.0

1)W

hite

850

n g=

1.58

(0.0

1)H

uman

hair

stra

nds

400–

600

1.45

(304

nm,0

.6%

)E

llips

omet

ry,

valu

esde

pend

onpa

ram

eter

sof

thic

knes

sfo

rcu

ticle

surf

ace

roug

hnes

sla

yer

(fro

m30

4to

359.

7nm

)an

dai

rin

clus

ion

(fro

m0.

6to

5.7%

),R

ef.1

422

400–

600

1.46

(299

.5nm

,0.1

%)

400–

600

1.47

(308

.7nm

,0.8

%)

400–

600

1.46

(273

.7nm

,2.2

%)

400–

600

1.50

(327

.5nm

,4.7

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340 Chapter 7

Tab

le7.

6(C

ontin

ued)

Tis

sue

λ,n

mn,

n gC

omm

ents

Gly

cate

d(g

luco

sefr

om40

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800

mg/

dl)

820

1.41

5→1.

385

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oglo

bin

(hum

an,o

xyge

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d)25

014

70(0

.03)

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s.13

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80,

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nel

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ents

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spec

trom

eter

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oglo

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7g/

l30

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441

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3)40

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(0.0

3)50

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413

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3)58

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406

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n g=

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08–0

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)


342 Chapter 7

Table 7.7 Values of Cauchy coefficients of dispersion Eq. (7.32) (see Ref. 1357).

Tissue sample A B ×10−3 C ×10−9

Porcine muscle|| 1.3694 0.073223 1.8317Porcine muscle⊥ 1.3657 1.5123 1.5291Porcine adipose 1.4753 4.3902 0.92385Porcine small intestine 1.3563 4.3905 0.92379Ovine muscle|| 1.3716 5.8677 0.43999Ovine muscle⊥ 1.3682 8.7456 –0.1653Human whole blood 1.3587 1.4744 1.7103Human blood plasma 1.3194 14.578 –1.7383

Figure 7.10 Schematic of a laser refractometer based on the principle of total internalreflection (see Ref. 1357).

with λ in nanometers, and values of the Cauchy coefficients as presented inTable 7.7. Measured mean values with standard deviation for four wavelengthsare presented in Table 7.6. Porcine (or ovine) muscle samples labeled as || and ⊥are the same sample, with the tissue fibers oriented in parallel and perpendicular tothe interface, respectively.

An expression for human blood plasma received in Ref. 1357 was extrapolatedto shorter wavelengths from 400 to 1000 nm:1009, 1359

nbp(λ) = 1.3254 + 8.4052 × 103λ−2 − 3.9572 × 108λ−4 − 2.3617 × 1013λ−6.

(7.33)

For modeling of the behavior of the refractive index of tissues, blood, and theircomponents, one may use a remarkable property of proteins: that equal concen-trations of aqueous solutions of different proteins all have approximately the samerefractive index, npw.1360 Moreover, the refractive index varies almost linearly withconcentration, Cp:

npw(λ) = nw(λ) + βp(λ) · Cp, (7.34)

where nw is refractive index of water and βp is the specific refractive increment;Cp is measured in grams per 100 ml (g/dl). For example, the refractive index



Table 7.8 Values of specific refractive increment, βp, mea-sured by Abbe refractometer on the wavelength 589 nm forthe proteins (see Ref. 1360).

Protein βp, dl/g

Total serum (human) 0.00179Euglobulin 0.00183Pseudoglobulin 0.00181Total albumin 0.00181Recrystallized albumin 0.00181Lipoprotein 0.00170–0.00171Hemocyanin Helix 0.00179

Octopus 0.00184Carcinus 0.00187

Egg albumin 0.001813Sheep CO hemoglobin 0.001945Globin (ox) 0.00178CO hemoglobin (ox) 0.00193–0.00195

of human erythrocyte cytoplasm, defined by the cell-bounded hemoglobin solu-tion, can be found from this equation at βp = 0.001942, valid for a wavelength of589 nm; i.e., for normal hemoglobin concentration in cytoplasm of 300–360 g/l, theRBC refractive index nRBC = 1.393−1.406.48 Because the scattering coefficient ofblood, which is mostly defined by hemoglobin refractive index, is not significantlydependent on the wavelength in the range of 580–800 nm,48 this value of β canbe used for estimating the refractive index of a hemoglobin solution in the NIRrange. Values of specific refractive increment, βp, for other proteins measured byan Abbe refractometer at a wavelength of 589 nm are presented in Table 7.8.1360

Other materials of specific biological interest are the carbohydrates, lipoids, andnucleic acid compounds. The first two usually have low values of β in the regionof 0.0014–0.0015; nucleic acids have higher values, 0.0016–0.0020.1360

The wavelength dependence of the specific refractive increment of the oxy-genated native hemoglobin solution, βHb (λ), normalized to the refractive indexof pure water, nw(λ) [see Eq. (7.34)], is presented in Table 7.9.1380 The estimatederror, which includes the error of the determination of the hemoglobin concen-tration and refractive index, is ±0.00003. Therefore, the derivation of a meanconstant normalized specific refractive increment of (βHb/nw) = 0.00199 dl/g forthe spectral regions 310–355 nm and 500–1100 nm is possible, because the stan-dard deviation of an averaged value of (βHb/nw) in these regions is ±0.000036 andthe same range as the estimated error for the determination of (βHb/nw) for a fixedwavelength.

The spectral dependencies of refractive indices for oxy- and deoxyhemoglobinin the 450–820 nm wavelength range were obtained in Ref. 1391. These and laterdeterminations225, 1325, 1362, 1393, 1394 are based on absorption spectral measurements(see Fig. 7.11) and conversion of the received imaginary part of the complex refrac-tive index [see Eqs. (3.16) and (3.17)] to its real part by using Kramers–Kronigrelationships.225, 1325, 1362, 1391, 1393–1395 These relations follow from the principle of


344 Chapter 7

Tab

le7.

9W

avel

engt

h-de

pend

entv

alue

sof

spec

ific

refr

activ

ein

crem

ento

fhem

ogl

obin

,βH

b(λ

),no

rmal

ized

tore

frac

tive

inde

xof

pure

wa

ter,

n w(λ

)[s

eeE

q.(7

.34)

],w

ithan

estim

ate

der

ror

of±0

.000

03;o

xyge

nate

dna

tive

hem

ogl

obin

solu

tion;

Fres

nelr

eflec

tanc

em

easu

rem

ents

usin

ga

mod

ified

inte

gra

ting

sphe

resp

ectr

omet

er;d

ata

from

Ref

.138

0(m

ore

com

plet

eda

taar

epr

esen

ted

inth

isre

fere

nce)

.

Wav

elen

gth,

nmβ

Hb

(λ)/

n w(λ

),dl

/gW

avel

engt

h,nm

βH

b(λ

)/n w

(λ),

dl/g

Wav

elen

gth,

nmβ

Hb

(λ)/

n w(λ

),dl

/gW

avel

engt

h,nm

βH

b(λ

)/n w

(λ),

dl/g

250

0.00

221

350

0.00

1989

450

0.00

2156

620

0.00

1964

260

0.00

2105

360

0.00

1983

460

0.00

2109

640

0.00

1954

270

0.00

2048

370

0.00

186

470

0.00

2078

680

0.00

197

280

0.00

2044

380

0.00

1774

480

0.00

2056

760

0.00

1958

290

0.00

2047

390

0.00

1694

490

0.00

2033

800

0.00

1939

300

0.00

202

400

0.00

1664

500

0.00

2005

840

0.00

1935

310

0.00

1998

410

0.00

1799

520

0.00

1983

900

0.00

1998

320

0.00

2007

420

0.00

2117

540

0.00

1981

980

0.00

2017

330

0.00

2021

430

0.00

2273

560

0.00

1992

1060

0.00

204

340

0.00

201

440

0.00

221

580

0.00

2004

1100

0.00

2056



Figure 7.11 Absorption spectra of deoxy- and oxyhemoglobin. −εdλ, pH = 5.5–9.5, �; −εo

λ,pH = 5.5–10.0, • (see Ref. 1311).

causality, which demands the real and imaginary parts of the complex index ofrefraction to be a mutual Hilbert transform (Hi) as

n′ (ν) − 1 = Hi[n′′(ν)

],

n′′ (ν) = Hi−1[n′ (ν) − 1

], (7.35)

where ν = 1/λ.Thus, the original formula for the determination of n′(λ) on the basis of measure-ments of μa(λ) = (4π/λ)n′′(λ) has the view

n′(ν) = 1 + 2

π

∫ ∞

0

n′′(ν′)ν′dν′

(ν′)2 − (ν)2. (7.36)

It follows from this relation that to calculate the index of refraction for a singlewavelength λ = 1/ν, one has to know absorption spectra over the whole interval[0, ∞]. Another problem is to provide integration in the vicinity of the wave-length of interest. To overcome these difficulties, suitable boundary conditionson the finite integral can be determined; analytical continuation of experimen-tal data before integration, or series expansion of experimental data also can beused.225, 1325, 1362, 1391 For numerical integration of Eq. (7.36), a proper step ofintegration and a symmetrical region around the ν = 1/λ of interest should bechosen.1362, 1391 When the series expansion method is used, the n′′ spectrum maybe presented as a sum of several peak functions, usually Gaussian or Lorentzian,which correspond to absorption bands within the measured spectral range.1325, 1362

Because the Hilbert transform is linear, the spectrum of the index of refractionis simply the sum of the corresponding Hilbert transforms of these peak functions.References 1325 and 225 used this approach to determine the index of refraction ofRBCs in the wavelength range from 400 to 1000 nm, and Faber et al.1362 conducted


346 Chapter 7

Figure 7.12 Spectral dependencies of the index of refraction (real part) for: (1) RBCs, 100%oxygenation of hemoglobin and its mean concentration in RBCs of 340 g/l (see Refs. 225and 1325); (2) oxygenated (100%) hemoglobin; and (3) deoxygenated hemoglobin at aconcentration of 140 g/l, which corresponds to the mean concentration of hemoglobin inwhole blood (see Ref. 1362).

this analysis for a wavelength ranging from 250 to 1000 nm for both oxygenatedand deoxygenated hemoglobin. These data are presented in Fig. 7.12.

The Kramers–Kronig equations allow for adequate reconstruction of the refrac-tive index spectral function from absorption measurements of an aqueous solutionof hemoglobin in the range from 250 to 1000 nm, with obligatory consideration ofthe dispersion properties of the solvent,1394 in this case, water. This was confirmedby direct measurements of the refractive index of hemoglobin.1379, 1380, 1384 In theseexperiments,1384 a commercially available multiwavelength digital refractometer,DSR-α (Schmidt & Haensch, Germany), was used, with nine wavelengths cover-ing the entire visible range: 401.5, 435.8, 486.1, 546.1, 587.6, 589.3, 632.8, 656.3,and 706.5 nm (see Tables 7.10 and 7.11). For measurements of the washed RBCs,light scattering considerably influences the spectral characteristics of hemoglobin,but the correctly chosen geometry of the experiment and subsequent processing ofthe data by using Mie theory can significantly improve the quality of informationobtained.1393

To account for the dispersion of absorbing bands in the UV and far-IR regionswithin the spectral range of interest (visible and NIR), absolute measurements ofrefractive index for at least one wavelength chosen in the studied spectral range, butfar from the absorption bands, should be provided. Such measurements may serve



Table 7.10 Refractive index of deoxygenated hemoglobin (Hb)a and oxygenatedhemoglobin (HbO2)b, measured by DSR-λ digital multiwavelength refractometer (Schmidt &Haensch, Germany) at different wavelengths and for different hemoglobin concentrations.Measurements at zero concentration correspond to pure solvent (PBS, pH at 7.4); to min-imize evaporation of water in the sample chamber, measurements were conducted at20 ± 0.01◦C; refractive index of hemoglobin at 37◦C is approximately 0.001–0.002 lowerthan that at 20◦C for all wavelengths and is primarily influenced by the refractive index ofwater in which it is dissolved; measuring error is 0.001 (see Ref. 1384).

Concentration, g/l Wavelength, nm401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5

Deoxygenated hemoglobin (Hb)0 1.345 1.342 1.339 1.336 1.335 1.335 1.334 1.333 1.33220 1.349 1.347 1.343 1.34 1.339 1.339 1.337 1.337 1.33630 1.35 1.348 1.345 1.342 1.34 1.34 1.339 1.338 1.33740 1.351 1.35 1.346 1.343 1.342 1.342 1.341 1.34 1.33850 1.353 1.352 1.348 1.345 1.343 1.343 1.342 1.341 1.3460 1.354 1.354 1.349 1.346 1.345 1.345 1.343 1.343 1.34170 1.355 1.355 1.35 1.347 1.346 1.346 1.344 1.344 1.34280 1.357 1.357 1.352 1.349 1.348 1.348 1.346 1.345 1.34490 1.359 1.359 1.354 1.35 1.349 1.349 1.347 1.347 1.345100 1.36 1.36 1.355 1.352 1.35 1.35 1.349 1.348 1.347110 1.362 1.363 1.357 1.354 1.352 1.352 1.35 1.35 1.348120 1.363 1.364 1.358 1.355 1.353 1.353 1.352 1.351 1.35130 1.365 1.366 1.36 1.356 1.355 1.355 1.353 1.353 1.351140 1.365 1.367 1.361 1.357 1.356 1.356 1.354 1.354 1.352

Oxygenated hemoglobin (HbO2)0 1.345 1.342 1.339 1.336 1.335 1.335 1.334 1.333 1.33220 1.349 1.347 1.343 1.34 1.339 1.339 1.338 1.337 1.33630 1.35 1.348 1.345 1.342 1.34 1.34 1.339 1.338 1.33740 1.352 1.35 1.346 1.343 1.342 1.342 1.34 1.34 1.33950 1.354 1.351 1.348 1.345 1.343 1.343 1.342 1.341 1.3460 1.355 1.353 1.349 1.346 1.345 1.344 1.343 1.342 1.34170 1.357 1.354 1.35 1.347 1.346 1.346 1.344 1.344 1.34280 1.359 1.356 1.352 1.349 1.348 1.348 1.346 1.345 1.34490 1.36 1.358 1.353 1.35 1.349 1.349 1.347 1.347 1.345100 1.362 1.359 1.355 1.352 1.35 1.35 1.349 1.348 1.347110 1.364 1.361 1.356 1.353 1.352 1.352 1.35 1.35 1.348120 1.366 1.362 1.358 1.355 1.353 1.353 1.352 1.351 1.35130 1.367 1.364 1.359 1.356 1.354 1.354 1.353 1.352 1.351140 1.369 1.366 1.361 1.358 1.357 1.357 1.355 1.354 1.353

aDry hemoglobin was in the form of methemoglobin. To obtain solutions of Hb with concentrations of0–140 g l−1, sodium dithionite was added to all samples at a concentration of 10 g l−1. The amount of theoverall refractive index of hemoglobin solution by which the refractive index increased with the addition ofsodium dithionite was subtracted.bTo convert methemoglobin to HbO2, sodium bicarbonate at a concentration of 15 g l−1 was used. The amount ofthe overall refractive index of hemoglobin solution by which the refractive index increased at addition of sodiumbicarbonate was subtracted.

as reference data and can be conducted, for example, using an Abbe refractometerfor hemoglobin solutions or the OCT technique for whole blood.1362, 1384, 1387, 1388

Another technique, which, in principle, allows for refractive index measurementsof blood and other bioliquids at a few separate wavelengths, is shown schemat-ically in Fig. 7.13. This conventional method uses an equilateral small angle


348 Chapter 7

Table 7.11 Effective refractive indices at zero concentration, n0(λ) = nw(λ) [see Eq. (7.34)],and specific refraction increments for Hb and HbO2 (see Ref. 1384).

Wavelength, nm

401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5n0 1.345 1.343 1.34 1.337 1.336 1.336 1.334 1.334 1.33βHb(λ), dl g−1 0.00146 0.00177 0.00154 0.00148 0.00147 0.00147 0.00144 0.00146 0.0014βHbO2 (λ), dl g−1 0.0017 0.00163 0.0015 0.0015 0.00147 0.00148 0.00144 0.00145 0.00143

Figure 7.13 Schematic of the hollow prism refractometer for the measurement of the indexof refraction of blood and other bioliquids (see Ref. 1354).

(of 10 deg) hollow prism made from thin quartz slides and the following expressionfor calculation of the refractive index:1354

n = sin(A+δm

2

)sin

(A2

) , (7.37)

where A is the prism angle and δm is the angle of minimum deviation.A Nomarski polarizing interference microscope was successfully used to mea-

sure the refractive index of fixed and intact dry erythrocytes taken from healthy anddiabetic patients.1389 It was shown that for intact RBCs at physiological pH 7.3,hyperglycation of hemoglobin leads to a higher refractive index; at maximum, itincreased from 1.55 at norm to 1.65 for diabetics. The increase, followed-up sat-uration, and damping of the refractive index of solutions of hemoglobin or wholeblood with glucose at concentrations of increased glucose were found by usingOCT measurements.1387, 1388 The results for the hemoglobin solution at concentra-tion of 140 g/l, which is characteristic for blood at normal physiological conditions,are shown in Fig. 7.14.

According to Eq. (7.34), the initial refractive index of hemoglobin solutionof 140 g/l in water with zero concentration of glucose at 820 nm is expected asnHb140 = 1.355. To evaluate the contribution of glucose at different concentrationsto the mean refractive index of the solution, supposing noninteracting hemoglobinand glucose molecules, the weighted average of refractive indexes [see Eq. (3.2)]of the glucose solution in water, nglw, and hemoglobin, nHb, should be calculated as

nHb+gl = fglwnglw + (1 − fglw)nHb, (7.38)



Figure 7.14 Experimental and reconstructed data for refractive index change of humanhemoglobin at glucose concentration increase in solution (see Ref. 1388). OCT refractome-ter working on 820 nm, hemoglobin concentration of 140 g/l at pH = 7.3. (1) Raw data;(2) calculated data using Eqs. (7.38) and (7.39) for noninteracting hemoglobin and glucose;(3) reconstructed on the basis of Eq. (7.40), refractive index of the glycated hemoglobinfraction.

where fglw is the volume fraction of the glucose solution. In experiments, thevolume fraction of glucose solution was kept constant at fglw = 0.86, which cor-responds to a hemoglobin concentration of 140 g/l (14%). In this equation, therefractive index of dry hemoglobin, nHb, is presented. The value of nglw can becalculated by using the expression238, 467, 468

nglw = nw + 1.515 × 10−6 × Cgl, (7.39)

where Cgl is the glucose concentration in mg/dl. Because nw can be found for 820nm from Eq.(6.5) as nw = 1.328 and Cgl is known, nglw can be calculated for eachconcentration of glucose.

The refractive index of hemoglobin, nHb, can be estimated from Eqs. (7.34)and (7.38) when glucose concentration is zero. From Eq. (7.34), it followsthat nHb140 = 1.355; thus, from Eq. (7.38), nHb140 = fwnw + (1 − fw)nHb, and forfw = 0.86 and nw = 1.328, nHb = 1.521, which correlates with experimental datafor the refractive index of dried RBCs of normal blood.1389 Therefore, nHb+gl canbe found for a solution with different glucose concentrations and a constant con-centration of hemoglobin. According to Eq. (7.38), the mean refractive index fornoninteracting molecules at an increase of glucose concentration of 10 times (from40 to 400 mg/dl) causes only a slight increase of the refractive index in the rangefrom 1.355 to 1.356 [see linear dependence (2) in Fig. 7.14].


350 Chapter 7

In contrast, the experimental data show that the refractive index of ahemoglobin solution at an increase of glucose concentration from 40 to 400 mg/dlchanges more effectively, from 1.355 to 1.361 [curve (1) in Fig. 7.14]. Theobtained degree of refractive index increase, its saturation, and the subsequentfall can evidently be explained using the concept of interaction between glucoseand hemoglobin molecules, when different forms of glycated hemoglobin (GHb)with new molecular structures and optical properties are originated.1396 The vol-ume fraction of GHb in the blood of diabetic patients linearly depends on the meanblood glucose (MBG) in the plasma, which is described by the following empiricalequation:1396

fGHb = 2.7 × 10−4 MBG (mg/dl) + 0.058. (7.40)

This relation allows one to reconstruct the refractive index of the glycated portionof the total hemoglobin by using the general relationship, Eq. (7.38). The finalresult of the reconstruction is presented by curve (3) in Fig. 7.14. To understand thebehavior of the index of refraction of GHb, the classical theory of light dispersionin condensed matter can be used. This theory produces the following formula forthe refractive index:1397

n = 1 + αNq2

Mq. (7.41)

where α is the wavelength-dependent coefficient, N is the number of molecules,q and Mq are the charge and mass of the charge of the molecule capable for oscil-lations at its own frequency at light excitation. From this equation, it follows thatthe refractive index of hemoglobin is a square-law function of charge and inverselyproportional to the mass of molecular charge. Each protein has several differentside groups (R), which define a molecule’s charge. According to Ref. 1389, thecharge of an R-group of hemoglobin molecules may be increased at glucose bind-ing, but at the same time, the increased mass of molecular charge at hemoglobinglycation decreases the refractive index. These facts may explain the obtainedchanges of refractive index in the experiments. At glucose concentrations from 40to 200–300 mg/dl, the increase in charge of the R-group of GHb molecules is higherthan that of the mass of molecular charge and the refractive index increases. At glu-cose concentrations higher than 200–300 mg/dl due to significant increases in Mq

and charge saturation, refractive index dependence saturates and even decreaseswith glucose concentration.

Certain other reasons may affect the refractive index change, such as uncon-trolled hemoglobin oxygen saturation (see Fig. 7.13)1361, 1362 and/or increase inhemoglobin’s affinity to oxygen at glucose elevation (up to 200% increase inaffinity for 15–20 mM of glucose was found by the authors of Ref. 1398).

Because the refractive index of tissue and blood components defines their scat-tering properties, measured scattering parameters may have an advantage whenevaluating the refractive index of tissue and blood components and their meanvalues.1292, 1310, 1368–1373, 1383, 1386, 1393, 1399–1401 Let us discuss this technique in more



detail.1399 For a monodisperse system of spherical scatterers, the reduced scatteringcoefficient can be described by the following expression, written in a more generalform than Eq. (7.27):

μ′s = N0 π aF(fs)Qs(ns, n0, a, λ)(1 − g), (7.42)

where N0 is the number of scatterers in a unit volume; a is their radius; F(fs) is thefunction accounting for the density of particle packing; fs is the volume fractionof scatterers; ns is the refractive index of the scatterers; n0 is the refractive indexof the ground material; λ is the wavelength; and Qs and g are factors of scatteringefficiency and anisotropy, which are calculated from Mie theory.129, 212, 214

Determination of the reduced scattering coefficient of a tissue sample usingintegrating sphere or spatially resolved techniques and corresponding algorithmsfor the extraction of the scattering coefficient, such as inverse adding–doubling orMC; knowledge about the refractive indices of the scatterers and the ground mate-rial at one of the wavelengths; and experimental or theoretical estimations for meanradius of the scatterers allows one to solve the inverse problem and reconstruct thespectral dependence of the refractive index of scatterers for a given spectral depen-dence of the refractive index of the ground material.1399 Similar measurements andtheoretical estimations of a tissue sample before and after its prolonged bathing insaline or other biocompatible liquid with known optical characteristics allow oneto evaluate the spectral dependencies of both refractive indices of the scatterers andthe ground material.

Let us consider a few examples. The major scatterers in a human sclera arelong collagen fibers with a wide range of diameters and a mean value of 100 nm.Fibers are arranged quasi-randomly in the bundles (see Chapter 3).769, 1402 Becauseof characteristic structure sizing and multiple crossings of bundles, this systemcan be approximated by a monodisperse system of spherical scatterers with simi-lar spectral properties. In that case, the Mie-equivalent scatterer radius is equal to250 nm. This value of particle radius is fitted to values of Mie-equivalent radiusreceived for in vivo measurements of skin, in which the scattering properties aremostly defined by the dermis and by fibrous tissue [see Eqs. (3.31) and (3.32)].Using experimental spectral dependence for the reduced scattering coefficient andaccounting for a scleral sample that has been placed into a physiological solutionfor a long time, the interstitial fluid was replaced by a physiological solution whoserefractive index is similar to that of water, and the spectral dependence for refrac-tive index of the scatterers was reconstructed.1292, 1400 The spectral dependence forwater, described by Eq. (6.5), was used at reconstruction. The following approx-imated formula for the refractive index of the material of effective scatterers ofscleral tissue, valid within the spectral range from 400 to 800 nm, was received asa final result of the reconstruction:

ns(λ) = 1.4389 + 1.5880 × 104λ−2 − 1.4806 × 109λ−4 + 4.3917 × 1013λ−6.

(7.43)

In fact, this dispersion relation should be similar to the spectral dependence of theindex of refraction of hydrated collagen because 75% of dry weight of sclera is


352 Chapter 7

attributable to collagen.769 The estimated value of the refractive index of normallyhydrated scleral collagen (68% of hydration for a whole tissue) of n = 1.474,238

corresponding to direct refraction measurements for whole sclera at a wavelengthof 589 nm,769 is accurately fitted to the value calculated from this semi-empiricalrelation.

A similar analysis of experimental data of the scattering properties of normaland immersed human skin in the spectral range from 400 to 700 nm allows one toreconstruct spectral dependences of both refractive indices for material of effectivescatterers, nss(λ), and ground (interstitial liquid) material, nsi(λ),1292

nss(λ) = 1.4776 − 1.7488 × 104λ−2 + 6.7270 × 109λ−4 − 3.3390 × 1014λ−6.(7.44)

nsi(λ) = 1.3510 + 2.1342 × 103λ−2 + 5.7893 × 108λ−4 − 8.1548 × 1013λ−6.(7.45)

Using the law of Gladstone and Dale [Eq. (3.1)] and these expressions, one canderive the dispersion formula for a whole skin as1292

nskin(λ) = 1.3090 − 4.3460 × 102λ−2 + 1.6065 × 109λ−4 − 1.2811 × 1014λ−6.

(7.46)

This is a more precise formula for describing the refractive index of skin thanEq. (7.29), which was received from the simplest suppositions for a skin model asa mixture of water and proteins with a constant refractive index.

For tissue optics, this is of great importance to determine the dispersion prop-erties of melanin, which is contained in skin, hairs, eye sclera and iris, and othertissues. Melanin granules are the major backreflecting particles in OCT and small-scale spatially resolved spectroscopy of skin. The above-described spectroscopicstudies of water suspensions of natural melanin, where the mean radius of parti-cles was determined by using electronic microscopy, allow us to solve the inverseproblem and to reconstruct the wavelength dependence of the refractive index ofmelanin particles in the range from 350 to 800 nm as1292, 1401

nM(λ) = 1.6840 − 1.8723 × 104λ−2 + 1.0964 × 1010λ−4 − 8.6484 × 1014λ−6.

(7.47)

An original method for measuring the refractive index of tooth dentin matrix, basedon optical immersion and taking advantage of its tubular structure, was proposedin Ref. 1403. Samples of freshly cut tooth dentin after treatment to remove organiccompounds from within tubules were filled with an immersion liquid. The refrac-tive index of liquid was selected so that light scattered by the sample was minimal.This value was used as the average index of refraction of the intertubular space oftooth dentin, which turned out to be n0 = 1.553 ± 0.001 for visible light.

A short pulse time delay technique was also successfully applied for refractiveindex estimation of normal breast tissue (sample of thickness d = 0.8 mm) andmalignant breast tissue (d = 0.85 mm).31 Using the known thickness of the sample



and the measured shift, �t, of the transmitted pulse peak relative to the delay timemeasured through a layer of air of the same thickness, the mean phase refractiveindex, n, of a tissue sample can be calculated. Very short pulses should be used insuch measurements; thus, a group of different wavelengths propagates in a mediaand the material dispersion (dn/dλ) should be accounted for by introducing thegroup refractive index:

ng = n − λ

(dn

dλ

). (7.48)

The time delay in the pulse arrival for a tissue sample of thickness d is31

�t = d

c0

(ng1 − ng2

), (7.49)

where c0 is the light velocity in a vacuum, ng1 is the effective (mean) group refrac-tive index of a tissue, and ng2 is the group refractive index of the homogeneousreference medium (air). The effective group refractive index of a tissue is

ng1 = fsngs + (1 − fs) ng0, (7.50)

where fs is the volume fraction of the scatterers composing a tissue, ngs is thegroup refractive index of the scatterers, and ng0 is the group refractive index of theground material of a tissue. The values of the phase refractive index of the above-mentioned two samples were calculated to be n = 1.403 for normal and 1.431 formalignant tissue.31

As it was already shown, OCT dynamic and spatially confined measure-ments of refractive index and scattering coefficients of tissue and blood are veryimportant for monitoring physiological changes in living tissues.1300–1302, 1305–1307,

1309, 1331–1341, 1361, 1362, 1387, 1388 For basic principles and applications of OCT,see Chapters 8 and 14. OCT provides simple and straightforward measure-ments of the index of refraction both in vitro and in vivo.635, 1301, 1302, 1331–1341,

1361, 1362, 1387, 1388, 1404–1418 The in-depth scale of OCT images is determined by theoptical path length, �zopt, between two points along the depth direction. Because abroadband light source is used, the optical path length is proportional to the grouprefractive index, ng, and geometrical path length, �z, as1282

�zopt = ng�z. (7.51)

Usually, ng∼= n. This simple relation is valid for a homogeneous medium and can

be used in in vitro studies when geometrical thickness of a tissue sample, �z, isknown.

Occasionally, both refractive index and thickness of a tissue sampleshould be measured simultaneously. In this case, a two-step procedure can beapplied.1405, 1407, 1413 First, a stationary mirror is placed in the sample arm of aninterferometer to determine the geometric position of the mirror, supposing thatthe group refractive index of air is equal to unity (z1). Then, a tissue sample with


354 Chapter 7

unknown ng and d should be placed before the mirror in the sample arm. Twopeaks from the anterior (z2) and posterior (z3) surfaces of the sample will appear,with the distance between them equal to a sample optical thickness [see Eq. (7.51)],and the position of the mirror (z4) will be shifted by (ng − 1)d due to the samplewhose group refractive index is greater than that of air. Thus, the calculation of thegeometrical thickness and the group refractive index proceeds as follows:

d = (z3 − z2) − (z4 − z1); ng = (z3 − z2)/d. (7.52)

For in vivo measurements of the index of refraction, a focus-tracking methodthat uses OCT to track the focal-length shift that results from translating the focusof an objective along the optical axis within a tissue was introduced1407 and furtherdeveloped.1301, 1302, 1408–1412 For the refractive index evaluation, the coincidence ofthe maxima of the interference pattern and spatial focus, registered as a signal max-imum, is needed. At least two points along the depth direction have to be probed toestimate a mean value of the refractive index between them. Usually, a multistepmeasurement is provided. The geometric average refractive index for a fiber/lensfocus tracking system is defined by the following expression:1301, 1302

n = √ngn = nobj√

1 − �zL1�zFiber

, (7.53)

where nobj is the refractive index of the objective in the sample arm, �zL1 is thechange in position of the first objective lens, and �zFiber is the fiber tip position inthe sample arm. The difference between both refractive indices is usually small,only a few percent, and can be ignored in practice. For a piecewise homogeneousmedium along the depth direction, the slope �zL1/�zFiber has to be evaluated at thefocus tracked condition (�zL1 positioned for maximum signal).

Bifocal optical coherence refractometry, which is based on simultaneous mea-surements of the optical path length difference between two foci, was recentlysuggested.1410, 1411 The primary advantage of this technique is that it avoids theneed to physically relocate the objective lens or the sample during an axial scan.When employing a relatively low NA objective lens in the sample arm, the ratioof the optical path length difference between two foci, measured in the medium,�zf-opt, and in air, �zf, is described by the expression1411

�zf−opt

�zf≈ ngn

[1 + 1

2(NA)2

(1 − 1

n2

)]. (7.54)

For a typical value of tissue index of refraction n = 1.4 and NA = 0.2, the secondterm in the square parentheses is only 1% of the magnitude of the ratio. Accountingfor this estimation and that ng

∼= n, a much simpler relation, as used in Ref. 1301,can be found as

�zf−opt ≈ n2�zf. (7.55)

Received relations [see Eqs. (7.51)–(7.55)] for refractive index evaluationassumed homogeneous media under study. Tissues and blood are inhomogeneous



Figure 7.15 Blood sedimentation in a cuvette of L = 1.1 mm thickness. Dynamic OCT in-depth image (λ = 820 nm) of whole blood sample slightly diluted by saline (13%) taken froma healthy volunteer (woman, 35 years old) (see Ref. 1331).

media with high scattering. Thus, these relations should be modified. For exam-ple, the modified Eq. (7.51) can be applied to describe dynamic OCT images forblood samples at sedimentation (see Fig. 7.15).1331 The OCT image demonstratesthat in a process of blood sedimentation, the mean refractive index of a blood layeris reduced (the line, showing the reflectance of the posterior surface of a cuvette,moves up with time). Such behavior can be understandable through the mechanismof the reduction in bulk scattering due to cell aggregation.

When the refractive index of the scatters, ns, differs little from the groundmedium, n0, the scattered field, Esc(r), at position r can be written as the followingiterative series:614

Esc(r) = αE1(r) + α2E2(r) + . . . , (7.56)

where

α = (ns − n0)/2πn0. (7.57)

The first term in Eq. (7.56) accounts for single-scattering events, the Rayleigh–Gans approximation; the second term accounts for all double-scattering events.Values of Esc(r) in the direction of propagation of the incident light (along thepositive z-axis) compose the forward-scattered light. This portion of the scatteredlight adds to the incident wave, slightly changing both its phase and magnitude,which can be expressed as614

exp

[ik

(z + L

�n

n0

)], (7.58)


356 Chapter 7

where k = 2π/λ is the wave number, λ is the wavelength within the medium ofindex n0; and L is the thickness of the scattering medium. The real part of thequantity �n expresses the phase change of the transmitted light, so it should beinterpreted as an index change of the medium due to light scattering. The imaginarypart of �n leads to an exponential decay in the transmitted wave caused by thescattered light escaping from the propagating light.

The refractive index, n� , of the medium is614

n� = n0 + �n = n + n2 − n2

nQ (λ/lc), (7.59)

where n is defined by the refractive indices of tissue or blood compounds [seeEq. (3.1)]; for a two-compound medium, it is equal to

n = fsns + (1 − fs) n0, (7.60)

where fs is the volume fraction of scattering particles, n2 is the mean-square valueof refractive index fluctuations, Q (λ/lc) refers to the form of scatters and theiraggregation, and lc is the correlation length of a randomly distributed refractiveindex fluctuations. Here, Q = 1.17 in the limit of large correlation length, lc � λ,(large particles) and Q = 0 in the limit of small lc (Rayleigh limit). In the case thatindex fluctuations take the form of parallel cylinders, Q = 0.67 for the large lc.

In the process of blood sedimentation, a two-phase system of plasma and RBCsis formed. Each phase has its own volume (thickness after separation) and refrac-tive index. Let us define the time-dependent thickness of the RBC layer as H(t),then the thickness of the upper clear plasma is [L − H(t)] (see Fig. 7.15). The aver-age refractive index of the layer of thickness L, containing two layers with differentrefractive indices, can be written in the form

nsed(t) = [L − H(t)]

Ln + H(t)

Ln� , (7.61)

where n and n are defined by Eqs. (7.59) and (7.60). Because n� is always largerthan n and the general sedimentation process is expressed as H(t)/L → Hct (bloodhematocrit), the total refractive index must decrease with time.

For describing the influence of time-dependent refractive index changes onOCT images during blood sedimentation, n should be replaced by n� in Eq. (7.51).The initial refractive index before sedimentation begins can be estimated fromthe experimental OCT image presented in Fig. 7.15 for whole blood slightlydiluted by saline. The experimental value of �zopt (distance between upper andlower bright lines at zero time) is equal to 1.533 mm or for thickness of theblood vessel �z = 1.1 mm, from relation �zopt

∼= n��z we can find n� = 1.394.Accounting for the fact that the whole blood refractive index is nb = 1.400, we canestimate the expected value of the refractive index, n�(t = 0), from n�(t = 0) =fbnb + (1 − fb)nsaline, where fb is the volume fraction of whole blood in the sampleand nsaline is the index of saline. For fb = 0.87 and nsaline = 1.330, the expectedvalue of n� = 1.391 is well fitted to the measured value.



The experimental value of �zopt at 10 min is equal to 1.483 mm;thus, nsed(t = 10 min) = 1.348. Accounting for this, from the OCT image,where (L − H)/L = 0.55, H/L = 0.45, and n = fbpnbp + (1 − fbp)nsaline = 0.87 ×1.340 + 0.13 × 1.33 = 1.339, we can evaluate n� from Eq. (7.61) as n� = 1.359and the corresponding relative index fluctuations of the RBC layer from Eq.(7.59)as [(n2 − n2)/n] ∼= 0.017 for Q = 1.17.

Results of in vitro and in vivo measurements of phase and group refractiveindices of tissue, blood, and their compounds using the discussed techniques andcertain others are summarized in Table 7.6.


Chapter 8

Coherent Effects at theInteraction of Laser Radiationwith Tissues and Cell Flows

This chapter considers coherent effects that accompany the propagation of laserradiation in tissues and the interaction of laser radiation with cell flows. Theseeffects include diffraction, formation of speckle structures, interference of specklefields, and scattering from moving particles. Principles of quasi-elastic light scatter-ing (QELS) spectroscopy, diffusion wave spectroscopy (DWS), full-field speckleimaging (LASCA), confocal microscopy, OCT, digital holographic and interfer-ential microscopy, SHG imaging, and nonlinear Raman scattering microscopy arediscussed.

8.1 Formation of Speckle Structures

Speckle structures are produced as a result of the interference of a large num-ber of elementary waves with random phases that arise when coherent light isreflected from a rough surface or passes through a scattering medium.45, 76, 77,

82, 83, 112, 113, 129, 136, 139, 221, 223, 555, 608, 1423–1459 The speckle phenomenon is a 3D inter-ference effect that exists in all points of space at which the reflected or transmittedwaves from an optically rough surface or volume intersect. Generally, there aretwo types of speckles: subjective speckles, which are produced in the image spaceof an optical system (including an eye), and objective speckles, which are formedin a free space and are usually observed on a screen placed at a certain distancefrom an object. Because the majority of bio-objects are optically nonuniform, irra-diation of such objects with coherent light always generates speckle structures thateither distort the results of measurements (and consequently, should be eliminatedin some way), or provide new information concerning the structure and motionof a bio-object and its components. In this tutorial, we will primarily discuss theinformation aspects of speckle fields.

359


360 Chapter 8

W

I

x

ϕ

Lc

σh

v

(a)

(b)

(c)

I

σI

x, t

laser

laser

<I>

Figure 8.1 Formation and propagation of speckles (a), observation of speckles (b), andintensity modulation (c); w is the scattered wave (see Ref. 1424).

Figure 8.1 schematically illustrates the principles of the formation and prop-agation of speckles produced in the regime of transmission and reflection ofcoherent light in an optically nonuniform media, and Fig. 8.2 shows real specklepattern formed at He-Ne laser beam transmission through a thin layer of ahuman epidermal sample. The average size of a speckle in the far-field zone isestimated as

dav ≈ λ

ϕ, (8.1)

where λ is the wavelength and ϕ is the angle of observation.Displacement of the observation point over a screen, x, or the scanning of a

laser beam over an object with a certain velocity, v (or an equivalent motion of theobject itself with respect to the laser beam), when the observation point remainsstationary generates spatial or temporal fluctuations of the intensity of the scatteredfield. These fluctuations are characterized by the mean value of the intensity, 〈I〉,and the standard deviation, σI [see Fig. 8.1(b)]. The object itself is characterizedby the standard deviation, σh, of the altitudes (depths) of inhomogeneities and thecorrelation length, Lc, of these inhomogeneities (random relief).

Because many tissues and cells are phase objects,77, 257, 263, 267–270, 555, 1373 thepropagation of coherent beams in cells and tissue slices can be described within


Coherent Effects at the Interaction of Laser Radiation with Tissues and Cell Flows 361

Figure 8.2 Speckle pattern produced at He-Ne laser beam transmission through a thinhuman skin epidermal sample (skin epidermal strip).

the framework of the model of a random phase screen (RPS).75 The amplitudetransmission coefficient of an RPS is given by

ts(x, y) = t0 exp {−i�(x, y)}, (8.2)

where t0 is the spatially independent amplitude transmission; �(x, y) is the randomphase shift introduced by the RPS at the (x, y) point. Such spatial phase fluctua-tions may be attributable to variations in the refractive index, n(x, y), or the RPSthickness, h(x, y), from point to point. For thin transmitting and reflecting RPSs,we have

�(x, y) = 2π

λ{n(x, y) − 1} h(x, y),

�(x, y) = 4π

λh(x, y),

(8.3)

respectively. Phase fluctuations of the scattered field are characterized by the stan-dard deviation, σφ, and the correlation length, Lφ. Generally, there are two typesof RPSs: weakly scattering RPSs, (σ2

φ < 1), and deep RPSs, (σ2φ � 1).

The ideal conditions for the formation of speckles, when completely developedspeckles arise, can be formulated in the following manner:

1. Coherent light irradiates a diffusive surface (or a transparency) characterizedby Gaussian variations of optical length �L = �(nh) with the probabilitydensity distribution

p(�L) = {2πσ2

L

}1/2exp

{− (�L)2

2σ2L

}. (8.4)


362 Chapter 8

2. Standard deviation of relief varies, σL � λ; both the coherence length oflight and sizes of the scattering area considerably exceed the differencesin optical paths caused by the surface relief, and many scattering centerscontribute to the resulting speckle pattern.

Statistical properties of speckles can be divided into statistics of the first andsecond orders. Statistics of the first order describe the properties of speckle fieldsat each point. This description usually employs the intensity probability densitydistribution function, p(I), and the contrast

VI = σI

〈I〉 ,σ2I = ⟨

I2⟩ − 〈I〉2 , (8.5)

where 〈I〉 and σ2I are the mean intensity and variance of the intensity fluctuations,

respectively. In certain cases, statistical moments of higher orders are employed.For example, in addition to contrast, generally defined as

VI =(μ2

μ1

)0.5

, (8.6)

we can introduce the asymmetry parameter

Qa = μ3

μ1,52

, (8.7)

which provides additional information concerning the scattering object. Here, thestatistical moments are defined as

μn = (N − 1)−1N∑

j=1

(Ij − μ1)n. (8.8)

For ideal conditions, when the complex amplitude of scattered light hasGaussian statistics, the contrast is VI = 1 (developed speckles), and the intensityprobability distribution function (PDF) is represented by a negative exponentialfunction:223

p(I) = 1

〈I〉 exp

{− I

〈I〉}

. (8.9)

Thus, the most probable intensity value in the corresponding speckle pattern isequal to zero; i.e., destructive interference occurs with the highest probability.

Equation (8.9) is plotted as curve 1 in Fig. 8.3; as shown, the most probablespeckle is dark. The intensity PDF described by this equation can be produced onlyby the interference of light that is all polarized in the same manner, resulting ina similarly polarized speckle pattern.1426–1430, 1450, 1460 Thus, the scattering surfacecannot depolarize the scattered light. Materials into which the light does not pen-etrate and is scattered only a single time generally produce speckle patterns withan intensity distribution in accordance with Eq. (8.9). On the other hand, materials



Figure 8.3 Theoretical intensity probability distribution function, p(I), of a fully developedspeckle pattern [curve 1, Eq. (8.9)] and the incoherent combination of two speckle fields[curve 2. Eq. (8.10)] (see Ref. 1436).

into which the light penetrates and is subject to multiple scattering, such as mostbiological tissues, tend to depolarize the interfering light.

Laser speckle patterns originating from most biological tissues are not fullydeveloped in the sense that their intensity distribution does not follow a negativeexponential relationship [Eq. (8.9)]. Such speckle patterns may have a distinctlydifferent intensity of PDFs, best thought of in terms of an incoherent combinationof two speckle fields. Many speckle interferometers function by allowing two inde-pendent speckle patterns to interfere.223, 1425–1429, 1433–1447 The speckle patterns caninterfere either coherently or incoherently. In the case of coherent combination, thestatistical properties of the resulting third speckle pattern remain fundamentallythe same as the two original patterns, typically following Eq. (8.9). However, inthe case of an incoherent combination of two speckle fields, the final intensity PDFdoes not obey negative exponential statistics, but instead follows the equation1436

p(I) = 4I

〈I〉2 exp

{− 2I

〈I〉}

. (8.10)

The shape of this relationship is shown as curve 2 in Fig. 8.3. The intensity PDFof individual speckle patterns arising from most biological tissues obeys this equa-tion. The reason is as follows: coherent light scattered from most biological tissuesproduces randomly polarized speckle patterns and any two orthogonally polarizedcomponents of scattered light are incoherent with one another. Thus, single specklepatterns arising from biological tissues that randomly polarize the speckle patterncan be considered to be the incoherent combination of two or more speckle pat-terns. Figure 8.4 shows the measured intensity PDF of a backscattered specklepattern arising from illuminating a sample of porcine skin with an expanded He-Ne


364 Chapter 8

Figure 8.4 Measured intensity probability distribution function, p(I), of the speckle field gen-erated by illuminating a sample of porcine skin with a He-Ne laser (633 nm) compared tothat predicted by an incoherent combination of two fields [Eq. (8.10)] (see Ref. 1436).

laser (633 nm). It is clear that the intensity PDF of the scattered light from the skinmore or less follows that predicted by Eq. (8.10).

Partially developed speckle fields are characterized by the contrast VI < 1. Thiscontrast may be lower for the following reasons:

1. If a uniform coherent background with intensity Ib is added to the specklefield, then we have

VI = (1 − ρ2b)1/2, (8.11)

where ρb = 〈Ib〉 / (〈Ib〉 + 〈I〉) . For example, with a decrease in the roughnessof a surface (or the nonuniformity degree of a solid scatterer), we have σ2

ϕ →0. Under these conditions, the strong specular (nonscattered) component ofthe coherent beam interferes with the speckle field. In the limiting case of anideal plane surface (a uniform medium), speckles vanish, VI = 0.

2. If a uniform incoherent background arises (e.g., due to lowering of the coher-ence of the light source or multiple scattering in the medium), then wehave

VI = 1 − ρb. (8.12)

For Gaussian statistics and a Gaussian correlation function of phase fluctua-tions, the propagation of intensity of the speckle field in a free space along thez-axis behind the RPS is described by the expression75



σ2I (z) = σ2

ϕ

2

{1 + 1

1 + D2

}, (8.13)

where D = zλ/πL2ϕ is the wave parameter. For a weakly scattering RPS

(σ2ϕ � 1), the contrast of the speckle field is always less than unity. For a deep RPS

(σ2ϕ � 1), the contrast reaches its maximum in the Fresnel zone (D ∼= 1) when

zmax = (2π/λ)(L2ϕ/σϕ), V > 1. The fact that the contrast is higher than unity

implies that dark areas predominate in the speckle pattern. The appearance of themaximum of intensity fluctuations is attributable to the focusing of scattered wavesbehind the RPS. In the Fraunhofer zone, we have VI → 1.

The intensity distribution for light transmitted through an RPS can be repre-sented in the following form:75, 223

I�(x, y) = Ic(x, y) + Is(x, y), (8.14)

Here, Ic(x,y) is the intensity of light transmitted in the forward direction (the spec-ular component) and Is(x, y) is the intensity of the scattered component. For ascattered field with Gaussian statistics, the intensity, I(0), at the center of the beamand the radius, rs, of the scattered beam in the observation plane are determined bythe following relations:

I(0) ∼= I0(0) exp(−σ2ϕ), (8.15)

rs∼= zλ

πLϕ

, (σ2ϕ � 1),

rs∼= zλ

πLϕ

σϕ, (σ2ϕ � 1),

(8.16)

where I0(0) is the intensity of the incident beam at its axis.For both weakly scattering and deep RPSs moving with velocity v in the direc-

tion perpendicular to the laser beam with radius w, the correlation time of intensityfluctuations in the scattered field is given by1450

τc∼=

√2 · w

v. (8.17)

This relationship holds true for a Gaussian incident beam when the observationplane lies in the Fraunhofer zone.

For phase objects with σ2ϕ � 1 and a small number of scatterers, N = w/Lϕ,

contributing to the field at a certain point in the observation plane, the contrast ofthe speckle pattern is greater than unity:1427

VI ={

1 − 2

N+ σ2

ϕ

4Nexp

[2πLϕ

λσϕ

sinθ

]2}1/2

, (8.18)

where θ is the angle of observation (scattering angle). The statistics of the specklefield in this case are non-Gaussian and nonuniform (i.e., the statistical parametersdepend on the observation angle).


366 Chapter 8

Statistics of the second order demonstrate how fast the intensity changes frompoint to point in the speckle pattern, i.e., they characterize the size and distribu-tion of speckle sizes in the pattern. The statistics of the second order are usuallydescribed in terms of the autocorrelation function of intensity fluctuations, G2(τ),and its Fourier transform, S (ω), representing the power spectrum of a randomprocess:

G2(τ) = 〈I (τ) I (t + τ)〉,S (ω) = 〈I〉2

2π

∫ ∞

−∞cos (ωτ)

[g2 (τ) − 1

]dτ,

(8.19)

where t is the temporal variable; τ is the change in variable; the angular brackets,〈〉, stand for the averaging over the time; g2 (τ) = G2 (τ) / 〈I〉2 is the normalizedtemporal intensity correlation function; and 〈I〉2 is the average intensity.

To describe comparatively small intensity fluctuations, it is convenient toemploy an autocorrelation function, G2 (�ξ), of the fluctuation intensity compo-nent and the corresponding structure function, DI(�ξ),

G2 (�ξ) = [I(ξ) − 〈I〉] · [〈I(ξ + �ξ) − 〈I〉〉], (8.20)

DI(�ξ) = ⟨[I(ξ + �ξ) − I (ξ)]2⟩,

DI(�ξ) = 2[G2(0) − G2(�ξ)

],

(8.21)

where ξ ≡ x or t is the spatial or temporal variable; �ξ is the change in variable.The angular brackets, 〈〉, stand for the averaging over an ensemble or the time.

Analysis is usually performed in terms of normalized autocorrelation andstructure functions. An autocorrelation function is preferable for the analysisof intensity fluctuations caused by comparatively large inhomogeneities in thescattering object. At the same time, the structure function is more sensitive to small-scale intensity oscillations. Figures 8.5 and 8.6 display typical autocorrelation and

rI1.0

0.5

1.28 x, mm

(a)

(b)

(c)

1.0

0.5

1.0

0.5

0.0

0.0

0.0

2.56

(x)

normal skin

psoriatic

psoriatic

Figure 8.5 Normalized autocorrelation functions of intensity fluctuations in speckles r I(x)for thin layers of normal(a) and psoriatic human epidermis (b and c) probed with a focusedlaser beam (see Refs. 77 and 555).



DI(r–)

101

100

10–1 100 101

r–

normalenamel caries

Figure 8.6 Difference between structural functions of speckle fluctuations for the scatteringof a focused laser beam from normal (upper line) and pathological (caries) (lower line)human tooth enamel (see Refs. 77 and 555).

structure functions measured for two types of normal and pathological tissues—epidermis of human skin and human tooth enamel.77, 555, 1446 These plots clearlyillustrate the difference in the sensitivity of these functions to spatial fluctuationson different scales.

8.2 Interference of Speckle Fields

Generally, owing to the considerable contribution of bulk scattering, the reflec-tion of laser radiation from a biological object generates the formation of partiallydeveloped speckle structures with comparatively small sizes of speckles, a contrastdifferent from unity, and random polarization of light in individual speckles. In theelementary case when reflected light in speckle structures retains linear polariza-tion, the intensity distribution at the output of a dual-beam interferometer can bewritten as1447, 1448

I(r, t) = Ir(r) + Is(r) + 2 [Ir(r)Is(r)]1/2 |γ11(�t)| cos {��I(r) + ��I(r) + ��I(t)},(8.22)

where Ir(r) and Is(r) are intensity distributions of the reference and signal fields,respectively; r is the transverse spatial coordinate; γ11(�t) is the degree of temporalcoherence of light; ��I(r) is the deterministic phase difference of the interferingwaves; ��I(r) = �Ir(r) − �Is(r) is the random phase difference; and ��I(t) is thetime-dependent phase difference related to the motion of an object. Specifically, forlongitudinal harmonic vibrations with amplitude l0 and frequency �v, we have


368 Chapter 8

Figure 8.7 Laser wave front matching speckle interferometer (see Ref. 1449): 1, He-Nelaser (633 nm); 2, prism; 3,4,5, objectives; 6, reference mirror; 7, multilayered object;8, beam splitter; 9, photodetector; 10, scanning platform; AFG, audio-frequency generator;ADC, synchronized analog-to-digital converter; PC, personal computer.

��I(t) = 4π

λl0 sin(�vt). (8.23)

In the absence of speckle modulation, ��I(r) governs the formation of regularinterference fringes. On average, the output signal of a speckle interferometerreaches its maximum when the interfering fields are phase-matched [��I(r) =const within the aperture of the detector], focused laser beams are used (speck-les with maximum sizes are produced), and a detector with a maximum area isemployed.

For a large-aperture photodetector, when it does not resolve amplitude–phasespatial variations in the interference field, the modulation depth of the photoelectricsignal of the interferometer with focused beams can be expressed as1449

β =∣∣∣∣sin u

u

∣∣∣∣ , u = π(NA)2�z

λ, (8.24)

where (NA) is the numerical aperture of the objective in the subject arm of thespeckle interferometer (see Fig. 8.7); �z is the longitudinal displacement of theobject.

8.3 Propagation of Spatially Modulated Laser Beams in aScattering Medium

For tissue surface microprofiling and shape diagnostics, measurement of the trans-lation of rough surfaces, laser anemometry of biological fluids, and cytometricpurposes, tissues or cells under study are probed with spatially modulated laserbeams (for example, beams with regular interference).5, 22, 76, 77, 472, 555, 1441, 1460–1467

Interferential methods take advantage of the easy tuning fringes of spatial modu-lation, including very small spacing between fringes, �I = λ/2θI (θI is the anglebetween the wave vectors of the interfering fields), which is comparable to the sizesof inhomogeneities of the sample. The use of modulated beams with large distancesbetween interference fringes that considerably exceed the sizes of inhomogeneities



results in the appearance of new correlation effects in the scattered field, and con-sequently, provides an opportunity to investigate random phase objects by meansof speckle technologies.472, 555, 1441, 1465–1467 In this case, the interference fringes ofaverage intensity display a contrast varying along the direction of propagation, z.If the beam diameter and separation between the fringes are sufficiently large, thefringes modulate the speckle field, and the evolution of the contrast of average-intensity fringes along the z-axis is determined by the statistical parameters of theobject and the separation between the fringes.

A spatial–temporal optical modulator ensures the formation and the motionof fringes.472, 555, 1441, 1465–1467 Average-intensity interference fringes are registeredby a photodetector with a slit oriented along the fringes. The width aperture isemployed for averaging the speckle modulation of the scattered field. The modula-tion depth of the photoelectric signal is equal to the relative contrast of interferencefringes:

VI(z)

VI0

= |μ(z)| (8.25)

where VI(z) is the contrast of average-intensity fringes, VI0 is the contrast in theinitial laser beam, and |μ(z)| is the modulus of the transverse correlation coefficientof the complex amplitude of the scattered field. Special phantom specklegrams withsmoothly varying and oscillating correlation coefficients of the boundary field havebeen developed for the experimental modeling of tissues and cellular structureswith different statistical properties of phase inhomogeneities.472, 1441

Figure 8.8 presents theoretical and experimental dependencies for the spatialevolution of the relative contrast of fringes obtained for phantom specklegramswith nearly Gaussian correlation coefficient, Kϕ(�x), of phase fluctuations of theboundary field. These dependencies allow us to reconstruct statistical parametersof the phase object, including Kϕ(�x).472, 555, 1441, 1465–1467

When a spatially modulated light beam is focused by using a diffraction-limited optical system with an aperture >ΛI, two spatially separated light spots are

1.0

0.8

0.6

0.4

0.2

0 100

V/V0

z, mm

σ =1.3, L =5.6μm, a=2.5Φ Φ

σ =1.12, L =7.8μm, a=2Φ Φ

Φ Φ

σ =0.625, L =6.4μm, a=2.45Φ Φ

20 40 60 80

I

Figure 8.8 Experimental and theoretical dependencies (see Ref. 472) of the relativefringe contrast, V I/V I0, on the distance z from an object for phantom specklegrams witha smoothly varying correlation coefficient of phase fluctuations of the boundary fieldK�(�x) = exp{–|�x|/L�}a.


370 Chapter 8

produced in the area of focusing. The optical scheme for such a system is presentedin Fig. 8.9. Because two different areas of an object are irradiated, the interaction ofthese light spots with a scattering medium generates two completely nonidentical(noncorrelated) speckle fields in the diffraction field. If the separation between theinterference fringes satisfies the inequality ΛI < dav (the average size of specklesin the observation plane), then the diameter of the beam waist meets the inequality2w0 > Lϕ. In this situation, regular interference fringes oriented in a random man-ner from speckle to speckle are observed within the limits of a single speckle. Inthis case, the contrast of fringes depends only on the relation between the intensi-ties of the interfering fields, not on the statistical properties of an object. If ΛI > dav

and 2w0 > Lϕ, no fringes occur in the scattered field [see Fig. 8.10(b)]. However,when an object moves in the transverse direction, a set of average-intensity inter-ference fringes arises [see Fig. 8.10(c)]. The contrast of this pattern is determinedby the statistical properties of the object.

The speckle method for testing random phase objects with the use of aspatially modulated beam provides the opportunity to determine such statisticalparameters as the standard deviation (σϕ) and correlation length (Lϕ) of phasefluctuations.472, 555, 1441, 1465–1467 Strictly speaking, this method can be applied tophase objects with smooth irregularities and Gaussian statistics. However, thisapproach can be also employed to study objects with non-Gaussian statistics or

Figure 8.9 Experimental setup for investigating the contrast of interference fringes inducedby focused, spatially modulated laser beam scattering by a random phase object (seeRef. 472).

Figure 8.10 Interferograms observed without an object (a), with a stationary object (b), andwith a moving object (phantom specklegram) (c) (see Ref. 472).



sharp inhomogeneities, but calibration is required in this case. Direct measure-ments using a sufficiently fast detection system make it possible to analyze objectsin real time, which is especially important for the investigation of tissue and cellu-lar structures, particularly for creating optical topographic schemes. This techniquecan be employed for studying thin layers of human epidermis, thicker transparenttissues of the front segment of the human eye (cornea and crystalline lens), andsclera in the process of optical clearing (enhanced translucence) under conditionsof mechanical or osmotic stresses.238, 555, 768 Along with the monitoring of statis-tical parameters of tissues, this approach should be useful for the development ofa new generation of laser interferential retinometers, i.e., devices for determiningretinal visual acuity in the human eye.5, 473, 1441 Because the interference pattern isstatistically averaged as a focused spatially modulated laser beam is scanned, evenpatients with a turbid (cataractous) crystalline lens can see interference fringes (seeFig. 8.10).

8.4 Dynamic Light Scattering

8.4.1 Quasi-elastic light scattering

Quasi-elastic scattering of light, photon-correlation spectroscopy, spectroscopyof intensity fluctuations, and Doppler spectroscopy are synonymous termsrelated to the dynamic scattering of light, which underlies a noninvasivemethod for studying the dynamics of particles on a comparatively large timescale.5, 78, 79, 112, 113, 555, 1460–1463, 1468, 1469 The implementation of the single-scatteringregime and the use of coherent light sources are of fundamental importance in thiscase. The spatial scale of testing of a colloid structure (an ensemble of biologicalparticles) is determined by the inverse of the wave vector modulus, |q|−1, definedby Eq. (3.39):

|q| = 4πn

λ0sin

θ

2, (8.26)

where n is the refractive index of the ground substance of the scattering medium (oraverage refractive index of the ground and scatterer materials, n = n) and θ is theangle of scattering. With allowance for self-beating due to photomixing of the elec-tric components of the scattered field on a photodetector, we can write the intensityautocorrelation function in the form of Eq. (8.19), which, for Gaussian statisticsand ergodicity of the random process, is related to the first-order autocorrelationfunction, G1(τ), by the Siegert formula:

G2(τ) = 〈I〉2 + βsb |G1(τ)|2 , (8.27)

where τ is the delay time; βsb is the parameter of self-beating efficiency, whichis determined according to experimental setup; βsb ≈ 1 for the ideal experimentalarrangement. More practically, Eq. (8.27) can be presented as


372 Chapter 8

G2(τ) = A[1 + βsb |g1(τ)|2], (8.28)

where A = 〈i〉2 is the square of the mean value of the receiver photocurrent, or thebaseline of the autocorrelation function, and

g1(τ) =⟨

E(t)E∗(t + τ)

|E(t)|2⟩

(8.29)

is the normalized autocorrelation function of the optical field.For a monodispersive system of Brownian particles, we have

g1(τ) = exp(−�Tτ), (8.30)

where �T = q2DT is the relaxation parameter and DT = kBT/6πηrh is the coef-ficient of translation diffusion; kB is the Boltzmann constant; T is the absolutetemperature; η is the absolute viscosity of the medium; and rh is the hydrodynamicradius of a particle. Many biological systems are characterized by a bimodal dis-tribution of diffusion coefficients, when fast diffusion (DTf) can be separated fromslow diffusion (DTs) related to the aggregation of particles.5, 1469–1471 In this case,the first-order autocorrelation function is written as

g1(τ) = p1 exp(−q2DTfτ) + p2 exp(−q2DTsτ), (8.31)

where p1 and p2 are coefficients proportional to the concentration and efficiency ofscattering of small and large particles, respectively. The goal of quasi-elastic scat-tering spectroscopy is to reconstruct the distribution of scattering particles in sizes,which is necessary for the diagnosis or monitoring of a disease by the analysis ofaggregation or disaggregation of cells or cell structures. Various particle suspen-sions, including nanoparticles used for specific labeling in the diagnosis or therapyof cancer and other diseases, can be characterized by this method.

8.4.2 Dynamic speckles

The specific features of the diffraction of laser beams from moving phase screensmotivate speckle methods for the structural diagnostics and monitoring of biologi-cal flows and motion parameters of tissues, including biovibrations, which are easyto implement from the technical point of view.22, 76, 82, 83, 1433–1439, 1442–1448, 1472–1478

The fluctuations of individual speckles can be analyzed to provide informa-tion about the movement of the scatterers producing the fluctuations. This analysiscan be based either on the techniques of photon correlation spectroscopy or laserDoppler velocimetry. It is not intuitively obvious that time-varying speckle andDoppler-induced fluctuations are identical. The theory of time-varying specklestarts with the classical (though random) interference pattern produced when lightbeams of the same frequency interfere. The fluctuations are caused by changesin the optical path lengths of the interfering beams caused by the movement ofthe scatterers. Doppler fluctuations, on the other hand, are explained by the beatingeffect that occurs when two waves of slightly different frequency are superimposed,



the difference being attributable to the frequency shift induced by the Dopplereffect when light is scattered by a moving object. Thus, the speckle explanation isbased on the superposition of waves of the same optical frequency, whereas in theDoppler explanation, the superimposed waves have different frequencies. Despitethese apparent differences in approach, it can be shown that, mathematically, thesetwo explanations lead to identical equations linking the intensity fluctuations tothe velocity distribution of the scatterers.82, 83 Thus, the two approaches are simplydifferent ways of examining the same physical phenomenon.

In the case of diffraction of a sharply focused Gaussian beam from a movingRPS with the Gaussian statistics of phase inhomogeneities and a Gaussian correla-tion function, the power spectrum of intensity fluctuations in the far-field zone canbe represented in the form of homodyne (I) and heterodyne (II) parts:1472

S (ω) ={

C1(2b)0.5 exp

[−bω2

2

]}I

(8.32)

+ {C2b0.5

(exp

[−b(ω − ω0)2] + exp

[−b(ω + ω0)2])}

II

Here, ω = 2πfλ/v is the unscaled frequency; f is the modulation frequency; v isthe velocity of a moving RPS,

b = L2c + 2Mw2

0

4M,

and

ω0 = 4πM

(w0Lc

)2 (x0

z

)1 + 2M

(w0Lc

)2 ,

where M is the parameter that depends on RPS dispersion of heights (σh) andirradiating wavelength (λ); w0 is the radius of the beam waist; x0 is a fixed pointwhere speckles are observed in the moving frame of reference; and z is the distancebetween the scattering and observation planes.

For a weakly scattering RPS (e.g., model of a thin blood vessel), we haveM = 1 and C1 � C2. For a deep RPS (e.g., model of a thick blood vessel), wehave M ∼ (σh/λ)2 and C1 � C2. In the case of thin vessels, we should expectthe appearance of a high-frequency peak in the spectrum of intensity fluctuations(the heterodyne part of the spectrum) owing to the interference interaction of thespecular and scattered components. The specular component (in transmission orreflection) serves as a reference wave. The position of the peak on the frequencyscale depends on the observation angle (x0/z). Because the standard deviation ofprofile fluctuations is small (σh � λ), spectrum S (ω) of intensity fluctuations fea-tures only high-frequency components. By contrast, in the model of a deep RPS,because the specular component is suppressed (due to scattering), interferenceinteraction vanishes and the spectrum features only low-frequency components (thehomodyne part).


374 Chapter 8

1.0

0

0.5

1

S(ω

ω 2πλ/Lc×

σ = 0.3λh

x = 2z0

σ = 0.01λh

x = 2z0

σ = 0.01λh

x = 00

)/Smax

Figure 8.11 Normalized theoretical power spectra of intensity fluctuations for dynamicspeckles arising from the interaction of a focused laser beam (w0 = 10λ) with phase objectscharacterized by various degrees of nonuniformity (σh) for different observation angles(x0).1481

S( f )/S1.0

0.5

0 0.2 0.4 0.6 0.8 1.0f, kHz

max

x = 00

x =3w /200 π

Figure 8.12 Scattering from a random flow: normalized experimental spectra of fluctuationsfor dynamic speckles at different observation angles (x0); w0 ≈ 2.3λ; spectra are averagedover 256 realizations of instantaneous spectra (see Ref. 1481).

The aforesaid is illustrated by theoretical and experimental spectra presentedin Figs. 8.11 and 8.12. Thus, the statistical characteristics of transmitted (reflected)light essentially depend on the observation angle and the degree of nonuniformityof an object. Such statistics of speckles are associated with a small number ofscatterers and can be classified as statistically nonuniform non-Gaussian statis-tics [Eq. (8.18)]. Similar to the case of spectroscopy of quasi-elastic scattering(Doppler spectroscopy), the frequency shift is a linear function of both the velocityof a scatterer and the observation angle of speckles only when the number of scat-terers irradiated by a laser beam is sufficiently large. If the number of scatterers issmall, N = (w0/Lc) < 5, we should expect an additional strong dependence of thefrequency shift on N, in accordance with the theoretical dependence presented inFig. 8.13.



1.0

0.8

0.6

0.4

0.2

00/Lc1 3 4 5

ω0/2π(x0/z)

ω2

Figure 8.13 Normalized theoretical dependence of the central frequency in the spectrumof intensity fluctuations on the number of scatterers, Ns = w0/Lc (see Ref. 1481).

8.4.3 Full-field speckle technique: LASCA

One problem of using the temporal statistics of time-varying speckle is that mea-surements are made at only one point in the speckle pattern (a single speckle). If anarea needs to be analyzed, it is necessary to scan the detector over the field of view.If a map of velocity distribution is required, some method of scanning the area ofinterest is necessary. Such a map is of particular importance if blood flow is to beused as a diagnostic tool. A linear CCD array was used to simultaneously monitor aline of speckles, and a scanning mirror extended this to a 2D area.1479, 1480 To char-acterize a local blood flow, the ratio of the mean intensity to the intensity differencein the speckle pattern was utilized; a quantity called normalized blur was a measureof velocity. In particular, a microcirculation map of the retina of a rabbit eye wasreceived upon illuminating the retina with light from a diode laser, scanning andstoring the speckle images, and then calculating the differences between successiveimages. These measurements correlated with invasive methods.1480 Scanning hasalso been applied to the laser Doppler technique,1481–1483 and commercial scanningDoppler systems are currently on the market that can provide full-field monitoringof capillary blood flow over quite large areas of the body.

However, nonscanning, or full-field, techniques for monitoring capillary bloodflow are more attractive. The contrast of a speckle pattern used as a measure oftime integration of a fluctuating speckle pattern can be employed as a detectingparameter to provide a full-field technique. If the integration time is comparablewith the period of the intensity fluctuations caused by dynamic light scattering, it isclear that the effect will be a blurring of the recorded speckle pattern—a reductionin the speckle contrast.

In the early 1980s, the use of such time-integrated speckle led to a technique forflow visualization that simultaneously achieves full-field operation and very simple(and cheap) data collection and processing (see Refs. 82, 83, 112, 1435, 1439, and1484–1488). Originally called single-exposure speckle photography, it was devel-oped primarily for the measurement of retinal blood flow. The basic technique wassimply to photograph the retina under laser illumination, using an exposure timethat is on the same order as the decorrelation time of the intensity fluctuations.It is clear that a very short exposure time would “freeze” the speckle and resultin a high-contrast speckle pattern, whereas a long exposure time would allow the


376 Chapter 8

speckles to average out, leading to low contrast. In general, the velocity distribu-tion in the field of view is mapped as variations in speckle contrast. Subsequenthigh-pass optical spatial filtering of the resulting photographs converted these con-trast variations to more easily visualized intensity variations. Later work introduceddigital image processing of the speckle photographs, including color-coding of thevelocities. More recently, the method has been developed into a fully digital, real-time technique for the mapping of skin capillary blood flow.82, 83, 1484, 1485 Becausethe method is no longer photographic, it is now called laser speckle contrast anal-ysis (LASCA). A closely related technique has been used as a remote methodfor sensing heartbeats;1489 a TV camera was used to record the speckle patternproduced by a vein, which was digitized frame by frame, and then the speckle con-trast was computed and plotted as a function of time; a minimum in this contrastindicated the occurrence of a heartbeat.

LASCA uses only a laser with diverging optics, a CCD camera, a frame-grabber, and a personal computer. Specially developed software computes the localcontrast and converts it to a false-color map of contrast (and hence, of veloc-ity). The contrast is quantified by the ratio of the standard variation of intensityfluctuations to the mean intensity, σI/<I> [see Eq. (8.5)]. The image is a time-integrated exposure, but for most flow fields (including, for example, capillaryblood flow), the exposure is sufficiently short to render the technique effectivelyreal-time. Figure 8.14 shows the simplicity of the basic setup. Light from the laseris diverged by simple optics to illuminate the area under investigation. The CCDcamera images the illuminated area and the image is observed on the PC moni-tor. On receiving an instruction from the PC, the frame grabber captures an imageand the software immediately processes it to produce a false-color contrast mapindicating velocity variations. This is typically accomplished in less than one sec-ond, making the technique effectively real-time. The operator has several options attheir disposal, including the number of pixels over which the local contrast is com-puted, the scaling of the contrast map, and the choice of contour colors. The mostimportant of these is the choice of the number of pixels over which to compute the

Figure 8.14 Basic setup for LASCA (laser speckle contrast analysis) (see Ref. 1435).



speckle contrast: too few, and the statistics will be questionable; too many, and spa-tial resolution will be lost. In practice, a square of 7 × 7 or 5 × 5 pixels is usuallya satisfactory compromise.

As claimed above, the principle of LASCA is very simple. A time-integratedimage of a moving object exhibits blurring. In the case of a laser speckle pattern,this appears as a reduction in the speckle contrast, defined (and measured) as theratio of the standard deviation of the intensity to the mean intensity. This occursregardless of the “movement” of the speckle. For random velocity distributions,each speckle fluctuates in intensity. For lateral motion of a solid object, on theother hand, the speckles also move laterally and become “smeared” on the image;however, a reduction in speckle contrast still occurs. For fluid flow, this situationmight be a combination of both these types of movement. In each case, the problemfor quantitative measurements is the determination of a relationship between thespeckle contrast and the velocity (or velocity distribution).

The higher the velocity, the faster the fluctuations and the more blurring thatoccurs in a given integration time. By making certain assumptions, the followingmathematical relationship between the speckle contrast and the temporal statisticsof the fluctuating speckle can be found:1435

σ2s (T) = 1

T

∫ T

0g2 (τ) dτ, (8.33)

where σ2s is the spatial variance of the intensity in the speckle pattern; T is the

integration time and g2 (τ) is the autocovariance of the temporal fluctuations of theintensity of a single speckle; g2 (τ) is defined in Eq. (8.20). This equation definesthe relationship between LASCA and techniques that use the intensity fluctua-tions in laser light scattered from moving objects or particles. LASCA measuresthe quantity on the left-hand side of Eq. (8.33); photon correlation spectroscopy,laser Doppler, and time-varying speckle techniques measure the quantity on theright-hand side. Additionally, LASCA uses image speckle, whereas most tem-poral techniques use far-field speckle. However, this does not detract from thefundamental equivalence of the two approaches expressed in Eq. (8.33).

All techniques allow the correlation time, τc, to be determined. In the case ofphoton correlation, this parameter is measured directly. In the case of LASCA,some further assumptions must be made to link the measurement of specklecontrast with τc.

Depending on the type of motion being monitored, various models can be usedto find a relation between the speckle contrast and τc for a given integration time,T . For example, for the case of a Lorentzian velocity distribution, this relation hasthe view (see also Fig. 8.15)1435

σs

〈I〉 =[τc

2T

{1 − exp

(−2T

τc

)}]1/2

. (8.34)

Among all temporal frequency measurement techniques (photon correlation spec-troscopy, laser Doppler, and time-varying speckle), LASCA suffers the problem


378 Chapter 8

Figure 8.15 Variation of speckle contrast with the ratio of decorrelation time (τc) tointegration time (T) for the Lorentzian model of LASCA (see Ref. 1435).

of relating τc to the velocity distribution of the scatterers. It is not straightforwardand depends on the effects of multiple scattering, size and shape of the scatteringparticles, non-Newtonian flow, non-Gaussian statistics resulting from a low num-ber of scatterers in the measuring volume, and spin of the scatterers, among otherfactors. Many studies are currently examining these effects, and the question isfar from settled. Because of the uncertainties caused by these factors, it is com-mon in all these techniques to primarily rely on calibration rather than on absolutemeasurements. At the same time, many research groups are working on the con-struction of adequate models and description of the unique relationship betweenmeasured correlation time and particle velocity distribution.82, 83, 1433–1445, 1451–1459,

1472–1480, 1484–1488, 1488

To measure the temporal statistics of fluctuating speckle patterns, it is neces-sary to monitor the intensity of a single speckle. To do this accurately, the apertureof the detector must be smaller than the average speckle size. Otherwise, somespatial averaging will occur and the first-order statistics will be corrupted (someaccuracy may also be lost from the second-order statistics). For LASCA, the matteris more complicated because it computes the local speckle contrast within a squareof pixels, and the size of the square is under the control of the operator. The largerthe square sampled for each measurement, the better the statistics. However, it isalso important to sample a sufficiently large number of speckles as well as pixels:if the speckles are much larger than the pixels, as suggested above, fewer specklesare sampled. This means that the viable speckle size is more restricted. If it is toosmall, each pixel samples more than one speckle, leading to speckle averaging andloss of measured contrast. If it is too large, not enough speckles are sampled toensure accurate statistics. Thus, speckle size needs to be carefully controlled. Thiscan be done by fixing the aperture of the imaging optics, which alone determinesthe speckle size,1425 but it removes operator control regarding the amount of lightentering the camera, because the shutter speed (the other available variable) hasalready been determined to select the range of velocities to be measured. Unlessthe dynamic range of the camera is very large, this can be a significant restriction



and can require the use of neutral density filters to ensure usable light levels at thedetector.

Another problem that has occurred with LASCA is its failure to realize thefull range of contrasts that should theoretically be available. A stationary objectshould provide a speckle contrast of unity (σI =<I>, in accordance with thewell-established speckle statistics theory and experiment). A fully blurred specklepattern produced by rapidly moving scatterers should have zero contrast. TheLorentzian model [see Eq. (8.34) and Fig. 8.15], for example, suggests that, fora given T , the dynamic range of the technique corresponding to contrasts between0.1 and 0.9 should be approximately 2.5 orders of magnitude in τ (and hence, invelocity). In practice, contrasts of only 0.6 were being measured, even for station-ary random diffusers.83 One possible cause is the CCD camera dark current. Byconducting some data preprocessing, it is possible to remove the effect of the darkcurrent and to achieve a measured speckle contrast for the stationary diffusing sur-face equal to 0.95, very close to the expected theoretical value of 1.0 for a fullydeveloped speckle pattern.1484 Other problems with LASCA concern the statis-tics owning to the Gaussian profile of the laser beam and the nonlinearity of theCCD camera.1484 However, many of these problems are also characteristic to laserDoppler, photon correlation, and other time-varying speckle techniques.

To summarize, the LASCA technique offers a full-field, real-time, nonin-vasive and noncontact method of mapping flow fields, such as capillary bloodflow.82, 83, 112, 1435, 1439, 1484–1488 It uses readily available off-the-shelf equipment, andsoftware operation is user-friendly, using the Microsoft Windows NT interface.Laser Doppler, photon correlation spectroscopy, and time-varying speckle arerelated techniques, but work by analyzing the intensity fluctuations in the scatteredlaser light. Because they are essentially methods that operate at a single point in theflow field, some form of scanning must be used if a full-field velocity map of theflow area is required. Typical scanning laser Doppler systems require minutes tocomplete this scan. LASCA achieves this goal in a single shot by utilizing the spa-tial statistics of time-integrated speckle. The technique produces a false-color mapof blood flow in less than a second, without the need for scanning. The primary dis-advantage of LASCA is the loss of resolution caused by the need to average overa block of pixels for producing the spatial statistics used in the analysis. However,the advantage of real-time operation without scanning outweighs the problem ofloss of resolution, especially for biomedical applications.

The availability of diode arrays and matrices, and the design of CMOS cam-eras, has eliminated the need for scanning in all previously described methods,and significantly enhanced the ability of speckle methods, including inven-tion of combined speckle methods with spatial and temporal averaging.1439, 1440,

1443, 1444, 1490, 1491

8.4.4 Diffusion wave spectroscopy

DWS is a specific class of studies in the field of dynamic light scattering,related to the investigation of the dynamics of particles within very short time


380 Chapter 8

intervals.73, 80, 81, 555, 1433, 1437, 1438, 1492–1501 A fundamental difference between thismethod and the spectroscopy of QELS is that this approach is applicable in thecase of dense media with multiple scattering, which is very important for tis-sues. DWS is uniquely suited for measurements of the average sizes of particlesand their motion within turbid, macroscopically homogeneous, highly scatter-ing media. In recent years, DWS has become known by a more accurate term:diffusion-correlation spectroscopy (DCS).1495

Despite the defined similarity between experiments on DWS and conven-tional experimental schemes of correlation spectroscopy of optical mixing [seeEq. (8.28)], the DWS theory is based on a qualitatively different interpretation ofradiation propagation in strongly scattering media. It is thereby assumed that dueto multiple scattering, each photon that has reached the given observation pointof the detector experiences a great number of scattering events, N. The succes-sive scattering acts taking place at the instant of time t at the scattering particleslocated in points r1(t), r2(t), . . . , ri(t), . . . , rN(t) in the medium with wave vectorsk1, k2, . . . ki, . . . , kN result in the formation of field E(t), whose total phase change,�φ(t), is determined as1492

�ϕ(t) =N∑

i=0

ki(t)[ri+1(t) − ri(t)

], (8.35)

�φ(t) is dependent on the total path length, s, of each photon migrated from thesource, r0, to the detector, rN+1, points (Fig. 8.16):

s =N∑

i=0

|ri+1(t) − ri(t)| =N∑

i=0

(ki

|ki|) [

ri+1(t) − ri(t)]

. (8.36)

Quantity s is related to N by the relation s = Nls, where ls = (μs)−1. In highlyscattering media, e.g., human skin, s can be considered as a statistically indepen-dent random walk. The distribution function of photon migration paths, p(s), in themedium is determined as the probability that light will cover s moving from pointr0 to point rN+1:1492

p(s) =( c

4πsD

)3/2exp

(c |r0 − rN+1|2

4sD

). (8.37)

Here, D is the photon diffusion coefficient [see Eqs. (1.26) and (1.27)] and c is thespeed of light in the medium.

Field E(t) interferes with field E(t + τ), scattered slightly later at the sameseries of the scattering particles at the instant of time t + τ (see Fig. 8.16). Thetime required by the photons to travel the entire optical path in the medium is muchshorter than the characteristic time for changing the position of scattering parti-cles in the medium. Thus, as a result of particle motion, the phase between fieldsE(t) and E(t + τ) will fluctuate, or be different at different instants of time. This



Figure 8.16 Schematic diagram of coherent radiation propagation through a randomlyinhomogeneous semi-infinite medium with strong scattering, in which light passes from theradiation source (S) toward the detector (D): (•) shows the location of scattering particles atthe instant of time (t + τ) and (◦) indicates the location of scattering particles at the instantof time τ.

predetermines temporal fluctuations of the scattered radiation intensity recorded inthe far zone. The patterns of the intensity fluctuations (speckles) can be visualizedon a screen or sensed by a homodyne detector.1496

Quantitatively, these fluctuations are described by the temporal field autocor-relation function

G1(τ) =<E(t)E∗(t + τ)>, (8.38)

determined as1497

G1 (τ) = I0

∑j=0,∞

p(sj) exp

(−N

6

⟨q2⟩ ⟨

�r2 (τ)⟩)

, (8.39)

where I0 =< |E(t)|2>, < · · ·> denotes an ensemble average, q is the change in thewave vectors ki and ki+1:

q = |ki − ki+1| = 2k0 sinθ

2. (8.40)

Respectively,

⟨q2⟩ = ⟨

4k20(1 − cos θ)

⟩ = 2k0 (1 − 〈cos θ〉) = 2k0lsltr

, (8.41)

where k0 = |ki| = |ki+1|, θ is the angle between directions ki = ki+1 (i.e., angleof the ith scattering act), and ltr is the transport length of the photon free path(which corresponds to the mean distance where a photon completely loses its initialdirection of motion) [see Eq. (1.16)].

In an elementary situation when particles move independently of each other,their positions are represented by Gaussian random quantities, and the change inthe photon momentum for each scattering event is independent of the position


382 Chapter 8

of a particle, the path-dependent normalized first-order autocorrelation functionis written as80

g1(τ, s) = exp

{−4π2

3λ2

⟨�r2 (τ)

⟩ s

ltr

}. (8.42)

Here, s is the total photon path length.In a dense medium, we have s � ltr. Therefore, in contrast to the case of single

scattering, the correlation function, g1(τ, s), is sensitive to the motion of a particleon the length scale on the order of λ[s/ltr]−1/2, which is generally much less than λ.Thus, DWS autocorrelation functions decay much faster than analogous functionsemployed in QELS.

Substituting Eq. (8.41) in Eq. (8.39), we determine that the normalizedtemporal field autocorrelation function, g1(τ) = G1(τ)/< |E(t)|2>, has the form

g1 (τ) =∞∫

0

p(s) exp

(−1

3k2

0

⟨�r2 (τ)

⟩ s

ltr

)ds. (8.43)

As shown, that similar to the conventional dynamic light scattering technique,78, 79

the change in g1(τ) is determined in terms of their mean-square displacement⟨�r2 (τ)

⟩, with the difference that the slope of g1(τ) increases in proportion to the

average number of scattering particles. This has been verified directly by Yodhet al., using a pulsed laser and gating the broadened response to select photon pathlengths of a specific length.1498 For the CW illumination, Eq. (8.43) is valid, giventhe assumption that the laser coherence length is much longer than the width of thephoton path length distribution.

For a system that multiply scatters laser radiation, the transport of tempo-ral field correlation function is accurately modeled by the correlation diffusionequation,1499 i.e.,[

D∇2 − cμa − 1

3cμ′

sk20

⟨�r2 (τ)

⟩] · G1(r, τ) = −cS(r). (8.44)

Here, G1(r, τ) is determined by Eq. (8.38), and is a function of position r and cor-relation time t; its units of intensity are energy per area per second. Here, D is thephoton diffusion coefficient, k0 is the wavenumber of the light in the medium, cis the speed of light in the medium, and S(r) is the distribution of light sourceswith units of photons per volume per second. Similar to μa, describing losses ofcorrelation attributable to photon absorption, 1

3μ′sk

20

⟨�r2 (τ)

⟩is a loss term repre-

senting the losing of correlation attributable to dynamic processes. The correlationdiffusion equation [Eq. (8.44)] is valid for turbid samples with the dynamics ofscattering particles governed by Brownian motion

⟨�r2 (τ)

⟩ = 6DBτ. When τ = 0,there is no dynamic absorption, and Eq. (8.44) reduces to the steady-state photondiffusion equation described by Eq. (1.17). The correlation diffusion equation canbe modified to account for other dynamic processes, such as random and shear



Figure 8.17 Schematic diagram of DWS experimental arrangement: 1, laser with a coher-ence length that is greater than or equal to the total photon path length, s, owing to multiplescattering; 2, fiber-optic probe, a multimode irradiating fiber and a single-mode detectingfiber; 3, detecting system, a PMT or an APD, operated in the photon counting mode andconnected with a digital multichannel autocorrelator; 4, blood perfused tissue.

flows, and turbulence. In the case of combined Brownian motion with random andshear flows, the correlation diffusion equation becomes1500, 1501(

D∇2 − cμa − 2cμ′sk

20DBτ − 1

3 cμ′sk

20

⟨�V2

⟩τ2

− 115 cμ

′−1s �2

effk20τ

2)

G1 (r, τ) = −cS (r). (8.45)

Here, the fourth and fifth terms on the left-hand side arise from random and shearflows, respectively. It was assumed that, for random flow, the velocity distribution isisotropic and Gaussian; thus, the mean square displacement

⟨�r2 (τ)

⟩ = ⟨�V2

⟩τ2,

where⟨�V2

⟩is the second moment of the particle velocity distribution (mean

square velocity); �eff is the effective shear rate. The dynamical absorption for flowin Eq. (8.45) increases as τ2 compared to the τ increase for Brownian motionbecause particles in flows travel ballistically; also, DB,

⟨�V2

⟩, and �eff appear

separately because the different dynamical processes are uncorrelated.A schematic diagram of a DWS experimental arrangement is presented in

Fig. 8.17. It may consist of a multimode optical fiber, which transports a laserbeam with an adequate coherence length (greater than or equal to the total pho-ton path length, s, owing to multiple scattering). Laser radiation diffusely scatteredwithin the sample is then collected by means of a single-mode optical fiber, whichallows the fluctuations of the light intensity within the coherence area of the scat-tered radiation to be recorded by the detecting system, which includes a PMT or anavalanche photodiode (APD), operated in the photon counting mode and connectedwith a digital multichannel autocorrelator. Then, the output signal is processed withan autocorrelator to the temporal intensity correlation function, G2(τ) [Eq. (8.19)],which is related to the normalized temporal field autocorrelation function, g1(τ)[Eq. (8.29)], by the Siegert relation [Eq. (8.28)]. Further subsequent analysis ofthe determined g1(τ) can be performed similarly to the conventional dynamiclight scattering approach, in which the autocorrelation function is evaluated by itsrepresentation in a semilogarithmic scale.

8.5 Confocal Microscopy

Confocal laser scanning microscopy, which employs the confocal principle (withtwo optically conjugate diaphragms or small-sized slits in the object and imageplanes) for the selection of scattered photons coming from a given volume


384 Chapter 8

Figure 8.18 Principle of confocal microscope (see Ref. 1514).

(Fig. 8.18), is a well-developed imaging technique for medical investigations.1, 3, 28,

76, 120, 122, 168, 351, 1110–1112, 1124, 1125, 1128, 1167, 1168, 1176, 1177, 1187, 1225, 1363, 1381, 1502–1529 Themost impressive results on 3D imaging of living tissues on the subcellular level,particularly skin and eye retina, have been obtained by using confocal microscopy.The spatial resolution of this technique provides an opportunity to recognizedifferent types of cells and simultaneously observe moving blood cells in microves-sels.972, 1512 Confocal optical sectioning is used in different microscopies of tissuesand cells, such as fluorescence1110–1112 and Raman scattering,1167, 1168, 1176, 1177, 1187

that were already described in preceding chapters, as well as in reflectancespectroscopy,1128, 1506, 1512, 1526 the principles of which we will discuss in thissection.

In a conventional microscope, the lateral and axial resolutions are not inde-pendent. The great advantage of a confocal microscope is that the axial resolutionis enhanced, which results in the optical sectioning capability of confocal micro-scopes.1128, 1502–1505 The lateral resolution of a confocal microscope is inverselyproportional to the NA of the microscope objective lens:1512

�x = 0.46λ

NA. (8.46)

The predicted resolution, �x, is 0.4 μm with 1.2-NA water-immersion objectivelens at wavelength λ = 1064 nm. The axial resolution is more sensitive to theNA of the microscope objective lens. Therefore, to obtain the maximum axialresolution, and hence, the best degree of optical sectioning, it is preferred touse microscope objectives with the largest NA. The full width at half-maximumof the axial irradiance distribution defines the axial resolution or optical sectionthickness:1512

�z = 1.4nλ

(NA)2, (8.47)



where n is the refractive index of the objective lens immersion medium. The pre-dicted axial resolution �z is 1.4 μm with 1.2-NA water-immersion objective lensat wavelength λ = 1064 nm and n = 1.35. The lateral (�x) and axial (�z) resolu-tion of the confocal microscope measured for the scattering medium with n = 1.35at λ = 1064 nm for a 1.2-NA objective lens were 0.7 and 3 μm, respectively.1512

The differences in predicted and measured resolution can be attributed to sphericalaberration. For an oil immersion microscope objective with NA of 1.4, and bluelight wavelength of 442 nm, the lateral resolution is 0.14 μm and the axial or depthresolution is 0.23 μm.1128

The lateral resolution of conventional (conv) and confocal (conf) microscopescan be compared.1128, 1504 If the image of a single-point specimen is viewed inreflected light by conventional microscopy, the image intensity distribution isgiven by

Iconv(r) =[

2J1(

2πλ

NA · r)

2πλ

NA · r

]2

, (8.48)

where J1 is the first-order Bessel function and r is the lateral distance in the focalplane. For the confocal case in the presence of the pinhole, the image is nowgiven by

Iconf(r) =(

2J1(

2πλ

NA · r)

2πλ

NA · r

)4

. (8.49)

For the confocal case, the image is sharpened by a factor of 1.4 relativeto the conventional microscope. With a confocal microscope, the resolution isapproximately 40% better than in a conventional microscope.

Let us consider axial resolution in a confocal microscope for imaging bothpoints and planes.1128, 1504, 1505 If a confocal microscope is scanned axially, so thatthe intensity of light reflected from a plane mirror is detected as a function of thedistance the mirror moves toward the focal plane, the intensity of the reflected lightis given by a simple paraxial theory as follows:1505

Iconf(z) =[

sin(υ(z)

2

)υ(z)

2

]2

. (8.50)

The symbol υ(z) is a normalized axial coordinate related to the real axial distance,z, by

υ = 8π

λnz sin2

(α2

), (8.51)

where n sinα = NA. At the focal plane, the intensity of the reflected signal ismaximal. These equations are valid for imaging plane reflectors. For point or linereflectors, Eq. (8.50) becomes

Iconf(z) =[

sin(υ(z)

2

)υ(z)

2

]4

. (8.52)


386 Chapter 8

Figure 8.19 Schematic of the confocal probing technique: L1, L2, and L3, short-focuslenses (f = 8 mm) forming in pairs a small-aperture collimator; d1 and d2 limitingdiaphragms with diameters of 10 μm; zf, depth of focal point immersion into the mediumunder study; L, laser source; D, detector of optical radiation; and n0 and n1, refractive indicesof the external and studied media (see Ref. 1521).

The optical sectioning is weaker for a point or a line than for a plane. All of theseequations refer only to bright field imaging in the reflection mode. For fluorescenceimaging, which is incoherent light imaging, all of the equations are different.1128

Image quality is not only dependent on resolution, but on the contrast of the image.The principle of the out-of-focal-plane rejection in a confocal microscope is

shown in Figs. 8.18 and 8.19. The reflected light from the focal plane passesthrough the pinhole and reaches the detector. In the case of an unfocused system,the reflected light is spread out over a region larger than the pinhole; only a verysmall amount of the light from out of the focal plane passes the pinhole and isdetected. An important problem in confocal microscopy is the optical aberrationsthat are introduced by the specimen and or the instrument itself.1128

The high image contrast and high spatial resolution of reflection confocalmicroscopy (RCM) are achieved by probing a small (10–100 μm2) volume of thetissue. The localization of a desired signal within the measured volume of suchsmall dimensions becomes possible as a result of mutual optical matching betweenthe laser radiation source, the measured volume, and the photodetector. The fieldsof view of the light source and photodetector are limited by pinholes, which aremounted in the plane of object and image (Fig. 8.19).1521 If the penetration depth,



zf, of the lens focus into the tissue does not exceed three to four lengths of thephoton mean free path, lph [see Eq. (1.8)], then such pinholes ensure that photonsreflected strictly back by the tissue and cell components within the probed volume(so-called ballistic photons) dominate in the detected signal. Only these photonscarry valid information that allows one to reconstruct the internal structure of themedium under study.

As zf increases, i.e., when the focus penetrates deeper into the scatteringmedium, the fraction of ballistic photons in the detected signal decreases, whereasthe fraction of photons scattered by the medium increases. Under typical conditionsof experiments with biological tissues, RCM allows one to distinguish ballisticphotons against a background of the totality of the medium-scattered photons, untilzf becomes higher than lph by a factor of 5–8. In other words, because of the intensemultiple light scattering characteristic of most of tissues, the RCM makes it pos-sible to obtain an image of the cellular structure of skin, for example, located at adepth of 300–400 μm at most.1502, 1510–1512

Figure 8.20 shows the results of MC simulation of spatial distribution, J(r),of the probability density of the effective photon optical paths, performed fora confocal probing scheme with a focus of the objective lens immersed into ahomogeneous scattering medium to a depth of zf = 300 μm. The parameters ofRCM are presented in Fig. 8.19. As expected, when zf does not exceed 3–4 MFPs(μs ≤ 100 cm−1 or, equivalently, lph ≥ 100 μm), clearly pronounced photon focus-ing at a depth of 300 μm is observed in the spatial distribution of the density ofeffective optical photon paths [Fig. 8.20(a)].

If zf amounts to 8–20 MFPs (μs = 266 − 400 cm−1 and, correspondingly,lph = 25 − 37.5 μm), then the tendency of probing radiation focusing in the tissueis maintained [Fig. 8.20(b)]. However, the central focal spot region is much largerthan in the case of a less scattering medium [Fig. 8.20(a)]. With a further increase inthe medium scattering coefficient (μs ≥ 1000 cm−1) and the corresponding short-ening of photon MFP (lph ≤ 10 μm), the incident radiation becomes defocused,although its narrow directivity remains unaltered [Fig. 8.20(c)].

These data (Fig. 8.20) clearly illustrate the possibility of localizing the focusedprobing laser radiation inside a homogeneous, multiply and anisotropically scat-tering (g = 0.9), and weakly absorbing (μa = 0.1 cm−1) medium upon probing bythe RCM.

For calibration of confocal microscopes, specially designed tissue phantomsare used (see, for example, Ref. 1225).

8.6 Optical Coherence Tomography

Methods of interferometry and tomography of tissues and organs with the use ofpartially coherent light sources have progressed rapidly in recent years,1, 3, 8, 17, 18,

28, 45, 76, 77, 84, 102, 108–111, 116, 126, 127, 129, 135, 136, 138, 139, 142, 146, 147, 156, 196, 355, 362, 555, 624, 636,

711, 751, 887, 1163, 1226–1229, 1234, 1300–1302, 1305–1307, 1331–1341, 1361, 1362, 1388, 1404–1417, 1530–1564,

1566–1568 which has provided the grounds for organizing a special international con-ference.8, 45, 116 OCT was first demonstrated in 1991.1530 Imaging was performed


388 Chapter 8

Figure 8.20 Spatial distribution, J(r ), of the probability density of the effective pho-ton optical paths calculated for homogeneous (n1 = 1.4), multiply [μs = 10 (a), 26.6(b), and 100 mm−1 (c)], and anisotropically (g = 0.9) scattering, and weakly absorbing(μa = 0.01 mm−1) media upon probing by reflection confocal microscopy in the geometrypresented in Fig. 8.19 and zf = 300 μm (see Ref. 1521). (See color plates.)

in vitro in the human retina and in atherosclerotic plaque to provide examples ofimaging in transparent, weakly scattering media as well as highly scattering media.A brief historical review and analysis of the fundamentals of low-coherence inter-ferometry and tomography are presented by Fercher and coworkers,84, 142, 1532, 1533

who also discussed ophthalmologic applications of these methods. An overviewof the early development of optical low-coherence reflectometry and some recentbiomedical applications is given by Masters.1562 State-of-the-art monographs andtutorials describing principles and biomedical applications of OCT have beenpublished.127, 135, 136, 146, 147, 156, 196

Different terms are employed in the literature to specify this method of inves-tigation: dual-beam coherent interferometry or laser Doppler interferometry, OCT,



or optical coherence reflectometry. The tomographic scheme differs from the inter-ferometric scheme by additional transverse scanning, which allows one to obtaintopograms of various tissue layers.

OCT is analogous to ultrasonic imaging, which measures the intensity ofreflected infrared light rather than reflected sound waves from the sample. Time-gating is employed so that the time for the light to be reflected back, or echo delaytime, is used to assess the intensity of backreflection as a function of depth. Unlikeultrasound, the echo time delay on the order of femtoseconds cannot be mea-sured electronically due to the high speed associated with the propagation of light.Therefore, a time-of-flight technique has to be engaged to measure such ultra-shorttime delay of light backreflected from the different depth of sample. OCT usesan optical interferometer illuminated by a low coherent light source to solve thisproblem.

This technique is conventionally implemented with the use of a dual-beamMichelson interferometer. If the path length of light in the reference arm is changedwith a constant linear speed, v, then the signal arising from the interference betweenthe light scattered in a backward direction (reflected) from a sample and light inthe reference arm is modulated at the Doppler frequency

fD = 2v

λ. (8.53)

Owing to the small coherence length of a light source,

lc = 2ln(2)

π· λ2

�λ, (8.54)

where �λ is the bandwidth of the light source with a Gaussian line profile, and theDoppler signal is produced by backscattered light only within a very small region(on the order of the coherence length lc) corresponding to the current optical pathlength in the reference arm. If a multimode diode laser or a superluminescent diode(SLD) with bandwidth of 15–60 nm (λ ∼ 800−860 nm) is employed, the longitu-dinal resolution falls within the range of 5–20 μm. For a titanium sapphire laserwith a wavelength of 820 nm, the bandwidth may reach 140 nm. Correspondingly,the resolution is 2.1 μm.45, 84

A typical scheme of a dual-beam Michelson interferometer with a low-coherence source and the principle of operation of such a device are shown inFig. 8.21, which illustrates ophthalmologic applications of this technique.1532, 1533

Let us consider the interference of light reflected from the front surface of eyecornea (1) and pigment epithelium of retina (2). Under these conditions, each ofthe two beams, E′ and E′′, is split into two beams, E′

1, E′2 and E′′

1 , E′′2 . Suppose that

d is the geometric distance between the reflective surfaces of the eye. Then, thecomponents of the field are characterized by additional delay times and the totalfield of light beams reflected from the eye is written as

E(t) = E1(t) + E2(t − τ) = E′1(t) + E

′′1(t − δ) + E

′2(t − τ) + E

′′2(t − δ − τ),

(8.55)


390 Chapter 8

M''

SLD

DB

LM' E'

(1) (2)

d

PD

2d2L

E'' E'

E2''

E'1'

E'1

E'2

Figure 8.21 Dual-beam Michelson interferometer with a partially coherent source of exci-tation for ophthalmologic applications (see Refs. 1532 and 1533): SLD, superluminescentdiode; M′ and M′′, interferometer mirrors; DB, dual beam; and PD, photodetector.

where τ = 2nd/c0 and n is the refractive index of a medium between two reflec-tive surfaces. When quasi-monochromatic sources are used, the interfering beamsconsist of groups of waves, and n should be replaced by the group refractive index

ng = n − λdn

dλ. (8.56)

We should take into account that the coherence length of light increases in a dis-persive medium, and spatial resolution lowers. This is especially noticeable forbroadband laser systems. Specifically, for a titanium sapphire laser with a band-width of 140 nm, the coherence length is equal to 2.1 μm for air (in the absenceof dispersion) and 60 μm for water (in a layer with a thickness of 24 mm).1548

According to Ref. 1548, the coherence length in a medium is

l′c =

{l2c +

[d

dng

dλ�λ

]2} 1

2

, (8.57)

where d is the thickness of the medium. Hence, we find that if the thickness of atissue being probed is not large (on the order of 1 mm), the additive to the coherencelength owing to dispersion may remain small. For example, for a titanium sapphirelaser with the largest bandwidth, this addition is the same order of magnitude asthe coherence length in free space.

Figure 8.22 presents a typical waveform of the interference signal correspond-ing to in vivo probing of the fundus of human eye with the use of partially coherentbeams of the interferometer shown schematically in Fig. 8.21. By analyzing sucha signal, one can very accurately determine the thickness of the layer of nervefibers (the distance between ILM and GCL, 75 μm). Along with geometric parame-ters, partially coherent interferometry provides an opportunity to determine optical



1.0

0.5

031.0 31.5 32.0

75 mm

I, arb. units430 mm

ILM

GCL

RPE

CH1

CH2

mm

Figure 8.22 Interference signal (in arbitrary units) obtained by in vivo probing of the fundusof the human eye. The wavelength of radiation of a superluminescent diode is 825 nm, andits coherence length is 12 μm (see Refs. 1532 and 1533); ILM, inner boundary layer; GCL,ganglion layer; RPE, retinal pigment epithelium; and CH1 and CH2, choroid layers. Thedistance is measured relative to the cornea.

parameters of tissues, such as scattering and absorption coefficients and the refrac-tive index. The dependence of these parameters on the physiological state of atissue allows one to obtain reliable diagnostic data in both ophthalmology and otherfields of medicine. It was demonstrated that the spatial resolution of the interfer-ence technique is approximately an order of magnitude higher than that providedby the conventionally employed ultrasonic diagnosis. In addition, owing to its con-tactless character, the interference technique does not require eye anesthesia. Theresults of measurements obtained with the use of the interference technique arecharacterized by high reproducibility and easily can be interpreted even by nonex-perts.1532, 1533 In addition to the determination of geometric and optical parametersof the rear segment of the human eye (thickness of the fundus and its components),low-coherence interferometry can successfully be used to measure the thickness ofthe cornea with resolution on the order of 1.6–3.5 μm, which is necessary for mon-itoring during conventional and laser surgical operations aimed at changing therefraction of cornea; for assessing various corneal pathologies, including edema;and for measuring the depth of the front eye chamber and the axial length of aneye. The latter possibility is particularly important when cataracts are treated sur-gically, because an error of 0.2–0.3 mm in determining the axial length of an eyegenerates an error in eye refraction of approximately one dioptry.1532, 1533

OCT can also be described on the basis of the principles of the hetero-dyne technique.1568 Figure 8.23 shows a typical fiber-optical scheme, where twobeams—signal and local oscillator beams—are generated from a broadband sourcesuch as SLD. The signal beam is incident on the sample; the transmitted or scat-tered light is superposed with the local oscillator beam in the balanced detector.Owing to the broad spectrum of the light, and therefore to the small longitudi-nal coherence length, the light from the sample and the local oscillator beam onlyinterfere if their path length is matched within the coherence length of the light.By increasing the path length of the local oscillator beam, �l, with the reference


392 Chapter 8

Figure 8.23 Typical fiber-optic OCT system. Light from the SLD is split up by a beam splitterinto a LO beam and a signal beam that is incident on to the medium (tissue) under investi-gation. The reflected field is superposed with the LO beam reflected from the longitudinallyscanned reference mirror; the superposed field is measured by a detecting-demodulatingsystem (see Ref. 1568).

mirror, MR, the local oscillator beam will interfere only with those parts of thesignal field that have traveled the same distance �l in the medium. Therefore, sig-nal field contributions from different photon path lengths in the sample can beselected. In practice, the reference mirror is moved at a fixed speed, and the het-erodyne beat signal resulting from the Doppler shift of the local oscillator beamreflected from the moving mirror is simultaneously recorded [see Eq. (8.53)]. Bymoving the laser beam in a 2D raster and taking vertical scans for each point, a 3Dimage can be obtained.

Figure 8.24(a) shows an example of a time-modulated interference signaldetected by the photodetector. If the detected ac signal is band-pass filtered withrespect to the central Doppler frequency (as the center frequency), then it isrectified and low-pass filtered. The output of the low-pass filter is the envelopeof the time-modulated ac interference signal, which is equivalent to the cross-correlation amplitude. Figure 8.24(b) provides an example of the detected envelopecorresponding to Fig. 8.24(a).

OCT performs cross-sectional imaging by measuring the time delay and mag-nitude of optical echoes at different transverse positions, essentially by the useof low-coherence interferometry. A cross-sectional image is acquired by perform-ing successive rapid axial measurements while transversely scanning the incidentsample beam onto the sample (see Fig. 8.25). The result is a 2D data set, whichrepresents the optical reflection or backscattering strength in a cross-sectionalplane through a biological tissue. The systems implemented by the fiber-opticcouplers, matured in the telecommunication industry, offer the greatest advan-tage for the OCT imaging of biological tissues because they can be integrated intoalmost all currently available medical imaging modalities, such as endoscopes and



Figure 8.24 Low-coherence interferometer output signals: time-modulated ac term of inter-ference signal (a), corresponding signal after demodulation (cross-correlation amplitude,i.e., envelope) (b) (see Ref. 1336).

Figure 8.25 OCT image (right, lower) is generated by performing measurements of thereflected signal time delay and magnitude of backscattered light intensity (left) over a rangeof transverse positions (upper). As an example, the OCT image of ceramic material withglazing that models a hard tissue (tooth or bone) is presented (see Ref. 1336).

microscopes.108, 109, 111, 1306, 1416 Figure 8.23 gives an example of the fiber-opticversions of OCT.

Numerous fiber-optical OCT systems are described in the literature (see forexample, Refs. 1, 108, 109, 111, 127, 136, 142, 146, 147, 156, and 196). In thesesystems, light from a low-coherence light source is coupled to a single-mode fibercoupler in which half of the light power is conducted through the single-mode fiberto the reference mirror. The remaining half enters the sample via proper focusingoptics. The distal end of the fiber in the sample arm serves a dual role as a coherentlight receiver and spatial filter analogous to a confocal pinhole. Because the dcsignal and intensity noise generated by the light from the reference arm add tothe interference signal, the system is prone to excess photon noise. One way toreduce this type of noise is to use a balanced detection configuration that cancels


394 Chapter 8

the background noise components by subtracting the photocurrents generated bytwo photodetectors.1336, 1568 The interference signals at the output of the detectorsadd because they vary out of phase.

OCT has the advantage that it can achieve extremely high axial image res-olution independently of the transverse image resolution. The axial resolution isdetermined by the coherence length of the light source in use, i.e., Eq. (8.54), whichis independent of the sampling beam focusing conditions. The lateral or transverseresolution achieved with an OCT imaging system is determined by the focusedspot size limited by the NA of the lens used to deliver the light onto the sample,and the wavelength in conventional or confocal microscopy [see Eqs. (8.48) and(8.49)]. To calibrate an OCT system, several types of specialized tissue phantomshave been designed.1226–1229

8.7 Digital Holographic and Interferential Microscopy

Another example of the use of lasers and coherent light sources in biology andmedicine is the digital holographic microscopy, which utilizes the classical prin-ciple of holography, but in which a digital camera is used as a recording tool,e.g., a CCD camera.179, 250, 260, 262, 263 Figure 8.26 introduces the concept of build-ing an inverted digital holographic microscope (DHM), developed on the basisof commercially available research microscopes for the study of transparent sam-ples, such as living cells.263 The light source is a laser (second harmonic ofNd-YAG laser, λ = 532 nm), the emission of which is divided into an object wave(illuminating the object) and a reference wave. For coherent light transportation,single-mode polarization-maintaining optical fibers are used. To provide objectillumination, light is directed through the microscope condenser. The referencewave is sent directly to the interference block, which is associated with one port ofthe microscope, designed to connect the camera. The beam splitter makes a smallrelative shift between the wavefronts of the object and reference waves. Formedby the superposition of these waves, a hologram is recorded by CCD camera andtransmitted to the image processing system for the reconstruction and further exam-ination of digital holograms. The registration time of the hologram depends on thematrix photoreceiver, which, for a CCD camera, is typically less than or equalto 1 ms.

The literature describes a variety of methods for the numerical reconstructionof digital holograms. A holographic method with a spatial phase shift (SPS) hasbeen quite suitable for use in the reconstruction of digital holograms, assumedin the preceding geometry for slightly divergent wavefronts of object and refer-ence waves.263 A numerical SPS algorithm can eliminate the effects of zero-orderintensity and double images, and provides compensation for wavefront aberra-tions of the object wave relative to the reference wave. The SPS method, appliedto the reconstruction of digital holograms, has successfully been used to imageand study living cells.260, 262, 263 Intensity distribution, IHP(x, y, z0), in the hologramplane (HP) located in plane z = z0 is formed by the interference of the object wave,O(x, y, z = z0), and the reference wave, R(x, y, z = z0):263



Figure 8.26 Optical schematics of a digital holographic microscope built on the basis of theinverse microscope using the modular integration principle. HP: hologram plane (plane ofCCD sensor) (z = z0), zIP is the location of the image (z = z0 + �z) (see Ref. 263).

IHP(x, y, z0) = O(x, y, z0)O∗(x, y, z0) + R(x, y, z0)R∗(x, y, z0)

+ O(x, y, z0)R∗(x, y, z0) + R(x, y, z0)O∗(x, y, z0),

= IO(x, y, z0) + IR(x, y, z0) + 2√

IO(x, y, z0)IR(x, y, z0) cos �φHP(x, y, z0),(8.58)

where IO = OO∗ = |O|2 and IO = RR∗ = |R|2 (the asterisk denotes the complexconjugate quantities). The parameter �φHP (x, y, z0) = φR(x, y, z0) − φO(x, y, z0)is the phase difference between waves O and R in plane z = z0. In the presenceof an object in the optical path of wave O, the phase distribution is given byφO (x, y, z0) = φO0(x, y, z0) + �ϕS(x, y, z0), where φO0(x, y, z0) is the phase of theobject wave itself, and �ϕs(x, y, z0) is the phase change due to the object. Forareas not occupied by the object, �φHP (x, y, z0) is determined by a mathematicalmodel:263

�φHP (x, y, z0) = φR(x, y, z0) − φO0(x, y, z0)

= 2π(Kxx2 + Kyy

2 + Lxx + Lyy). (8.59)


396 Chapter 8

The parameters Kx, Ky in Eq. (8.59) describe the divergence of the object waveand the properties of lenses of the microscope. Constants Lx, Ly define a linearphase difference between the O- and R-waves due to misalignment of the experi-mental geometry. For a quantitative phase estimate based on the measurement ofIHP(x, y, z0), in the first stage, a complex object wave O(x, y, z = z0) in the holo-gram plane is determined pixel-by-pixel by the solution of a system of equationsobtained through substituting Eq. (8.59) in Eq. (8.58). To determine the intensitiesof the adjacent sections, for example, within a 5 × 5 area, the pixels around thecurrent pixel of the hologram are accounted for by applying an algorithm to calcu-late the spatial phase shift. This algorithm is based on the assumption that only thevalue of the phase shift between object O(x, y, z0) and reference R(x, y, z0) waves�φHP (x, y, z0) = φR(x, y, z0) − φO0(x, y, z0) is rapidly changing in the space of thehologram plane. In addition, the intensity of the object wave is assumed to remainconstant in the area around a given point of the hologram, for which the numericalevaluation is made. This condition is accurately satisfied in the case of an optimalratio between the magnification of the microscope and matrix receiver in use.

Parameters Kx, Ky, Lx, Ly cannot be obtained with the required precision fromdirectly analyzing the geometry of the experiment. Therefore, they are determinedwith the help of an iterative fitting procedure on the basis of preliminary studies inthe absence of the sample (see Ref. 260).

Regarding an ordinary microscopy with white light illumination, obtaining asharp image is also required for DHM. However, in DHM, if the object is notimaged sharply in the HP, for example, because of mechanical or thermal insta-bilities, the image sharpness can be adjusted in the second stage in the processof further transporting the object wave to the image plane. During the transporta-tion, parameter �z is selected so that the holographic image has a sharp peak,in accordance with the microscopic image in white light. The next criterion toobtain a sharp image of the object is to eliminate the influence of diffraction effectsat coherent light illumination, which are minimized algorithmically. As a resultof applying these algorithms and the parametric model for the phase difference,�φHP, in Eq. (8.59), the reconstructed holographic images do not contain ghostimage or zero-order signals.

From object wave O(x, y, zIP), in addition to amplitude modulo |O(x, y, zIP)|,which defines an ordinary image of the object, phase information of object�ϕS(x, y, zIP) is simultaneously reconstructed:

�ϕS(x, y, zIP) = φO (x, y, zIP) − φO0(x, y, zIP)

= arctanIm {O (x, y, zIP)}Re {O (x, y, zIP)} (modulo 2π). (8.60)

After removing uncertainty due to phase 2π, data obtained from Eq. (8.60) may beused in quantitative phase contrast microscopy.

In the transmission mode, as shown in Fig. 8.26, measured phase informa-tion about a semitransparent object is determined by its thickness and refractiveindex and by the refractive index of the environment. Information is missing



from the literature about the refractive indices of many types of living cells.Therefore, in recent years, new interferometric and holographic methods havebegun development for measuring the refractive index of the components ofliving cells and studying the correlation between cell refraction and their functionalstates.179, 249–251, 254, 255, 257, 260, 262, 263, 267, 268 For example, using a DHM, integral val-ues of the refractive index of neurons were measured.249 In these measurements,it is necessary to control the thickness of the sample.260 Similar problems withthickness control have occurred for Hilbert transform phase microscopy withmicrofluidistic equipment.254 In Refs. 261 and 263, DHM images of sphericalcells in suspension were obtained and their radius and integral refractive indexwere estimated. In Ref. 251, the refractive index and size of a cell were measuredindependently by a dual-wavelength DHM system in combination with environ-ment dispersion control by adding an exogenous dye. Reference 250 describesa method of tomographic DHM refractometry of cells by registration of multi-ple phase-contrast images of a rotating sample. Similar results were obtained withphase Fourier microscopy255 and diffraction microscopy,265 in which the dense cellobject was transilluminated in different directions. Nevertheless, in all cases, itwas not possible to conduct independent measurements of the thickness (size) andrefractive index.

For a case in which the cells are in a medium with refractive index n0, andthe integral cell index of refraction, ncell, is known, then the thickness of the cell,H(x, y, zIP), can be determined based on measurements of the difference betweenoptical path lengths for light passing through the cell and the surrounding medium(�ϕcell):260

H(x, y, zIP) = λ�ϕcell(x, y, zIP)

2π· 1

ncell − n0, (8.61)

where λ is the wavelength of light. In principle, the measured parameter �ϕcell

allows one to estimate the shape of the cells. Nevertheless, Eq. (8.61) must be usedwith caution because, for example, various toxins and osmotic reactions can affectboth the size and refractive index of the cell (see Refs. 200 and 260).

Figure 8.27 illustrates the processing and presentation of recorded digital holo-grams. Figs. 8.27(a) and 8.27(b) show digital holograms of a living cell carcinomaof the human pancreas (Patu8988T), taken with an inverted DHM (Fig. 8.26)working in transillumination mode (microscope objective 40×, NA = 0.65), anda reconstructed holographic amplitude image that corresponds to the image ina bright field microscope with coherent laser light illumination. Figure 8.27(c)presents a reconstructed image of the phase contrast accounting for modulo 2π[Eq. (8.60)]. Figure 8.27(d) shows data for continuous phase distribution, with theexception of 2π uncertainty, representing the change in the optical path lengthof light passing through the cell compared with the environment. Figure 8.27(e)shows a pseudo 3D image of the cell in the gray chart. Cell thickness alongthe marked dotted line in Fig. 8.27(d), calculated on the basis of Eq. (8.61) forncell = 1.38, n0 = 1.337, and λ = 532 nm, is shown in Fig. 8.27(f). The first deriva-tive with respect to the x coordinate for data, presented in Fig. 8.27(d), defines


398 Chapter 8

Figure 8.27 Example showing image processing and representation in DHM: digital holo-gram of a human pancreas carcinoma cell (Patu8988T) (a), its reconstructed holographicamplitude image (b), quantitative phase contrast image (modulo 2π) (c), unwrapped phasedistribution (d), gray level coded pseudo-3D plot of the unwrapped phase image (e), cal-culated cell thickness along the dashed white line in (d) (f), DHM differential interferencephase contrast (DHM DIC) image (g) (see Ref. 263).

the differential interference phase-contrast DHM. This method is comparable tothe well-known Nomarski technique of differential interference phase contrast,but with additional advantages of digital focus adjustment and resulting sensitivitycontrol.

An interference phase microscope for high-precision quantitative study of indi-vidual cells is shown in Fig. 8.28. Similar to the previously described holographicmicroscope, it is based on an inverted microscope with single-mode fiber-optic ele-ments and a CCD camera as a detector.252 As a coherent light source, a helium-neonlaser with a wavelength of 632.8 nm is used. Signal processing for the estima-tion of optical (or phase) thickness is based on a Hilbert transform algorithm.This is designated Hilbert phase microscopy (HPM). The concept of the Hilberttransform in the spatial scale provides quantitative phase images through recordingonly one spatial interferogram. Thanks to the single-shot nature of the registration,the HPM has a short acquisition time, limited only by the recording equipment;therefore, it provides accurate measurements of the optical length (phase) shift at



Figure 8.28 Quantitative interferential phase microscope integrating an inverted micro-scope with the principle of HPM (A) (see Ref. 252); quantitative assessment of the shapetransformation associated with the RBC during a 10-s period (B), the profiles in (b) and (d)are measured along the profiles indicated by the white arrows in (a) and (c).

nanometer scale in millisecond or smaller time scales, characteristic for manybiological phenomena.

In a microscope with a 100× objective lens, the output of a single-mode fiber isthe field for illumination of an object. All fibers are mechanically fixed to not gen-erate additional phase noise in the system. The lens is configured so that the imageof an object passing through the beam-splitting cube is formed in the plane of theCCD camera. In the reference arm, the output field of the other single-mode fiberis collimated and expanded by a telescopic system consisting of a different objec-tive lens and the same lens. The reference beam is a plane wave, which interfereswith the image field. The reference field is slightly mismatched by the direction inrelation to the object field, so that uniform fringes are formed at an angle of 45 degwith respect to the x- and y-axes. The CCD camera (C7770, Hamamatsu Photonics)has a recording rate of 291 f/s at full resolution of 640 × 480 pixels with exposuretime of 1–1.5 ms. Fringes were recorded by using six pixels for the period. Thespatial distribution of intensity associated with the interferogram in one directionis given by the well-known expression

I(x) = IR + IS(x) + 2[IRIS(x)]1/2 cos[qx + φ(x)], (8.62)

where IR and IS are the intensity distributions of the reference and object fields,respectively; q is the spatial modulation frequency of fringes; and φ(x) is a spatiallymodulated phase attributable to the object that is the subject of study. When usinghigh spatial frequency filtering and the Hilbert transform, φ(x) is determined ateach point of a single-shot image. As an illustration, Fig. 8.28(b) presents dynamicimages of the erythrocyte. The possibilities of obtaining cell dynamic images andusing them for morphometry in the nanometer spatial and millisecond time scalesare demonstrated.

The dynamic profile of the geometric thickness of the cell can be directlyobtained from the phase measurements as H(x, y, t) = (λ/2π�n)φ(x, y, t), where


400 Chapter 8

�n = (ncell − n0) is the difference between the average refractive index of the celland the environment, which is called the contrast of refractive index (CRI).252 Fromthis, it follows that the possibility of determining the momentary volume of the cellis V(t) = ∫

H(x, y, t)dxdy.Thus, interference and holographic methods and their new modifications are

promising for studying intracellular dynamics.179, 249, 263, 265, 267, 268 For the diagno-sis of cell functional status, the relationship between the optical path differenceand the macroscopic parameter of the medium, i.e., refractive index, is of funda-mental importance. The advances and perspectives of coherence interferometry forstudies of intracellular dynamics are discussed by Tychinsky.267, 268 Measurementsof cell CRI confirmed the diagnostic value of the refractive index. For example,changes in the CRI at hypotonic stress were found in DHM studies of neurons249

(see Fig. 8.27). The spatial-temporal changes in RBC phase thickness were demon-strated by using HPM (see Fig. 8.28).252 In the same work, by studying a singleRBC hemolysis, it was shown that the cell volume is reduced quite slowly, by 50%in 4 s, which is determined by RBC membrane rigidity; this also has diagnosticapplications.

As we discussed previously [see Eqs. (8.58)–(8.62)], the equivalent model of abiological object is crucial for the application of interferential methods to the diag-nosis and interpretation of results. Usually, an optically heterogeneous real objectis represented as a uniform sphere with an equivalent refractive index. In certaincases, it is possible to divide the structural elements and to determine their CRI.Contribution to the optical path difference (OPD) gives the geometrical thickness,H, and CRI �n, so their separation and accurate determination of the refractiveindex of the object are essential for the detection of weak effects. To separate thecontributions to the OPD of H and the refractive index of the object, for example,two immersion media with precisely known indices of refraction can be used.249

A cuvette that contains the cells, made from a material with a known refractiveindex, is essentially a reference object, both in form and refractive index. Thisprocedure applied in HPM with a common pathway has provided highly accuratemeasurements, insensitivity to vibrations, and millisecond temporal resolution.253

Free of special markers, interferential methods are significantly less invasivethan, for example, methods using fluorescent dyes or nanoparticles. Organelles ofcells are easily differentiated by phase contrast. Dimensions of organelles are typ-ically smaller than or comparable to the wavelength, so the spatial resolution ofthe amplitude-based optical methods is limited by diffraction at the aperture ofthe objective lens. However, interferential methods in the study of phase objectspotentially have spatial super-resolution, significantly smaller than the diffractionlimit.267

Studies by Tychinsky et al.267, 270 were conducted using an Airyscan coher-ent phase microscope (CPM), the optical scheme of which is shown in Fig. 8.29.The microscope is a modification of a Linnik microinterferometer, wherein thesource of coherent radiation is a helium-neon laser (λ = 632.8 nm). To register theinterferential signal and convert it to local phase values, the linear-periodic modu-lation of the phase of the reference wave was produced. The coordinate-sensitive



Figure 8.29 Coherent phase microscopy (see Refs. 267–270): Airyscan Coherent PhaseMicroscope based on the Linnik interferometer and He-Ne laser (λ = 633 nm) with linear-periodical phase modulation of the reference wave (a); phase for each pixel in theinterferential image is determined at its scanning by the spatially sensitive photoreceiver–electronic dissector LI-620 (Electron, St. Petersburg, Russia). Representation of modulationsignal and interferometer’s response: phase modulation of the reference wave, U(t), causesmodulation of photoreceiver’s current I(t)[Ui (t)] (b); local phase values are determined frompulse duration τ (two values τ1 and τ2 are shown); sampling frequency and the speed ofimage collection is determined by the modulation frequency of 1 kHz (or 1 ms per pixel);noise-limited sensitivity hmin ≈ 0.5 nm.

photodetector (dissector) and electronic unit with analog-to-digital converter wereused to detect interferential signals. The principal difference from other methodsof phase imaging is that the OPD measurement is performed sequentially for eachpixel. The frequency and image sampling rate are determined by input frequencyof 1 kHz (or 1 ms per pixel). The resulting phase images included high spatial reso-lution of 100 nm for static images and 25 nm for dynamic images. One significantadvantage of the method is the possibility of random access to image points. Amicroscopic field of view may vary within 5–50 μm, depending on the objectivelens in use; the maximum dimension of the images by one coordinate has reached1024 pixels. The noise-limited sensitivity to the optical thickness measurementswas approximately hmin = 0.5 nm.

Interpretation of phase images is based on the concept of object representationin the form of a spatially inhomogeneous optical medium with a refractive index,n(r, t), in a limited region of space. The OPD represents the measured value. In theapproximation of eikonal or geometrical optics for a thin, transparent, and spatiallyinhomogeneous medium (cell), the OPD depends on the physical thickness, H, andCRI—the difference between the refractive index, n(r, t), of a cell and the exter-nal environment, n0 [see Eq. (8.61)]. In Fig. 8.30(a), a cell model is shown as alocal inhomogeneity with transverse dimensions d and H. A wave from a coherentsource passing through the cell experiences deformation of the wavefront (spatialmodulation), which is converted in the interferential microscope to the distribu-tion of OPD or phase thickness. This initial information is digitally encoded inthe topogram [see Fig. 8.30(b)]. Figures 8.30(c) and 8.30(d) show a topogram forphase thickness and a profile of a cell (human tissue culture HCT 116) along aselected section line, respectively. In the topogram [Fig. 8.30(c)], areas of different


402 Chapter 8

Figure 8.30 Optical model of a cell (see Ref. 269): cell is represented in the form of opti-cal inhomogeneity, n(x , y , z, t), in the immersion medium with a refractive index n0 (a); thewavefront of the incident plane wave is modulated by the optical inhomogeneities of thecell (b); distorted wavefront is converted to a topogram in an interferential microscopethat is a digitized 2D distribution of optical path (phase) difference h(x , y ); phase thick-ness profile h(x) is received by the cross-sectioning of the topogram along a scanningline; (a) and (b) phase image of unstained cell (tissue culture cells HCT 116): (a) on thetopogram contrast nucleus and less contrasting border of the cytoplasm with the environ-ment, marked by contour line, are shown; (b) in the diametric cross section, h(x), of thecell, phase images of optically denser nucleus and nucleolus are clearly shown; on the pro-file of the phase thickness the dimensions for which the CRI of nucleus and nucleolus arecalculated.

optical thicknesses are highlighted by pseudo-color; the contrasted nucleus andemphasized contour line of cell boundary are visible. In a typical cross sectionof the phase image of an unstained cell [Fig. 8.30(d)], its nucleus and nucleo-lus are clearly distinguished by the difference in optical (phase) thickness. Thecytoplasm of the cell in the phase thickness profile has a weak, sometimes evennegative contrast, owing to the simultaneous projection of the contributions ofelements of the multilayer structure and the various cell organelles in the planeof the cell phase image. For this reason, the width of the region adjacent to thecell boundary is significantly bigger than the actual thickness of the cytoplasmicmembrane.



As noted previously, the phase image in plane (x, y) is a 2D distribution of theoptical path difference of h(x, y, t) = ∫

[n(x, y, z, t) − n0]dz, which largely dependson the difference between the refractive indices of the object n(x, y, z, t) and theexternal environment, n0. Image phase contrast of organelles increases with theirCRI �n, which is equal to the difference between the average index of refrac-tion of the cell, <n(x, y, z, t)>, and immersion medium, n0. However, this relationmay be used only if there is a priori information about the size of heterogeneityand the volume for which the average value <n(x, y, z, t)> is determined. For thecase in which averaging is expected over the entire volume of the object, the max-imum phase thickness, �h, can be represented as �h = �nH = (<n(x, y, z, t)>−n0)H.

In many cases, the approximation of cell irregularities by spherical or cylin-drical shapes is sufficient, and the measured transversal dimension, d, in the phaseimage may be used as an equivalent geometric thickness, H.249, 254 For determiningthe CRI as an informative magnitude, it is possible to use an approximation H ∼= d,for which �n = �h/H ∼= �h/d, where �h is the maximum phase thickness and dis the transverse dimension in the phase images.

Intensive temporal fluctuations of recorded signals are usually observed on thesteep sections of the phase thickness profile and have been associated with themetabolic activity of a cell. Registration of these temporal fluctuations for a spe-cific local area of the cell is the basis of dynamic phase microscopy. This methodis illustrated in Fig. 8.31. Periodically, during tens of seconds, the phase thicknessprofile along the scan line at a fixed interval (up to hundreds of milliseconds) ismeasured, and data are stored in a matrix form, h(x, t) (track diagram), in the com-puter’s memory. For example, as shown in Fig. 8.31, in the cross section of thetrack diagram, there are characteristic fluctuations in the vicinity of the nuclearmembrane and in the nucleolus.

Figure 8.31 Illustration of dynamic phase microscopy (see Ref. 269): for the phase image(topogram), periodically during the time on the order of tens of seconds, the measurement ofphase thickness profile along the scan line at fixed intervals (up to hundreds of milliseconds)was conducted and stored in the computer memory in the form of a matrix h(x , t) (trackdiagram); in the section of the track-diagram in the vicinity of the nuclear membrane and inthe area of nucleolus characteristic, temporal fluctuations are shown.


404 Chapter 8

8.8 Second Harmonic Generation and Nonlinear RamanScattering

SHG is a new, high-resolution, nonlinear optical imaging modality for thestudy of intact tissues and cellular structures.177, 1133, 1134, 1141, 1146, 1156, 1160, 1161, 1569,

1570–1573, 1575, 1577–1602 SHG is a second-order nonlinear optical process that can onlyarise from media lacking a center of symmetry, e.g., an anisotropic crystal, or at aninterface such as membrane. It can be used to image highly ordered structural pro-teins without exogenous labels, as well as biological membrane probes with highmembrane specificity.

Collagen, as a primary component of connective tissues, has an appreciablenonlinear susceptibility for SHG. The helix of collagen secondary structure isnoncentrosymmetric, satisfying a condition for SHG, which self-assembles intohigher order structures. Collagen has been shown to have a dominant uniaxialsecond-order nonlinear susceptibility component aligned along the fiber axis. Insuch multicomponent tissues as skin, SHG light is mostly generated within dermis,not cellular layers like epidermis or subcutaneous fat.

SHG techniques have many advantages connected with dividing of incidentwavelength and selectivity to tissue structure, which allow one to easily reject sur-face reflection and multiple scattering of the incident light in the upper epitheliallayer without using a gating technique. As in the case of multiphoton fluorimetry,excitation light is in the NIR wavelength range, which is not excessively stronglyscattered by tissue, and the SHG signal is generated in a very small volume oftissue occupied by the focused laser beam. This provides high spatial resolution,acceptable in many cases for the in-depth probing and separation of excitation anddetection signals. Tightly focused laser beams with high power density and veryshort pulse duration in the range of tens or hundreds of femtoseconds allow for thegeneration of harmonics in undamaged living tissue, due to the brief interactionof radiation with tissue and the low overall energy—less than that needed for ion-ization of molecules. In addition, SHG polarimetry is an effective tool to probecollagen orientation in tissues.1575, 1576, 1578, 1579, 1600

In general, the nonlinear polarization of a material can be expressed as1571

P = χ(1)E + χ(2)EE + χ(3)EEE+, . . . , (8.63)

where P is the induced polarization, χ(n) is the nth order nonlinear susceptibil-ity, and E is the electric field vector of the incident light. The first term describesnormal absorption and reflection of light; the second, SHG, sum, and difference fre-quency generation; and the third, both two- and three-photon absorption, as well asthird harmonic generation and coherent anti-Stokes Raman scattering (CARS).

SHG, by contrast to two-photon fluorescence (see Subsection 5.2), does notarise from an absorptive process. Instead, an intense laser field induces nonlinear,second-order polarization in the assembly of molecules, resulting in the productionof a coherent wave at exactly twice the incident frequency (or half the wavelength).The spectral and temporal profiles of two-photon excited fluorescence and SHG arealso different. For two-photon fluorescence, the width of the emission spectrum isdetermined by the relative geometries of the ground and excited molecular states,



and the emission lifetime is related to the oscillator strength of the transition andis typically on the order of a few nanoseconds. In SHG, by contrast, both thespectral and temporal characteristics are derived from the laser source: the band-width scales, as 1/

√2 times the bandwidth of the excitation laser; and, owing to

the coherence of the process, the SHG pulse is temporally synchronous with theexcitation pulse.

A simplified expression for SHG signal intensity has a form1571

I(2ω) ∝[χ(2) E (ω)

τp

]2

τp, (8.64)

where χ(2) is the second-order nonlinear susceptibility, E(ω) and τp are thelaser pulse energy and width, respectively. As in two-photon fluorescence [seeEqs. (5.13)–(5.16)], the signal is quadratic with peak power, but because SHG isan instantaneous process, a signal is generated only during the duration of the laserpulse. The macroscopic value, χ(2), can be expressed in terms of the first molecularhyperpolarizability, β, as

χ(2) = ρM 〈β〉 , (8.65)

where ρM is the density of molecules and the brackets denote orientational average.This underscores the need for a noncentrosymmetric region, because 〈β〉 wouldvanish for an isotropic distribution of dipole moments. It follows from Eqs. (8.64)and (8.65) that the SHG signal depends on the square of the molecular surfacedensity, whereas the intensity of two-photon fluorescence is linear with the densityof fluorophores [see Eq. (5.11)].

Within the two-level system model, β is given by1571

β = 3e2

2h3

ωgefge�μge[ω2

ge − ω2] [

ω2ge − 4ω2

] , (8.66)

where e is electron charge; hωge, fge, and �μge are the energy difference, oscillatorstrength, and change in dipole moment between the ground and excited states,respectively. Although SHG is not an absorptive process, the magnitude of theSHG wave can be resonance-enhanced when the energy of the second harmonicsignal overlaps with an electronic absorption band. It follows from Eq. (8.66) that βgrows large when the fundamental frequency of the laser approaches the electronictransition; then, the total second-order response is a sum of the nonresonant andresonant contributions:

χ(2)total = χ(2)

nonres + χ(2)res. (8.67)

Depending upon the specific properties of the molecule and the excitation wave-length, the resonant contribution can dominate, resulting in enhancement of anorder of magnitude or more.

SHG microscopy has been successfully used to produce high-resolutionimages of living cells,1571 3D imaging of endogenous structural proteins in tis-sues,1572 and biomolecular arrays in cells, tissues, and organisms.1573 In vivo


406 Chapter 8

dynamic imaging of collagen in normal tissues and in its modified state in thetumor is described in Ref. 1574, and the generation of polarized SHG images ofcollagen are discussed in Refs. 1575, 1576, 1579, and 1584, including images ofrat tail tendon1575 and dermis of human skin.1579

SHG microscopy allows one to study many biochemical and biophysical pro-cesses, such as collagen nanostructure by analyzing the susceptibility tensor of thesecond order;1599 spatial orientation of the fibrous structures of tissues;1600 struc-tural changes in mixed collagen gels (types I and V) as a marker to record changesin human breast stroma with cancer;1590 microstructural and mechanical propertiesof collagen gel;1594 the mechanism of reversible dissociation of collagen in tissuesunder the influence of glycerol;1578 the role of myosin in the formation of SHGsignals from muscle sarcomeres;1585 the twist angles of myosin and collagen;1596

and the electrical activity in intact neural networks.1591

In Ref. 1591, the SHG excitation was provided by a high-powered fiber laseroperating in the 1064-nm spectral range (see Fig. 8.32). The scanning head of therandom access second-harmonic generation (RA-SHG) microscope was developedby using two acousto-optical deflectors (AODs) crossed at 90 deg. To compen-sate for the larger dispersion attributable to two crossed AODs, an acousto-opticalmodulator placed at 45 deg with respect to the two axes of the AODs was used. Amicroscope objective focused the excitation light into the tissue. The SHG signalwas collected in the forward direction and detected with a GaAsP photomultiplier(PMT) module. Figure 8.32(b) presents an SHG image of rat cerebellar slice atthree different depths of 10, 50, and 100 μm. Examples of SHG signals includethose of a Purkinje cell (red arrow), granule cell (yellow arrow), and interneuron(blue arrow). These images were acquired with the same laser power across allthree depths.

SHG, as a method of nonlinear multiphoton imaging, has considerable poten-tial for clinical studies.1597 For example, it is possible to quantify the status ofa disease such as osteogenesis imperfect;1587 to monitor the restructuring of theextracellular matrix in ovarian cancer;1589 to visualize skin lesions;1592 to quan-titatively analyze the structure of collagen in the human dermis under healthyand pathological states;1593 and to obtain images of the cornea after intrastromalfemtosecond laser ablation.1580

The primary advantage of the nonlinear methods is that labeling is rarelyneeded; however, new types of markers, such as ZnO nanoparticles with a strongnonlinear response, can be useful, for example, in the study of nanoparticle dif-fusion in tissues and their use as local generators or quenchers of free radicals inthe treatment or prevention of dental and skin diseases.1157–1161 The SHG methodwith and without nanomarkers is a prospective technique for in vivo nonlinearcytometry.173, 179, 182, 1147, 1152, 1155, 1156

Because the SHG method is technically implemented by using similar exper-imental equipment to multiphoton fluorescence and CARS, these methods areoften used together as part of a multimodal approach to gather more informa-tion about fundamental processes in tissues and cells (see for example, Refs.1577, 1601, and 1602). CARS is formally described in terms of four-wave



Figure 8.32 RA-SHG microscope (see Ref. 1591). RA-SHG microscope arrangement: afiber laser (λ = 1064 nm) provided the excitation light, which comprised 200 fs width pulsesat 80-MHz repetition rate. The laser beam was adjusted for optimal linear polarization via ahalf-wave (λ/2) plate. Beam passes were made through 45-deg AOM for angular spreadingprecompensation. A second half-wave (λ/2) plate was placed after the AOM to optimizethe diffraction efficiencies of the two orthogonally mounted AODs: AOD-x and AOD-y . Ascanning lens (SL) and a microscope tube lens (TL) expanded the beam before it wasfocused onto the specimen by the objective lens. The SHG signal was collected by an oilimmersion condenser, band-pass filtered (BFP) and focalized by a collection lens (CL) into aGaAsP PMT (photomultiplier) (a). SHG image of rat cerebellar slice at three different depthsof 10, 50, and 100 μm. Examples of SHG signals from a Purkinje cell (red arrow), granulecell (yellow arrow) and interneuron (blue arrow). The images were acquired with the samelaser power across all three depths (b). (See color plates.)

mixing,5, 181, 1171, 1172, 1601–1608 as indicated by the molecular vibrational state dia-grams in Figs. 5.11 and 8.33. CARS is a third-order nonlinear optical process inwhich three excitation fields interact to produce a fourth field, which is detected.In general, two laser beams with frequencies νpump and νS are tuned to determinetheir difference, νpump − νS, to be equal to the frequency, νvib, of a vibrationaltransition of the sampling molecules. Then, the probing laser beam with fre-quency, νprobe, resonantly generates a fourth enhanced field with frequency νAS =


408 Chapter 8

Figure 8.33 Molecular energy levels and transitions involved in the CARS process (seeRef. 181).

νpump + νvib. Figure 8.33 presents these transitions characteristic to the CARSprocess. Typically, only two laser beams are used to generate the CARS signal,because a so-called frequency-degenerate optical scheme with νpump = νprobe canbe applied. The intensity of the CARS signal depends quadratically on the modulusof the induced third-order polarization, P(3) in the sample [see Eq. (8.63)]:

IAS ∝ ∣∣P(3)∣∣2 , (8.68)

where P(3) depends on the third-order optical susceptibility, which can be presentedas a sum of the nonresonant and resonant contributions:

P(3) = [χ(3)

nonres + χ(3)res

]EpumpEprobeES (8.69)

The primary advantages of CARS compared to conventional Raman, in addi-tion to the opportunity to amplify the signal by more than four orders of magnitude,are direct signal generation, narrow band, and a complete absence of the influ-ence of AF because the signal is generated at wavelengths shorter than that ofexcitation. In Ref. 1577, the SHG method in combination with two-photon fluores-cence allowed the authors to obtain in vivo images of cells and extracellular matrix.Investigation of the effect of DMSO on the dynamics of skin optical clearing byquantitative multimodal nonlinear microscopy (SHG/CARS) is presented in Ref.1601; and simultaneous multimodal imaging for in vivo studies of the dynamics ofbiological processes, integrating multiplex coherent anti-Stokes Raman scattering(M-CARS), SHG, and two-photon fluorescence, is described in Ref. 1602.

When integrating with a laser scanning microscope, CARS can provide videoimages. The method was used for imaging and monitoring the lipid vesicles in



HeLa cells and membrane of lysed erythrocytes; growing fat droplets in liv-ing adipocytes; transporting organelles within living cells; and storing lipidsin nematode Caenorhabditis elegans upon the registration of CARS signal at2845 cm−1.1605 It was shown that CARS imaging is not destructive to cells understudy if the measurement does not exceed 5 min.1605

Principles and prospects for development of CARS as a technique for noninva-sively obtaining specific information about the chemical and molecular structure ofan object without the use of exogenous markers and, and its biological and medicalapplications, are discussed in Refs. 1171, 1172, 1603, and 1604. Ex vivo study ofmouse brain using M-CARS in comparison with results of the classical histologicalanalysis confirmed the potential of the method as an ideal tool for chemoselectiveimaging in tissues.1606 It is shown that the method enables quantitative analysisof CARS images, which is necessary, for example, for the real-time diagnosis ofbreast cancer.1607 In particular, functional imaging of cell and tissue structuresusing CARS and corresponding image processing algorithms make it possi-ble to distinguish cancerous lesions from normal tissue and benign proliferativelesions.

A commercially available micro-endoscope was used for minimally invasivemultimodal nonlinear video imaging of cellular processes in the spinal cord of liv-ing mice.1608 The system allows for obtaining CARS images of myelin sheaths andfluorescence detection at two-photon excitation from microglial cells and axons.Despite its small diameter, a micro-endoscope provides high-speed multimodalimaging in a sufficiently large region of tissue and with sufficient resolution tomeasure small differences in the thickness of the myelin sheaths and motility ofmicroglial cells.

A typical probing depth of nonlinear microscopy and spectroscopy is less than300 μm owing to the strong scattering of many tissues under study.1609 However,the use of tissue optical clearing technology by replacing the water with other fluidshaving a similar refractive index to that of proteins200, 201, 1609, 1612 can significantlyreduce scattering and reach a probing depth greater than 2 mm. A more detaileddescription of the tissue optical clearing method is presented in the next chapter.

8.9 Terahertz Spectroscopy and Imaging

The terahertz frequency range, which occupies an intermediate position betweenthe IR and microwave frequency ranges (1 THz → 1 ps → 300 μm → 33 cm−1 →4.1 meV → 47.6 K) (see Fig. 8.34), is relatively less studied in the whole rangeof electromagnetic waves from radio to x-rays. Efficient sources of radiation haveappeared only in the last two decades, primarily due to the development of laserswith ultrashort pulses. Excited by laser pulses, terahertz (THz) radiation is promis-ing for applications in biology and medicine because of the following importantfeatures: (1) many vibrational transitions of biomolecules are found in this range;(2) the heterogeneity of tissues that causes strong scattering of electromagneticradiation in the visible and NIR does not cause measurable scattering in theTHz range; (3) the refraction of different types of tissues varies greatly; and (4)


410 Chapter 8

Figure 8.34 Terahertz spectral range.

excitation by ultrashort pulses allows one to explore a wide range of frequenciesin a single measurement and provide high temporal resolution.178 Therefore, thedevelopment of THz spectroscopic methods for studying tissues, providing detec-tion and imaging of metabolic and pathological processes, has recently been ofgreat interest. Also, THz spectroscopy allows, in a single measurement, the deter-mination of the complex index of refraction of the medium under study, which isimportant for the development of a functional THz tomography with high sensi-tivity to changes in the concentration of metabolites and accurate marking of theboundaries of the pathological process.

To generate THz pulses, several methods can be used. Typically, photoconduc-tive dipole antennas, a semiconductor surface, or nonlinear crystal work as THzpulse generators. In the first two methods, radiation is generated by the formationof transient photocarriers in a semiconductor irradiated by short light pulses and bythe photocurrent pulse caused by the action of external or internal electric fields.For a nonlinear crystal, the optical rectification phenomenon is used when a signalis generated in a different frequency in the THz range.

Terahertz pulses can be detected by a similar photoconductive antenna or byusing the electro-optical effect in a nonlinear crystal. During propagation, theTHz pulse induces birefringence in the crystal; at a given instant, the polarizationstate of the probe laser pulse changes proportionally to the THz field amplitude.Experimentally, the power difference of orthogonally polarized components of theprobe laser pulse or a current induced in the antenna, depending on the time delaybetween terahertz and optical probe pulses, are measured. The sensitivity of thedetector, as well as the efficiency of THz wave generation is defined by phase-matching conditions and nonlinear susceptibility of the crystal, its length, andduration of the laser pulse. In general, when a semiconductor device is replacedby a nonlinear optical device, the frequency range of a spectrometer is shifted fromthe lower (0.5 ± 0.45 THz) to the higher frequency region (2 ± 1.5 THz).

One of the principles of THz time-domain spectrometry upon excitation bya femtosecond laser radiation is presented in Fig. 8.35.178 The type of THz gen-erator and detector is selected depending on the nature of the absorption of thesample and the frequency range of interest. For example, in Ref. 178, the authorsused 90-fs laser pulses at 790 nm, a low-temperature grown GaAs semiconductorsurface as a THz generator, and a 0.3-mm-thick <110> ZnTe crystal as an electro-optical detector. By using the Fourier transform of the temporal pulse profile, thespectrum of the complex index of refraction containing information about the real



Figure 8.35 Principle (a) and detailed schemes (b) of terahertz time-domain spectrometerat excitation by a femtosecond laser (see Ref. 178).

part of the index of refraction and absorption coefficient (imaginary part of indexof refraction) of the medium can be calculated. In most of the experimental studiespresented in Ref. 178, a 50-ps sampling time of the signal with 1024 counts and300 ms acquisition time of each count were provided. This allowed for perform-ing more than 103 measurements with the SNR in the spectral range from 0.3 to2.5 THz with a spectral resolution of 10 GHz. The laser and terahertz pulses hada repetition time period of 12 ns; the energy of the THz probing pulse was 10−13

J. Such low pulse energy should not damage any tissue. Even in the case of res-onant absorption, only a small fraction of the spectral components of the pulse isabsorbed in the sample.

A specific feature of pulsed THz spectroscopy is the possibility of directlymeasuring electromagnetic field magnitude and direction, which contains phaseinformation. To calculate the optical properties of tissue, it is necessary to recon-struct optical parameters from the measured transmission spectra, T(ω). From theexperiment and subsequent Fourier transform of the temporal profiles of pulses, weobtain the incident THz pulse amplitude, Eref(ω), and the amplitude, Esample(ω),


412 Chapter 8

of the transmitted pulse. Then the transmission coefficient of the sample can bereproduced as

T(ω) = Eref

Esample= T0(ω) · FP(ω) · RL(ω) , (8.70)

where T0(ω) provides basic information about the medium through which the THzpulse is travelling (absorption coefficient and index of refraction):

T0(ω) = exp{−i

(nsample − nair

)dω

c

}; (8.71)

FP(ω) describes the reflections of pulses in parallel plate and Fabry–Perot modes:

FP(ω) ={

1 − R2 (ω) exp(−i2nsampled

ω

c

)}−1; (8.72)

RL(ω) describes the reflection losses at the boundaries of the sample:

RL(ω) = 4nsamplenair(nsample + nair

)2 = 1 − R2 (ω) . (8.73)

Here, we use the complex refractive index, denoted as n(ω) = n′(ω) − i · n′′(ω)for the medium in which the absorption is accounted for by the imaginary part,n′′(ω) = α(ω) · c/ω;ω = 2πf is the angular frequency, d is the sample thickness,R(ω) = (nsample − nair)/(nsample + nair) is the complex reflection coefficient, c is thespeed of light, and nsample and nair are the refractive indices of the sample and air,respectively, nair ≈ 1;α is the absorption coefficient for the field, which is twiceless than the power absorption coefficient.

Assuming that RL (ω) ≈ const and FP (ω) ≈ 1, we can use Eq. (8.70) todetermine

α(ω) = 1

d

{ln |T (ω)| + ln

[1 − R2

av

]}, (8.74)

where Rav = (nav − 1)/(nav + 1) is the average reflection coefficient, nav is the realpart of the refractive index of the sample averaged in the range of measured fre-quencies. The average refractive index, nav, is determined by the time delay, �t, ofpulse propagating through the sample:

nav = 1 + c · �t

d, (8.75)

and the frequency dependence of the refractive index, n′(ω), is calculated from theexpression

n′(ω) = 1 + arg{T (ω)} · c

ωd. (8.76)

In a more rigorous approximation, one is able to account for reflections on theinterfaces of the sample, the so called, Fabry–Perot modes. This is important in the



case of a large refractive index of the sample material and its preparation as a thinplate, e.g., upon measurement of sliced tooth specimens or compressed tablets ofsugars and other biologically important compounds.

For the analysis of the characteristic absorption bands of substances found intissues or biological fluids, it is possible to draw a simple model for the dielectricfunction (permittivity) as a sum of Lorentz oscillators:

ε(ω) = ε0 +∑

j

fjω2j

(ω2j − ω2) − iγjω

, (8.77)

where ωj,γj, fj are the eigenfrequencies, dumping factors, and oscillator strengths,respectively; ε0 is the low-frequency permittivity; j is the number of resonances inthe selected frequency range.

For certain objects, transmittance spectroscopy is poorly applicable becauseof strong absorption (e.g., tissues containing water) or the large size of the objectin in vivo studies. In this case, reflectance spectroscopy is generally used when thecomplex reflection coefficient, Rp (ω), containing information about the absorptioncoefficient and refraction of the medium under study, is measured:

Rp(ω) = n2(ω) cos(θ) −√

n2(ω) − sin2(θ)

n2(ω) cos(θ) +√

n2(ω) − sin2(θ), (8.78)

which is characterized by amplitude Rp and phase ϕp; Rp = Rp · eiϕp , where theindex p indicates the p-polarization of the radiation in the plane of incidence, andθ is the angle of beam incidence measured from the normal. Here, the Fresnelformulas accounting for the complex index of refraction of the medium are used.

In the study of tissues, it is important to provide an appropriate probing depthand account for a layered tissue structure. Eq. (8.78) provides information onlyabout the interface (effective depth, where a reflected signal is formed, that is oftens of microns). However, during the study of layered tissues, such as skin, whenlayer thickness is approximately 100 μm or more, reflected pulses from differentsurfaces can be separated over time. Further, it is possible to apply Eq. (8.78) foreach layer with reflectance and transmittance of the medium (layer) between thesurfaces through which radiation passes twice. In the visible range, this techniqueis developed for a three-layer model of the skin,1059 which can be well adapted tothe terahertz range.

To study soft tissues, bioliquids, or aqueous solutions, attenuated total reflec-tion (ATR) spectroscopy is more appropriate. In this case, it is possible to controlthe penetration depth, δ, of the field into tissue or fluid:178

E(z) = E0 exp(− z

δ

), (8.79)

where

δ ≈ λ

π

(n2

pr sinθ − n2sample

) 12

. (8.80)


414 Chapter 8

Figure 8.36 Probing depth of ATR spectroscopy (see Ref. 178). Sample index of refractionis changed from 1 to 2.5; penetration depth, δ, of terahertz waves for different frequencies(a); different incident angles, θ (b); schematics of wave interaction with Dove prism (c).

For a silicon Dove prism (1.5 × 2 cm base, apex angle of 90 deg, refractiveindex of silicon in THz range at 3.42, practically negligible dispersion and absorp-tion), desirable sensitivity to water concentration in soft tissue can be obtained (seeFig. 8.36). The prism, placed in a collimated THz beam, conserves the beam direc-tion. The spectrum of transmitted radiation measured for a clean prism basis is usedas a reference. To measure the reflection spectra, the sample should be attached tothe prism base (or a drop of a liquid should be placed on the surface of the prism).

The primary advantage of the ATR method relative to reflection spectroscopyis the simplicity of reference spectra measurement; additionally, reflection ampli-tude is maximal. The primary difficulty of the ATR method is an optical contactproblem for hard sample studies. It has been shown that existence of a 10-μm layerof air between the prism surface and the matter under study is critical for gatheringinformation about tissue. For liquid samples, optical contact is always preferred.Equation (8.78) (Fresnel formula) describing reflection is also valid for ATR, butone should account for refraction of prism material, npr, and substitute n by n/npr

in this equation.The prism scheme is more convenient for soft tissue studies, and can be used

in in vivo studies, because a sample attaching to the prism base forms a flat, smoothinterface with the tissue sample. The in vivo measured ATR spectra of finger skin(male, 32 years old, Caucasian skin; skin site is within base of thumb) are presentedin Fig. 8.37. Because the ATR method provides measurements only for superficial



Figure 8.37 In vivo ATR reflection spectra (amplitude and phase spectral dependencies forATR reflection coefficient) of the human skin (average of six measurements, male, 32 yearsold, Caucasian skin, skin site is within base of the thumb) (see Ref. 178).

tissue layers up to 10–30 μm, the skin was probed only within the stratum corneum.In this layer, water content is minimal and equal to 15% (by weight); the maincontent is formed by proteins (70%) and lipids (15%).241 As a result, the skinreflection spectrum is considerably different from the water reflection. One cancontrol evanescent field penetration depth by changing the incidence angle; thus,the essential surface properties of the samples can be investigated with accuracy upto λ/50.

The study of biological tissues (Fig. 8.38) has shown that they have strongand comparable absorption, but their refractive indices are considerably differ-ent. The latter allows one to detect pulses reflected from different layers ofthe tissue if the signal-to-noise ratio in a time-domain terahertz spectrometer isimproved. Significant differences in the refractive index of various tissues allows

Figure 8.38 Absorption spectra of soft and hard tissues measured in vitro; values of theindex of refraction, n, were averaged for entire frequency range (see Ref. 178).


416 Chapter 8

Figure 8.39 Tooth absorption (a) and refraction (b) spectra; each line corresponds todifferent local tooth areas (see Ref. 178). Tooth dentine absorption spectrum in the fre-quency range from 0.2 to 2.5 THz can be approximated by the quadratic dependenceα(f ) = A + B1 · f + B2 · f 2 (empty circles). The averaged coefficients A, B1, B2 are 13, −21,and 36, respectively (for f measured in THz and α in cm−1). The refractive index dispersiononly weakly varies in different tooth samples, with much higher index of refraction for toothenamel.

the amplitude of reflected pulses from the boundaries of the various layers to bemeasured, which is important to identify signals carrying spectroscopic informa-tion and for constructing THz tomographic tools. The absorption and refractionspectra of different tissues have similar shapes. This is partly explained by thepresence of water in these tissues (the absorption spectrum of water has a similarshape, but the absorption coefficient of water is higher). The absorption spectraof different biological molecules also display similar shapes (linear or quadraticincrease in absorption and decrease in the refractive index with frequency). Theabsence of characteristic lines in the spectra of dry tissues can be explained by theoverlap of many spectral lines in the high-frequency range. Fat tissue is satisfacto-rily transparent, with mild dispersion characteristics of the absorption spectrum inthe region of 2–2.5 THz. Hence, by measuring the delay of THz pulses reflectedfrom the tissue interfaces between skin dermis and fat and fat/muscle layers, itappears to be possible to measure the thickness of the fat layer.

The monitoring of pathological changes in tooth tissues requires knowledgeabout the optical properties of tooth tissues in the terahertz frequency range. Thetransmission spectra of different tooth samples were measured locally (the diam-eter of the probe beam was 1 mm) by using the time-domain THz spectrometershown in Fig. 8.35 (see Fig. 8.39), including dentine areas with different concentra-tions and orientations of dentine tubules. Although the water content in dentine andenamel is relatively small, it affects their optical properties, which was also demon-strated by other methods. The absorption spectra of different samples withoutpathology are similar. In contrast, the refractive index averaged over measured fre-quencies is practically the same (n = 2.4) for all dentine samples and considerablylarger for enamel (n = 3.2). The refractive index dispersion varies only slightlyin different tooth samples. The absorption spectrum can be approximated by thequadratic dependence α(f ) = A + B1f + B2f 2 (at least in the frequency range from



0.2 to 2.5 THz), where the coefficient B2 plays the primary role. The averagedcoefficients A, B1, and B2 are 13, −21, and 36, respectively (for f measured in THzand α in cm−1). Terahertz tooth spectra may be important for the development ofterahertz tooth spectroscopy and tomography, particularly for diagnostics of certaindiseases related to water content in tooth tissues (tooth hardness) and for in vivomonitoring of tooth liquor and drug delivery.


Chapter 9

Controlling Optical Propertiesof Tissues

This chapter describes the fundamentals and advances of controlling tissue opticalproperties. As a major technology, the optical immersion method using exogenousoptical clearing agents (OCAs) is discussed. Water transport in a tissue, and tissueswelling and hydration upon its interaction with an OCA, are considered. Opticalclearing properties of fibrous and cell-structured tissues are analyzed by using spec-trophotometry, frequency domain, fluorescence, IR vibrational, Raman, terahertz,and polarization measurements, confocal microscopy and OCT, as well as nonlin-ear spectroscopy techniques, such as two-photon fluorescence, SHG, and CARS.In vitro, ex vivo, and in vivo studies of a variety of human and animal tissues,such as eye sclera, skin, muscle, fat, cerebral membrane (dura mater), digestivetract tissue, tendon, blood vessels, and blood, are presented. OCA delivery, tis-sue permeation, and skin reservoir function are discussed. Imaging of cells andcell flows in optical clearing is also discussed. Some important applications ofthe tissue immersion technique are described, such as glucose sensing and preci-sion tissue laser photodisruption, as well as other techniques of controlling tissueoptical properties, such as tissue compression and stretching, noncoagulating andcoagulating temperature action, and tissue whitening.

9.1 Fundamentals of Controlling Optical Properties of Tissueand Brief Review

Reflection, absorption, scattering, and fluorescence in living tissues and blood canbe effectively controlled by various methods.1, 6, 9, 10, 24, 26, 29, 48, 49, 54, 57, 61, 62, 76, 77,

90, 91, 95, 96, 162, 163, 166, 178, 200, 201, 221, 238, 264, 351, 392, 393, 452, 463, 467, 469, 555, 608, 621, 622, 654, 738,

764, 766, 769, 781, 791, 792, 810, 826, 991, 1006, 1010, 1059, 1177, 1191, 1194, 1257, 1258, 1271, 1292, 1293, 1306, 1331,

1336, 1343, 1359, 1362, 1383, 1387, 1389, 1399, 1400, 1418, 1439, 1470, 1486, 1487, 1521, 1547, 1578, 1579, 1609, 1811

Staining (sensitization) of biological materials is extensively used to study themechanisms of interaction between light and their constituent components, and fordiagnostic purposes and selective photodestruction of the individual components

419


420 Chapter 9

of living tissues. This approach underlies the diagnosis and photodynamictherapy (PDT) of malignant neoplasm, UV-A photochemotherapy of psoriasisand other proliferative disorders, angiography in ophthalmology, and many otherapplications in medicine.

In visible and NIR ranges, tissues and biological liquids are low absorbingbut highly scattering media (see Table 7.1). Scattering defines spectral and angularcharacteristics of light interacting with living objects, as well as its penetrationdepth; thus, optical properties of tissues and blood may be effectively controlledby changes in scattering properties. It is possible to control the optical (scattering)properties of living tissue by using various physical and chemical actions such ascompression, stretching, dehydration, coagulation, UV irradiation, exposure to lowtemperature, and impregnation by chemical solutions, gels, and oils. All of thesephenomena can be understood if we consider tissue as a scattering medium thatshows all optical effects characteristic to turbid physical systems. It is well knownthat the turbidity of a dispersive physical system can be effectively controlled bymatching the refractive indices of the scatterers and the ground material. This isdesignated the optical immersion technique. Another possibility for controlling theoptical properties of a disperse system is to change its packing parameter and/orscatterer sizing (see Chapters 1–3).

In vivo control of tissue optical properties is very important for many medicalapplications. A number of laser surgery, therapy, and diagnostic technologiesinclude tissue compression and stretching for better transportation of a laserbeam to underlying layers of tissue. The human eye compression techniqueallows one to perform transscleral laser coagulation of the ciliary body andretina/choroid.392, 769, 1257 The possibility of selective translucence of the uppertissue layers should be very useful for developing eye globe imaging techniquesand for detecting local inhomogeneities hidden by a highly scattering medium infunctional tomography. Results on the control of human sclera optical properties bytissue impregnation with OCAs, which are typically hyperosmotic chemical agents,such as x-ray contrast (trazograph or hypaque), glucose, and PEG, were alsoreported.6, 24, 61, 77, 200, 221, 238, 781, 810, 949, 1338, 1613, 1615, 1623, 1627, 1686, 1687, 1697, 1728, 1729, 1743,

1758, 1766, 1811

In general, the scattering coefficient, μs, and scattering anisotropy factor, g,of a tissue is dependent on refractive index mismatch between cellular tissuecomponents: cell membrane, cytoplasma, cell nucleus, cell organelles, melaningranules, and extracellular fluid. For fibrous (connective) tissue (eye scleralstroma, corneal stroma, skin dermis, cerebral membrane, vessel wall noncellu-lar matrix, female breast fibrous component, cartilage, tendon, and skeletal ormyocardium muscle), index mismatch of interstitial fluid and long strands ofscleroprotein (collagen-, elastin-, or reticulin-forming fibers), or muscle cell sar-coplasm and immersed filaments (structural proteins, such as myosin, actin, ortitin), is important.63, 64, 85, 96, 200, 222, 774, 776, 1613, 1615, 1621, 1622 Refractive index match-ing is manifested in the reduction of the scattering coefficient (μs → 0) andincrease of single scattering directness (g → 1). For skin dermis and eye sclera,μs reduction can be very high.200, 238, 766, 768, 781, 1613, 1615, 1630, 1729, 1768 For hematous


Controlling Optical Properties of Tissues 421

tissue like the liver, its impregnation by solutes with different osmolarity also leadsto refractive index matching and reduction of the scattering coefficient, but theeffect is not as pronounced as for skin and sclera because cells change size as aresult of osmotic stress.1621, 1622

Soft tissue is composed of closely packed groups of cells entrapped in a net-work of fibers through which interstitial fluid percolates. At a microscopic scale,the tissue components have no pronounced boundaries; thus, tissue can be consid-ered as a continuous structure with spatial variations in the refractive index. Aspreviously discussed, to model such a complicated structure as a collection of par-ticles, it is necessary to resort to a statistical approach (see Chapter 3). The tissuecomponents that contribute most to the local refractive index variations are the con-nective tissue fibers (either collagen-, elastin-, or reticulin-forming), which formpart of the noncellular tissue matrix around and among cells; and cell membrane,cytoplasmic organelles (mitochondria, lysosomes, and peroxisomes), cell nuclei,and melanin granules.63, 64, 85, 96, 200, 222, 774, 776, 1613, 1615, 1621, 1622 Figure 3.1 shows ahypothetical index profile formed by measuring the refractive index along a linein an arbitrary direction through a volume of tissue and corresponding to the sta-tistical mean index profile. The average background index, n0, is defined as theweighted average of refractive indices of the cytoplasm and the interstitial fluid,ncp and nis [see Eq. (3.2)]. The refractive index of a particle can be defined as thesum of the background index and the mean index variation, <�n>, described byEqs. (3.3)–(3.5).

For a two-component model, the mean refractive index of a tissue, n, is definedby the refractive indices of its scattering center material, ns, and ground matter, n0,n = fsns + (1 – fs)n0 [see Eq. (7.60)]. The ns/n0 ≡ m ratio determines the scatteringcoefficient. For example, in a simple monodisperse model of scattering dielectricspheres (Mie theory) μ′

s is defined by Eq. (7.27), where μ′s ∼ (m – 1)2. It fol-

lows from Eq. (7.27) that only a 5% increase in the refractive index of the groundmatter (n0 = 1.35 → 1.42), when that of the scattering centers is ns = 1.47, willcause a sevenfold decrease of μ′

s. In the limit of equal refractive indices for non-absorbing particles and background material, m = 1 and μ′

s → 0. In living tissue,the relative refractive index is a function of its physiological or pathological state.Independent of the specificity of tissue state, the refractive index of the scatterersand/or the background may be changed (increase or decrease); correspondingly,light scattering may increase or decrease.

Light scattering and absorption of particles that compose tissue or blood can becalculated by Mie theory. The relevant parameters are the size (radius a) of the par-ticles, their complex refractive index, the complex refractive index of the dielectrichost (ground material in tissues or plasma in blood), n0, and the relative refrac-tive index of the scatterers and the ground materials, m = n′

s/n0. The imaginarypart of the complex refractive indices is responsible for light losses attributableto absorption. Mie theory yields the absorption and scattering efficiencies and thephase function from which the absorption and scattering coefficients, μs = ρσsca

and μa = ρσabs, and g are calculated; ρ is the density of scatterers (particles). The


422 Chapter 9

corresponding scattering and absorption cross sections, σsca and σabs, and g-factorare described by Eqs. (3.53), (3.54), and (3.55), respectively.

The transport scattering coefficient increases strongly with the ratio of the realpart of scatterer index and the background medium index, n′

s/n0, especially for0.1–1 micron-sized particles (see Fig. 6.2).1193, 1194 For fully matched refractiveindices of scatterers and background material, the scattering coefficient reduces tozero and the scattering anisotropy factor is maximal and approaches 1 for particleslarger than 1 μm.

However, in practice, total index matching cannot always be provided, so othermechanisms of tissue clearing may be essential. Sometimes, the action of hyper-osmotic chemical agents or strong mechanical compression may lead to reversibleor irreversible changes in the size of scatterers. The wavelength dependencies ofscattering parameters for systems with partially matched refractive indices of scat-terers and background (n′

s/n0 = 1.07) are shown in Fig. 6.3. This level of matchingis typical for many normal connective and cell-structured tissues. The spectral vari-ation in the relative index has been neglected in calculations, but may be relevantin practice. If particle size and ratio of refractive indices are fixed, the wavelengthdependencies are caused by spectral variations in the ratio of the wavelength tothe particle size. For particles with a similar refractive index to that of the host(see Fig. 6.3), the scattering coefficient of the particle systems with very small orlarge diameters of particles is almost independent of the wavelength in the rangefrom 400 to 800 nm, whereas that of a system with intermediate-diameter par-ticles decreases with wavelength. The same tendency in wavelength dependence(no dependence for very small and large scatterers, and decreased dependence forintermediate diameters) is expected for the scattering anisotropy factor.

It follows from this consideration that reduction of scattering may be associatednot only with refractive index matching, but also with changes in the sizing of thescattering system. Both aggregation to large particles and disaggregation to smallparticles will lead to scattering damping, but the scattering anisotropy propertiesof the newly formed system should be quite different. The latter can be used forunderstanding the tissue clearing mechanisms associated with particle sizing andrefractive index matching. Conceptually, for many situations, the leading mecha-nism of tissue clearing might be refractive index matching because the equalizingof refractive indices of scatterers and surrounding media always takes place at tis-sue immersion, dehydration, or compression, and the sensitivity of the scatteringproperties to refractive index matching is very high.

As a particle system, whole blood shows pronounced clearing effects, whichmay be accompanied by induced or spontaneous aggregation and disaggre-gation processes as well as RBC swelling or shrinkage upon the applicationof biocompatible clearing agents with certain osmotic properties.200, 1009, 1010,

1331, 1336, 1359, 1646, 1650, 1700, 1702

It is possible to achieve marked impairment of scattering by means ofintratissue administration of appropriate OCAs. Conspicuous experimental opti-cal clearing in human and animal sclera; human, animal, and artificial skin; humangastrointestinal tissues; and human and animal cartilage and tendon in the visible



and NIR wavelength ranges induced by the administration of x-ray contrast agents(verografin, trazograph, and hypaque); glucose; propylene glycol; polypropyleneglycol-based polymers (PPGs); PEG; PEG-based polymers; glycerol; and othersolutions has been described in Refs. 24, 61, 77, 162, 163, 166, 200, 221, 238,467-469, 555, 621, 622, 766, 781, 791, 792, 810, 826, 1293, 1306, 1319, 1332,1418, 1439, 1486, 1487, 1547, 1578, 1613–1615, 1623–1640, 1642–1645, 1651,1652, 1662, 1673, 1674, 1676, 1677, 1685–1698, 1702–1705, 1706–1709, and1714–1811.

Coordination between refractive indices in multicomponent transparent tis-sues showing polarization anisotropy (e.g., cornea) leads to its decrease.5, 10, 200

In contrast, for highly scattering tissue with hidden linear birefringence or opti-cal activity, its impregnation by immersion agents may significantly improvethe detection ability of polarization anisotropy due to reduction in backgroundscattering.200, 621, 622, 1697, 1698

Concentration-dependent variations in scattering and transmission profiles inα-crystalline suspensions isolated from calf lenses are believed to be related toosmotic phenomena.1618 Osmotic and diffusive processes that occur in tissuestreated with verografin, trazograph, glucose, glycerol, and other solutions are alsoimportant.200, 238 Osmotic phenomena appear to be involved when optical proper-ties of biological materials (cells and tissues) are modulated by sugar, alcohol, andelectrolyte solutions. This may interfere with the evaluation of hemoglobin satura-tion through oxygen or identification of such absorbers as cytochrome oxidase intissues by optical methods.1621, 1622

Experimental studies on the optical clearing of normal and pathological skinand its components (epidermis and dermis) and the management of reflectance andtransmittance spectra using water, glycerol, glycerol–water solutions, glucose, sun-screen creams, cosmetic lotions, gels, and pharmaceutical products were conductedin Refs. 57, 306, 383, 469, 555, 766, 826, 1336, 1418, 1547, 1578, 1610, 1613–1615, 1626–1632, 1634, 1635, 1638, 1640, 1643, 1645, 1653, 1691, 1695, 1702,1703, 1706–1709, 1711, 1714, 1715, 1717–1724, 1726, 1730–1736, 1738, 1739,1741, 1742, 1744, 1746–1757, 1760–1765, 1767, 1776, 1781, 1785–1791, 1801,1802, 1808, and 1809. The control of skin optical properties was related to theimmersion of refractive indices of scatterers (components of keratinocytes in epi-dermis; collagen and elastic fibers in dermis) and ground matter, and/or reversiblecollagen dissociation.200 In addition, some of the observed effects appear to havebeen attributable to the introduction of additional scatterers or absorbers into thetissue or, conversely, to their washing-out.

A marked clearing effect through hamster,766 porcine,1720 and human1336, 1630,

1632, 1638 skin; human and rabbit eye sclera;61, 1625 and rabbit dura mater1439

occurred for an in vivo tissue within a few minutes of topical application (eye, duramater, skin) or intratissue injection (skin) of glycerol, glucose, propylene glycol,trazograph, and PEG, and PPG polymers.

Albumin, a useful protein for index matching in phase contrast microscopyexperiments,1360, 1383, 1619, 1620 can be used as the immersion medium for tissue studyand imaging.58, 96 Proteins smaller than albumin may offer a potential alternative


424 Chapter 9

because of the relatively high scattering of albumin. Occasionally, medical diagno-sis or contrasting of a lesion image can be provided by the enhancement of tissuescattering properties by applying, for instance, acetic acid, which has been suc-cessfully used as a contrast agent in optical diagnostics of cervical tissue.58, 96,

1663, 1668, 1812, 1814 It has been suggested that the aceto-whitening effect in cervicaltissue is attributable to the coagulation of nuclear proteins. Therefore, an aceticacid probe may also prove extremely significant in the quantitative optical diagno-sis of precancerous conditions because of its ability to selectively enhance nuclearscatter.58, 96

Evidently, the loss of water by tissue seriously influences its optical properties.One of the major reasons for tissue dehydration in vivo is the action of endogenousor exogenous osmotic liquids. In in vitro conditions, spontaneous water evaporationfrom tissue, tissue sample heating at noncoagulating temperature or freezing in arefrigerator, impel tissue to lose water. The action of hyperosmotic OCAs alsoleads to tissue dehydration, which may be strong.200, 1742, 1752 Typically, in visibleand NIR, far from water absorption bands, the absorption coefficient increases bya few dozen percent and scattering coefficient by a few percent due to more closepacking of tissue components caused by its shrinkage. However, the overall opticaltransmittance of a tissue sample increases owing to the decrease of its thickness bydehydration.764, 765 Specifically, in the vicinity of strong water absorption bands,the tissue absorption coefficient decreases due to a lower concentration of waterdespite the higher density of tissue following dehydration.

It is possible to significantly increase transmission through a soft tissue bysqueezing (compressing) or stretching it.200, 1059, 1319, 1617, 1803, 1807 The optical clarityof living tissue is attributable to its optical homogeneity, which is achieved throughthe removal of blood and interstitial liquor (water) from the compressed site. Thisresults in a higher refractive index of the ground matter, whose value becomessimilar to that of scatterers (cell membrane, muscle, or collagen fibers) [see Eq.(7.27)]. Closer packing of tissue components at compression makes the tissue aless chaotic and more organized system, which may scatter less due to coopera-tive (interference) effects.654, 1616 Indeed, the absence of blood in the compressedarea also contributes to altered tissue absorption and refraction properties. Certainmechanisms underlying the effects of optical clearing and changing of light reflec-tion by tissues upon compression and stretching were proposed in Refs. 61, 62, 200,654, 768, 769, 1059, 1257, 1319, 1341, 1616, 1628, 1629, 1678, and 1803–1807.

Long-pulsed laser heating induces reversible and irreversible changes in theoptical properties of tissue.764, 765, 1662 In general, the total transmittance decreasesand the diffuse reflectance increases, showing nonlinear behavior during pulsedlaser heating. Many types of tissues slowly coagulated (from 10 min to 2 h) in a hotwater or saline bath (70–85◦C) exhibit increases in their scattering and absorptioncoefficients (see Table 7.1).

UV irradiation causes erythema (skin reddening), stimulates melanin syn-thesis, and can induce edema and tissue proliferation if the radiation dose issufficiently large.54, 1059, 1656, 1657 These photobiological effects may all be respon-sible for variations in the optical properties of skin and need to be taken into



consideration when prescribing phototherapy. Also, UV treatment is known tocause color development in the human lens.794

Natural physiological changes in cells and tissues are also responsible for theiraltered optical properties, which may be detectable, and thus, used as a measureof these changes. For example, measurements of the scattering coefficient allowone to monitor glucose166, 467, 469, 534, 991, 996, 999, 1006, 1008, 1191, 1192, 1650, 1683, 1684, 1761, 1765

or edema1682 in the human body, as well as blood parameters.763 A nearly parabolicdependence between the scattering coefficient and Hct values in thin blood layershas been demonstrated [see Eq.(3.23)].763 Many papers report the optical charac-teristics of blood as functions of hemoglobin saturation with oxygen. Alterationsto the optical properties of blood caused by changes in Hct value, temperature, andparameters of flow can be found in Tables 7.1–7.4 and 7.6.

9.2 Tissue Optical Immersion by Exogenous Chemical Agents

9.2.1 Principles of optical immersion technique

Let us consider the principles of the optical immersion technique based on theimpregnation of a tissue or dilution of blood by a biocompatible chemical agent,which also may have certain hyperosmotic properties. Any connective (fibrous) tis-sue can be effectively impregnated by a liquid agent or its solution. As an exampleof fibrous tissue, human sclera will be analyzed.

A model of the human sclera in a local region can be represented as a slab withthickness d that is filled by thin and long dielectric cylinders (collagen fibers) withaverage diameter ∼100 nm and refractive index nc = 1.474 (see Fig. 9.1).238, 791, 792

The cylinders are located in planes that are parallel to the slab surface, but withineach plane, their orientations are random (see Fig. 3.5). The space between col-lagen fibers is filled by homogeneous ground substance with refractive index n0

= 1.345. A considerable mismatch in refractive indices between collagen fibersand ground substance makes the system turbid, i.e., causes multiple scattering andpoor transmittance of propagating light. The refractive index of the backgroundis a controlled parameter and may be changed in the range from 1.345 to 1.474,which transitions the system from multiple to low-step or even single-scatteringmode. For nc = n0 = 1.474, the medium becomes totally homogeneous and opticallytransparent if the absorption of scatterers is small.

The described model of tissue is applicable to any fibrous tissue, includingskin dermis and muscle. Indeed, refractive indices and fiber diameters and theirspacing should be changed. The transmission of collimated light by a tissue layerof thickness z is defined by the Bouguer−Beer−Lambert law [see Eq. (1.1)]:

Tc = I(z)/I0 = exp(−μtz), (9.1)

where I0 and I(z) are the intensities of the incident and detected light, respec-tively; μt = μa + μs is the attenuation coefficient. As listed in Table 7.1 for thehuman sclera at wavelength λ = 800 nm, the absorption coefficient μa

∼= 1.6 cm−1

and reduced scattering coefficient μ′s = μs(1 − g) ∼= 38 cm−1. For g = 0.9, μs

∼=380 cm−1.


426 Chapter 9

Figure 9.1 Schematic representation of human scleral sample and the geometry of lightirradiation (see Ref. 238).

Owing to the fibrous structure of the sclera, it is quite reasonable to assumethat the dynamics of fluid diffusion within the tissue can be approximated by freediffusion.238, 1685, 1815 Therefore, to describe the dynamics of the change in refrac-tive index and corresponding decrease in the scattering coefficient when a chemicalagent diffuses within the interfibrillar substance of a tissue, we used a model of freediffusion with the approximate solution of diffusion equation238, 1815

∂Cf(x, t)

∂t= Df

∂2Cf(x, t)

∂x2, (9.2)

where Cf(x, t) is the fluid concentration, Df is the coefficient of diffusion, and x isthe spatial coordinate. This equation is applicable for cases in which the rate ofthe process is not limited by membranes, such as the diffusion of substances inthe interfibrillar space or when a substance in solution has a high rate of perme-ation through membranes.1815 For a plane slab with thickness d, which is placed atmoment t = 0 in a solution with initial concentration of the agent Ca0 [initial con-centration of the agent within the slab is equal to 0; i.e., t = 0; 0 ≤ x ≤ d; Ca(x, 0)= 0; boundary conditions are Ca(0, t) = Ca(d, t) = Ca0], Eq. (9.2) has the followingsolution describing the time-dependent distribution of agent concentration withina sample:238, 1758, 1815

Ca(x, t) = Ca0

{1 − 4

π

[exp

(− t

τ

)sin

(πx

d

)+ 1

3exp

(−9t

τ

)sin

(3πx

d

)

+1

5exp

(−25t

τ

)sin

(5πx

d

)+, ...

]}, (9.3)



where

τ = d2

π2Da, (9.4)

Da is the agent diffusion coefficient.The ratio of the amount of dissolved matter, mt, at moment t to its equilibrium

value, m∞, is defined as1815

mt

m∞=

∫ d0 Ca(x, t)dx

Ca0d

= 1 − 8

π2

{exp

(− t

τ

)+ 1

9exp

(−9t

τ

)+ 1

25exp

(−25t

τ

)+, ...

}. (9.5)

This ratio, in turn, defines the volume-averaged concentration of an agent,Ca(t), which, in the first-order approximation has the view238, 1652, 1685

Ca(t) = 1

2

∫ d

0Ca(x, t)dx ∼= Ca0

[1 − exp

(− t

τ

)], (9.6)

Equations 9.3 through 9.6 allow one to determine the time-dependent concentra-tion of chemical agents with relatively low molecular weight at depth x within atissue sample, or time variations of the total amount of these agents in the sam-ple if the diffusion coefficient, Da, of these molecules in tissue is known. On theother hand, measurement of Ca(t) makes it possible to estimate the Da value ofimplanted molecules in the interstitial fluid of the tissue. For low molecular weightcompounds, the values of their diffusion coefficients in their own media are approx-imately 10−5cm2·s−1; for water, Da = 2.5·10−5cm2·s−1, and Da = 0.5·10−5cm2·s−1

for saccharose.1815

When an agent is administrated through only one sample surface, this situationalso may take place for in vivo topical agent application and Eq. 9.6 is still valid,but with another expression for the characteristic diffusion time:1758

τ = 4d2

π2Da. (9.7)

Equations (9.3)–(9.7) were received for diffusion through a homogeneous slab.Because of its fibrous structure, a tissue can be presented as a porous material thatleads to modification of the chemical agent diffusion coefficient

Da = Dai

p. (9.8)

Here, Dai is the chemical agent diffusion coefficient within the interstitial fluid andp is the porosity coefficient, defined as

p = V − VC

V, (9.9)


428 Chapter 9

where V is the volume of the tissue sample and VC is the volume of collagen fibers.To describe the diffusion of larger molecules, the theory of hindered diffusion

through a permeable membrane should be used.238, 1685, 1815 Based on Fick’s law,which limits the flux of matter, J (mol·cm2·s−1), to the gradient of its concentration:

J = −DadC

dx, (9.10)

for stationary transport of matter through a thin membrane of thickness l, wehave1815

J = Pa(C1 − C2), (9.11)

where Pa = Da/l is the coefficient of permeability, and C1 and C2 are theconcentrations of molecules in two spaces separated by a membrane.

Using Eqs. (9.10) and (9.11), it is possible to determine variations in the con-centration of molecules inside a closed space with volume V, surrounded by apermeable membrane with area S by using the following equation:1815

dC2

dt= PaS

V(C1 − C2). (9.12)

For a large external volume when C1 can be considered as a constant, Eq. (9.12)has an approximate exponential solution in a similar form to Eq. (9.6),1815 withC2 = Ca, C1 = Ca0, and

τ = V

PaSor

Rl

3Dafor a spherical membrane, (9.13)

where R is the radius of the membrane (of a cell or tumor necrotic core).Upon tissue impregnation by a chemical agent, the refractive index of the

background (interfibrillar) media, n0, is a time-dependent function of the agentconcentration, which penetrates into a sample, Ca(t), and is defined by Eq. (9.6).The time-dependent volume fraction of the agent within the tissue sample fa is pro-portional to its concentration, Ca, thus, by using the law of Gladstone and Dale [seeEq. (3.1)], we can write

n0(t) = n0i(t)f0(t) + nafa(t), (9.14)

where f0(t) + fa(t) = 1, n0i is the initial (intrinsic) index of refraction of the groundmedium prior to tissue impregnation by an agent. For application of nonosmoticor low-osmotic agents, the initial refractive index of the interfibrillar space can beconsidered as independent of time n0i(t) ∼= n0i(t = 0).



The expression for the scattering coefficient, derived for a system of non-interacting thin cylinders with a number of fibrils per unit area, ρs, has theform238, 1685

μs∼= ρs

(π5a4n3

0

λ30

)(m2 − 1)2

[1 + 2

(m2 + 1)2

], (9.15)

where ρs = fcyl/πa2, fcyl is the surface fraction of the cylinders’ faces, a is thecylinder radius, m = ns/n0 is the relative index of refraction of cylinders (scatterers)to the background (interfibrillar space), and λ0 is the wavelength in vacuum.

As a first approximation, it is reasonable to assume that the radii of the scat-terers (fibrils) and their density cannot be significantly changed by chemicals (notissue swelling or shrinkage take place), the absolute change of n0 is not very high,and variations in μs are caused only by the change in the refractive index of theinterstitial (interfibrillar) space with respect to refractive index of the scatterers.Then, considering that a majority of tissues have m ≈ 1, the ratio of the scatteringcoefficients at a particular wavelength as a function of refractive index ratio m canbe written in the following form:238, 1685

μs2∼= μs1

(m2 − 1

m1 − 1

)2

. (9.16)

Indeed, this relation describes changes in tissue scattering properties attributableto a refractive index match or mismatch caused by changes in refractive indicesof the scatterers, the background, or both. A similar equation for Mie sphericalparticle systems follows from Eq. (7.27). Owing to square dependence, the sen-sitivity to index matching is very high; for instance, for m1 = 1.1 and m2 = 1.01,μs2

∼= 0.01μs1.For the immersion technique, the refractive index of the scatterers, ns, is usually

kept constant during tissue impregnation by an agent. Thus, we can use Eq. (9.14)to rewrite Eq. (9.16) in a form that is specific for tissue impregnation by an agentwith weak osmotic strength:

μs(t) = μs(t = 0) ×[

nsn0(t) − 1

]2

[ns

n0(t=0) − 1]2 . (9.17)

A more rigorous approach to calculate the scattering coefficient must be basedon the consideration of light scattering by a densely packed systems of thindielectric cylinders or spherical particles with a particular size distribution (seeChapters 1–3).

To estimate changes in tissue collimated transmittance caused by agent diffu-sion into a sample (see Fig. 9.2), Eqs. (9.1), (9.6), (9.14), and (9.17) should be usedin combination. Usually, immersion agents do not have strong absorption bandswithin the wavelength range of interest; thus, the absorption coefficient often maybe considered as a constant value. Indeed, the diffuse transmittance and reflectance


430 Chapter 9

Figure 9.2 Schematic representation of diffusion of the immersion agent into a tissuesample and light transmittance and scattering (see Ref. 1652).

as well as differential scattering characteristics (angular dependent scattering) fora tissue sample can be calculated if the behavior of g at optical immersion isknown. For Mie particles, the behavior of the g-factor attributable to refractiveindex matching can be analyzed by using Eq. (3.55). Corresponding calculationsfor the normalized reduced scattering coefficient and g-factor in the framework ofMie theory at different wavelengths and sizes of spherical scatterers are presentedin Figs. 6.2 and 6.3. To evaluate the relation of these calculations to OCA diffusionkinetics, one can use Eqs. (5.6), (5.14), and (5.17).

For in vivo studies, the backreflectance geometry of the measurements is vital,thus, Eqs. (9.6), (9.14), and (9.17) should be used with Eqs. (1.33) or (7.13), ortheir analogous equations used for interacting particles (see Chapters 1–3).

9.2.2 Water transport

Water balance in living tissues is one of the critical features of tissue condition. Attissue interaction with diffusion of external or internal molecules (proteins, sugars,alcohols, or polymers), tissue water should be involved in the molecular displace-ment processes.238 Water may be transported through a membrane (a certain tissuelayer) by an increased concentration of dissolved substance in one of two parts ofthe system. This happens for membranes more permeable for water than for dis-solved material and is called osmosis.238, 1815 The simplest case of water transportis when a membrane is permeable for water and totally unpermeable for moleculesof dissolved substances. However, in general, biological membranes are perme-able for both water and dissolved substances, but their degrees of permeability canbe quite different. This is the most complicated case to describe, but the situationbecomes simpler when water and dissolved substance permeate by the same pathsinside a membrane [such as interfibrillar spaces (pores) in fibrous tissues, whichare filled by the interstitial fluid containing water]. In this case, fluxes of water anddissolved substance interact, and each flux is dependent on the degree of interac-tion. Such interaction between the stationary fluxes can be accurately describedwithin the framework of irreversible thermodynamics.1815



Assuming that, in a system, there is only one type of dissolved molecule (i.e.,two fluxes move through a membrane: the water flux, JW, and dissolved matter,JS, which are proportional to the gradients of the chemical potential of water anddissolved matter), we can define the volumetric flux as1815

JV = JWVW + JSVS, (9.18)

where VW and VS are the partial mole volumes, in a form

JV = Lp(�p − σRT�CS). (9.19)

The flux of dissolved matter can be expressed as1815

JS = RTω�CS + CS(1 − σ)JV . (9.20)

Here, in Eqs. (9.19) and (9.20), Lp is the phenomenological coefficient indicatingthat the volumetric flux can be induced by rising hydrostatic pressure, �p;σ is thereflection coefficient [σ = −(Lpd/Lp), where Lpd is the phenomenological coef-ficient indicating, on one hand, the volumetric flux that can be induced for themembrane by the osmotic pressure RT�CS, and on the other, the efficiency of theseparation of water molecules and dissolved matter]; ω = (LD − Lpσ

2)CS, whereLD is the phenomenological coefficient characterizing the interchange flux inducedby osmotic pressure RT�CS; and CS is the average concentration of dissolvedmatter in two interacting solutions.

For the ideal partially permeable membrane, σ = 1. For membranes that arepermeable for molecules of dissolved matter, 0 < σ < 1. Equations (9.19) and(9.20) are valid for solutions with a low concentration. The volumetric flux for apartially permeable membrane described by Eq. (9.19) has the same mechanism ofcreation for both hydrostatic and osmotic pressure. Thus, for pores (fibrous) mate-rials (such as sclera, derma, muscle, and dura mater), it is expected that osmoticpressure induces the flux of water due to increasing hydrostatic pressure, but notthrough independent diffusion of water molecules caused by their concentrationgradient, because this entails considerably more resistance.1815

9.2.3 Tissue swelling and hydration

When applying a chemical agent, changes in the pH level of the environmentare very important, because swelling or shrinkage of tissue is expected.1816 Theswelling or shrinkage of a fibrous tissue is caused not only by the increase(decrease) of collagen (elastin) fibril size, but also by the increase (decrease) ofthe sample volume due to the rise (diminution) of the mean distance between fib-rils. It is well known that a change of the environmental pH to the more acid oralkaline sides from a colloid isoelectric point increases the degree of swelling.This is explained by the appearance of a positive or negative charge of colloidparticles, and therefore, by an increase in the degree of hydration. In general, theinitial pH condition of the tissue under study and the acid or alkaline nature of theimpregnated solution may lead to different dependencies of tissue thickness or vol-ume on chemical agent concentration (or time of impregnation) owing to changes


432 Chapter 9

in pH. Such behavior of a tissue sample should be taken into account when opti-cal measurements are used for the estimation of tissue properties. For example, theswelling or shrinkage was monitored for different initial conditions of scleral tissuesample preparation and solutions used.238, 555, 1625, 1686, 1687

A detailed study of the swelling of bovine sclera and cornea as a function ofpH and ionic strength of the bathing medium, using an equilibration technique thatprevents the loss of proteoglycans during swelling, is presented in Ref. 779. X-raydiffraction was used to measure the intermolecular spacing (IMS), fibril diametersand D-periodicity, and interfibrillar spacing (IFS) of collagen as functions of pH,ionic strength, and tissue hydration. Hydration, H, was defined as

H = Weightwet − Weightdry

Weightdry. (9.21)

It was found that both tissues swelled least near pH 4 (the isoelectric point), thathigher hydrations were achieved at low ionic strength, and that sclera swelledapproximately one-third as much as cornea under most conditions. The IMS in bothtissues decreased as the ionic strength increased; for scleral hydration H ∼= 2.5 andpH 7.0, IMS changed from 1.71 to 1.61 nm at 33-fold increase of ionic strength.The IMS experienced virtually no change from hydration; when H > 1, H = 3.2 isphysiological hydration; the corresponding mean values for the cornea were 1.75± 0.04 nm (n = 12) and for the sclera were 1.65 ± 0.02 nm (n = 9) at pH 7.4. Fordehydrated tissues (H = 0), the mean spacing was 1.25 ± 0.02 nm (n = 2) for thecornea and 1.27 ± 0.01 nm for the sclera.

The packing of fibrils, defined as IFS2, is another important parameter thatdetermines the control of tissue light scattering. For bovine cornea at physiologi-cal pH 7.4, the IFS2 decreased linearly from approximately 9.2 × 103 nm2 for ahighly hydrated tissue (H = 9.7) to approximately 2.1 × 103 nm2 at 10-fold lesshydration, and was equal to 4.2 × 103 nm2 at physiological H = 3.2. Both fibrildiameters [mean value 39.0 ± 1.1 nm (n = 6)] and D-periodicity [mean value64.50 ± 0.35 nm (n = 6)] of corneal collagen were essentially independent ofhydration and pH when hydration was above unity. This means that the fibrilspreferentially absorb the initial water, then remain at a relatively constant diam-eter. The remaining unchanged value of D-periodicity with hydration indicates nosignificant changes in the dimensions along the axis of the fibrils during swelling.These same tendencies are expected for the sclera, as a collagen-based medium.The volume of tissue at a given hydration may be expressed in terms of the dryvolume. The corresponding expression describing the volume of the cornea underhydration can be written as779

VH = VT(1 + 1.066 · H). (9.22)

This equation should apply equally to any volume of tissue, i.e., to the volumeassociated with each fibril.

The swelling of scleral tissue is following similar principles as those of corneawith the same isoelectrical point around pH 4, but at a lower level of swelling. As



noted in Ref. 779, there are several reasons for the low hydration of the sclera: thelow concentration of proteoglycans; high collagen content and larger fibrils witha smaller combined surface area than in the cornea; and structural peculiaritiesconnected with the fibrils arranged in bands, which may branch and interweave.

It was found by the authors of Ref. 779 that the high light scattering (lowtransmittance) of bovine cornea increased more rapidly with hydration (even belowphysiological hydrations) at pH values around the isoelectric point. For example,at pH 5, transmittance was approximately 98% for H = 2; 87% for H = 3.2; andonly 12% for H = 6. In contrast, the light scattering at higher pH values (6–8)changed slowly with hydration: transmittance was higher than 90% for each levelof hydration from 1 to 7, with the local maximum of transmittance of 98% forH = 4. According to current models, discussed in detail in Chapter 3, cornealtransparency at a given wavelength depends on certain structural parameters suchas fibril diameters, density of fibril packing, position of each fibril relative to itsneighbors, and refractive indices of collagen and the interfibrillar matrix; changesin one or more of these parameters may be sufficient to decrease or increase lightscattering.

From these studies, it follows that to improve corneal transparency, causedby stromal edema, hypertonic drops extracting sufficient water from tissue may beused. As shown in Ref. 779, sodium chloride should be better than other hypertonicpreparations for the treatment of corneal edema, because, if used frequently, it mayalso reduce swelling pressure in the stroma and decrease the fibril diameter.

The connection between H (mg water per mg dry tissue weigh) and corneald (in mm) is described by the following empirical formulas:1413, 1688, 1689

for rabbit cornea

H = 10 · d − 0.42, (9.23)

and for bovine cornea

H = 5.3 · d − 0.67. (9.24)

9.3 Optical Clearing of Fibrous Tissues

9.3.1 Spectral properties of immersed sclera

Normally eye sclera (see Section 3.6 and Fig. 3.24) is a turbid medium that isnontransparent in the visible range.768, 769 The origin of scleral spectra formationcan be understood on the basis of light scattering by a system of polydispersive,irregularly arranged collagen cylinders immersed in the ground substance with alower refractive index (see Chapter 3)791 and strong absorption bands.768, 769, 781

With natural thickness of 0.6–0.8 mm, this tissue shows multiple scattering andlooks like white matter. The transition from multiple to low-step/single scatteringcan be provided by drying a tissue sample768, 769 [Fig. 3.24(c)] or impregnating itby an immersion liquid.238, 781, 791, 1338, 1685, 1728, 1729, 1743, 1766, 1811

Figure 9.1 is a schematic representation of the human scleral sample struc-ture and geometry of light irradiation. Analytical approaches for describing the


434 Chapter 9

propagation of light in the sclera are valid only when strongly simplifying assump-tions are used, which make the model substantially less adequate. Thus, the directsimulation of photon migration in a medium using MC simulation was used forcalculating spectral characteristics and photon statistics.238, 791 The MC simulationof the sclera transmission and reflection spectra was conducted by using the prob-ability function for the free photon path, l (see Subsection 1.1.3). The orderingof scatterers (thin dielectric cylinders) was taken into account by using the exper-imental radial distribution function, g(r), obtained from electron micrographs ofthe human sclera770, 791 (Fig. 3.6). It was assumed that ordering affects only eachindividual event of the interaction between a photon and a particle. As the angulardependence of the scattered light intensity by a particle, the scattering indicatrixfor a fiber with a diameter corresponding to the modal value of the size distributionwas used: 120 nm. The effect of the multiple scattering is included automaticallyin the simulation procedure of the photon path by the MC method; in these sim-ulations, the spatial distribution of scattering centers was assumed as completelyarbitrary. This approximation is valid if the dimension of the region of local order-ing of scattering particles is far smaller than the mean free path of a photon in themedium, which takes place for the sclera.

The results of such modeling for a scleral sample (1 mm-thick, 120 nm meanfibril diameter, and 285 nm mean separation between collagen fibrils; refractiveindex, nc = 1.474; and initial refractive index of interfibrillar space, n0 = 1.345)are presented in Figs. 9.3–9.6. The collimated transmittance represents a fractionof photons leaving a tissue layer in a direction that differs from that of the inci-dent radiation no more than by ±0.5 deg, which corresponds to their entrance intothe aperture of a spectrometer. Total transmittance and diffuse reflectance spectra,accounting for real geometry (losing a certain amount of scattered light) of the inte-grating spheres used in experiments, were also calculated. The calculations wereperformed for different values of the refractive index of the background substance,from 1.345 to 1.450, corresponding to different levels of matching indices. It isclear that the model describes the major features of normal and immersed tissuespectra in the visible range. A comparison of calculated and experimental spec-tra (see Fig. 9.7) shows that refractive index matching can be considered as theprimary mechanism responsible for tissue-enhanced translucence.

The MC simulation technique allows one to describe the transition of tissuescattering mode from complete diffusion to coherence (ballistic photons dominate)caused by refractive index matching. This transition is accurately illustrated by thehistograms in Figs. 9.4–9.6. The numbers of backscattered and forward-scatteredphotons collected by integrating spheres were calculated. These histograms showthat for sclera with unmatched or slightly matched refractive indices (n0 = 1.370),there is a broad distribution of the number of scattering events (with the meanvalue of 25–30 collisions for NIR) undergone by forward-traveling photons, whileno ballistic photons (the coherent part of transmitted light) are visible. For fairlymatched refractive indices, certain ballistic photons come into being. In particu-lar, for moderately matched refractive indices (n0 = 1.410), the unscattered and



Figure 9.3 Collimated (a) and total (b) transmittance spectra as well as diffuse reflectance(c) spectra of the human sclera of 1 mm thickness calculated by Monte Carlo for differentrefractive indices matching a geometry very close to the experimental one (see Fig. 9.7);refractive index of collagen fibrils nc = 1.47 and interfibrillar material n0 = 1.35, 1.37, 1.39,1.41, 1.43, and 1.45 (see Refs. 651 and 791).

low-step scattered photons dominate in both directions—forward and back—witha mean number of collisions for the forward traveling NIR photons of 3–4 and arather extensive ballistic component. For strongly matched indices (n0 = 1.450),the ballistic component dominates and both scattering components in forward andbackward directions are small. In the NIR, the optical clearing of tissue and trans-formation of scattering mode from multiple to low, or even single steps, beginsmuch earlier than for visible light. A strong ballistic component formed at tissueclearing gives perspective to the coherent-domain diagnostic methods to be morewidely used in biomedicine.

The total transmittance, diffuse reflectance, and collimated transmittance weremeasured in the 200–2200 nm wavelength range by using commercially avail-able Varian Cary 5E, 500, or 2415 spectrophotometers with an internal integratingsphere.238, 766, 1636, 1637, 1685 To reconstruct the absorption and reduced scattering


436 Chapter 9

Figure 9.4 Distributions of the number, Nph, of forward (F) and backscattered (B) photonscalculated by Monte Carlo that have undertaken a definite number of collisions, Ns, beforeescaping the human scleral slab of 1 mm thickness (two integrating sphere geometry) forslightly matched refractive indices of collagen fibrils and interfibrillar material (nc = 1.474,n0 = 1.370): λ = 400 nm (a); λ = 600 nm (b); λ = 800 nm (c) (see Refs. 651 and 791).

coefficients of tissue from such measurements, the IAD1270 or IMC methods wereapplied.1625

For in vitro and especially in vivo studies of tissue optical clearing, fiber-optic grating-array spectrometers such as LESA-5, 6, 7 (BioSpec, Russia), andPC1000, PC2000, USB2000 (Ocean Optics Inc., USA) are suitable for fast spec-tra collection in a course of immersion agent action.1059, 1293, 1439, 1625, 1630, 1643, 1645,

1651, 1652, 1695, 1698 Typically, the spectral range of interest is from 400 to 1000nm and the spectrometer fiber probe consists of seven optical fibers. One fiber



Figure 9.5 Distributions of the number, Nph, of forward (F) and backscattered (B) photonscalculated by Monte Carlo that have undertaken a definite number of collisions, Ns, beforeescaping the human scleral slab of 1 mm thickness (two integrating sphere geometry) forpartly matched (midlevel) refractive indices of collagen fibrils and interfibrillar material (nc =1.474, n0 = 1.410): λ = 400 nm (a); λ = 600 nm (b); λ = 800 nm (c) (see Refs. 651 and 791).

transmits light to the object, and six fibers collect the reflected radiation. Themean distance between the irradiating and receiving fibers is approximately200 μm for PC1000 and LESA-6, and approximately 2 mm for LESA-5. Thespectrometers are calibrated by using a white slab of BaSO4 with a smoothsurface.

Spectra were measured in vitro with human sclera samples.238, 1685 The sclerawas carefully purified from ciliary body and retina, washed, and cut into pieces


438 Chapter 9

Figure 9.6 Distributions of the number, Nph, of forward (F) and backscattered (B) photonscalculated by Monte Carlo that have undertaken a definite number of collisions, Ns, beforeescaping the human scleral slab of 1 mm thickness (two integrating sphere geometry) forstrongly matched refractive indices of collagen fibrils and interfibrillar material (nc = 1.474,n0 = 1.450): λ = 400 nm (a); λ = 600 nm (b); λ = 800 nm (c) (see Refs. 651 and 791).

10 × 10 mm in area. The sclera sample was placed into a cell of volume 1 ml filledwith osmotic liquid or physiological solution. Three different types of chemicalagents were used for scleral optical clearing in Refs. 238 and 1685. The primaryexperiments were performed by using x-ray contrast agent trazograph (a deriva-tive of 2,4,6-triiodobenzene acid) with molecular weight of approximately 500,and its 60% and 76% solutions in water. Some measurements were performed fortwo optical clearing agents (OCAs) with quite different molecular weights, such as



Figure 9.7 Experimental spectra of human scleral samples measured for different timeintervals of administration of trazograph-60. Spectra were measured 1 min after the samplewas immersed in solution, and then at 2-min intervals. Measurement time for an individualspectrum, scanning from higher to lower wavelengths, was approximately 85 s. Collimatedtransmittance, Tc; sample thickness, 0.6 mm (a). Total transmittance, T t; sample thickness,0.7 mm (b). Diffusion reflection, Rd; sample thickness, 0.7 mm (heavy pigmented tissue)(c) (see Refs. 238 and 1685).

glucose (∼180) and polyethylene glycol (PEG) (6000 or 20,000). At room temper-ature measured by an Abbe refractometer, refractive indices of some of the agentswere as follows: trazograpth-60, n = 1.437; trazograph-76, n = 1.460; PEG (6000)solutions: n = 1.368 (0.4 g/ml), 1.394 (0.6 g/ml), 1.403 (0.8 g/ml), and 1.469(1.0 g/ml); glucose solutions: n = 1.363 (0.2 g/ml), 1.378 (0.3 g/ml), 1.391 (0.4g/ml), and 1.415 (0.54 g/ml). For the glucose–water solutions, the refractive index


440 Chapter 9

at any wavelength in the visible and NIR, where glucose has no strong absorptionbands, can be estimated by using Eq. (6.5) and (7.39).

The typical transmission spectra, Tc(λ) and T t(λ), and diffusion reflection spec-tra, Rd(λ) measured by the integrating sphere spectrophotometer for different timeintervals of trazograph-60 administration, are presented in Fig. 9.7.238, 1685 It is clearthat the untreated sclera is poorly transparent for visible and NIR light. Trazographadministration makes this tissue highly transparent: up to 70–75% at 600–800 nmfor the sample kept in solution for 7–10 min. In addition, its spectral reflectivitydecreased from 35–40% to 13–15% in this wavelength range.

In general, for many of measured samples, it can be concluded that foruntreated scleral samples transmittance was less than 1–2% in the range 400 to500 nm and increased up to 6–30% for NIR wavelengths, depending on the sam-ple thickness and pigmentation. Trazograph, or other agent administration, not onlyleads to increased transmittance but changes the form of the spectral curve: on aver-age, for the short wavelengths, collimated transmittance increased from 1–2 to 20%(10–20 times) and for the long wavelengths, from 20–30 to 50–80% (∼2.5 times).

For the optically cleared sclera, the collimated light makes the primary con-tribution to transmittance. Direct measurements performed for a 0.75-mm-thickscleral sample treated with trazograph-60 for 40 min showed that transmittance forthe detector acceptance angle of 30 deg, T30

∼= 35% at 400 nm and ∼= 85 % at 840nm, Tc

∼= 27% at 400 nm and ∼= 85% at 840 nm. Additionally, the CCD images ofa laser beam transmitted through the sclera at different levels of optical clearing,presented in Fig. 9.8, show the process of the formation of ballistic groups of pho-tons (see the center of the pattern) upon reduction of scattering multiplicity. Theseimages also qualitatively support the calculated statistics of photon interactions attissue clearing (Figs. 9.4–9.6).

The efficiency of tissue clearing depends on the concentration and temperatureof the solutions. For bovine sclera at room temperature (18.5◦C), the maximumcollimated transmittance at 450 nm is in the range Tcmax = 13% (trazograph-60),22% (glucose, 45%), 39% (trazograph-76), 46% [PEG (6000), 80%]; and at 700nm Tcmax = 73% (glucose, 45%), 76% (trazograph-60), 99% [trazograph-76 andPEGs (6000 and 20,000), 80%].1692 The maximal transmittance is achieved at 15–30 min. At physiological temperature, this time interval is considerably shortened.For example, for a PEG 20,000 solution (80%), the time interval for maximal tissueclearing changed from 27 min at 18.5◦C to 12 min at 38◦C.

The time-dependent collimated transmittance of a scleral sample measured at633 nm concurrently with trazograph-60 administration is presented in Fig. 9.9. Itshows the dynamics of tissue clearing. Similar characteristics were measured forglucose and PEG administration. The registration of the dynamic response of theintensity transmission can be used to estimate diffusion coefficients of the interact-ing fluids: water and agent (trazograph, glucose, glycerol, and PEG). Based on thetheoretical background given earlier, we can estimate the coefficient of diffusionof the agent by assuming that water and agent have the same paths for diffusion.The following set of equations gives simple algorithms for determination of the



Figure 9.8 Specklegrams recorded at two different moments of time in the far-field zonefor a sample of translucent human eye sclera irradiated with a focused beam of He-Ne laser(633 nm). Enhanced translucence was provided by trazograph-60 in a cuvette during 2.5(a) and 10 min (b) (see Ref. 555).

diffusion coefficient: Eqs. (9.1), (9.4), (9.6), (9.14), and (9.17). More sophisti-cated algorithms accounting for tissue swelling and shrinkage, and appropriate tothe inverse optical problem solving (IAD, IMC) measuring procedures, are alsoavailable.1177, 1625, 1651, 1652, 1686, 1729

Data for diffusion coefficient values of different samples of the human scleraare collected in Table 2 of Ref. 200. The estimated values of DT, calculated usingapproximately 30 magnitudes of Tc measured for different time intervals for eachsample, have quite reasonable rms errors and differences in mean values fromsample to sample. As shown in Fig. 9.9, rms values include the low-frequencyoscillations of Tc(t), which can be caused by spatial–temporal fluctuations of theagent diffusivity upon interacting with tissue structure. On average, the DT val-ues are not far from the values of Da for the diffusion of low-weight molecules inwater.1815

For the hyperosmotic agents, fluid transport within tissue is more complicatedbecause there are at least two interacting fluxes; thus, the model for describing these


442 Chapter 9

Figure 9.9 Time-dependent collimated transmittance (dots) of a 0.5-mm-thick scleral sam-ple measured at 633 nm concurrently with administration of trazograph-60 (see Ref. 238).Solid and dashed lines represent the mean value and the upper and lower limits of Tcobtained by calculating Tc using experimental data: DT = (1.46 ± 0.19) × 10−5 cm2s−1.

processes should be more complicated and should include monitoring of additionalmeasurement parameters, such as the refractive index of the chemical agent, tissueweight and/or thickness, and osmotic pressure in a process of tissue clearing. Suchmonitoring of the refractive index of trazograph-60 in a bath during a process ofscleral clearing gave 1.4370 (t = 0), 1.4321 (12 min), 1.4222 (20 min), and 1.4025(40 min). Measurements of the weight of tissue samples before and after admin-istration of the agents gave the following values: trazograph-60 (sample 5 × 8 ×0.6 mm3), 54 mg (t = 0) and 51 mg (34 min); glucose (40%, pH 3.5) (sample 10 ×11 × 0.5 mm3), 82 mg (t = 0) and 66 mg (20 min); PEG (6000) (1 g/ml) (sample 8× 10 × 0.5 mm3), 65 mg (t = 0) and 48 mg (60 min). Thus, the relative decreasesof the sample weight are 5.5% for trazograph-60, 15.5% for 40% glucose, and28% for PEG (6000). Both experiments with refractive index and weighting showdifferences in the osmotic properties of the agents and their tissue dehydration abil-ities, which are in the ranges of low (trazograph-60), midlevel (40% glucose), andhigh [PEG (6000)]. It follows from the experiment that in optical clearing of thesclera, trazograth-60 dominates the process of the replacement of interfibrillar fluid(mostly water) because trazograph-60 has a refractive index higher than water. Arather large reduction of refractive index in the bath with the sample indicates thatwater effectively escapes tissue and the small loss of sample weight indicates thatwater is replaced by trazograph-60. Thus, we may assume that, in the system, thereare two approximately equal fluxes moving through a tissue layer: the water flux,JW, directed out of a layer and a dissolved matter, JS, directed into a layer, whichare proportional to the gradients of the chemical potential of water and dissolvedmatter [see Eq. (9.19)].1815 For glucose and especially for PEG, dehydration playsan important role due to the inequality of two fluxes: JW out of a tissue layer isstronger than JS flux into a layer. Thus, structural changes of collagen fibrils andIFS caused by tissue dehydration and described in Subsection 9.2.3779 should beaccounted for in the tissue clearing model based on tissue dehydration.

The interaction of OCA penetrating inside a tissue with collagen fibrils maybe responsible for quasi-periodic low-frequency (3–4 min of period) oscillations



of the light transmittance that are clear in Fig. 9.9. The oscillating character ofthe tissue response may be explained as a multistep origin of fluid diffusion.238, 555

The first step of OCA penetration into tissue leads to refractive index matching ofinterstitial fluid and hydrated fibril collagen—the significant translucence of tis-sue growth. The second step is characterized by the interaction of OCA, containedwithin the renovated interfibrillar liquid, with fibril collagen, which leads to colla-gen dehydration and consequent growth of its refractive index; this slightly breaksdown optical matching and causes a slight decrease in transmittance. The subse-quent disbalance of water–OCA concentrations leads, in turn, to the penetrationof an additional amount of OCA into the sample, which reestablishes refractiveindex matching and corresponding light transmittance—this is the origin of thethird step. The individual inertia of each of these processes may establish quasi-periodic oscillations, with the period and amplitude depending on parameters ofthe nonlinear system. Rather regular oscillations of OCT image depth of hamsterand rat skin with periods close to 2.5 and 3.5 min, respectively, were also found attissue immersion by glycerol.1721

Measured values of osmotic pressure for trazograph-60 were equal to 4.3 and7.1 MPa for trazograph-76.238 For untreated sclera, the value of osmotic pressurewas equal to 0.74 MPa, which increased after the administration of trazograpth-60for 30 min up to 5.02 MPa. On one hand, the osmotic pressure causes the gen-eration and intensity of flows [see Subsection 9.2.2 and Eqs. (9.19) and (9.20)],but on the other hand, rather strong osmotic pressure may destroy tissue structure.A direct histological study showed that there are no serious, irreversible changesin the cellular and fibrous structure of the human sclera following a rather longperiod of OCA administration.1693 For example, for trazograph-60, this period is atleast approximately 30 min, after which rather minor changes in tissue structure,characterized by moderate tissue swelling, were observed.

The reversibility of tissue structure changes following OCA administrationalso demonstrate data in Fig. 9.10,555, 1694 which show that the multiple–single scat-tering transition (i.e., optical translucence or improvement of linear polarization)is reversible when the OCA bath is replaced by a physiological solution, and viceversa when the OCA is administrated again.

The theoretical and experimental results show that the administration of OCAsto the sclera affects the refractive index matching of the collagen fibrils and inter-fibrillar fluid, leading to dramatic changes (a reduction) in the scattering propertiesof the sclera. For different OCAs, refractive index matching can be implementedin different ways: (1) water can leave the interfibrillar space and exit the sample(dehydration); (2) the administered fluid can enter the tissue and fill up the inter-fibrillar space, and water can partly leave the interfibrillar space and partly exitthe sample. The first mechanism is characteristic only for highly hyperosmoticagents. For fibrous tissue, similar to sclera, the second mechanism is preferable forall tested chemical agents because their molecule sizes are much lower than themean cross section of interfibrillar space, which is approximately 185 nm, whenthe diameter of the largest molecule of PEG (20,000) should be less than 5 nm.Indeed, the structure of interfibrillar matrix and molecular structural properties


444 Chapter 9

Figure 9.10 Temporal dependencies for the values of mean speckle intensity, 〈Is〉, and itspolarization components, 〈I⊥〉 and 〈I||〉, measured in the paraxial region of a sample ofhuman sclera with a thickness of 0.4 mm and averaged over the scanning trajectory (1.5mm): 1, 2, 3, sequential measurements with a sample that was first placed in trazograph-60, then in physiological solution (0.9% NaCl), and then again in trazograph-60; λ = 633 nm(see Ref. 1694).

may influence diffusion; thus, the diffusivity of foreign molecules and correspond-ing strength of water flux is different for different agents. Water fluxes in thesclera were strongly induced by PEGs, midlevel by 40% glucose, and weakly bytrazograph-60 (see weight measurements).238

The dynamics of tissue optical clearing using OCA is defined by a character-istic time response of approximately 3 to 10 min. This agrees well with resultsobtained by Rol,769 but they used point-wise mechanical stress or local heat-ing induced by a laser beam. Actually, as follows from Eq. (9.19), osmotic andhydrostatic pressure caused, for example, by mechanical stress, have the samemechanism for inducing fluid flux, and the time response is defined by water diffu-sion through the interfibrillar space. Thus, optical clearing using local mechanicalstress should be generally equivalent to the action of a hyperosmotic agent, becauselocal stress collects water from the compressed site and diminishes the tissue layerthickness. In practice, optical clearing with OCAs may be more preferable thanmechanical stress, because there are more possibilities to control the time/spatialresponses and efficiency using various chemical agents; in addition, the function ofthese agents may be combined (tissue optical clearing and treatment).

These results are general and can be used to describe many other fibrous tis-sues. The human sclera can be considered as a living scattering etalon in the visiblerange, like white glass (see diffuse reflectance spectra in Fig. 9.7). For example,due to a simpler structure and more stable and controllable parameters of sclera incomparison with skin, light scattering technologies of glucose monitoring designedfor skin measurements467, 469, 991, 1006, 1008 may be more effective for applicationto sclera. With this connection, it is interesting to analyze changes in the colorof sclera during clarification.622, 791 This change from transmission and reflectionspectra in Fig. 9.7 was quantitatively estimated by calculating the chromaticitycoordinates for the MKO 1964 color system. From the calculated color triangles,



Figure 9.11 Experimental setup for in vitro and in vivo measurements of the collimated lighttransmittance and reflectance spectra (see Ref. 1625). In vitro measurements: 1, opticalfiber; 2, aluminum jacket; 3, neutral filters; 4, sclera sample; 5, OCA; 6, 0.5 mm pinhole; 7,cuvette.

it follows that the native sclera has a reddish tint in the transmitted light; how-ever, this does not appreciably change the visual perception because of its very lowtransmission coefficient. During sclera clarification, its color whitens. In the diffusereflectance, the native sclera is white, as is visually observed. Upon clarification,the sclera color in the reflected light slightly shifts from white to bluish.

To more precisely study time-dependent transmittance and reflectance of tis-sue, a fiber-optic photodiode array or CCD spectrometer, providing fast collectionof spectra, should be used. This is especially important for the determination of dif-fusion coefficient in in vitro studies and in in vivo monitoring of tissue clarification.Using the fiber-optic photodiode array spectrometer shown in Fig. 9.11, detailedin vitro measurements for human sclera were conducted upon tissue impregnationby various solutions, such as glucose, trazograph, verografin, and propylene gly-col, which do not have strong absorbing bands within the spectral range of interest,400–800 nm.1651 In in vitro study, the conjunctiva and ciliary body, as well as theretina with choroid, were removed. The mean thickness of samples was approxi-mately 0.5 mm. They were fixed on a plastic plate with a 5 × 5 mm2 square aperture(effectively impregnated by a chemical agent via both surfaces of the sample) andplaced in a 5-ml cuvette filled with the solution under study.

To understand the mechanisms of scleral tissue optical clearing, the collimatedtransmittance spectra and change of the scleral sample weight were measured con-currently with the administration of glucose solution. Figures 9.12–9.14 illustratethe dynamics of transmittance spectra and typical weight change. It is clear that the


446 Chapter 9

Figure 9.12 Time-dependent collimated transmittance spectra of the human sclera sampleimpregnated by a 40%-glucose: (1) 10 s; (2) 1 min; (3) 2 min; (4) 3 min; (5) 4 min; (6) 5 min;(7) 6.5 min; and (8) 8.5 min after the scleral sample was immersed in 40% glucose (seeRef. 1625).

untreated sclera is a poorly transparent media for visible light. Glucose administra-tion makes this tissue highly transparent. As shown in Fig. 9.13, the characteristictime response of sclera optical clearing is approximately 5 min.

Based on these measurements and accounting for the use of commerciallyavailable 40% glucose from the drug store, which has a low pH of 3.5, the fol-lowing model of action of osmotically active liquid on a fibrous tissue seems tobe adequate. During the first stage, which takes place approximately 5 min after asample is placed in glucose solution, substantial optical clearing was accompaniedby a decrease in the sample thickness. Thus, we may suppose that optical clear-ing occurs due to two main mechanisms: (1) refractive index matching betweencollagen fibers and penetrated glucose; and (2) glucose osmotic action that dehy-drates tissue, resulting in up to 25% decrease of thickness. During the late stageof glucose administration, to the seventh minute, the optical clearing process sat-urates concentrations in the system, due to equilibration of fluids (glucose, water,proteins, and salts), and the thickness slightly increases. From the seventh to fif-teenth minutes, the inclusion of thickness change (increase to initial thickness) inoptical clearing is clearly shown on the background of the inclusion of saturatedmolecular fluxes; collimated transmittance slightly decreases, but still remainsvery high. Further tissue swelling with time up to 20% of the initial thickness tothe twenty-first minute does not seriously influence tissue transmittance. Despitethe complex behavior of tissue thickness following administration of this specificchemical agent—40% glucose at pH 3.5—thickness variations do not stronglyaffect optical clearing. Such nonmonotonous behavior of tissue thickness—initialshrinkage and late swelling—can be explained using results of Ref. 779, where it



Figure 9.13 Time-dependent collimated transmittance of the human sclera sample mea-sured at 420 nm (squares); 589 nm (circles); 630 nm (upward triangles); and 700 nm(downward triangles) concurrently with administration of 40% glucose (see Ref. 1625).

was experimentally shown that for bovine sclera, hydration (swelling) may changefrom H = 2.48 for pH 7, close to physiological, to H = 7.15 for pH 3. In our case,this means that at the first stage when tissue pH is close to physiological pH, itis not seriously affected by glucose (a small amount is penetrated into the sclera)and the dehydration of tissue is dominant due to osmotic action of glucose; how-ever, during the late stages of glucose administration due to the large amount ofglucose penetrating tissue and permeating the bath, the pH of the whole system oftissue/glucose bath decreases and swelling takes place.

These effects of tissue shrinkage and swelling are important but not dominantduring glucose action, thus the experimental data for the collimated transmittance(Figs. 9.12 and 9.13) and the time-dependent measurements of changes in tissuesample thickness under OCA action (Fig. 9.14) can be used to estimate the glu-cose diffusion coefficient in sclera.654, 1292 A detailed model of glucose transport infibrous tissue is described in Ref. 1652. Equations (9.1), (9.6), (9.14), and (9.17)are the basis for this model, which can be used for reconstruction of the diffusionconstant. The estimated average value of the diffusion coefficient of 40% glucosetransport in the scleral sample is equal to DG = (3.45 ± 0.46) × 10−6 cm2s−1

at temperature 20◦C. This value is not far from the values of Da for diffusion oflow-weight molecules (such as sucrose or glucose) in water at zero concentration(3.6–5.2) × 10−6 cm2s−1 at 12–15◦C.1815, 1817, 1818 When hyperosmotic agents areused, the diffusion coefficient should be similar to that of water diffusion in a tissue,because this is the primary flux in the system. For dependence on tissue structure,


448 Chapter 9

Figure 9.14 Calculated time-dependent thickness of the human sclera sample (MonteCarlo simulation was the best fit for the experimental data of collimated transmittance shownin Figs. 9.12 and 9.13) (see Ref. 1292).

this value should be equal to or greater than the value of diffusion coefficient ofwater in water, DW = 2.5 × 10−5cm2s−1.

Diffusion coefficient is a function of dimension and form of diffusingmolecule:1815

Da = const × M−S. (9.25)

For small molecules, S = 1/2, and for spherical molecules diffusing in water (largeproteins), S = 1/3. In general, parameter S for diffusion in water is in the range0.3–0.5, and for diffusion through a biological membrane, it is approximately 3.5.For example, changing molecular weight, M, from 45 to 122 during diffusion inwater changes the diffusion coefficient from 1.6 × 10−5 to 0.8 × 10−5 cm2s−1

(twofold); for the diffusion of the same molecules through a plasmatic membrane,the change is from 1.4 × 10−8 to 2.0 × 10−10 cm2s−1 (70-fold).1815

9.3.2 Scleral in vitro frequency-domain measurements

The dynamical response of optical properties (modulation depth and phase shift ofintensity modulation of backscattered light) of the human eye sclera with respect tointervals of OCA administration can be measured using a photon-density wave (fre-quency domain) technique (see Section 1.3).1626 When intensity of the light sourceis modulated at a frequency ω, a photon-density wave is induced in a scatteringmedium as follows:1, 4, 129

A(r) = Adc + Aacexp[−i(ωt−θ)], (9.26)

where Adc, Aac, and (ωt − θ) are the dc and ac components of the amplitude of thephoton-density wave and its phase, respectively.



Figure 9.15 Frequency-domain measurements. Time-dependent changes in amplitudeof optical signal from the human eyeball in situ after trazograph-60 injection (a) andtrazograph-60 drops in the vicinity of the detector fiber tip for several source–detectorseparations (1.14, 2.08, and 3.5 mm) (b) (see Ref. 1626).

Photon-diffusion theory provides independent determination of the absorptionand reduced scattering coefficients from the measurements at a single modulationfrequency. The expressions for the measured quantities as phase delay, θ, and acamplitude, Aac, have been presented elsewhere1, 4, 129 (see Sections 1.3 and 11.2).These expressions depend on the source-detector separation, rsd, reduced scatteringcoefficient, μ′

s, and absorption coefficient, μa.Data shown in Fig. 9.15 represent the temporal changes of ac amplitude dur-

ing trazograph-60 administration for three different source–detector separationsand two different techniques of immersion solution administration: by injectionand drops. The intensity and phase of photon-density waves generated by a NIRoptical source were measured for several source–detector separations. The lightsource was a laser diode with a wavelength of 786 nm and 4-mW power at theend of coupled multimode fiber (core diameter of 62.5 μm).1626 The intensitymodulation depth of approximately 80% at a frequency of 140 MHz was pro-vided by modulating the injection current of the laser diode. The experimentalsetup was designed at the University of Pennsylvania. A multifiber detection sys-tem with small source–detector separations, together with a Dicon multichannelfiber-optic switcher, was used for immersion experiments on the human sclerain situ for a whole eyeball. The clearing of scleral tissue was observed duringthe first 3 min of trazograph-60 administration by injection. For small source–detector separations—approximately 1–2 mm—and a relatively large one—3.5mm—the temporal dependencies are quite different. Keeping in mind that dur-ing the first 3 min after injection of the OCA, the positive time scale correspondsto a decrease in scattering owing to tissue immersion, the opposite tendencies ofthese dependencies can be understood as follows. For the small source–detectorseparation close to the exact geometry of backreflectance, the intensity of reflectedlight decreases along with a decrease scattering; and for rather large separations,when lateral photon diffusion effects are important, intensity first increases with


450 Chapter 9

decreased scattering, but if scattering continues to decrease, intensity will lessen.That is why a local maximum on a curve for a separation of 3.5 mm was observed.At the third minute after OCA injection, owing to its diffusion into neighbor tis-sue regions, amplitudes for all separations have a tendency to reach initial values.Another technique of OCA administration by drops shows the same tendencies asfor injection for small and large separations, but essential changes to the amplitudeshappen momentarily after chemical agent drops are applied, and then amplitudesslowly change in opposite directions. This behavior depends on the specific fea-tures of OCA application, which are (1) superficial impregnation (underlines theimportance of surface immersion effect); (2) continuous renovation of the OCA onthe tissue surface (many drops during the measurement interval).

This study, performed under circumstances that are very similar to in vivo mea-surements, also shows that the impregnation of eye sclera by a hyperosmotic OCAaffects the matching of reversible refractive indices of the collagen fibrils and inter-stitial media, which leads to dramatic reduction in the tissue scattering ability, upto 60% in ac signal change for 10–12 min upon application of trazograph-60.

9.3.3 Scleral in vivo measurements

In vivo measurements were conducted for a rabbit eye by using the experimen-tal setup presented in Fig. 9.11. Experimental spectra and dynamic response onselected wavelengths are shown in Figs. 9.16 and 9.17.1625, 1729 The surface tem-perature of the rabbit eyes was ∼38◦C. Here, 40% glucose was used as a chemicalagent for scleral optical clearing, administered in the form of eye drops. A signif-icant decrease of the reflectance during the first 5 min of glucose administrationwas observed. Dips appearing at 420, 530, and 570 nm are caused by blood per-fusion. The lower reflectance at 420 nm is caused by the strong absorption ofblood. Evidently, faster decay at this wavelength reflects blood perfusion dynam-ics due to eye conjunctiva and sclera inflammation induced by light irradiationand osmotic action of glucose. Because blood absorption has less influence at 630to 700 nm, measured dynamic responses can be used for in vivo estimation ofdiffusion coefficients for glucose in scleral tissue.

Experimental data presented in Figs. 9.16 and 9.17 show that for in vivomeasurements, reflectance decreases up to twofold; this value of decrease iscomparable with in vitro studies for trazograph-60 immersion [see Fig. 9.7(c)].Transmittance measurements are difficult to provide in in vivo experiments; thus,to estimate translucent efficiency during optical immersion, we may use resultsof in vitro measurements of collimated transmittance that show up to 26-foldincreases in transmittance. Using MC modeling based on experimental data andthe arrangement used for in vivo and in vitro measurements, in vivo and in vitroclearing efficiency can be correctly compared.1696 The calculated ratios of maximal(untreated tissue) to minimal (well treated tissue) diffuse reflectance, Rd, for in vitroand in vivo measurements show the same tendency of change with the wavelength.Differences in the absolute values of this ratio (∼=1.2 for in vitro and ∼= 2 for in vivoat 700 nm), which are higher for the in vivo case, can be explained by a multilayered



Figure 9.16 In vivo time-dependent reflectance spectra of a rabbit eye sclera measuredconcurrently with administration of 40% glucose solution: (1) 1 min; (2) 4 min; (3) 21 min;(4) 25 min; (5) 30 min after drop of glucose into the rabbit eye (see Refs. 1625 and 1729).

Figure 9.17 In vivo time-dependent reflectance of a rabbit eye sclera measured con-currently with administration of 40% glucose at 420 nm (downward triangles), 630 nm(squares), and 700 nm (upward triangles) (see Refs. 1625 and 1729).

structure of the living tissue (consisting of the conjunctiva, the Tenon’s capsule,the sclera itself, the ciliary muscle, and the ciliary pigmented epithelium), someof which are extremely absorbing. The living tissue seems to be more effectivelycontrolled by immersion phonomena due to the stronger influence of absorbing


452 Chapter 9

layers, which reduce the fluence rate of the backscattered photons as the light pen-etrates more deeply inside tissue (due to reduction of the scattering coefficient),where absorption is maximal for this specific tissue. Less scattering causes shorterphoton migration paths and less probability for photons to be absorbed.

Other reasons for more effective control are the blood perfusion and metabolicactivity of living tissue, which cause more effective impregnation of tissue atphysiological temperature, even though the agent was only applied to the exte-rior surface of the sclera. In general, the rate of agent diffusion in a tissue increasesfrom the minimal rate for fixed tissue samples, when additional bonds are formedbetween the protein molecules hindering, agent transport, to midlevel for freshtissue samples, and highest for in vivo immersion.200

It is also important that the total transmittance for the in vivo case is three-to sixfold more effectively controlled by tissue immersion than that for separatedscleral samples measured in vitro. The total transmittance of the anterior eye layersmeasured at the posterior interface of the sclera determines the laser energy appliedto the ciliary body when its coagulation is needed. The collimated transmittance,in turn, determines the efficiency of laser irradiation through the sclera at a localarea of the eye bottom to destroy a tumor, for example.

The time-dependent light absorption fractions for different layers of the rabbiteye at 700 nm calculated using MC simulation for tissue impregnated by 40%glucose are shown in Fig. 9.18. The initial values of the scattering and absorptioncoefficients for various tissue layers were taken from Refs. 392 and 393. The time-dependent diffuse reflectance, total transmittance, and light absorbed fractions attissue immersion were calculated by using the previously discussed in vivo studies.According to graphs of Fig. 9.18, due to the significant translucence of the upperlayers of the rabbit eye, the lower absorbing layers of the eye membrane, such asciliary body components, are sufficiently irradiated, and thus absorb light well. Itis found that as far as the light absorption fraction in the conjunctiva and the sclerais decreased, it is considerably increased in the ciliary body. This confirms thedeclared possibility of using OCAs for the transscleral selective photodestructionof the ciliary body.61, 769, 781, 1811

It is shown that administration of OCAs to a fibrous tissue allows one to effec-tively control its optical characteristics. The dynamics of optically clearing scleraltissue are characterized by a time response of approximately 5–10 min, which isdefined by the diffusivity of an immersion agent in a tissue, tissue condition (intactor fixed), and tissue thickness. The shrinkage and swelling of tissue may play animportant role in the tissue clearing process. During prolonged OCA administra-tion (for example, glucose at pH 3.5), tissue shrinkage at the first step of clearingmay be replaced by swelling, which, in turn, may cause saturation or even slightreduction of tissue optical transmittance.

Dynamic optical characteristics can be used for the determination of diffusioncoefficients of endogenous (metabolic) and exogenous (chemical agent) fluids inhuman tissues. Obtained values for diffusion coefficients of glucose, trazograph,and PEG (6000) in intact human sclera correspond well to values of the diffusioncoefficient for small molecules diffusing in water.200



Figure 9.18 Time-dependent light absorption fractions for different layers of rabbit eye at700 nm, calculated using Monte Carlo simulation for tissue impregnated by 40% glucose.Squares correspond to conjunctiva, circles to sclera, upward triangles to ciliary muscle, anddownward triangles to ciliary pigment epithelium (see Ref. 1696).

9.3.4 OCT monitoring of OCA and drug delivery in eye scleraand cornea

OCT provides cross-sectional images of tissues over typical penetration depthsof 1 to 3 mm. Although OCT is a unique and useful imaging modality withthe capability of 3D imaging that enables precise depth-resolved assessments ofthe optical properties of tissues, the relatively shallow penetration depth is con-sidered a serious limitation for many imaging and diagnostic applications. Thepenetration depth of OCT is fundamentally limited by the attenuation of ballis-tic light propagation via scattering and absorption. As an OCT beam penetratesdeeper into tissue, the signal strength diminishes. Tissue optical clearing meth-ods have been shown to be very effective for enhancing the imaging depth andcontrast.1336, 1341 To quantify the signal strength at a particular depth and the per-meation rates of different compounds in tissues, methods based on OCT signalslope (OCTSS) or OCT amplitude (OCTA) analysis have been developed.1337, 1341

In the first approximation, the OCTSS plotted on a logarithmic scale is proportionalto the total attenuation coefficient of the tissue, μt [see Eqs. (1.1) and (9.1)]:

ln

(I (z)

I0

)≡ OCTSS = −μtz = − (μs + μa) z, (9.27)


454 Chapter 9

where μs and μa are the scattering and absorption coefficients, respectively.Because μs μa in the NIR spectral range,

ln

(I (z)

I0

)≡ OCTSS ≈ −μsz. (9.28)

The scattering coefficient of a tissue depends on a refractive index mis-match between the interstitial fluid (ISF) and the tissue components (collagenfibers and cells). In a simple model of scattering dielectric spheres, μs can beapproximated as271

μs = 3.28πr2ρs

1 − g

(2πr

λ

)0.37 (ns

nISF− 1

)2.09

, (9.29)

where g is the tissue anisotropy factor, r is the radius of scattering centers, ρs isthe volume density of the scattering centers, λ is the wavelength of the incidentlight, and ns and nISF are the refractive indices of the scattering centers and ISF,respectively. If the refractive index of the scattering centers remains constant andis higher than the refractive index of ISF, the diffusion of molecules inside themedium reduces the refractive index mismatch between ns and nISF, and, hence,the scattering coefficient is also reduced:

μs = 3.28πr2ρs

1 − g

(2πr

λ

)0.37 (ns

nISF + δnmol− 1

)2.09

, (9.30)

where δnmol is the molecularly induced increase of the refractive index of ISF.Therefore, an increase in OCA concentration of tissue will increase the refractiveindex of ISF, which will decrease the scattering coefficient as a whole.

Alternatively, the change in local concentration of scattering particles suchas cell components or collagen fibers can change scattering. The mean refractiveindex of tissues can be calculated by the law of Gladstone and Dale [see Eqs. (3.1)and (9.14)] as a weighted average of refractive indices of collagen fibers or cellcomponents (ns) and interstitial fluid (nISF):

ntissue = fsns + (1 − fs) nISF, (9.31)

where f s is the volume fraction of collagen fibers and/or cell components in tis-sues. Therefore, changes in the volume fraction of tissue components f s (e.g., byshrinkage or swelling of the tissues) will either change the overall refractive indexof the tissues or change it within a localized volume where these structural effectstake place.

The OCTSS method utilizes the calculation of the average permeability coef-ficient, P [see Eq. (9.11)], of the tissue layer. The permeability coefficient can be



Figure 9.19 OCT signals recorded at different times to indicate region and depth for bothOCTSS and OCTA analysis methods (see Ref. 1341).

computed by dividing the thickness of the region used to calculate the OCTSS,zregion, by the time of molecular permeation in the monitored region, tregion:1338

P = zregion

tregion. (9.32)

Prior to the addition of molecules, the baseline signal would remain relatively con-stant. Only after application will the changes in the OCTSS be observed. The timeinterval can be calculated as the time when saturation was achieved (after diffusion)minus the time at which the molecules first reached the region of interest (tregion).

Alternatively, the OCTA method of measurement can be used to calculate thepermeability coefficient at specific depths within the tissue from

P (z) = zi

tzi. (9.33)

Here, zi is the distance from the surface of the tissue where the measurementsare performed and tzi is the time of agent diffusion to that depth. Figure 9.19schematically shows the principles of OCTSS and OCTA methods for monitoringof OCT signal kinetics.

Optical clearing efficiency can be estimated by the change in the optical signalobtained from the tissue after the addition of the clearing agent as a percentagechange. Formally, percentage change at a certain depth of a tissue can be defined as

%OC = I2 − I1

I1× 100, (9.34)

where I1 is the optical intensity prior to the addition of the OCA and I2 is the opticalintensity after the OCA has diffused through that particular depth. For example, aspresented in Figs. 9.20 and 9.21, 40% glucose can induce an approximately 10%clearing effect in the upper layer of rabbit sclera, which increases to 22% in thelayers below.1339


456 Chapter 9

Figure 9.20 Schematic diagram showing experimental protocol during in vitro experimentswith cornea and sclera (laser beam configuration is shown for experiment with cornea) (a).2D OCT images of rabbit sclera during a glucose diffusion experiment recorded at 0 min (i),20 min (iii), and 53 min (v); and corresponding 1D signal distribution of the OCT images (ii),(iv), and (vi) (b). OCT signal slope as a function of time recorded from sclera during glucosediffusion experiment (c) (see Ref. 1339).

These experiments proved the capability of the OCT technique to quantify thepermeability coefficient and clearing efficiency of glucose or any other agent in dif-ferent tissue layers. Glucose, in particular, was monitored in two different regions:the uppermost region, which includes bulbar conjunctiva and episclera, and thelower region, which is mostly stromal tissue. The bulbar conjunctiva is a thin,translucent mucous membrane that covers the sclera. This epithelial layer cover-ing the episclera is thought to create a natural barrier that slows the penetrationof OCAs. Glucose travels faster when it is past the outermost layer. Another rea-son for the difference in the permeability coefficient of glucose in these two regionscould have been the diverse anatomical properties of collagen bundles in each layer.Collagen bundles show a wide range of width and thickness among the layers ofthe sclera. They tend to be wider and thicker toward the inner layers, thereforecreating more spacing for analytes to diffuse through more easily.

Additionally, this study suggests that more effective clearing occurs in the innerthan upper regions. Penetration of glucose into the episclera could have been pri-



Figure 9.21 Optical clearing efficiency at different depths in rabbit sclera during the 40%glucose diffusion experiment (see Ref. 1339).

Table 9.1 Mean value of permeability coefficient (P) of certain agents and drugs inrabbit cornea and sclera (see Refs. 1338 and 1339).

Drug Cornea: P ± SD, × 105, cm·s−1 Sclera: P ± SD, ×105, cm·s−1

Water 1.68 ± 0.54 (n = 8) 1.33 ± 0.28 (n = 5)Ciprofloxacin (0.3%) 1.85 ± 0.27 (n = 4) 1.41 ± 0.38 (n = 3)Dexamethasone (0.2%) 2.42 ± 1.03 (n = 7) —Metronidazole (0.5%) 1.59 ± 0.43 (n = 5) 1.31 ± 0.29 (n = 4)Mannitol 1.46 ± 0.08 (n = 4) 0.62 ± 0.11 (n = 5)Glucose — Epithelium: 0.60 ± 0.04 (n = 5)Glucose — Stroma: 2.84 ± 0.68 (n = 5)

marily through the intercellular spaces of the epithelial layer; thus, less glucoseenters the epithelial cells than the stromal tissue, and the refractive-index match-ing for organelles inside the cells is worse than that for the collagen fibers outsidethe cells. The disparity in the collagen fibril sizes among the various layers in thesclera could also have been the reason for the dissimilarity in the clearing efficiencyamong different regions in the tissue. This result for enhanced clearing efficiency ofthe scleral stroma correlates well with the studies using a fiber-optic spectrometer(see Subsection 9.3.1).

Permeation of various molecules and drugs has been quantified in the scleraand cornea of the eye.1338, 1339 Table 9.1 lists examples for the permeation rates ofvarious molecules and drugs in the rabbit sclera and cornea measured by using theOCTSS method described above.

9.3.5 Dura mater immersion and agent diffusion rate

Optical clearing of the human dura mater is important for cerebral optical diag-nostics, phototherapy, and laser surgery. The dura mater is a typical fibrous tissue


458 Chapter 9

Figure 9.22 Visual changes in the in vitro turbid rabbit dura mater and measured opticalchanges before and after epidural application of glycerol. Native dura mater placed overthe resolution target, bar = 1 mm (a). One-minute application of glycerol, bar = 1 mm (b).Transmittance spectra for native dura mater measured at application of glycerol for 1, 2,and 10 min (c) (see Ref. 1439).

and demonstrates the same optical clearing behavior as eye sclera, cornea, or skindermis and muscle, but has its own diffusion coefficient, characteristic time, anddegree of clearing, defined by its structure. The first results from in vitro experi-mental studies of the optical clearing of human and rabbit dura mater under actionof mannitol, glucose, and glycerol solutions at various concentrations are presentedin Refs. 1293, 1439, 1634, 1652, and 1688.

Figure 9.22 illustrates the dynamic changes in the turbidity of rabbit duramater after application of glycerol.1439 A resolution target was placed under asample. After treatment of glycerol for 1 min, the target, which was not visibleunder the native dura mater [Fig. 9.22(a)], was viewed through the specimen[Fig. 9.22(b)]. Results of the measurement of optical properties [Fig. 9.22(c)]confirm the visually observed reduction in scattering. Figure 9.22(c) shows theincrease in transmittance within the wavelength range of 400–750 nm as a func-tion of the time the sample was soaked in glycerol. The hemoglobin absorptionbecame much more prominent after application of glycerol [Fig. 9.22(c)]. Thisindicates that the quality of images received by techniques based on the detectionof hemoglobin absorption spectra can be significantly improved upon reducing thescattering of the tissue upper layers. In vivo studies of glucose and glycerol actionon rabbit dura mater at the open cranium and application of an epidural agentalso confirm the concept of effective optical clearing of fibrous tissue.1439 The totaloptical clearing was achieved very rapidly: 50 s after tissue treatment by glycerol.

Figure 9.23 presents the collimated transmittance spectra and temporal depen-dencies of the spectral components for the human dura mater samples impregnatedby glucose solution. It is clear that glucose is another very effective agent for duramater clearing. Using such measurements for glucose and mannitol and the algo-rithm described in Refs. 1625 and 1652, the diffusion coefficients for 40% glucose



Figure 9.23 Collimated transmittance spectra (a) and corresponding temporal dependen-cies (b) measured for the human dura mater sample in a course of administration of 40%glucose solution in a bath (see Refs. 1634 and 1652).

and mannitol solution (0.16 g/ml) were found: DG = (5.43 ± 0.88) × 10−6cm2s−1

and DM = (1.67 ± 0.21) × 10−6cm2s−1.200, 1652

9.4 Skin

9.4.1 Introduction

Skin has a very complicated structure, as schematically presented in Fig. 9.24.It possesses a protective function, preventing the penetration of pollutions and


460 Chapter 9

Figure 9.24 Human skin structure.

microorganisms into the body. The outermost cellular layer of skin is epidermis,which consists of stratum corneum (SC) (mostly dead cells) and four layers of liv-ing cells. SC is a lipid–protein biphasic structure, having a thickness of only 10–20μm on most surfaces of the body. Owing to cell membrane keratinization, tightpacking of cells, and lipid bridges between them, SC is a dense medium with poorpenetration for foreign molecules.1819, 1820 The excellent diffusional resistance ofthe SC makes the transdermal delivery of immersion agents and water loss by skindifficult. To understand the transport and barrier functions of the skin, it is impor-tant to have knowledge about the distribution of water and ions within the differentlayers.1821, 1822 Water content is known to influence various physical characteristics,such as brittleness, elasticity, tensile strength, viscoelasticity; barrier characteris-tics; electrical resistance; thermal conductivity; and appearance. The SC receiveswater from within the body, but water may also be taken up from the environment.



From within the body, water reaches this tissue from the sweat glands and by dif-fusion from underlying tissues. The in vivo diffusion of water across the SC is apassive process that can be modified through application of hyperosmotic agents.The water content of the innermost layer of the SC is in equilibrium with the adja-cent moist granular layer. The outside cell layer, however, is in equilibrium with theenvironment and is certainly drier than the innermost cornified layer. Thus, thereexists a concentration gradient, causing transepidermal water loss (TEWL).

No significant difference was found for diffusion across the epidermis and SC.The diffusion coefficient, D, of the flow of water through a stationary macromolec-ular gel (the tissue) corresponds to viscose flow through a very fine porous medium.As has been determined in strongly hydrated SC, D is approximately 4 orders ofmagnitude lower than self-diffusion coefficient in water.1821 The diffusivity (D) ofwater in SC increases from ∼3 × 1010 to 109 cm2s−1 as humidity, H, increasesfrom 46 to 81%. The average water content of the SC, as measured in Ref. 1822, is54%, while other authors arrived at a water content as low as 15 to 40% in the samelayer. The rate of diffusion of molecules with molecular weight of 119 in the SCof volunteers is in the range from ∼1010 to 3.5 × 1010 cm2s−1.1820 The hydrationof the dermis is not significantly different from that of the viable cell layers of theepidermis.1822

Dermis is the next thickest layer of the skin, which is mostly fibrous tissuethoroughly supplied by blood, and thus, can be easily impregnated by exogenousor endogenous liquids (immersion agents). Subcutaneous tissue contains a largeportion of fat cellular layer, which is much less penetrative for diffusing moleculesthan dermis. This specific structure of skin defines the methodology of its effectiveoptical clearing, which is related to the immersion of refractive indices of scatterers(keratinocyte components in epidermis; collagen and elastin fibers in dermis) andground matter.57, 200, 306, 766, 1578, 1630, 1726 Experimental studies of optical clearing ofskin using water, glycerol, glycerol–water solutions, glucose, propylene glycol,oleic acid, DMSO, sunscreen creams, cosmetic lotions, gels, and pharmaceuticalproducts were conducted in Refs. 57, 200, 306, 383, 469, 555, 766, 826, 1336,1418, 1547, 1578, 1610, 1613–1615, 1626–1632, 1634, 1635, 1638, 1640, 1643,1645, 1653, 1691, 1695, 1702, 1703, 1706–1709, 1711, 1714, 1715, 1717–1724,1726, 1730–1736, 1738, 1739, 1741, 1742, 1744, 1746–1757, 1760–1765, 1767,1776, 1781, 1785–1791, 1801, 1802, 1808, 1809 and 1823.

9.4.2 In vitro spectral measurements

Table 9.2 illustrates the efficiency of the action of different immersion agents onthe transmittance of stripped samples of human skin (30–40 μm in thickness) takenfrom volunteers using glass substrate–glue technology.1726 Because of the smallthickness of the sample, with a few layers of dried and living keratinocytes and theagent supplied through the living cell layer, the rate and efficiency of immersionwere very high.

An in vitro study of rat dorsal skin impregnated by anhydrous glycerol, whenthe agent was applied to the dermal side of the skin sample, showed a power


462 Chapter 9

Table 9.2 Efficiency of OCA action on 30–40-μm-thick skin stripping sample, expressedas a ratio of mean transmitted intensities after (IA) and before (IB) lotion application; n isthe index of refraction of the lotion (see Ref. 1726).

OCA Glycerol–water–urea solutions DMSO50%

Ultrasoundgel

n 1.449 1.380 1.356 1.354 1.348 1.396 1.337IA/IB 12.8 3.7 4.9 5.9 4.1 7.9 5.3

wavelength dependence of the reduced scattering coefficient in the wavelengthrange from 500 to 1200 nm, described by Eq. (3.30), μ′

s ∼ λ−h.766 Measurementsgave the following data for the reduced scattering coefficient at 500 nm andh-parameter: μ′

s≈ 50 cm−1 and h = 1.12 for normal skin, which subsequentlydecreased in μ′

s (500 nm) and h with increased time in glycerol (mostly due tothe dehydration effect), μ′

s≈ 30 cm−1 and h = 1.09 for 5 min, μ′s≈ 20 cm−1 and

h = 0.85 for 10 min, μ′s≈ 12 cm−1 and h = 0.52 for 20 min, and μ′

s≈ 23 cm−1 andh = 0.9 for the rehydrated sample kept in physiological PBS solution for 20 min.A 60 % decrease in hydration was estimated on the basis of changes in the waterabsorption peaks and a 21.5% corresponding decrease in thickness was found fromthe native tissue to that treated with glycerol for 20 min. The rehydration processcaused the thickness and turbidity of the sample to move back toward their ini-tial states, but during the course of 20 min rehydration, the turbidity (μ′

s) did notreach its initial state. Accounting for a relatively short period of time (∼20 min) foroptical clearing of skin samples approximately 1 mm in thickness766 in this exper-iment, and for the high viscosity of glycerol, its action as a hyperosmotic agentshould have mostly drawn interstitial water out of the tissue; at a slower rate, itshould have replaced the water and salts of the ground substance. Twenty minutesof rehydration are also not sufficient for water to reenter all of the cells and colla-gen fibers in the tissue, thus the scattering coefficient and spectral power parameter,h, for rehydrated tissue are slightly lower than their initial values.

More prolonged administration of glucose (up to 6 h) and glycerol (up to45 min) into the fresh rat skin samples was conducted at room temperature inthe course of tissue collimated transmittance measurements.1695, 1703 These studieswere performed to clarify the mechanisms of skin optical clearing and to optimizethe technique. To avoid tissue damage and to provide a less viscous chemical agent,a glycerol–water solution (88%) and 40% glucose, both available in drugstores,were used as immersion agents. Skin samples were 0.57–0.90 mm in thicknessand 1 × 1 cm2 in area; some contained whole skin including epidermis, dermis,and hypodermic fatty layer, and for others, the fatty layer was removed. Hairs wereremoved by tweezers and the immersion agent was applied to both sides of the sam-ple in a bath. Figures 9.25 and 9.26 illustrate the typical collimated transmittancespectra and optical clearing kinetics. It is clear that the untreated rat skin is poorlytransparent for the visible light. Both glucose and glycerol administration make thistissue highly transparent, showing the 15-fold increase of collimated transmittance



Figure 9.25 Collimated transmittance spectra of the rat skin sample measured concurrentlywith administration of 88% glycerol at different time intervals (sample thickness of 0.9 mm)(see Ref. 1695).

for glucose [Fig. 9.26(a)] and 10-fold increase for glycerol [Fig. 9.26(c)] at 700nm for the samples with fatty layer kept in solution for 45 min. The efficiencyis substantially greater for samples with fatty layer removed [Fig. 9.26(b)]: anapproximately 50-fold transmittance increase is measured for glucose solutionat the same wavelength during the same time interval, with further increases oftransmittance and its saturation for more prolonged time intervals.

Table 9.3 presents characteristics (refractive index and osmolality) of a varietyof chemical agents with different optical clearing potential (OCP), defined as theratio of values of tissue reduced scattering coefficient before and after agent action,OCP ≡ μ′

s (before)/μ′s (after).1717 OCP was measured in vitro at agent application to

the dermis side of human skin by using a Franz diffusion chamber after a 20-minapplication time. Table 9.3 indicates no correlation between OCP and refractiveindex for agents with indices in the range from 1.43 to 1.48, and no correlation withosmolality in a wide range from 1643 to 26,900 mOsm/kg, but the highest valuesof OCP from 2.4 to 2.9 are provided by agents having both the highest refractiveindex and osmolality, such as glycerol, 1,4-butanediol, and 1,3-butanediol.

It is evident that the penetration rate of OCA into skin is much slower than thatfor sclera or dura mater, which takes only 8–10 min to be saturated by trazographor glucose solutions. In comparison with the sclera and dura mater, no saturation ofthe clearing process was observed up to 6 h if the fatty layer was not removed. Thisphenomenon can be connected with the low permeability of the epidermal and fattissue cellular layers for any molecules, which slows both fluxes—water flux fromthe tissue and immersion agent flux from the outside into the tissue. Saturation ofthe optical transmittance can be expected when the equilibrium state in the immer-sion agent/water diffusion process is achieved, i.e., when concentrations of water


464 Chapter 9

Figure 9.26 Time-dependent collimated transmittance of the rat skin samples (1 h afterautopsy, hairs were removed using tweezers) measured at different wavelengths in a courseof administration of immersion solution in a bath. Sample thickness 0.73 mm, with hypo-dermic fatty layer, immersion agent of 40% glucose (a); sample thickness 0.57 mm, withremoved hypodermic fatty layer, immersion agent of 40% glucose (b); sample thickness 0.9mm, with hypodermic fatty layer, immersion agent of glycerol–water solution (88%, vol/vol)(c) (see Refs. 1702 and 1703).

and immersion agent inside and outside tissue are approximately equal. For skinwith epidermis and fatty layer, such saturation was not reached even after 6 h ofglucose administration, but with removed fatty layer, saturation was found after 1 h.

Using the previously discussed algorithm described by Eqs. (9.1), (9.6), (9.14),and (9.17) and experimental data (see Fig. 9.26), the diffusion coefficient of waterin the skin under the action of glycerol can be estimated. Such estimation is validfor agents with strong osmotic strength, because water flux dominates in the sys-tem. The mean value of the diffusion coefficient, averaged for six rat skin samplesat 20◦C for glycerol–water solution penetration, mostly from the dermal side ofthe skin, is equal to (5.12 ± 2.27) × 10−7 cm2s−1, which is approximately twoorders less than the diffusion coefficient of water in water, DW

∼= 10−5cm2s−1

(see Ref. 1818), or one order less than water diffusion in intact human lens,



Table 9.3 OCA characteristics and in vitro measured OCP following agentapplication to dermis side of human skin by using a Franz diffusion chamber;OCP is defined as the ratio of values of tissue reduced scattering coefficientbefore and after agent action, OCP ≡ μ′

s(before)/μ′s(after), and was measured

after 20 min application time (see Ref. 1717).

OCA Refractiveindex

Osmolality,mOsm/kg

OCP

Glycerol 1.47 14,550 2.9 ± 0.850% trimethylolpropanol (TMP) 1.43 6830 2.2 ± 0.3100% TMP 1.47 13,660 2.1 ± 0.71,3-butanediol 1.44 22,050 2.4 ± 0.71,4-butanediol 1.44 26,900 2.8 ± 0.5Ethylene glycol 1.43 22,640 1.9 ± 0.6MPDiol glycol (1,3-diol, 2-methyl-propane) 1.44 23,460 2.3 ± 0.2P-0062a 1.48 1643 2.0 ± 0.5

aP-0062 is a polyethylene glycol–based prepolymer developed at University of California, Irvine.

DW∼= 3.0 × 10−6cm2s−1 (see Ref. 1177). For a subcutaneous fat-free sample,

40% glucose action is characterized by a higher diffusion rate,200 D = (3.1 ± 0.1)× 10−6 cm2s−1, which may be attributable to more effective penetration of glucoseinto tissue.

Using near infrared spectroscopy (800–2200 nm), mass and water loss mea-surements; transdermal skin resistance measurements; and enhancers of skinpermeability such as dimethyl sulfoxide (DMSO) and oleic acid, a monounsatu-rated fatty acid, were compared for propylene glycol (PG) application onto theepidermal surface of samples of fresh porcine skin with thickness of 1.52 ± 0.18mm.1691 It was shown that, when compared with DMSO as an enhancer, oleicacid has a similar synergetic optical clearing effect. Accounting for clinical safetyreasons, oleic acid could be one of the optimal choices as an enhancer for opti-cal clearing of skin, because it is recognized as safe and free of side effects,and DMSO has some potential toxicity. After application of oleic acid solution(0.1 M of oleic acid and PG-40) the total transmittance measured on the wave-length of 1278 nm of the skin sample increased by 41% and 58%, respectively, for30 and 60 min treatment, while diffuse reflectance decreased by 39% and 47%,respectively.

The difference in apparent absorbance [diffuse reflectance spectra were trans-formed into apparent absorbance, A = log(1/Rd)] between two wavelengths of1936 and 1100 nm was adopted to monitor the change in water content.1336, 1636,

1637, 1676, 1690, 1691 It is important that oleic acid solution provided the greatestwater loss in comparison with the other tested solutions: 37% and 46% after30 and 60 min treatment, respectively. As for DMSO-50, water loss was 15%and 20%; PG-80: 20% and 29%; and PG-80+DMSO-50: 34% and 44%, after30 and 60 min treatment, respectively. However, the mass loss upon applicationof oleic acid solution was the lowest among the tested solutions: after 30 min,PG-80 provided 10.9% of mass loss; PG-80+DMSO-50: 6.4%; and oleic acid


466 Chapter 9

Figure 9.27 Spectral changes for pig skin sample before and after treatment by 1,2-propanediol [1,2-propylene glycol (1,2-PG)], over the wavelength range of 400–1700 nmmeasured by integrating sphere: transmittance after treatment by the agent at time inter-vals of 0, 10, 20, 30, 40, 50, and 60 min (from bottom to top) (a); correspondingreflectance spectra (from top to bottom) (b); corresponding reconstructed reduced scatter-ing coefficient spectra (from top to bottom) (c); and corresponding reconstructed absorptioncoefficient spectra (from top to bottom) (d) (see Ref. 1742).

(0.1 M)+PG-40: 6.3%. Greater mass loss was obtained after 60 min of appli-cation of these agents; PG-80: 14.2%, PG-80+DMSO-50: 9.9%, and oleic acid(0.1 M)+PG-40: 8.3%. The comparison of water and mass loss data providenice confirmation of the basic concept of optical clearing, that refractive indexmatching is achieved by two main diffusing processes: water flux from tissue(dehydration) and agent flux into tissue (replacement of interstitial water by theagent).

Figure 9.27 presents integrating sphere spectral measurements over the wave-length range of 400–1700 nm for the pig skin sample before and after treatmentby 1,2-propanediol (1,2-propylene glycol).1742 It is clear that after treatment by theagent for 60 min, transmittance was significantly increased and reflectance corre-spondingly decreased for the entire spectral range. The reconstructed spectra forreduced scattering and absorption coefficients allow for the prediction of opticalclearing mechanisms, one of which is related to tissue dehydration. Experimental



Figure 9.28 Relative reduction of water content (a) and reduced scattering coefficient (b)after 10-, 30-, and 60-min treatment with OCAs, where 1,2-PG stands for 1,2-propylene gly-col (1,2-propanediol); 1,4-BG is 1,4-butylene-glycol (1,4-butanediol); PEG-200 is polyethy-lene glycol 200; PEG-400 is polyethylene glycol 400; 70% Gly is 70% glycerol–watersolution (see Ref. 1742).

data, presented in Fig. 9.28, demonstrate a strong correlation between opticalclearing efficiency and tissue dehydration. Additionally presented are the rela-tive reduction of water content in skin [estimated using absorption peak at 1450nm; see Fig. 9.27(c)] and decay of reduced scattering coefficient after 10-, 30-,and 60-min treatment with 1,2-propanediol, 1,4-butanediol (1,4-butylene-glycol),PEG-200, PEG400, and 100% glycerol and 70% glycerol–water solution.1742 Itfollows that 100% glycerol has the best skin clearing ability among other testedOCAs and provides maximal tissue dehydration.

A method of accelerating penetration of the index-matching compounds byenhancing skin permeability through creating a lattice of microzones (islets) oflimited thermal damage in the SC was recently proposed.1718, 1752, 1801 A combina-tion of a flashlamp system (EsteLux, Palomar Medical Technologies, Inc.) and aspecially designed appliqué with a pattern of absorbing centers (center size ∼75μm, lattice pitch ∼450 μm) has been used to create a lattice of islets of damage


468 Chapter 9

(LID).1824 Several index-matching agents, including glucose and glycerol, havebeen tested. A high degree of optical clearance for full-thickness pig, rat, chicken,and human skin in vitro and in vivo has been demonstrated with 40% glucose and88% glycerol solution after creating an LID with a few optical pulses (fluence of14–36 J/cm2, 20 ms pulse duration).1718, 1825

To enhance skin permeation for OCA and drugs, a fractional laser microabla-tion (FLMA) technique is also used.1719, 1801 A Palomar Lux2940 (Palomar MedicalTechnologies, Inc.) machine built on the basis of an erbium laser (λ = 2940 nm) isa specially designed system for FLMA. Usually, a mode of laser generation usingthree subsequent pulses with ∼1 J of energy in each pulse and pulse duration of5 ms is applied for skin perforation. This system is equipped with different head-pieces providing multibeam operation modes. For example, the headpiece used inRef. 1801 allowed the authors to create 169 vertical conical channels within a skinarea of 6 × 6 mm. Diameter of each channel on the skin surface was ∼100 μm,with distance between them of ∼500 μm and mean channel depth of ∼200 μm.

9.4.3 In vivo spectral reflectance measurements

In vivo topical application of glycerol, glucose, x-ray contrasts, PG, cosmeticlotions, and gels also made human skin more translucent within a time periodfrom a few minutes to a few hours.1547, 1626, 1706, 1708 Water loss or increaseby means of moisturizing substances seriously influences skin optical proper-ties.1166, 1707, 1710, 1820, 1822 NIR reflectance spectroscopy is used as a method todirectly determine changes in free, bulk, and protein-bound water and to assessscattering effects in skin for the evaluation of skin care products.1708 The follow-ing spectral bands are associated with water: free water, 1879 nm; bulk water,1890 nm; and protein-bound water, 1909 and 1927 nm. The effects of increasesin ambient humidity are associated with increased levels of free water in the skin,whereas moisturizers containing hydroxyethyl cellulose, PG, dipropylene glycol,and glycerol contribute to decreases in light scattering.1708 The water observed insuch experiments is primarily in the SC stratum because only a small part of thereflected light comes from the epidermis or below.

Noninvasive measurement of SC hydration can be performed by using ATR-FTIR spectroscopy.1166, 1709, 1820 Three absorption bands are relevant for determin-ing water content in the SC: 3300 cm−1 (3030 nm) for O-H and N-H vibrations;1645 cm−1 (6079 nm), amide I band; and 1545 cm−1 (6472 nm), amide II band.The intensity of the amide I band is pronounced in the presence of water due to thestrong absorption of water at 1645 cm−1 and the changes in the carbonyl absorptionunder the influence of water, whereas the intensity of the amide II band is due toprotein alone. The intensity ratio of the amide I/amide II bands, also called mois-ture factor, is assumed to be a relative measure of SC hydration.1709 Various SCmoisturizers based on glycerol, PG, sodium lactate, natural moisturizing vegetal,liposomes, butylene glycol, polyglycerylmethacrylate, and urea were used for anin vivo SC hydration study.1709 Depending on the composition and concentration,



maximal SC hydration could be reached in 0.5–2 h after application of the sub-stance on the surface of skin. For some substances, a considerable moisturizingeffect was detectable up to 8 h following application. Dual wavelength (1300 and1450 nm) optical coherence reflectance measurement is a prospective technique fordepth profiling water absorption within the skin.1710

To enhance OCA permeation through SC, a number of specific proceduresare usually applied, such as heating, electrophoresis, and sonophoresis.1703, 1706,

1751, 1754, 1757, 1801, 1819 To increase the efficiency of the topical application of OCAs,gelatin gels containing clearing agents (verografin, glycerol, or glucose) weredesigned.1706 The diffusion rate of the agents within the gel layer can be ratherhigh; this, along with comparatively large volume of the gel, provided a constantconcentration of OCA, equal to the agent content in the gel, at the skin surface. Forintact skin of a volunteer, the best dynamics, i.e., the rate and the degree of clearing(17%), were observed in the case of verografin gel [Fig. 9.29(a)]; after 40 min ofobservation, clearing still proceeded at a marked rate, whereas for glycerol gel, thecurve flattens out after 27 min; no clearing was observed in 40 min of glucose gelapplication.

Because the barrier function of the skin is primarily associated with SC, mea-surement was conducted on the skin after 30–50 μm epidermal glue stripping[Fig. 9.29(b)]. Application of glucose gel to skin without upper epidermis produceda rapid 10% drop of reflected light intensity. Glycerol gel gave better results; overthe time of observation, the decrease in reflected signal ranged up to ∼20%, whichwas twice that attained for intact skin. Surprisingly, no clearing effect of verografingel was observed.

An electophoretic applicator and gel with double the content of gelatin werealso applied to human skin optical clearing.1706 In Fig. 9.29(c), the results for glyc-erol gel are shown. When the active electrode was connected as anode, a ∼20%reduction of optical signal was attained. This value is comparable to the results withstripping, but the time of attainment of minimum signal is nearly halved. When theactive electrode was connected as a cathode, an increase of backreflectance wasobserved over the whole duration of measurement. The effect was attributed to thedevelopment of erythema.

It may be concluded that for the topical application of glycerol and glucosegels, the employment of epidermal stripping and electrophoresis techniques doeslead to enhancement of the dynamics of in vivo optical clearing of human skin. Thebest characteristics were obtained with electrophoretic administration of glycerolfrom anode. In the case of glucose, stripping and electrophoresis from the cath-ode produced similar results, but the application of glucose should be terminatedafter 10–12 min for the risk of deterioration of clearing by the development oferythema.

The administration of glucose or glycerol by intradermal injection into rator hamster skin decreases the reflectance and correspondingly increases tissuetransmittance.766, 1634, 1643, 1645, 1695, 1703, 1720, 1741, 1823 This effect was observed at allwavelengths during 15–18 min after glucose injection.1643, 1645 The greatest degreeof changes in tissue reflectance is found at the wavelengths from 580 to 750 nm,


470 Chapter 9

Figure 9.29 Backreflectance at 830 nm measured by a fiber-optic probe (rsd = 1.2 mm,source fiber 0.2 mm and detector fiber 1 mm in diameter) perpendicular to the skin surfaceat clearing gel (glucose: 3.9 ml 40% glucose and 0.2 g gelatin; glycerol: 1.3 ml glycerol, 0.1g gelatin, and 2.6 ml distillate water; verografin: 2.6 ml verografin-60, 0.1 g gelatin, and 1.3ml distillate water) application on intact skin (a); on skin after glue epidermal stripping (b);at electrophoretic application of gelatin gel with glycerol (1.3 ml glycerol, 0.2 g gelatin, and2.5 ml distillate water) (c) (see Ref. 1706).

where scattering dominates. At the 16th min, the reflectance of the skin wasminimal (maximal transmittance); it decreased approximately 3.5-fold at 700 nm,then tissue slowly returned to its normal state: at the 76th min, only a twofoldreduction of reflectance was observed. It was shown that glycerol injection causes amore prolonged effect of tissue optical clearing, but reflectance decreased slightlyless than for glucose injection. This can be explained by the higher viscosity ofglycerol and its mostly indirect action through tissue dehydration. The reaction ofthe rat skin to the injection of distillate water, as a model of nonosmotic agent, wasalso studied. A reduction of reflectance was observed only for a short period (thefirst minute) after injection. This was attributable to a much higher transmittanceof the injected water with respect to the surrounding tissues. At the second minute,water diffused into bulk tissue and the transparency of tissue was decreased—thereflectance spectrum was gradually elevated to its initial value. The injection ofwater does not cause immersion clearing of the skin.



Figure 9.30 Changes in skin reactions on injection of 40% glucose (a) and 75%-glycerol(b): �, diameter of VTW (DT); �, diameter of swelling area around VTW (DS); ∗,+ ratioDS/DT; ◦, diameter of swelling area at injection of distillate water (see Refs. 1643 and 1645).

The virtual transparent window (VTW), ∼4 mm in diameter, is created in theskin with the living time period of ∼30 min for 40% glucose and more than 60 minfor 75% glycerol. This window allows blood microvessels in the skin to be clearlyidentified by the naked eye.1643, 1644 A swelling white ring (edema) appeared aroundthe VTW after agent injection. The images of skin after intradermal injection ofglucose, glycerol, and water were recorded by a digital video camera. The diame-ters of swelling area (DS) and VTW (DT), and their ratio (DS/DT) were measured(Fig. 9.30).1643 For glucose injection, the diameter of the VTW was registered at thefirst minute after injection. At the second min, the diameter was slightly decreased.For the next 15 min, this diameter and that of the swelling area were unchanged.After the twentieth minute, a significant reduction of the VTW was observed.


472 Chapter 9

Figure 9.31 Reflectance spectra (a) and time-dependent reflectance (b) at three wave-lengths (420, 500, and 700 nm) of the human skin measured at hyperdermal injection of 0.1ml of 40% glucose into internal side of the forearm of the male volunteer for different timeintervals; (1) intact skin, (2) at 23 min and (3) at 60 min after injection (see Ref. 1630).

For glycerol injection, the diameter of the VTW was approximately the same, butthe swelling ring was larger, and both transmittance and swelling were observed fora longer period than at glucose injection [Fig. 9.30(b)]. The injection of distillatewater caused only the appearance of swelling at the injection site. The diameterof the swelling area decreased gradually and swelling disappears at the thirtiethminute after injection.

Figure 9.31 shows the reflectance spectra and the corresponding time-dependent reflectance for a few spectral components measured for a healthy humanvolunteer under intradermal 40% glucose solution.1630 The reflectance spectrashow a scattering background determined by the diffusion reflection of the skinlayers, with well-pronounced bands caused by blood optical absorption. Withinone hour after glucose injection, the skin reflection coefficient decreased, on aver-age, by a factor of 3.8, and then exhibited a slow increase, which indicates thatglucose was eliminated from the observation area and the skin reflectance tendedto restore itself to its initial level. Based on these results and the proposed skinclearing model, we may suggest that the main contribution to clearing in the firststage (first hour) is attributable to refractive index matching between the collagenfibrils of the dermis (n = 1.46) and the interstitial space (initially n = 1.36) to whichglucose (n = 1.39) diffuses. Estimated from the experimental data [Fig. 9.31(b)],the diffusion coefficient of glucose in dermis is DG = (2.56 ± 0.13) × 10−6 cm2s−1;this value is 3.6-fold less than for glucose diffusion in water at 37◦C, DG ≈ 9.2 ×10−6 cm2s−1, and reflects the characteristic of dermis permeability for glucose.

For application, it is important that skin preserves transparency (lowreflectance) for a few hours after injection, which is defined by glucose diffusionalong the skin surface, because upper and lower layers of the skin—epidermis andfat—have much lower permeability than dermis. For the optical clearing effectto remain visible, glucose should diffuse at least the distance l = 1.25–1.75 mmfor the fiber probe used in experiments (Fig. 9.11), i.e., the diffusing (optical



Figure 9.32 Frequency-domain backreflectance measurements for the small source-detector separations (see Ref. 1626). Time-dependent changes of the amplitude (a) andphase shift (b) of the signal for several source–detector separations (1.14, 2.08, and 3.5mm) for in vivo study of a human arm under 20 min glycerol administration.

clearing) time, τ ≈ l2/DG ≈ 1.7–3.3 h (accurately corresponds to experimentaldata) [Fig. 9.31(b)].

As is clear from Fig. 9.31(a), at dermis clearing (reduction of scattering), thecontrast of hemoglobin absorption bands is significantly higher than for control,but for prolonged immersion (curve 3) contrast is not very high. This result isvery important for contrasting of tissue abnormalities (tumors) associated withhemoglobin or other concentrations of probe absorbers (for instance, ICG dye).Therefore, there is an optimal immersion time interval (for human skin at glucoseinjection, this is 60 min), which allows one to see skin absorbers and localize themmore precisely at reduced scattering. Indeed, for prolonged immersion, the contrastdecreases due to fewer light interactions with absorption at low-step scattering.

9.4.4 In vivo frequency-domain measurements

The dynamical response of optical properties of the human skin treated by achemical agent can be measured using a photon-density wave (frequency domain)technique.1626 The intensity and phase of photon-density waves generated by theNIR optical source (786 nm) were measured at several source–detector separa-tions.1626 For small (1–3 mm) source–detection separation measurements, allowingfor examination of thin tissue layers, a special multichannel fiber-optic probe wasdesigned. It was used together with a Dicon multichannel fiber-optic switcher.Dynamical responses of optical properties (modulation depth and phase shift ofintensity modulation of the backscattered light) were measured for human skinvia intervals of administration of a chemical agent. Each separation was mea-sured during 10 s and averaged, corresponding to one point in Fig. 9.32. The


474 Chapter 9

Figure 9.33 Frequency-domain backreflectance measurements for large source–detectorseparation (2.5 cm) (see Ref. 1626). Raw experimental data of the phase and ac amplitudeof the optical signal (a) and calculation of the absorption and the scattering coefficients (b).Cosmetic gel with refractive index n = 1.403 has been used.

relative amplitude (normalized to the initial amplitude) and phase changes (the cur-rent phase minus the initial phase) during 20 min of glycerol topical applicationare shown in Fig. 9.32. Only scattering changes must be considered due to theextremely low absorption of glycerol at the measuring wavelength. The observedamplitude and phase changes are small, reflecting minor permeation of the epi-dermal cell layers to any chemical agent. Nevertheless, these measurements showthe sufficient sensitivity of the frequency-domain method to small changes in thescattering coefficient of the skin.

For large (2.5 cm) source–detector separation studies, the source and detectorfiber tips were mounted in a rubber pad and fastened to the surface of a humanforearm to avoid random moving artifacts. Cosmetic gel with refractive indexn = 1.403 was placed on the surface of the arm, and the phase and ac amplitudemeasurements were continuously provided. One sampling point corresponds to onesecond. The results of measurement during 30 min of gel administration are shownin Fig. 9.33(a). The temporal quasi-periodic fluctuations shown in the phase andamplitude of the optical signal are primarily caused by the heartbeats.

Results of the reconstruction of tissue optical parameters are shown inFig. 9.33(b). The initial values of μ′

s and μa for human skin were taken fromTable 7.1, and relative changes in these parameters were calculated with a runningaveraging procedure for every 5-s interval to exclude the influence of heartbeats.Corresponding temporal evolutions of the scattering and absorption coefficientswere received. This study shows no noticeable changes in absorption during thegel administration trial. A slight increase in the absorption can be explained byan increase of the water content in the skin due to the moisture effect of theapplied gel. The selected source–detector separation (2.5 cm) and correspondingmeasuring volume are too large to make the matching effect a useful procedure for



topical application of the gel. Only an approximately 6% reduction in the scatteringcoefficient, averaged over the large measuring volume, was observed. This meansthat the scattering coefficient of the upper (superficial) layers of the skin changedmore effectively. Refractive index matching of fiber tips and tissue surface is alsoimportant.

In vivo frequency domain measurements for immersed tissues show that therefractive index matching technique provided by the appropriate chemical agent orapplication of cosmetic preparation can successfully be used in tissue spectroscopyand imaging when reduction of scattering properties is needed.

9.4.5 OCT imaging

The typical OCT fiber-optic system employs a broadband light source (a superlu-minescence diode), delivering light at the central wavelength of 820 or 1300 nmwith a bandwidth of 25–50 nm. Such OCT system provides 10–20 μm of axial andtransverse resolution in free space with a signal-to-noise ratio up to 100 dB (seeSection 8.6).109, 110, 127, 136, 142, 156

The result of the OCT study is the measurement of optical backscattering orreflectance, R(z), from the tissue versus axial ranging distance, or depth, z. Thereflectance depends on the optical properties of tissue, i.e., the absorption and scat-tering coefficients (μa and μs), or total attenuation coefficient μt = μa + μs. Therelationship between R(z) and μt is, however, highly complicated because of thehigh and anisotropic scattering of tissue. However, for optical depths less than 4,reflected power can be approximately proportional to −μtz in exponential scaleaccording to the single scattering model,1336 i.e.,

R(z) = I0α(z) exp(−μtz), (9.35)

where I0 is the optical power launched into the tissue sample and α(z) is the reflec-tivity of the sample at the depth of z, which is linked to variations in the localrefractive index of the sample. The absence of a factor of 2 in the exponential, eventhough light twice passing through the sample before and after is backscattered,is attributable to interferential nature of the OCT signal, which gives informationabout local reflectivity and attenuation of tissue.1334, 1336 The mean square of thephotodetector heterodyne signal current, 〈i2(z)〉, received by an OCT system fromz is a product of two factors: the mean square heterodyne signal in the absence ofscattering, 〈i2〉0, and the heterodyne efficiency factor, �(z), describing the signaldegradation due to the scattering,1300, 1333, 1336 i.e.,

〈i2(z)〉 = 〈 i2〉0�(z), (9.36)

where factor 〈i2〉0 is defined as

〈i2〉0 = β2PRPSσb/π(wH)2 (9.37)

where β is the power to current conversion factor, PR and PS are the power ofreference and input sample arm beams, σb is the effective backscattering cross


476 Chapter 9

section, and wH is the 1/e irradiance radius at the probing depth in the absence ofscattering. More precisely, wH is defined in Refs. 1300 and 1333.

The heterodyne efficiency factor, �(z), contains the scattering effects. It hasbeen shown1300, 1333 that for only a single scattering contribution,

�(z) ≈ exp{−2μsz}. (9.38)

Factor 2 in the exponent of Eq. (9.38) accounts for the round-trip attenuationto and from depth z of in the sample arm. In the absence of absorption, μs canbe determined from the slope of the OCT signal. For media with absorption, μs

can be obtained by subtracting the absorption coefficient from the total attenuationcoefficient, μt = μs + μa, obtained from the slope of the OCT signal. Thus, themeasured signal in an OCT system is defined as1300, 1333, 1336

(⟨i2(z)

⟩)1/2 ≈ (⟨i2

⟩0

)1/2 [exp ( − 2μtz)

]1/2. (9.39)

The result of the OCT study is the measurement of optical backscattering orreflectance, R(z) ∝(⟨

i2(z)⟩)1/2

, from the tissue versus axial ranging distance, ordepth, z. Thus, using this definition we arrive at Eq. (9.35).

Measurement of OCT reflectance for two depths, z1 and z2, allows one toapproximately evaluate the attenuation coefficient and its temporal behavior dueto reduction of tissue scattering coefficient at agent immersion if reflectivity, α(z),is considered as weakly dependent on depth:

R(z1, t)

R(z2, t)≈ exp {−μt(t) [z1 − z2]} (9.40)

or

μt(t) = 1

�zln

[R(z1, t)

R(z2, t)

], (9.41)

where �z = |z1 − z2|. Because noise is inevitable in the measurement, a final resultshould thus be obtained by the use of a least-squares fitting technique to improvethe accuracy of the determined value of μt.

Optical clearing (enhancement of apparent transmittance), �T, by an agentapplication can be estimated using the following expression:

�T = Ra − Rs

Rs× 100%, (9.42)

where Ra is the reflectance measured from the backward surface of the sampleimpregnated by an agent, and Rs is that without impregnation (control).

Multiple scattering is a detrimental factor that limits OCT imaging perfor-mances: imaging resolution, depth, and localization. To improve the imagingcapabilities, the multiple scattering of tissue must be reduced. The immer-sion technique with application of biocompatible agents is a prospective tech-nique for OCT, because the depth and contrast of OCT images can easily be



Figure 9.34 Dynamic OCT images (λ = 820 nm) at 0 (a), 3 (b), 10 (c), 15 (d), 20 (e), and40 (f) min after topical application of 80% glycerol solution onto rat skin. Images performedright after the rat was sacrificed, all presented units are in millimeters, and the vertical axispresents the imaging depth (see Ref. 1631).

essentially improved at immersion.136, 139, 146, 147, 200, 1057, 1306, 1336, 1338, 1521, 1547, 1623,

776, 1624, 1631, 1633, 1636, 1638, 1673, 1677, 1721, 1759, 1780, 1826

OCT imaging combined with OCA immersion is a useful technology forskin disease diagnosis and monitoring. To illustrate the dynamics of skin opti-cal clearing after the application of glycerol, a set of OCT images (820 nm) ofa rat skin sample was recorded at regular time intervals over a period of 40 min(Fig. 9.34).1631 Both the index-matching effect, leading to enhanced depth capa-bility, and the localized dehydration effect, leading to the improvement of imagingcontrast, are clearly evident. Analogue results were received for fresh porcine andchicken skin for imaging at 1300 nm by 50% and 80% glycerol solutions by R. K.Wang. The OCT image of human skin with psoriatic erythroderma acquired sometime after the application of glycerol differs from the initial image by greater pen-etration depth and better contrast (Fig. 9.35). These image improvements facilitatethe identification of the important morphological phenomenon of acanthosis.1306

The possibilities of in vivo diagnostics of malignant melanoma, observation ofsubepidermal blisters, and control of the scattering properties of skin through thesaturation of skin with glycerol by its topical application were demonstrated on


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Figure 9.35 OCT images of skin with psoriatic erythrodermia (see Ref. 1306): before topi-cal application of glycerol (a); immediately after the application of glycerol (b); 20 min afterapplication of glycerol (c); after 80 min after application of glycerol (d); corresponding histol-ogy (e) (database of dermatological group of Prof. G.A. Petrova, Institute of Applied Physicsof the Russian Academy of Sciences).

Figure 9.36 OCT signals (in intensity-depth coordinates) obtained for in vivo probing ofhuman fingertip skin. Upper curve corresponds to skin saturated with glycerol. Scatteringcoefficient for the skin with glycerol is reduced: for the SC by a factor of two; for epidermisand upper dermis by 20%; and for deeper dermis layers by only 5% (see Ref. 1547).

the basis of OCT imaging of human skin both in vitro and in vivo.1547 Accordingto the estimates of the authors of Ref. 1547, the scattering coefficient for the SCwith glycerol is reduced by a factor of two (Fig. 9.36). For epidermis and upperdermis, the coefficient of scattering decreases by 20%. For deeper dermis layers,the coefficient of scattering lowers by only 5%. The effect on the enhancement ofboth imaging depth and contrast was found in in vivo studies of human skin opticalclearing upon topical application of the 50% propylene glycol solution.1632

The OCT images captured from the skin site of a volunteer following hyper-dermal injection of 40% glucose allowed one to estimate the total attenuationcoefficient [see Eq. (9.28)].1632 The attenuation initially decreases, and thenincreases with time. Such behavior correlates well with the spectral measurements



shown in Fig. 9.31 and also reflects the index matching induced by glucose injec-tion. The light beam attenuation in tissue, I/I0 ∼exp(−μtz), for intact skin (0 min)was found from OCT measurements to I/I0

∼= 0.14, and for immersed skin at 13min I/I0

∼= 0.30; i.e., intensity of transmitted light increased 2.1-fold. This valuealso correlates well with the spectral measurements.

The high sensitivity of the OCT signal to the immersion of living tissue byglucose allows one to monitor its concentration in the skin at a physiologicallevel.166, 991, 996, 1006, 1008, 1191, 1192, 1650, 1684, 1761, 1765 Although glycerol and glucose areeffective OCAs when injected into the dermis,766, 1632, 1645 they do not normallypenetrate well into intact skin. In recent OCT experiments with human skin invivo upon topical application during 90–120 min of combined lipophilic PPG andhydrophilic PEG–based polymers, both with indices of refraction of 1.47, whichclosely match that of skin scattering components in SC, epidermis, and dermis,it was shown that the polymer mixture can penetrate intact skin and improveOCT images to more clearly visualize dermal vasculature and hair follicles.1638

This composition may have some advantages in skin optical clearing due to thehydrophilic component, which may more effectively diffuse within living epider-mis and dermis. Its lower osmotic strength may also have some advantages, butthe optical clearing depth could not be improved radically in comparison with thetopical application of other clearing agents, such as glycerol, glucose, x-ray con-trast, and PG, because of principal limitations in the diffusion of the chemical agentthrough intact cell layers (see Table 9.3). Thus, to provide fast and effective opti-cal clearing of skin, the appropriate well-known or newly developed methods ofenhanced agent delivery should be applied. Some are discussed above.

Two examples of in vivo studies of skin optical clearing and OCA diffu-sivity are presented in Figs. 9.37–9.39. The time-domain OCT system used toimage the diffusion of glucose in the skin of anesthetized monkeys is shown inFig. 9.37(a).1765 The next two figures, Figs. 9.37(b) and 9.37(c), present the rep-resentative OCT signals obtained from monkey skin before adding 20% glucoseand 60 min after glucose diffusion and an OCTSS graph of monkey skin in thecourse of glucose diffusion, respectively. The permeability coefficient of 20% glu-cose in monkey skin, averaged for five independent experiments on four differentmonkeys, was found to be (4.41 ± 0.28) × 10−6 cm·s−1.1765

Enhanced optical clearing of rat skin at in vivo OCT in-depth imaging isdemonstrated in Figs. 9.38 and 9.39.1768 In-depth OCT reflectance profiles beforeand after the topical application of PEG-400 are shown, as the average of threeduplicate images, upon using massage and chemical enhancers, such as thiazoneand propanediol. Reflectance measured from a depth of 300 μm (see Fig. 9.38)at the application of PEG-400 as an OCA and physical (skin cleaning by tapestripping and massage) and chemical (thiazone and propanediol) enhancer of skinpermeability is compared for different enhancement protocols (see Fig. 9.39).These data illustrate the efficiency of the combined application of physical andchemical enhancers for skin impregnation by a particular OCA.


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Figure 9.37 Schematic drawing of the time-domain OCT system used to image the dif-fusion of glucose in the skin of anesthetized monkeys (a); representative OCT signalsobtained from monkey skin before adding glucose and 60 min after glucose diffusion (b);OCTSS graph of monkey skin during a 20% glucose diffusion experiment (c) (see Ref.1765).

9.4.6 OCA delivery, skin permeation, and reservoir function

The general principles of designing preparations that allow one to provide deeppermeation within skin for the improvement of its physiological properties are dis-cussed elsewhere (see, for example, Ref. 1827). As discussed earlier, the samecosmetic preparations with or even without corrections may serve as optical immer-sion compositions. This is the best solution when the immersion compositionimproves both the physiological and optical properties of the skin. However, the



Figure 9.38 Enhanced optical clearing of rat skin in vivo at OCT in-depth imaging: depthreflectance before and after the topical application of PEG-400, showing the average ofthree duplicate images at using massage and thiazone (a) and propanediol (b) as thechemical enhancers (see Ref. 1768).

Figure 9.39 Reflectance measured by OCT from a depth of 300 μm (see Fig. 9.38) uponthe application of different optical clearing agents after skin cleaning by tape stripping (seeRef. 1768). Saline + massage (control) (a); PEG-400 + thiazone, but no massage (b); PEG-400 only + massage (c); PEG-400 + thiazone + massage (d); PEG-400 + propanediol +massage (e).

excellent diffusional resistance of the SC makes the transdermal delivery of animmersion agent difficult.1819

Lipids define a high permeability of creams and lotions in the upper layers ofepidermis and hair follicles.1827 Ethers of fat acids with single atom spirits likeisopropyl myristate, isopropyl palmitate, and isopropyl laurate are very importantchemicals as components of deep-penetrating creams and lotions.

Technical lecithin [60% natural phospholipids (major phosphatidylcholine),30–35% plant oil, glycerol, and more] is a basis for many nourishing (nutritive)creams due to its possibility of penetrating deep into the skin.

Silicon wax and oils easily penetrate into the hair follicles via friction(rubbing), do not induce inflammation due to their low surface tension, and donot influence the thermal balance of the skin.


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Emulsions are oils in water and water in oils with particle sizes of morethan 0.1 μm. Emulsions like oils in water are widely used in cosmetics for deeppenetration into the skin, as providers for biologically active substances, and more.

Nourishing (nutritive) creams easily penetrate to the deep layers of the epi-dermis and prevent TEWL. Skin hydration can be provided by two mechanisms:osmotic or physiological. As hydrating substances, sodium lactate, pyrrolidonecar-boxylic acid, derivatives of amino acids and sugars, proteins, and mucopolysaccha-rides are usually used. As a hygroscopic component, glycerol is often used (usuallyless than 10% in composition). At present, glycerol is usually replaced by PG.

Currently, numerous creams and lotions providing sufficiently deep impregna-tion of the skin are available in the market of cosmetic products. Many cosmeticemulsions, gels, and lotions for skin hydration use gyaluronic acid (the best forTEWL); sea collagen (also good for TEWL); liposomes and nanospheres—fatparticles (for transportation of biologically active substances to the deep lay-ers of epidermis and hair follicles). As a rule, creams based on liposomes andnanospheres are used after application of peeling creams, for example, creams con-taining α-hydroxy acids (AHAs) or abrasive creams, which smooth the skin andallow liposomes and nanospheres to penetrate.

Liposomes have been suggested as a vehicle for dermal and transdermaldrug delivery, but knowledge remains poor about the interaction between lipidvesicles and human skin. In Ref. 1828, liposome penetration into the humanskin in vitro was visualized by using a confocal microscope. Liposomes wereprepared from phospholipids in different compositions and labeled with a flu-orescent lipid bilayer marker. Liposome compositions containing dioleoylphos-phatidylethanolamine (DOPE) were able to penetrate deeper into the SC thanthose from liposomes without DOPE, because liposomes containing DOPE mayfuse or mix with skin lipids in vitro and loosen the SC lipid bilayers. Among thefactors not affecting SC penetration were negative charge, cholesterol inclusion,and acyl chain length of the phospholipids. Fusogenicity of the liposome com-position appears to be a prerequisite for skin penetration. The liposome sizes,determined by the quasi-elastic light scattering method, were in the range of40–76 nm. The penetration depth into the skin in 72 h was in the range of 2–38 μm.Effective mixing of liposomes containing DOPE with a SC lipid bilayer happensin a few minutes.1828

Occlusion enhances the percutaneous absorption of a variety of com-pounds.1819 The effect is relatively independent of the structure of the compound.For example, hydration of the SC appears to enhance diffusion of water as wellas the percutaneous absorption of a homologous series of alcohols, phenols, andsteroids. Occlusion leads to a threefold increase in the percutaneous absorption ofseveral steroids applied from acetone vehicles. Occlusion reduces or blocks TEWLand the evaporation of volatile solvents or compounds from the surface of skin. Inturn, this results in a profound (300–400%) increase in the water content of theSC. Most transdermal preparations are partially or completely occlusive. Partialocclusion may also be obtained with formulations based upon petrolatum, oint-ments, or creams, although lotions offer little occlusive activity. In addition, baths



act to increase the water content of the SC and enhance percutaneous absorption.The effect of occlusion on the water content of the SC is relatively transitory, andtypically returns to normal levels within 15 min after removal of an impermeablewrap. Because TEWL also returns to normal level, it is likely that the reduction inbarrier activity is also transitory.

Water uptake by the SC under occlusive conditions is primarily localized inthe corneocytes. Hydration appears to have very little influence on the structureor properties of intercellular lipids. Full hydration of the SC by occlusion appearsto provoke the formation of water pools associated with rough structures. Thesestructures can be considered as small water channels, which reduce the diffu-sional path length and resistance of hydrophilic compounds. However, lipophilicand amphiphilic drugs may also profit from such shortened pathways.

One possible mechanism of occlusion action is that the swelling of the cor-neocytes directly alters the skin barrier function. Swelling of the corneocytes mayprovide an alternative penetration pathway, i.e., by facilitating entry into the cor-neocytes, increasing the diffusivity of compounds through the corneocytes, oraltering the structure of a minor lipid component.

In general, skin permeation enhancers act at the level of the SC.1819 The molec-ular bases to which their activity can be attributed include (1) an increase in thepartitioning of compounds into the SC; (2) an increase in the diffusivity of thecompound through the SC; and (3) a change in the penetration pathway.

The in vitro studies of passive transport of polar molecules like urea, mannitol,sucrose, and raffinose across intact and human epidermal membrane (HEM) pre-treated for 2 h with ethanol, and theoretical analysis of the hindered diffusion,showed that permeation pathways of HEM can be characterized by membraneporosity.1829 Effective pore radii estimates for intact HEM fell between 1.5 and2.5 nm, while similar estimates fell compactly between 1.5 to 2.0 nm for ethanol-pretreated HEM. Thus, an approximately 100-fold increase in permeability forethanol-pretreated HEM relative to intact HEM was explained by increased poros-ity of HEM upon the extraction of HEM lipids by ethanol pretreatment, whilecreating pores with effectively small radii.

Permeation decrease of up to three orders was found for large molecules (8000Da) in comparison with small molecules (∼200 Da).1830 The examination of thepermeation of macromolecules (up to 18 kDa) through ethanol-pretreated (2 h)HEM yielded estimates of effective pore size for this biological membrane in therange of 2.2–5.4 nm.1830 Radii with approximately twice larger pores in studieswith larger molecular size may reflect the existence of a distribution of pore sizes;probe permeants of larger molecular size may yield a larger average pore size thanthose determined with smaller molecular permeants.1829

Such behavior was also observed during skin penetration studies in whichethanol was topically applied.1831, 1834 In these studies, ethanol reduced the bar-rier of the SC owing to its interaction with intercellular lipids that resulted inenhanced SC permeation of topically applied substances, including aspirin. Effectsof ethanol/PG composition on macroscopic barrier properties of the skin were alsoanalyzed.1832


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Recently, ethanol evaporation through the skin was measured after oral intakeof ethanol (0.30 to 0.52 g per kg of body weight) at skin sites differing in thick-ness of the SC and the density of hair follicles and sweat glands.1835 The selectivesealing of the skin appendages had no significant influence on ethanol evapora-tion, which indicates that the evaporation of orally ingested ethanol mostly occursthrough the SC lipid layers. Thus, an influence of ethanol on the penetration oftopically applied products can be expected. However, in the study of Ref. 1035,orally administered ethanol had no effect on the penetration of a topically appliedUV filter substance. Presumably, the available concentration of ethanol within theSC was too small (a theoretical maximum of 1.7 mg per 1 cm2 skin surface) tosignificantly influence its permeation. Therefore, the effect of topically appliedsubstances should not be influenced by a single ethanol dose of 31.2 g, as usedin the study;1835 however, larger alcohol doses may significantly disrupt the skinbarrier function in the body.

Permeability of biological membranes may be induced not only by ethanol: anumber of various chemical agents may serve as enhancers of membrane perme-ation.1815, 1819 For example, polyenic antibiotics increase water permeation througha cell membrane as follows: twofold for Amphotericin B, more than 44-fold forglycerol, and more than 200-fold for urea.1815

DMSO, a polar aprotic solvent, is also a good enhancer.1637, 1727, 1735, 1736, 1819

This is a natural substance derived from wood pulp; it has the unique capabilityto penetrate living tissues, to associate with water, proteins, carbohydrates, nucleicacid, ionic substances, and other constituents of living systems; it possesses hygro-scopic and anti-inflammatory properties; and is FDA approved as a preservative oftransplanting organs and for interstitial cystitis treatment.1836

A concentration of approximately 60% is required for the activity of DMSOto disrupt human skin barrier function; enhancement ratios of 20–200 have beenreported.1819 DMSO provides irreversible disruption of the SC, perhaps by solu-bilizing the intercellular lipids and/or denaturing proteins. Unfortunately, DMSOhas certain side effects, such as skin irritation, chemical instability, degree of dam-age to the SC, and characteristic taste/odor of its oxidation products. Certain otherpolar aprotic solvents also have been experimentally used as enhancers, but onlyone, decylmethylsulfoxide, has found its way into practice.1819

There are a great variety of surfactants that reduce skin barrier function, clas-sified as nonionic, anionic, and cationic by the dependence of their charge atphysiological pH.1753, 1757, 1768, 1819 Certain unsaturated fatty acids increase percu-taneous agent absorption by reducing skin barrier function or by increasing thethermodynamic activity of compounds in some formulations.1819 The monoun-saturated fatty acid oleic acid (C18) is frequently chosen as an enhancer for awide variety of polar and moderately lipophilic compounds.1691, 1746, 1819 Oleic acidincreases TEWL in vivo by approximately 1.5- to twofold, consistent with a gen-eral decrease in skin barrier function. There is a well-established synergy betweenthe enhancing activities of oleic acid and propylene glycol vehicles.1691, 1748, 1819

Stripping of the SC represents the simplest approach to physicallyenhancing the percutaneous absorption of a compound across the skin [see



Fig. 9.29(b)].1706, 1819 Although it is not always suitable for therapeutic applicationsbecause of irritation responses, skin stripping is a very useful scientific tool forevaluating the maximum amount of agent percutaneous absorption that can beexpected from a topical application.1837, 1839

Ultrasound or phonophoresis (sonophoresis) techniques provide enhancedabsorption of low-molecular-weight compounds as well as proteins such asinsulin.757, 1751, 1754, 1801, 1819 A continuous or pulse exposure of US at a frequencyfrom 20 kHz to 10 MHz at intensity of up to 3 W/cm2 can be applied for up to10 min. The intensity is limited by heat production in the tissue. The enhance-ment activity of high-frequency US (5–10 MHz) is connected with the induction ofconvective pathways through hair follicles and disruption of the intercellular lipidlamellae; cavitation phonomena when small air bubbles are formed within the SCplays an important role in its permeation.

A low-frequency US may be particularly suitable for enhancement.1819 In vivoapplication of 20 kHz US to the skin of hairless rats for 1 h resulted in a 100-foldincrease in TEWL and sufficient delivery of insulin through the skin to reduce theblood glucose levels of rats.

Iontophoresis refers to the enhancement of agent percutaneous absorp-tion by the application of moderate (0.5 V/cm2) voltages across the skin [seeFig. 9.29(c)].1706, 1819 Iontophoresis is not restricted to charged ions, and the flux ofuncharged molecules across the skin is also enhanced in a process termed electro-osmosis. This results from the combination of a reduced SC barrier and an inducedsolvent convective flow. Iontophoresis appears to drive molecules through discretesites located in the SC, such as hair follicles and sweat glands. A quantitativecomparison of the flux of ions through appendages and through the intercellularlipid domain is estimated to be between 50% and 95% during iontophoresis.1819

Enhancement of percutaneous absorption by iontophoresis has been studied for awide variety of agents.1819 After a clinically relevant exposure of 0.16 mA/cm2 for1 h, the subsequent permeability of human skin in vitro was reduced tenfold. Thiseffect exists during and after application of the current and is fully reversible afterapproximately 24 h. At higher voltages (5–200 V/cm2) and short pulse exposureelectroporation of biological membranes may occur,1819 that also provides agentpermeation into a tissue.

It was shown recently that laser-generated stress waves (photomechanicalwaves) can also permeabilize the SC.1840, 1843 The permeability of the SC was firstdemonstrated with δ-aminolevulinic acid (ALA) as a probe. The permeability ofthe SC depends on the peak stress. The onset of the permeability of the SC isobserved at ∼380 bar and increases with increasing peak stress. The efficiency ofALA transport through the SC is nonlinear. A small increase in the peak stress,from 440 to 500 bar (14% increase in peak pressure), caused fluorescence intensity(protoporphyrin IX concentration induced by ALA application) to increase by∼200%. The application of stress waves causes no pain or discomfort and does notappear to affect the structure and viability of the skin. The change of the perme-ability of the SC is transient and its barrier function recovers within a few minutes.The increased permeability allows macromolecules to diffuse through the SC to


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epidermis and dermis. The maximum size of particles that have been transportedthrough the SC is 100 nm in diameter.1840 Thus, laser-generated stress wavescan facilitate the transdermal delivery of large particles and molecules, such asnovel probes (carbon, gold, melanin nanoparticles, quantum dots, or encapsulatedmolecular probes), encapsulated drugs, or plasmid DNA. The combined actionof laser-stress waves and anionic surfactant, such as sodium lauryl sulfate (2% ofw/v), enhanced the delivery of nanoparticles through the SC.1840 The applicationof sodium lauryl sulfate increases the size of the channels in the biomembraneand delays the recovery of the SC barrier function. The synergism of light andsurfactant action was manifested as a significant reduction in time interval forproviding similar SC permeation: only 5 min of the application of sodium laurylsulfate was sufficient at laser single pulse action (∼7 J/cm2), instead of a few hourswithout laser pulse, providing peak pressure of ∼600 bar and stress pulse durationof ∼250 ns.

It was also shown that laser-generated stress waves increase the permeabilityof the cell plasma membrane. Increased permeability of skin structures allows theintroduction of macromolecules into SC, cytoplasm of living epidermal cells, andfibrous dermis. Thus, stress waves have the potential to topically and noninvasivelydeliver chemicals into the deep layers of the skin.

As the possible mechanism of the recently proposed method of enhancing skinpermeability by creating a lattice of microzones of limited thermal damage in theSC by applying of a few consequent optical pulses,1718, 1719, 1801, 1825 the phase tran-sition of SC intercellular lipids from gel to liquid crystalline phases due to localheating can be considered.1361, 1844

Alternative techniques for the delivery of clearing agents based on injectionof an agent into the skin with a needle-free injection gun or laser skin surfaceablation, and combinations of these methods, are also under development.1720, 1721

A diode laser source with 980 nm wavelength in conjunction with an artificialabsorber on the skin surface was used to facilitate enhanced penetration of thetopically applied skin clearing agent glycerol into in vivo hamster and rat skin.1721

This technique provides sufficient skin surface heating, which leads to keratinocytedisruption and possibly skin surface ablation of less than 20 μm with a treatmentsite of 16 mm2 during laser beam scanning. Results indicate an improvement in theability to deliver NIR light of 1290 nm up to 36% deeper into in vivo rodent skinby using a laser fluence of less than 96 J/cm2. Higher fluences caused unwantedthermal denaturation of skin tissue.

SC ablation can be provided directly by application of pulsed erbium laserswith wavelengths of 2790–2940 nm corresponding to the strong water absorptionband.1845, 1846 Laser ablation of 12.6% of the surface area of porcine SC produced2.8- and 2.1-fold increases in permeability constant (Pa) for 3H-hydrocortisone and125I-γ-interferon, respectively.1845 These studies demonstrate that a pulsed (250 μspulse width) laser with wavelength of 2790 nm and 1 J/cm2 of fluence densitycan reliably and precisely remove the SC with 10–14 laser pulses, facilitating thepenetration of large molecules that cannot penetrate intact skin, such as 125I-γ-interferon.



Among such modalities tested by the authors of Ref. 1846, including skinmicrodermabrasion, iontophoreses, electroporation, and Er-YAG (λ = 2940 nm)ablation, laser ablation showed the greatest enhancement of ALA permeationthrough pig skin samples. The laser fluence was found to play an important rolein controlling the drug flux, producing fourfold to 246-fold enhancement ratiosrelative to the control. The skin permeation of ALA across microdermabrasion-treated skin was approximately 5–15-fold higher than that across intact skin. Theapplication of iontophoresis or electroporation alone also increased ALA perme-ation by approximately 15-fold and twofold, respectively. The incorporation ofiontophoresis or electroporation with the resurfacing techniques (laser ablation ormicrodermabrasion) caused a profound synergistic effect on ALA permeation.

For multiarea skin perforation, FLMA provided by a multibeam erbium laser(λ = 2940 nm) was examined with variable beam configuration (circular spots orlines), transverse spatial frequency of structured illumination and depth of skindamage.1801

The SC functions not only as a barrier against penetration of a clearingagent into skin, but also as a reservoir for topically applied substances.1847, 1848

Skin appendages, particularly sebaceous glands, also serve as reservoirs for clear-ing agents.1653, 1655, 1837, 1849 Therefore, for the development of technologies forthe topical application of clearing agents, knowledge about the reservoir func-tion is of fundamental interest. The long-term functioning of the reservoir ofthe SC in human skin was investigated in vivo by using laser confocal scanningmicroscopy and the tape stripping method where the long-term reservoir of the SCwas determined both qualitatively and quantitatively, depending on the polarityof the applied formulation.1847, 1848 Formulations with different physicochemi-cal properties were studied. A follicular long-term reservoir was only observedfor the hydrophilic sodium fluorescein after its application in PG. Follicularpenetration of dyes was also reported for the application of emulsions,1837 sol-vents such as ethanol and glycerol,1653, 1655 or 5-μm microspheres containing dyeand suspended in silicon oil at w/w concentration of 4%.1849 The penetrationdepth and reservoir properties of human skin in vivo for MB and ICG dissolvedin ethanol/glycerol solvents were recently reported.1653, 1655 These studies wereapplied for the improvement of sebaceous glands functioning for photodynamicacne treatment; the most intensive staining of sebaceous glands was just after the15–20 min massage and heating procedure. It was also shown that highly porousnylon microspheres suspended in silicon oil provide penetration depth of MB intohairless rat skin in vivo of up to 150 and 400 μm in 2 and 26 h, respectively.1849

The results of the study, described in Refs. 1653–1655 and 1847–1849, ledto the assumption that the better the penetration into the SC and the follicles,the longer the reservoir will remain there. Two pathways of dye release fromthe reservoir are possible: (1) desquamation of the SC and the release of sebum,respectively, or (2) penetration into the viable tissue.

In conclusion, the efficiency of topically applied UV skin filters may be signif-icantly reduced if inappropriate cosmetic compositions are used as ground material


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for such a filter. Two primary effects can be important: (1) reduction of light scat-tering in SC due to optical immersion and (2) inhomogeneous distribution of thetopically applied substances. Both effects lead to reduction in the efficiency ofUV filters: first, because of fewer interactions of migrating photons in skin withsunscreen material at less scattering; and second, because of the formation ofislands free of sunscreen, which do not block UV radiations. The second problemis analyzed in detail in Ref. 1839.

9.5 Optical Clearing of Digestive Tract Tissue

9.5.1 Spectral measurements

The mucosa is a gate for applying OCA to provide optical clearing of the tis-sues of the digestive tract, particularly stomach tissues. Mucosa consists of moistepithelium and the connective tissue immediately beneath it. Mucosal structureis almost identical to skin, with cell epidermal and fibrous dermal layers. Theabsence of the dead cell layer, such as SC of skin, makes normal mucosa morepermeable for chemical agents. Studies of optical clearing of stomach tissues arepresented in Refs. 1336, 1636, 1637, 1676, 1677, and 1691. Transmittance and dif-fuse reflectance measurements were performed over a range from 800 to 2200 nmfor 1.2–1.6-mm-thick frozen-thawed and fresh native porcine stomach cardiac andpyloric mucosa sections. Immersion solutions (glycerol/DMSO/water) of differentconcentrations were topically applied onto the epithelium surface of the sample,then spectra were acquired at time intervals of 5, 10, 20, and 30 min. The dif-ference in apparent absorbance (extracted from the diffuse reflectance) betweentwo wavelengths (1936 and 1100 nm) was used to estimate water content. Someresults are presented in Fig. 9.40. Figures 9.40(a) and 9.40(b) show that, over thewhole wavelength range investigated, the transmittance increased with time anddiffuse reflectance decreased over the range of 800–1370 nm. The greatest increasein transmittance was at 1278 nm, and the greatest decrease in reflectance was at1066 nm.

A strong correlation has been found between optical clearing and water des-orption.1636, 1637, 1676, 1690, 1691 At 30 min after treatment, 80% glycerol caused 15%water loss, whereas 50% glycerol and 50% DMSO caused 9% and 7% water losses,respectively. The patterns of optical clearing are similar to those of water desorp-tion. The water loss was maximal (∼19 %) and optical transmittance at 1278 nmwas also maximal (∼30%) for a mixture of 50% of glycerol and 30% of DMSO(synergetic effect).

Reduction in the scattering and water absorption allows one to obtain morepronounced signatures of absorbing bands of tissue components. In particular, thisis demonstrated by apparent absorbance spectra (1400–2200 nm) in Fig. 9.40(c),measured at application of 50% DMSO solution. The major features of these spec-tra are the bands near 1450 and 1936 nm, corresponding to the first overtone of OHstretch in water and the combination mode of OH stretch and HOH bends in water,respectively. DMSO application significantly changes the absorbance spectrum of



Figure 9.40 Optical changes for fresh pyloric mucosa of porcine stomach before andafter application of immersion solution measured by spectrophotometer with an integratingsphere at the time intervals of 0, 5, 10, 20, and 30 min [(a) and (b) from bottom to top, and(c) from top to bottom], respectively. Total transmittance (a) and diffuse reflectance (b) overthe range 800–2200 nm after topical application of 80% glycerol onto the epithelium surfaceof the sample of thickness 1.6 ± 0.2 mm (see Refs. 1336 and 1636). Apparent absorbancespectra calculated from diffuse reflectance measurements over the range 1400–2200 nmafter application of 50% DMSO to sample of thickness 1.15 ± 0.12 mm (c) (see Ref. 1637).

the tissue. The peaks of 1730 and 1675 nm appeared at 5 min after DMSO admin-istration, i.e., with water loss (scattering and water absorption reduction), and maycorrespond to resolvable CH groups in lipids and proteins.

9.5.2 OCT imaging

In vitro studies of optical clearing of gastrointestinal tissues, such as stomach,esophagus, and colonic mucosa, were also performed by using an OCT imagingtechnique.1632, 1633, 1636, 1677, 1677, 1774 Figure 9.41 shows two OCT images of normalfresh human stomach tissue (fundus), intact and treated by 80% propylene gly-col solution. A clearer image with excellent differentiation of epithelium, isthmus,lamina propria, and muscular tissue is achieved following agent action.1632, 1633

Figure 9.42 illustrates M-mode OCT images obtained from repeated A-scansof a porcine stomach with the application of glycerol.1677 From the image, it is clearthat the penetration depth increases gradually with the increase of time. There is


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Figure 9.41 OCT images of a normal fresh human stomach tissue (fundus): without (a)and with (b) topical application of 80% propylene glycol solution. E, epithelium; LP, laminapropia; MM, muscularis mucosae (see Ref. 1632).

Figure 9.42 Time course of repeated OCT A-scans of porcine stomach tissue with theapplication of glycerol. Horizontal and vertical axes present time (min) and imaging depth(mm), respectively; registration of OCT signal starts at the time approximately 0.5 min afteragent application (see Ref. 1677).

a slope of the surface of the tissue. The downward trend of the tissue surface isattributed to the tissue dehydration induced by the chemical agent.

OCT in vitro studies of glucose diffusion in normal and diseased [esophagealsquamous cell carcinoma (ESCC)] human esophageal epithelium have demon-strated that cancerous tissue is more permeable for glucose.1774 The permeabilitycoefficient of 40% aqueous solution of glucose was measured as (1.74 ± 0.04)× 10−5 cm·s−1 in normal esophagus and (2.45 ± 0.06) × 10−5 cm·s−1 in ESCCtissues. However, during the same time interval for glucose application, opticalclearing efficiency, i.e., light penetration depth, was significantly smaller for theESCC tissues than that of normal esophagus tissues. This finding, in addition tothe quantification of optical clearing rate and efficiency, allows one to differentiatenormal and cancerous tissues due to their different responses to OCA.

The preceding experiments were performed on in vitro biological tissues. Thedynamic optical clearing effect induced by the chemical agent will differ from that



for in vivo cases. Because of the self-regulation and blood circulation of cells,the living tissues would experience less dehydration after the application of ahyperosmotic chemical agent.

9.6 Optical Clearing of Other Tissues

9.6.1 Muscle

The human body contains a large quantity of skeletal muscle. The principal func-tion of this tissue is to provide the movement of bones and body parts. Theinternal structure of the muscle consists of orientated muscle fibers surroundedby ISF, which primarily contains water and some dissolved salts and minerals.Owing to the heterogeneous composition of skeletal muscle, its refractive indexprofile presents localized discontinuities at the boundaries between the musclefibers and the ISF. It is known that human muscular fibers have a refractive indexof 1.41,1285 which is higher than the refractive index of ISF distributed aroundthe fibers. Considering the tissue optics of the muscle, mismatch of the refractiveindex between fibers and ISF will cause major light scattering for an optical beamtraveling inside.

Thus, skeletal muscle is another example of a tissue in which a significantdifference between refractive indices of scatterers and ISF is observed.1740 A modelfor rat muscle tissue that contains dry scatterers with a refractive index of 1.584distributed through the ISF, which is primarily composed of water with a refractiveindex of 1.333, was experimentally proved.1386 Actually, for natural rat muscle, theglobal refractive index is 1.398, water content is 0.756, and solid part content is0.244 with index of refraction of 1.584; thus, scatterers attributable to hydration oftheir material have a lower index of refraction equal to 1.41.1285 Skeletal muscle canbe submitted to optical clearing to reduce this refractive index mismatch.1850, 1851

The study of OCA diffusion into the tissue is significant for the understandingof the mechanisms involved in optical clearing and time efficiency of treat-ment.1613 Aiming to understand how OCAs interact with tissues, several studieswere conducted with results for the diffusion time for certain OCAs like dimethylsulphoxide,1791 glucose,1339, 1652, 1774, 1850, 1851 mannitol,1652 and glycerol1772 in dif-ferent tissues, including cancerous tissues.1774 Along with the experimental meth-ods, some mathematical models have been developed to describe agent diffusionin tissues.200, 1634, 1758

With the objective of studying OCA diffusion into skeletal muscle, a simplemethod can be adopted to estimate the diffusion time and coefficient of an OCA.This method is based on measuring the temporal spectra for collimated transmit-tance of tissue samples under treatment.238 For example, when aqueous solutionsof glucose at different concentrations are used as OCAs, from the adjustments ofexperimental data with models of free diffusion of glucose molecules in muscle tis-sue, the diffusion time for each treatment can be determined.1850, 1851 The analysisof the diffusion time as a function of glucose concentration in the solution allowsfor estimating the true diffusion coefficient of glucose in muscle tissue.1850, 1851


492 Chapter 9

Figure 9.43 Assembly for collimated transmittance measurements (see Ref. 1851).

Considering that glucose molecules undertake free diffusion when entering theinterstitial space of muscle tissue, which has a slab form with thickness d, andthat the agent simultaneously diffuses through both surfaces of the slab, the dif-fusion is characterized by Eq. (9.2). This equation allows for the determination ofthe time dependence of OCA concentration, Ca, at any unidirectional position, x,between the two surfaces. When OCA diffuses through two surfaces of the tissueslab, the diffusion time of OCA is related to the diffusion coefficient by Eq. (9.4).If the volume of solution is significantly higher than the volume of the slab, we candetermine the amount of dissolved matter, mt, at the moment, t, to its equilibriumvalue, m∞, according to Eq. (9.5). The ratio in this equation defines the volumeaveraged concentration of an agent, Ca(t), within the slab at time t. As a first-orderapproximation, this equation has a solution given by Eq. (9.6), from which a rela-tion between the time dependence of OCA concentration within the sample andits characteristic diffusion time, τ, is established. When using τ in Eq. (9.4), thecorresponding diffusion coefficient, Da, can be calculated. These two parametersestimate glucose diffusion in skeletal muscle.1851

To perform the study, the skeletal muscles from the abdominal wall of rat—Wistar Han species—were selected. After sacrificing one animal, the entire muscleblock from the abdominal wall was retrieved. From that block and by using acryostat, eight samples were sliced with an approximately circular form, 10 mmin diameter and 0.5 mm thickness. Using a measuring assembly presented incross section in Fig. 9.43, the collimated transmittance of the samples was mea-sured. The pinholes shown in this figure have a circular form to fix the sample.The sample holder has a central hole 1 mm in diameter to allow the passage oflight. After measuring the natural sample (control), the sample was immersed inan aqueous solution. The concentrations of glucose in the solutions were 20%,25%, 30%, 35%, 40%, 45%, 50%, and 54%. The total number of samples understudy was eight: one for each treatment. The agent was delivered by a lateralopening that is not shown in the cross-sectional representation in Fig. 9.43. Thecollimated transmittance was measured each second for whole spectra from 400to 1000 nm (for each second, 37 spectra were averaged) for a period of 30 min.Figure 9.44 represents the time variations of collimated transmittance for some ofthe treatments. Similar time dependences were obtained for the other treatments.



Figure 9.44 Time dependence for collimated transmittance observed for the treatmentswith: 20% glucose (a), 35% glucose (b), 40% glucose (c), 50% glucose (d) (see Ref. 1851).


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Table 9.4 Mean and standard deviation (SD) values for the diffusion time, τG/W, fordifferent treatments (n = 11) (see Ref. 1851).

Concentration of glu-cose in solution, %

20 25 30 35 40 45 50 54

Mean diffusion time, s 65.9 72.0 77.3 138.3 300.0 209.4 103.6 58.4SD, s 1.8 2.0 2.2 4.3 4.9 7.4 7.0 7.9

To determine the average time variation of collimated transmittance, data fordifferent wavelengths, each 20 nm between 600 and 800 nm, where the tissuespectral profile is mostly sensitive to scattering, were selected and processed. Alldisplaced and normalized data sets were adjusted with the equation

Tc (λ) = 1 − exp

(− t

τG/W

), (9.43)

where τG/W represents the diffusion time of the combined fluxes in each treatment[water (W) out and glucose (G) into the tissue].

As shown in Fig. 9.44, for the treatment with the lowest concentration ofglucose in solution (20%), a regime takes place of fast diffusion and slightlydecreasing saturation. This means that the immersion solution contains a largeamount of water comparable to tissue water content. Possibly, in this case, twowater fluxes are created: one is directed inside tissue and caused by differencesbetween water concentration inside and outside; the other is directed from thetissue and caused by the osmotic action of glucose. Therefore, because of thestrong involvement of small water molecules in the diffusion process, the totaltime response of the diffusion process is short (fast diffusion). After the satura-tion regime is reached, the tissue needs to compensate for its partial dehydrationcaused by glucose impact, so it starts to receive water from the solution to createa balance; tissue swelling may be created with some decay of collimated transmit-tance for longer times. Such decreasing behavior during saturation is not seen inthe other treatments presented in Fig. 9.44. Considering the various solutions inuse, as glucose concentration increases [Figs. 9.44(b) and 9.44(c)], the water con-tent of the solution becomes similar to the free water content in the tissue and waterflux decreases (it becomes approximately zero when the glucose concentration is∼40%) [Fig. 9.44(c)]. This means that only glucose diffuses freely in the systemand the diffusivity parameters depend only on diffusion parameters of larger glu-cose molecules, thus, we see the maximal value of the measured diffusion time[Fig. 9.44(c)]. However, at higher glucose concentration, we again see a decreasein diffusion time, τG/W [Fig. 9.44(d)], because water is again involved in the dif-fusion process, with the primary flux directed from tissue to surrounding solutiondue to glucose hyperosmolarity.

For a particular glucose concentration, the mean and standard deviation for thediffusion time, measured at 11 wavelengths, were calculated1851 (see Table 9.4).



Figure 9.45 Diffusion time, τG/W, as a function of glucose concentration in solution (seeRef. 1851).

Figure 9.45 shows the mean diffusion time of glucose as a function of glucoseconcentration in the solutions. This dependence reaches a maximum for a con-centration of 40.5%. This maximum indicates that an aqueous solution with thisconcentration of glucose would have the same amount of water as free water in thetissue. In such a case, no or very weak water flux occurs with only glucose flux intothe tissue. Thus, the obtained diffusion time of 302.9 s is mostly due to diffusionof glucose molecules, τG, and represents the true diffusion time of glucose in theskeletal muscle. Using this value and considering that the slab thickness is 0.5 mm,the diffusion coefficient of glucose in muscle can be calculated with the help ofEq. (9.4):

DG = d2

π2τG= 0.052

π2 × 302.9= 8.36 × 10−7 cm2 · s−1 (9.44)

From these measurements and analyses, we can also estimate the tissue to havea free water content of 59.5%. This value is smaller than 75.6% of total watercontent for the skeletal muscle of rat.1392 This means that the remaining 16.1% ofwater is bound to the tissue components and does not participate in the dehydrationmechanism during optical clearing, at least on the time scale of 30 min.

Because the single wavelength measurements of the collimated transmittanceare sufficient for quantification of diffusion parameters, brighter light sources, suchas lasers and LEDs, can be used to measure thicker tissue samples. Similar studiescan be performed with different OCAs to determine their diffusion properties inskeletal muscle and other tissues.

The behavior of specular reflectance at immersion optical clearing (IOC) isalso of great interest, because certain light scattering diagnostic techniques (seeSection 10.4), including polarization-sensitive methods, are based on the detec-tion of light scattered by superficial tissue layers, where specular reflectance anddiffusely scattered light dominate in the direction of the specular beam. The mea-suring assembly represented in Fig. 9.45(a) allows for measurements of temporalspecular reflectance spectra, RS(λ), at the angle of 8 deg within a certain small


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field of view around this angle.1850 The time evolutions for rat muscle tissue treat-ment with 40% glucose are represented in Fig. 9.45(b). Because of tissue surfaceroughness, refractive index mismatch at the interface, and light beam penetrationinto tissue, there is a great contribution of light scattering in the specular reflectedspectra. During tissue treatment on a short time scale, two leading mechanismsmight be involved—agent diffusion into the tissue and tissue dehydration. The firstmechanism causes refractive index matching of the top tissue layers and reductionin tissue surface roughness. The second mechanism mostly leads to better homo-geneity of the upper tissue layers due to better packing of scatterers and matchingof their refractive index regarding ISF, and therefore, eliminates inclusion of tissuebulk scattering into specular reflection. As a consequence, the measured specularreflectance decreases greatly in the first few seconds of the treatment and tendstoward the value determined by Fresnel’s formula.

In the study described in Ref. 1850, very fast (∼5 s) specular reflectance decay(twofold) for 40% glucose application was found. Because this is caused by fastglucose permeation via thin tissue layers, we can estimate the thickness of this layerfrom Eq. (9.4), based on the previously presented estimation of glucose diffusioncoefficient for muscle tissue, determined by Eq. (9.44):

lspecular = √DG · τspecular = √

5 × 83.6 × 10−4 cm ∼= 21 μm. (9.45)

From this estimation, it follows that an OCA superficially interacting with tis-sue can rapidly and efficiently eliminate light scattering from a tissue layer of acontrollable depth, and through this interaction, can improve polarization-sensitiveand light-scattering diagnostic technologies to be applicable for deeper layers.

9.6.2 Breast and lung

Several further studies investigated the possibility of differentiation between nor-mal and pathological tissues based on OCA molecular permeability rates in othertissue types, such as female breast1772,1773 and lung.1775 The corresponding studiesof esophagus tissues1774 are discussed in Section 9.5. In particular, it has beenfound that in pathological lung tissue with benign granulomatosis, adenocarci-noma tumor, and squamous cell carcinoma, the permeability coefficient of 30%glucose compared with that from normal lung tissue increases up to 32%, 113%,and 162%, respectively.1775 These findings make the IOC method a prospectivetechnique for early identification of pathological alternations of the tissues; IOCcan be considered as an additional biomarker of tissue pathology.

The permeability coefficient and percentage of OCT signal enhancement (%)upon application of 20% and 40% glucose, and 20% mannitol, to normal andcancerous breast tissues have been investigated in vitro.1773 These data are summa-rized in Fig. 9.47 and Table 9.5. As shown, the OCT technique could distinguishbetween normal and cancerous tissues due to the statistically significant differencebetween measured magnitudes of permeability coefficient and percentage of OCTsignal enhancement at IOC for these tissues. The comparison between magnitudesof permeability coefficient of two glucose–water solutions with concentrations of



Table 9.5 Percentage of OCT signal enhancement (%) inhuman breast tissue at IOC (see Ref. 1773).

Analyte Normal breast tissue Cancerous breast tissue

20% glucose 72.2 ± 12.3 37.8 ± 8.340% glucose 93.0 ± 11.7 58.2 ± 9.920% mannitol 51.2 ± 7.8 26.2 ± 7.2

Table 9.6 Mean permeation rate of 30% glucose in normal and pathological lung tissues atglucose delivery by SPD; OCT measurements (see Ref. 1775).

Permeation rate ±SD, × 105, cm·s−1

Normal lung (NL) Lung benigngranulomatosis(LBG)

Lung adenocarcinomatumor (LAT)

Lung squamous cellcarcinoma (LSCC)

30% glucose/SPD 2.01 ± 0.21 2.75 ± 0.28 4.53 ± 0.49 5.81 ± 0.62

20% and 40% showed that the permeability rate is slower for 40% glucose, whichaccurately fits the data presented in Fig. 9.45 (also see discussion nearby). It is alsoclear that the permeability of breast cancer tissue is better than that of normal breasttissue and that the OCT technique is capable of distinguishing the cancerous tissuesfrom normal tissues. In turn, the optical clearing efficacy has better performancefor higher than lower concentrated OCAs, and the efficacy in normal tissue is alsobetter than that in cancerous tissue, as presented in Table 9.5. These data clearlydemonstrate that the IOC method can potentially be applied for characterization ofbreast tissue and early diagnosis of breast cancer. Needle OCT probes1412 will beuseful for imaging and quantification of the morphology and metabolic activity ofcancerous breast tissue.

Another example of the successful application of the IOC technique for differ-entiation between normal and cancerous lung tissue is described in Ref. 1775. Tomake this technique more robust, these authors used US-mediated OCA enhanceddiffusion [sonophoretic delivery (SPD)] into normal, benign, and cancerous humanlung tissue in vitro. The Fourier-domain OCT system was used for the evaluation ofpermeability coefficients at SPD. SPD was provided at a frequency of 1 MHz andan intensity of 0.80 W/cm2 over a 3-cm probe. SPD and OCA were simultaneouslyapplied for 15 min. Experimental results for mean values of permeability coeffi-cient for the delivery of 30% glucose into normal lung tissue (NL), lung benigngranulomatosis (LBG) tissue, lung adenocarcinoma tumor (LAT), and lung squa-mous cell carcinoma (LSCC) are listed in Table 9.6. The permeability coefficientof 30% glucose/SPD strongly depends on tissue condition. It increases comparedwith that for the NL tissue to 36.8%, 125.4%, and 189.1% for the LBG, LAT,and LSCC tissue, respectively. Statistically significant differences (p < 0.05) werefound in magnitudes of permeability coefficient between all types of pathologyand NL tissue. These results suggest that the OCT functional imaging techniquecombined with US OCA delivery may become a powerful tool in early diagnosis


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Figure 9.46 Specular reflectance measuring assembly (a) and measurement results at ratmuscle tissue treatment with 40% glucose (b) during the first minute (upper) and 30 min(lower) (see Ref. 1850).

and monitoring of microstructure and functionality of pathologic human lung tis-sue. Endoscopic OCT technologies, described in Chapter 14, should be an optimalbasis for the corresponding hardware for in vivo studies.

9.6.3 Cranial bone

Skeletal and skull bones and teeth are typical representatives of hard tissues. IOCof these tissues also may be useful in a number of applications.1308, 1309, 1341, 1343, 1784

For example, the possibility of selective optical translucence of cranial bone may



Figure 9.47 Comparison of the mean permeability coefficients of 20% and 40% glucose,and 20% mannitol in normal (left bar) and cancerous (right bar) breast tissues (see Ref.1773).

be of great importance for brain optical functional imaging and laser therapy of anumber of brain diseases, including stroke.176

Bone consists of inorganic and organic matrices. The inorganic (mineral)matrix mostly contains hydroxyapatite [Ca10(PO4)6(OH)2], which is responsiblefor the compressive strength of bone. The main components of the organic matrixare collagen, other proteins, lipids, and blood cells. Normally, bone is composedof 50–60% mineral components, 20–30% organic material, 10–20% water, and<3% lipids.6 To briefly summarize the structural properties of bones, which areessential for understanding IOC mechanisms and efficiency, we will follow Ref.1342. It is important that the porosity of the bones is of 5–10%. Bone is com-posed of osteons and differentiated into cortical bone, which is dense and solidand surrounds the marrow space, and trabecular bone, which is composed of ahoneycomb-like network of trabecular plates and rods interspersed in the bonemarrow space. At microstructural level, cortical bone is organized into 200–300μm diameter secondary osteons, which are composed of large vascular channels(50–90 μm diameter) surrounded by circumferential lamellar rings (3–7 μm thick),with so-called “cement lines” at the outer boundary. At the nanostructural level,the lamellae are composed of organic type-I mineralized collagen fibers (up to15 μm in length, 50–70 nm in diameter, and formed by regular arrangement ofsubnanostructural collagen molecules), bound and impregnated with inorganic car-bonated apatite nanocrystals (approximately 30 nm in length and width, 2–3 nm inthickness).

Water is significantly important for living bone and is one of its majorcomponents. Bone water occurs at various locations and in different binding states:


500 Chapter 9

bound to the mineral or organic components, or free (bulk water). The strongestwater is bound in the apatite-like crystals (approximately 35 mg of water/g min-eral). Bulk water fills the pores of the calcified matrix, which form a network ofinterconnecting channels (the lacuna-canalicular system), which communicate theHaversian canals (the bone vascular system) with the osteocytes embedded in themineralized matrix. This communication network serves the transport of nutrients,waste products, and signaling molecules from the vascular system to the osteocytesand vice versa.

The refractive index of whole cranial bone at various stages of mineralizationranges from 1.555 to 1.564.1342 Bone tissue components have the following refrac-tive indices: apatite, >1.623; hydrated collagen (type I), 1.43; and lipids, ∼1.45(see Table 7.1).

The in vitro IOC of human and porcine cranial bone under the action of PGand glycerol was initially demonstrated in Refs. 1342 and 1343. For this study, fiveporcine and 10 human cranial bone samples were used. All bone samples were cor-tical (or compact) bones. The samples of human cranial bone were obtained frompostmortem examinations. The thickness of each bone sample was measured witha micrometer in several points over the sample surface and averaged. Thickness ofthe samples varied from 1.6 ± 0.1 to 5.0 ± 0.5 mm. The refractive indices at 589nm of PG and glycerol were measured as 1.43 and 1.47, respectively.

The measurements of bone reflectance were performed in the spectral rangeof 450–1000 nm by using a LESA-5 commercial spectrometer (BioSpec, Moscow,Russia) and a fiber-optical probe with seven optical fibers. All fibers had a 200 μmcore diameter, NA of 0.22, and distance between the delivering and receiving fibercenters of 290 μm. The total transmittance and diffuse reflectance measurementswere performed in the 800–2000 nm wavelength range by using a CARY-2415commercial spectrophotometer (Varian, Australia) with an integrating sphere. Forprocessing the experimental data, IAD was used (see Chapter 7), and the anisotropyfactor was fixed as 0.9.

In Fig. 9.48, reflectance spectra of cranial porcine bone upon its impregnationby PG are shown. In the spectra, spectral bands corresponding to blood absorptionin the visible range are clear. The action of immersion agent produces a ratherfast, strong decrease in the reflectance of the bone tissue in the whole spectralrange. This happens due to rapid impregnation of the upper tissue layers by theOCA and corresponding decrease of light scattering, and also indicates that bonebecomes more transparent with these layers. The depth of probing in this case wasapproximately 100–200 μm for the given center-to-center separation of the sourceand detector fibers.

Figure 9.49 demonstrates changes in optical parameters of human cranial bonein the spectral range 800–2000 nm before and after administration of glycerol.Absorption and reduced scattering coefficients were reconstructed by the IADmethod using the measured total transmittance and diffuse reflectance of the bonesample. In the NIR, the absorption bands of water at 978, 1192, 1464, and 1930nm, and lipid band at 1745 nm were clearly observed.1707, 1710 Overall, the admin-istration of hyperosmotic solutions into cranial bone tissue allows for effective



Figure 9.48 Reflectance spectra of cranial porcine bone with administration of propyleneglycol for different time intervals (see Ref. 1342).

Figure 9.49 Spectral dependencies of absorption and reduced scattering coefficients ofhuman cranial bone sample measured before (1) and after administration of glycerol duringone hour (2) (see Ref. 1342). Black circles represent data for untreated bone (see Ref.1309), and open circles represent untreated skull (see Ref. 1308).

control of its optical properties in the NIR. Because of the reduction in scatter-ing and absorption due to matching of the refractive indices of scatterers/ISF andtissue dehydration, the transparency of bone increases for particular wavelengths.Scatterers in bone tissues are large osteons, 200–300 μm in diameter, and 50–90μm diameter cavities between osteons, as well as nanostructures, all of which causethe complex characteristics of light scattering.

We can conclude that under 20-min action of PG, the decrease of bonereflectance probed within the depth of 100–200 μm can be 70%. Additional studyof tissue samples a few millimeters in thickness, using total transmittance and dif-fuse reflectance with integrating sphere, shows the decrease of both absorption andreduced scattering coefficient up to 20% and 30%, respectively, under the action


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of glycerol during one hour. This means that effective translucence of the super-ficial tissue layers has a strong impact on the overall tissue transmittance. Thepresented results can be useful for functional brain and bone-related imaging byOCT, reflectance spectroscopy, and other optical modalities.

In vivo studies for mice, which demonstrate with evidence that the turbidmouse skull became transparent within 25 min after application of innovative skulloptical clearing solution (SOCS), were pioneered by Zhu et al.1784 SOCS was com-posed of various biocompatible agents, whose main components included laurinol,weak alkaline substances, EDTA, dimethyl sulfoxide, sorbitol, alcohol, and glu-cose. Figures 9.50(a), 9.50(b), and 9.50(c) show typical white-light images of theintact mouse skull, treated skull, and removed skull rectangle area A; Figs. 9.50(d),9.50(e), and 9.50(f) show magnified white-light images of rectangle area A; andFigs. 9.50(g), 9.50(h), and 9.50(i) show speckle contrast images of the blood flowin vessels within area A. It is clear that the intact skull is turbid, and the corti-cal blood vessels are hardly distinguishable. After treatment with SOCS, the skullbecomes transparent and the cortical vessels can be observed clearly.

The minimum resolution diameter of a vessel was 14.4 ± 0.8 μm at imag-ing through the optically transparent skull after treatment with SOCS for 25 min[Fig. 9.50(e)], and 12.8 ± 0.9 μm for cranium window A with removed bone[Fig. 9.50(f)]. The speckle contrast images show that the only blood flow of afew large vessels can be measured hazily through the intact skull, whereas theblood flow distribution of cortical microvessels can be distinguished clearly indetail through the IOC skull, which is consistent with that through cranium win-dow A. Therefore, it can be concluded that the IOC method enhances the contrastof both white-light and speckle images, which provides nondestructive creation ofa transparent cranial window for accessing high-resolution cortical structural andfunctional information.

9.6.4 Tooth dentin

Molecular diffusion in the other hard tissues, such as human tooth750,751,1341,1705

and nail,1235, 1341 were also studied using the IOC technique. Diffusion of water anddental liquor is necessary for correct functioning of teeth. For example, water sup-ply affects tooth hardness.152 Monitoring and control of dental tissue permeabilityare important for recognition and healing of dental pathologies, disease treatment,and hygienic tooth whitening.

For example, OCAs such as PG, when used as dye vehicles, allow dye to exitfaster through the apical tooth foramen.1705 A comparable study1705 of PG anddistilled water as solutes for the dye demonstrated that the area and depth of pene-tration of dye dissolved in PG was significantly greater than that in distilled water(p < 0.0001). The overall mean time for dye to be released was 0.60 min for the PGgroup (n = 28) and 2.19 min for the distilled water group (n = 14). PG rapidly andmore effectively delivered dye through the root canal system, indicating its poten-tial use in pathology imaging and delivering intracanal medicaments. Fortunately,concentrated solutions of PG have marked germicidal efficiency, and its use as a



Figure 9.50 White-light images of intact mouse skull (a), transparent skull after SOCS treat-ment for 25 min (b), and with removed rectangle area A (c). Corresponding magnified whiteimages (d–f) and speckle contrast images and (g–i) are within rectangle area A shown in(a–c) (see Ref. 1784). (See color plates.)

vehicle may provide the potential for preventing or treating microbial infectionsthat invade and reside deeply within dentinal tubules.1705

One exciting OCT application is its use for diagnostics of disease-caused struc-tural changes in dental tissues.136, 156, 635, 636, 1341 Using OCT, the study of OCAdelivery to dentin samples can be implemented in two geometries (see Fig. 9.51):(1) the sample is placed in a cuvette that is filled up by an OCA, and OCT scanningis performed through this OCA layer, covering the sample (front-side impregna-tion); (2) the sample is glued to the cuvette opening and OCA diffuses via thebackside sample interface (backside impregnation). The samples were covered bya layer of hermetic lacquer that insulates diffusion of OCA into the tissue andprevents its evaporation, except for a window for OCA diffusion and light pen-etration in the case of single-side OCA impregnation, and two windows on theopposite sides of the sample in the case of backside OCA impregnation. In bothcases, because of slow diffusion and relatively thick samples, OCT scanning wasperformed repeatedly during a few hours. Figure 9.52 shows an example of exper-imental results for water diffusion in two geometries. The difference betweenthe A-scan behavior for front-side [Fig. 9.52(a)] and backside ([Fig. 9.52(b)]


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Figure 9.51 Schematics of diffusion agent application and OCT registration: front impreg-nation (a), back side impregnation (b); 1 is the cuvette with diffusion agent, 2 is the toothsample, 3 (black line) is the layer of the lacquer, the insulating diffusion of agent into thetissue and preventing its evaporation (see Refs. 750 and 751).

Table 9.7 Tooth dentin structural and diffusion properties obtained frommicroscopy and OCT (see Ref. 750).

Sample Thickness, mm Mean tubulediameter, μm

Agent Permeability coefficient,P ± SD, × 106 (cm·s−1)

1 0.9 0.60 ± 0.10 Water 3.04 ± 0.132 1.3 2.30 ± 0.15 Water 40.2 ± 2.43 1.2 1.60 ± 0.13 Water 2.09 ± 0.654 0.8 2.40 ± 0.55 44% glycerol 4.91 ± 0.67

impregnation may be explained by the competitive impact of the mean attenua-tion and backreflectance coefficients on OCT signal amplitude. Both coefficientsdecrease upon immersion agent action, but reduction of the attenuation coefficientimproves OCT signal amplitude from the sample depth, because the reduction ofthe backreflectance causes a corresponding decrease in OCT signal amplitude.One remarkable finding is that, in both cases, the mean slope of the OCT signaldecreases with time and agrees well with the characteristic times of slope decrease.

Application of an OCA through the backside of the sample is free of the arti-facts caused by the liquid layer over the sample during front-side application.Hence, backside OCA application was used in further experiments with otheragents.750, 751, 1341 Results of similar measurements conducted for other samplesunder diffusion of water and 44% glycerol aqueous solution are summarized inTable 9.7. They demonstrate strong correlation between the diffusion rate and thesample structure, i.e., the diameter and number density of tubules.

Studies of glucose diffusion in dentin and its impact on dentin permeabilityfor water and other agents are important for understanding and treatment of toothpathologies related to diabetes mellitus in humans.1341 Glucose might have a directeffect on the odontoblastic metabolism because it decreases type I collagen syn-thesis in mature human odontoblasts. It may also promote the formation of cariouslesions. It has been found that the permeability coefficient for 35% aqueous solu-tion of glucose is about two orders of magnitude smaller than that for water.1341 The



Figure 9.52 Examples of OCT monitoring of water diffusion in human tooth dentin: aver-aged A-scans taken at different time elapsed after in front (a) and back side (b) applicationof water (see Fig. 9.51); curve 1, initial state; 2, in 56 min; 3, in 209 min (a); curve 1, initialstate; 2, in 7 min; 3, in 78 min (b); mean OCT signal slope versus time for in front (c) andback side (d) application. Probed depths are 150–300 μm for (c) and 60–300 μm for (d)(see Refs. 750, 751 and 1341).

greater molecule size of glucose in comparison with water and the molecular bind-ing with tissue components can explain the unsatisfactory permeability of glucose.

To test glucose impact on dentinal tissue permeability for water, the diffusionprocess of water in dentin was investigated before and after long-term incubationof tooth samples with glucose.1341 The samples were kept in 35% aqueous glucosesolution for 5 days, then washed and dried in the same way as control measure-ments with intact samples. The permeability coefficients of samples intact andthose incubated with glucose were found to be (2.59 ± 1.63) × 10−4 and (3.86± 0.39) × 10−4 cm·s−1 respectively. Thus, the long-term glucose impact on toothdentin results in irreversible changes to the tissue structural properties that may beassociated with glycation of collagen contained in intertubular dentin. Owing tocollagen glycation, intertubular dentin became denser, and hence, tubules becamelooser with more space, which facilitates diffusion of the agent.


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Figure 9.53 Polarization images of a sclera sample (white light source, crossed polarizers).Images from left to the right correspond to 4, 5, 6, 7, 8, 9, 9.5, and 10 min of tissue impregna-tion by trazograph-60. Supporting wires of the sample are shown for the translucent tissue(see Refs. 654 and 1726).

9.7 Other Prospective Optical Techniques

9.7.1 Polarization measurements

Dynamics of polarization structure of a tissue image during immersion can eas-ily be observed using an optical scheme with a white light source and a tissuesample placed between two parallel or crossed polarizers. Figure 9.53 illustratesthe evolution of polarization images during scleral optical clearing.654, 1726 Insuch experiments, a tissue layer works as a phase plate (or a number of phaseplates653,1698,1850−1852), on which linear birefringence is spatially and temporallydependent. As scattering decreases with time due to refractive index matching, thebirefringence of the fibrillar structure of the sclera affects the transmittance of theoptical system. The spatial inhomogeneities of images may be attributable to spa-tial variations of the sample thickness and structure, both of which may influencethe efficiency of OCA impregnation and the corresponding phase shift between theorthogonal optical field components (see Chapter 2).622

Upon reduction of scattering the degree of linearly polarized light propagat-ing in sclera is improved. This is clear from experimental graphs in Figs. 9.10 and9.54.1697 Regarding immersed tissue, the number of scattering events decreases andresidual polarization degree of transmitted linearly polarized light increases. As aresult, the dynamics of tissue average transmittance and polarization degree aresimilar (see Fig. 9.10). It follows from Figs. 9.10 and 9.54 that tissue optical clear-ing leads to an increase of the depolarization length.36, 135, 138, 595, 650, 738, 1852, 1853 Dueto less scattering of the longer wavelengths, the initial polarization degree is thehighest for these wavelengths. Polarization imaging is a useful tool for the detectionof subsurface lesions, but it is effective only at depths smaller than the depolar-ization length.36, 594, 595 Optical clearing may substantially increase the depth ofpolarization imaging.



Figure 9.54 Time-dependent polarization degree, (I||−⊥)/(I||−⊥), of collimated transmit-tance measured in vitro at different wavelengths for the rabbit eye sclera at administrationof 40% glucose (see Ref. 1697).

The image contrast, C(t) = B(t)/Bmax, where B(t) is the current sample bright-ness and Bmax is the maximal brightness, characterizing the transmittance of linearpolarized light through a tissue sample, was used for quantitative evaluation of thediffusion process of an agent in a tissue. A white-light video-digital polarizationmicroscope is suitable for these measurements.621 Sections of the various connec-tive and vascular tissues of 0.1–1.5 mm thickness were studied. The immersionsolution was heated up to 36–40◦C and simply dropped onto the tissue sample sur-face. Figure 9.55 shows different rates of tissue optical clearing for vein and aortasamples caused by different interactions of these tissues with the immersion agent:a denser aorta is less penetrative for the agent than vein, therefore, its action onaorta is visible only in a few hours, whereas for a vein sample, about 10 min is suf-ficient to complete clearing. However, both tissues finally turn from initial turbid(multiple scattering mode) at t = 0 to less depolarized and more transparent state(less scattering mode), C(t) → 1.

Reduction of scattering with optical immersion makes it possible to more eas-ily detect the polarization anisotropy of tissues and to separate the effects of lightscattering and intrinsic birefringence on tissue polarization properties. It is alsopossible to study the birefringence of form with optical immersion, but when theimmersion is strong, the average refractive index of the tissue structure is similarto the index of the ground media, and the birefringence of form may be too smallto see because both phenomena are based on the refractive index mismatch: scat-tering due to irregular refractive index variations, and birefringence due to regularvariations [see Eqs. (2.2) and (2.3)].


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Figure 9.55 Experimental temporal dependencies for image contrast of linear polarizedlight transmitted through vascular tissue sections (aorta and vein vena cava inferior)measured by a white-light video-digital polarization microscope with the application oftrazograph-60 (see Ref. 621).

Upon the reduction of scattering tissue, birefringence can be measured moreprecisely; in particular, the birefringence of form and material can be separated. Forexample, for a translucent human scleral sample by its impregnation with a highlyconcentrated glucose solution (about 70%), the measured optical anisotropy622

�n = (ne – no) was equal to ≈ 10−3. This is 1.5–4.5-fold less than for otherbirefringent tissues described in Chapter 2 and is mostly explained by a reduc-tion in the inclusion of birefringence of form at optical immersion. The additionalmeasurements of the collimated transmittance allow one to estimate the refractiveindex of the ground substance of the translucent tissue, n2, using the expressionsfrom radiative transfer and Mie theories [see Eqs. (9.1) and (9.16)]. For humanscleral sample impregnated by 70% glucose solution, n2 was evaluated as 1.39.Using this value and that of the refractive index of hydrated collagen, n1 = 1.47,and �n = 103, collagen volume fraction, f 1, was calculated from Eq. (2.2) as f 1

∼=0.32, which correlates well with an estimation made in Section 3.6.

Figure 9.10 illustrates the reversibility of the polarization immersion effect.A polarization-speckle microscope working in transmittance mode was used toconduct these measurements.555, 1694 The sample was irradiated by a linear polar-ized focused laser beam, which was scanned along the trace of 1.5 mm upon thesample surface to average speckle modulation in the far zone where the analyzerand photodetector were placed. Two orthogonal linear polarized components of thetransmitted light were detected. Initially, the sample displays poor transmittance,with equal intensity components <I||> = <I⊥>, and multiple scattering takesplace. When the immersion agent acts in the fourteenth minute, <I||> prevailssubstantially over < I⊥ >, and the tissue becomes less scattered. The subsequent



action of the physiological solution washes out the immersion agent and returnsthe tissue to its normal state. The tissue becomes turbid again in the twenty-secondminute with no measured difference between the intensities of the orthogonallypolarized components. The secondary application of the immersion agent makesthe tissue less scattered and more polarization-sensitive with a maximum reachedat the twenty-eighth min.

Figure 9.56 shows the reversible loss of turbidity and birefringence in rodenttail tendon observed at glycerol (13 M) application.1578 The dark background ineach image demonstrates the extinction of illuminating light at crossed polarizersin the polarized light microscope used in measurements. Characteristic bandingpatterns observed in the tendon sample indicate ordered fibril organization. Thedistribution of pattern brightness corresponds to the distribution of a phase shiftbetween orthogonal optical field components [see Eq. (2.1)], and the backgroundsmooth brightness corresponds to light scattering. Loss of transmittance at the sam-ple edges and appearance of bright spots in the middle of the sample in the course ofglycerol action indicate refractive index matching of collagen fibers (not shown inthe image due to their small diameter). The complete refractive index matching atthe edge region happens earlier than in the middle of the sample, and causes tissueto completely lose scattering and birefringence in this region. In the middle regionof the sample, refractive index matching is not completed and scattering is mostlyreduced (loss of turbidity); thus, bright and dark areas corresponding to a certainphase shift are very clear. Tissue shrinkage under glycerol action due to tissuedehydration, as hypothesized by the authors of Ref. 1578, suggests that reversibledissociation of collagen fibers may influence the pattern formation. The rehydra-tion of the tissue sample in saline creates a fully visible banding structure in thecrossed polarizers due to the resumption of tissue birefringence and approximateturbidity to the initial states.

Practically all healthy connective and vascular tissues show the strong orweak optical anisotropy typical of either uniaxial or biaxial crystals.621, 622, 653, 1698

Pathological tissues show isotropic optical properties.29, 594, 595

The behavior of retro-reflected circularly polarized light from a scatteringmedium at its IOC is investigated experimentally on a tissue phantom in Ref. 738.For easy interpretation of the experimental results, the authors propose the use ofthe formalism of the Poincare sphere. The high sensitivity of the parameters of thereflected circularly polarized light to changes of phantom scattering properties wasdemonstrated (see Fig. 9.57). The improvement of polarization ability of the back-reflected circular polarized light at IOC with increase of concentration of OCA(glycerol) is clear.

9.7.2 Confocal microscopy

The increased transparency of the upper tissue layers can improve pene-tration depth, image contrast, and spatial resolution in reflection confocalmicroscopy.351, 1521, 1525, 1679 By MC simulations of the point spread function, itwas shown that the signal spatial localization offered by a confocal probe in the


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Figure 9.56 Reversible loss of turbidity and birefringence in rodent tail tendon followingglycerol (13M) application observed by polarized light microscopy at crossed polarizers.1578

Before glycerol application: banding patterns observed in tendon indicate ordered fibrilorganization (a). During glycerol application: loss of transmittance at the sample edgesand bright spots in the middle indicate refractive index matching of collagen fibers; com-plete refractive index matching at the edge region causes tissue to lose scattering andbirefringence, because in the middle sample region, the refractive index is not completedand scattering mostly is reduced (loss of turbidity) (b). Tissue sample after rehydration insaline (c). (Figure was kindly provided by Alvin T. Yeh and Bernard Choi.)



Figure 9.57 Polarization-sensitive measurements at optical clearing (see Ref. 738):schematics of the experimental setup (a): the circularly polarized light is produced by alaser diode (Thorlabs, Inc., 635 nm), using linear polarizer and quarter wavelength plate(λ/4), and is focused onto the sample surface; backscattered optical radiation is collectedat distance d away from the area of incidence and then passed through a quarter wave-length plate (λ/4) and linear polarizer (analyzer); normalized intensity of light backscatteredfrom milk and detected using a quarter wavelength plate and rotating analyzer on the wayto detector (b); each curve shows results for samples diluted by given amounts of watersolution of glycerol: 10%, 20%, 30%, 40%, 50%, 60%, and 70%. (See color plates.)


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Figure 9.58 Axial profile of a detector signal distribution before (a) and 20 min after (b)glycerol administration (intradermal injection) predicted by the numerical Monte Carlo sim-ulation for a confocal microscope focusing at (1) 300 μm, (2) 600 μm, (3) 900 μm into theskin. Confocal probe parameters are: lens diameter, 5 mm and focal length, 10 mm; pinholediameter is 10 μm; the height of the lens above the surface is 9.7 mm (see Fig. 8.19 andRef. 351).

skin tissues during their clearing is potentially useable for monitoring the reticulardermis (Fig. 8.20).1521 The results of the simulation predict that after 20 min ofchemical agent diffusion after intradermal glycerol or glucose injection, a signalcan be detected from tissues located twice as deep in skin.



A significant improvement to the confocal microscopy signal under glyceroladministration is clear from theoretical axial profiles of a detected signal (pointspread function) calculated for three different in-depth focuses (Fig. 9.58).351

9.7.3 Fluorescence detection

Fluorescence is a simple and effective method for the study of tissues and cells andis widely used for disease diagnosis and monitoring. However, in some cases, scat-tering can strongly modify the fluorescence spectra from deep-lying fluorophores,or even completely prevent a weak fluorescence to be detected or excitation radia-tion from penetrating deeply into the tissue. Therefore, the IOC method is of greatpotency for fluorescent diagnostics.1418, 1640, 1642, 1785, 1789

The improvement of the detected fluorescence signal traveling through skin inin vitro and in vivo experiments upon topical application of hyperosmotic OCAs,such as anhydrous glycerol (13 M, index n = 1.47) and pure DMSO (14 M, indexn = 1.47), and highly concentrated glucose (7 M, index n = 1.46), was demon-strated.1418 Fluorescence measurements were performed for hamster dorsal skinwith OCA applied to the subdermal side of the skin and rhodamine fluorescent filmplaced against the same skin side. Fluorescence was induced by a dye laser pulseat 542 nm, delivered to the skin epidermal side by a fiber bundle, and was detectedby a collection fiber bundle from the epidermal surface at wavelengths longer than565 nm. Skin flap window preparation in an area void of blood vessels was usedfor in vivo studies. Approximately equal enhancement of transmitted fluorescencewas achieved for in vitro and in vivo measurements (Fig. 9.59). On average, up to100% increase in fluorescence intensity is clear up to 20 min for glucose and glyc-erol application, and up to 250% for DMSO. A significantly greater increase in the

Figure 9.59 Comparison of the percent increase in fluorescent signal due to applicationof OCAs to the skin site: 100% glycerol, 100% DMSO, and 7M glucose (see Ref. 1418).Measurements conducted in vivo for the hamster dorsal skin with OCA applied to the sub-dermal side of the skin and rhodamine fluorescent film placed against the same skin side.Excitation wavelength was 542 nm and fluorescence was detected at wavelengths longerthan 565 nm.


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Figure 9.60 In vivo dynamics of human skin autofluorescence intensity (λexc = 337 nm)after intradermal injection of 0.1 ml of trazograph-76. Intensity values at different emissionwavelengths are normalized by correspondent initial values (see Ref. 1640).

case of DMSO is associated with its twice greater osmolarity than for glycerol andglucose at these concentrations.

Significant enhancements of both the sensitivity (∼fivefold) and spatial res-olution (∼threefold) for low-level light-emitting probes (broadband violet-bluechemiluminescence with a center wavelength of 425 nm) were demonstrated inin vitro experiments with a 3-mm-thick fresh porcine skin sample at topical appli-cation of 50% glycerol during 30 min.1642 In this case, the higher efficiency ofluminescent light transportation through the skin at immersion is connected withhigher initial scattering and absorption of skin at shorter wavelengths. Refractiveindex matching effectively damps light scattering, and thus, absorption of light isalso conducted, due to fewer photons circulating within a tissue.

In a theoretical study,1641 it was shown that by refractive index matching at theskin interface and use of a fiber-optical fluorescence probe, one can improve thecontrast and spatial resolution of the shallow sampling volume.

Both described model experiments accurately demonstrated changes in tissuelayer transmittance at optical immersion for light from a fluorescent source placedbehind a tissue layer. However, fluorophores are more often distributed within atissue layer, or a multilayered tissue structure may even contain many differentfluorophores. In this case, the behavior of the fluorescence signal at tissue immer-sion is not clearly evident, because the cross section for fluorescence emissiondepends on the amount of light absorbed by the fluorescent centers. Such crosssection decreases as multiple scattering decreases. Thus, at tissue optical clearinginstead of enhancement of a fluorescence signal, one can see its damping.1640, 1788

Evidently, this depends on the depth of the fluorophore and the layer of tissue thatis optically cleared.



Figure 9.60 illustrates that fluorescence can be damped under the reduction oftissue scattering due to refractive index matching.1640 These data were received invivo for human skin at intradermal injection of the immersion liquid, trazograth-76. This behavior of the AF signal means that the primary fluorophore (collagen)is in the dermis, where the immersion agent was inserted. However, with time, dueto greater in-depth penetration of the exciting light and less attenuation of inducedfluorescence by the upper layers of skin, fluorescence intensity increases. Tissueoptical clearing can be a helpful technology for determining the distribution anddifferentiation of endogenous or exogenous fluorophores within a tissue.

The increase of the sensitivity and spatial resolution of the bioluminescentand fluorescent imaging methods by IOC is discussed in Refs. 1785 and 1788.The possibility of practical use of the IOC method for the detection of salmonella(Salmonella typhimurium) directly through the skin of a pig was demonstrated bythe authors of Ref. 1786 upon the topical application of glycerol. Efficient fluores-cent imaging of tissues, required for reliable tracking of surgical intervention, wasrealized during IOC of the skin.1787

New possibilities of the IOC method for producing clear and highly resolved3D images of the structural elements of different tissues using fluorescenceconfocal microscopy are presented in Refs. 1794–1796, 1798, and 1854.

9.7.4 Two-photon scanning fluorescence microscopy

One new direction in tissue spectroscopy is associated with multiphoton fluores-cence scanning microscopy (see Section 5.2)114,122,131,137,1123−1162,1797 However,it has been shown that the effect of light scattering in multiphoton fluores-cence scanning microscopy drastically reduces penetration depth to less thanthat of the equivalent single-photon fluorescence while largely leaving resolutionunchanged.1132, 1138 This primarily happens due to excitation beam defocusing (dis-tortion) in the scattering media. Although some improvement in the penetrationdepth of two-photon microscopy can be obtained by optimizing the pulse shapeand repetition rate for the sample under investigation,1139 reduction of scattering isbelieved to be more effective for the improvement of penetration depth and imagecontrast.1609, 1610 Two-photon fluorescence microscopy provides high-resolutionimages of human skin in vivo.1140, 1141 Evidently, the technique is applicable formany other tissues, but normally, its probing depth is limited.

The first demonstration of two-photon in-depth signal improvement using theoptical immersion technique with hyperosmotic agents, such as glycerol, propyleneglycol, and glucose, was conducted by the authors of Ref. 1610 during ex vivoexperiments with human dermis. Thick (150 μm) slices of dermis excised duringplastic surgery were imaged within the same day. Images were collected in stacks,each comprising four images of 100 μm2 area taken at depths of 20, 40, 60, and80 μm from the surface of the sample. Before data acquisition, the sample wasimmersed in 0.1 ml of PBS to prevent drying and shrinkage. Then, the sample wasimmersed in 0.5 ml of an OCA and one image stack was acquired every 30 s for 6–7 min. Finally, the OCA was removed and the sample was immersed again in 0.1


516 Chapter 9

ml of PBS, to observe the reversibility of the clearing process. Glycerol and PGwere both used in anhydrous form, and glucose as a concentrated aqueous solution(5 M). The upper limit of tissue shrinkage was estimated as 2% in the course of6–7 min of OCA application.

The average contrast in each image and relative contrast (RC) were definedas1610

Contrast =Nlines∑i,j=1

∣∣Iij − ⟨Iij

⟩∣∣ , RC(%) = 100Contrast [OCA] − Contrast [PBS]

Contrast [PBS],

where⟨Iij

⟩is the mean intensity of the nearest eight pixels and Nlines = N – 2, with

N = 500; Contrast [OCA] and Contrast [PBS] are calculated for OCA and PBSimmersion, respectively. Contrast, as defined here, is linearly dependent on thefluorescence intensity and varies according to structures in the image. Hence, itsusefulness is primarily to enable comparison between images of the same sampleat the same depth maintaining the same field of view. Normalization to the totalintensity would be required to compare different images. RC also serves for thepurpose of comparison.

Figure 9.61(a) shows two typical image stacks: the first received for a sam-ple immersed in PBS and the second received 7 min after application of glycerol.The images show connective tissue in human dermis, which is primarily composedof collagen and elastin fibers. The enhancement of contrast, as well as increase ofpenetration depth (from 40 to 80 μm) and total intensity [i.e., the intensity summedover all pixels; Fig. 9.61(b)] are clearly shown in the images. The correspond-ing absolute and relative contrast levels are plotted in Figs. 9.61(a) and 9.61(d).RC has a value of 215% at 40 μm and dramatically increases with increasingdepth.

The effect on deeper layers is greater because of the cumulative effect of thereduction in scattering on the superficial layers of the tissue sample, which providesless attenuation of the incident and detected fluorescent light. The contrast is alsodependent on fluorescence intensity, which is proportional to the squared excitationintensity and mostly dependent on excitation beam focusing ability. Better focusing(less focused beam distortion) is achieved in less scattering media.

It was shown experimentally that application of each OCA among glycerol,PG, and glucose resulted in a contrast enhancement with varying degrees of effi-ciency and saturation. The dynamics and final contrast level attained depend onthe OCA and tissue depth. Saturation of contrast occurs most rapidly in superficiallayers of the sample. This is consistent with a diffusion model for the penetrationof the agent from the surface into the tissue [see Eqs. (9.2), (9.6), and (9.7)]; i.e.,if the contrast is proportional to agent concentration, then the saturation time at agiven depth will be proportional to the depth. According to the data of Ref. 1610,∗glycerol is the most efficient with respect to saturation level (RC = 49.7% at 20 μmdepth, ∼304% at 40 μm depth, ∼1900% at 60 μm depth, and ∼9260% at 80 μm

∗Numerical data for RC values were provided by David Sampson.



Figure 9.61 Two-photon microscopy of human skin ex vivo by use of glycerol as opticalclearing agent (see Ref. 1610). Image stacks for a skin dermis sample immersed in PBS(upper) and after immersion for 7 min in glycerol (lower) (a). Corresponding total intensity(b), contrast (c), and relative contrast (d).

depth), but also the slowest. PG provides RC ∼64% at 20 μm depth, ∼1090% at40 μm depth, ∼5640% at 60 μm depth, and ∼447% at 80 μm depth. However, glu-cose (5 M) is the worst with RC = 10.9% at 20 μm depth, ∼134% at 40 μm depth,∼471% at 60 μm depth, and ∼406% at 80 μm depth, but diffuses three timesfaster than glycerol and five times faster than PG. Diluted agents produced similartendencies in contrast enhancement and increase of penetration depth, providinghigher efficiency in both characteristics with increased OCA concentration.

However, some specificity was found in the action of three different OCAs: forpropylene glycol and glucose, slowing in the rate of contrast increase was observedfollowing the addition of PBS, rather than a decrease as for glycerol. Such behaviormay be associated with less inclusion of the dehydration mechanism in opticalclearing for propylene glycol and glucose, and more of these agents diffused intotissue in comparison with glycerol.

These data illustrate that, as in linear spectroscopy, refractive index matchingis the leading mechanism in the reduction of tissue scattering and two-photon sig-nal improvement. In contrast to in vivo single-photon fluorescence spectroscopy


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(see Fig. 9.60), where fluorescence intensity may decrease with decreased multi-ple scattering, a two-photon tomography signal is always increased owing to lessdistortion of the focused beam and less attenuation of a two-photon fluorescencesignal by superficial optically cleared tissue layers.

Because of the strong light scattering in tissues under study, the probing depthof modern nonlinear microscopes is less than 300 μm, but the use of IOC technol-ogy, by replacing the water in tissues with fluids with a refractive index similarto that of proteins, can significantly reduce the scattering, leading occasionalincreases in the probing depth in excess of 2 mm.1609

9.7.5 Second harmonic generation

Optical clearing seems to be a promising technique for the improvement of detectedsignals in multiphoton microscopy, nonlinear spectroscopy, and imaging of tis-sues.1578, 1579, 1611, 1792, 1793, 1797 On the other hand, these techniques might be usefulto the understanding of the molecular mechanisms of tissue optical clearing atimmersion and dehydration.

In skin, SHG (see Section 8.8) is provided mostly within dermis due toits primary component, collagen, which has appreciable nonlinear susceptibility.Evidently, due to optical clearing, less scattering in the epidermis for long incidentwavelength light (800 nm), and especially for backward SHG short wavelengthlight (400 nm), may improve SHG images of dermis collagen structures.

At 100% glycerol application to rodent skin dermis and tendon samples, aswell as to an engineered tissue model (raft), high efficiency of tissue optical clear-ing was achieved in the wavelength range from 400 to 700 nm, but SHG signal wassignificantly degraded in the course of glycerol application and returned back to itsinitial state after tissue rehydration by application of saline.1578 The loss of SHGsignal in Ref. 1578 is associated with the reversible dissociation of collagen fibersand corresponding loss of fibril organization under glycerol action. This explana-tion is slightly contradictory, because less organization of collagen fibers will leadto less transmittance.654 Because the significant effect of optical clearing at glyc-erol application is tissue dehydration, the explanation from the data of Ref. 1579seems to be more adequate. Using reflection-type SHG polarimetry, it was shownthat the SHG polarization signal (SHG radar graphs) for chicken skin dermis wasalmost unchanged (Fig. 9.62) and the SHG intensity decreased to approximatelyone-fourth at tissue dehydration.1579 Authors have hypothesized that the decreasein SHG intensity results in a change in linear optical properties, i.e., scatteringefficiency, rather than that of the efficiency of SHG radiation in the tissues. As itfollows from Fig. 9.62, the tissue fixation process also indicates nearly unchangedSHG polarization radar graphs with slightly increased SHG intensity. Because for-malin fixing induces crosslinking of collagen in tissues, this result may imply thatcrosslinking does not affect collagen orientation, but essentially contributes to theefficiency of the SHG signal.1579 These two examples clearly illustrate the depen-dence of SHG signal on light scattering of the sample, which decreased at tissue



Figure 9.62 SHG radar graphs received for native samples of chicken dermis (see Ref.1579). SHG signal distributions before and 5 h after formalin fixation (a, b); those beforeand 13 h after air drying (c, d).

dehydration and increased at fixation. Thus, to study tissue structure (collagen ori-entation) by using SHG, one of the methods providing light scattering suppressionmay be applied, such as SHG polarimetry1579 optical immersion technique,1792 or acombination.1793 For example, during SHG imaging of muscle tissue at applicationof 50% glycerol–water solution, the probing depth, defined on the level of 1/e, wasincreased up to threefold: from 70 to 210 μm.1792

Owing to significant differences between tissue structure and functioningunder in vivo and in vitro conditions, IOC mechanisms may be different for thesetwo cases. One attempt to study in vivo mechanisms of skin optical clearing wasundertaken in Ref. 1741 upon the application of glycerol–water solutions by usingdifferent measuring modalities, such as histological, TEM, and SHG imaging, toprove these mechanisms. IOC was provided by dermal injection of 20%, 30%, or75% glycerol–water solution into the dorsal skin of Sprague-Dawley rats. It wasfound that after injection of glycerol, the reflectance spectrum of skin decreasesquickly in the range of 400–900 nm with saturation and follows this with an


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Table 9.8 Changes in dermal thickness, d, 5, 10, and 30 min after injectionof glycerol–water solutions (see Ref. 1741).

OCA d, μm

5 min 10 min 30 min

Control 1459 ± 77 1459 ± 77 1459 ± 7720% glycerol 1444 ± 78 1530 ± 146a 1767 ± 90b

30% glycerol 1303 ± 97b 1405 ± 83 1580 ± 135b

75% glycerol 1194 ± 43b 1214 ± 72b 1287 ± 91b

aSignificant difference (p < 0.05).bExtremely significant difference (p < 0.01).

Table 9.9 Diameter of dermal collagen fibers 10 min after injec-tion of glycerol, TEM measurements [see Fig. 9.63(b) and Ref.1741].

OCA Diameter, nm

Control 109 ± 2020% glycerol 100 ± 1330% glycerol 98 ± 23b

75% glycerol 79 ± 13b

bExtremely significant difference (p < 0.01).

increase for a longer elapsed time after injection. The higher the concentration ofglycerol, the larger the observed reflectance decreases. Skin structure examinationby TEM and SHG imaging was conducted in 10 min after injection of glycerol, asthe optimal time for IOC. Figures 9.63(a) and 9.63(b) show the microstructure(histology) and ultramicrostructure (TEM) of skin samples, respectively. Thehistological results indicate that the thickness of the dermis decreases withincreased glycerol concentration. Changes in dermal thickness in three differenttime intervals, including 10 min, after injection of glycerol–water solutions aresummarized in Table 9.8. TEM images clearly show that collagen fibers in allgroups of measurements are arranged in order; however, 75% glycerol injectionsignificantly reduces the diameter of collagen fibers, whereas for smaller glycerolconcentrations, there are hardly any changes in collagen diameters compared withthe intact sample (see Table 9.9). All of these findings are very important becausethe collagen-fiber structure of skin is an essential source of the SHG signal.

To clarify the effects of OCAs on collagen fibers, a two-photon excitation fluo-rescence microscope working in SHG mode was used to image skin samples afterinjection of glycerol solution [see Fig. 9.63(c)]. To isolate the SHG signal, a band-pass filter at 395 nm (395/11, Sigma, USA) was placed in front of the PMT. Theimage integration time was 12.5 ms/pixel. Figure 9.63(d) shows the SHG imagesof collagen fibers in dermis. As shown, 10 min after injection of glycerol of dif-ferent concentrations, the SHG signal is still strong, which suggests no noticeable



Figure 9.63 Intact rat skin sample and samples cut in 10 min after in vivo injection of 20%glycerol, 30% glycerol, or 75% glycerol: histological images, 1 is epidermis, 2 is dermis, 3 isbreakpoint of skin by injector (a); TEM images of dermal collagen fibers (b); schematic dia-gram of two-photon excitation fluorescence microscope [titanium-sapphire laser generating790-nm, 100-fs, 80-MHz pulses coupled into an inverted microscope (FV1000, Olympus,Japan)] tuned to SHG imaging mode (c); SHG images (d) (see Refs. 1615 and 1741).

collagen dissociation as found in in vitro experiments, in which skin samples wereimmersed in extremely highly concentrated 13M-glycerol for 30 min,1578, 1730 theSHG signal was much weaker, and the bundled pattern could no longer be observedin SHG images due to collagen dissociation. Different results could be attributableto a difference between in vivo and in vitro skin, i.e., the metabolism removes someof the agent and decreases the local concentration of glycerol.

9.7.6 Vibrational, Raman, and CARS spectroscopy

Infrared vibrational spectroscopy is primarily used to monitor the diffusion ofOCAs in tissues, because many OCAs have characteristic absorption peaks in themiddle IR other than peaks of water in this range, and thus, can be identified on


522 Chapter 9

the background of the spectrum of water, which is difficult to do in NIR.1231, 1735

The dehydration of the tissue at IOC also can help in the identification of biologicalmolecules in tissues by their characteristic IR spectra on a background of reducedIR spectrum of water. Tissue actually becomes more transparent in this spectralrange, not only due to the reduction of scattering, but also because of a decrease inabsorption associated with water loss.

For example, in Ref. 1231, to measure the IR absorption spectra of tissue com-ponents and phantoms (water, polyacrylamide, Intralipid, collagen gels) as well ashyperosmotic OCAs (glycerol, 1,3-butylene glycol, trimethylolpropane, Topicare)in the spectral range of 2–15 μm, ATR-FTIR spectroscopy was used. Kinetics ofDMSO and glycerol permeability into pig skin in the in vitro experiment was stud-ied through imaging the spatial–temporal distribution of the OCA in the tissue byFTIR spectroscopy.1735

Confocal Raman spectroscopy is also used for in vivo monitoring of theOCA, particularly for DMSO permeability and penetration of OCA permeabilityenhancers into skin stratum corneum.1727 A significant increase of usually unde-tectable Raman signals from internal tissue layers can be achieved by opticalclearing of the superficial layers of tissue that hide the target.1790, 1791 In this way, invivo percutaneous Raman spectroscopy of rat tibia was provided under skin opti-cal clearing by topical application of glycerol.1790 Raman microspectroscopy waseffectively used for in vitro studies of the optical clearing processes in porcineskin.1791

Nonlinear Raman spectroscopy also finds application in the study of mecha-nisms of tissue optical clearing, such that presented in Ref. 1601, where the CARSsignal served as a reference for studying the effects of DMSO on the structure ofcollagen, and corresponding loss of SHG signal and reduction of light scattering inhuman skin.

9.7.7 Tissue clearing in the terahertz range

Basics of terahertz spectroscopy and imaging in tissues are presented in Section8.9. In this wavelength range, where scattering is very low, but absorption bywater, the primary component of tissue, is very high, the dehydration mechanism ofIOC1855 is important. The development of THz methods, providing detection andimaging of metabolic and pathological processes, is of great interest, especiallyas an additional channel of information in multimodal systems in combinationwith optical methods.178, 1856, 1859 In such applications, the use of IOC technologymay solve many problems with optical and THz methods, not only by reversiblereduction of light scattering, but also by the accompanied tissue dehydrationthat promotes greater tissue penetration for THz radiation, caused by reversiblereduction of absorption associated with water content in tissue.

Direct in vitro measurements of dehydration effects in pig muscle tissue forthe sample immersed in glycerol for 30 min showed a significant decrease in theabsorption of THz radiation in the frequency range of 0.1–1.5 THz, measured by



Figure 9.64 Attenuated total reflectance of terahertz radiation for normal and dehydratedpig muscle tissue samples; dehydration was provided at impregnation of a sample byglycerol solution during 30 min (see Ref. 178).

the attenuated total reflection technique (see Fig. 9.64).178 The weight loss of thesample was measured as 10% of its original weight, and integration over the visiblespectrum transmittance increased by 5%. This experiment also demonstrated thehigh sensitivity of probing THz radiation concentration of water in tissues, whichcan be one of the criteria for recognition of pathology.1859 Effects of dehydrationduring lyophilization (freeze-drying) of tissue samples taken from a number ofrat organs (kidney, diaphragm, liver, rectum, and stomach) on THz transmittancespectra in the range of 0.4–2.2 THz were investigated in Ref. 1857.

9.8 Imaging of Cells and Cell Flows

9.8.1 Blood flow imaging

Small blood microvessels can clearly be identified visually by the naked eye in invivo study of hamster766,1644 and rat1645 skin, when a transparent window in skinwas created by glycerol drops to the subdermal side of a native hamster dorsal skinflap window preparation,1644 or by intradermal injection of glycerol766,1645 or 40%glucose1645 (see Fig. 9.30). In in vitro study of fresh human fat tissue upon topicalapplication of a PG solution (50–80% with pure water), blood vessels were alsoobserved.1673

In addition to more precise visualization of the vessel network, immer-sion agents may influence the functioning of blood microvessels.766, 1439,

1486, 1487, 1644, 1645 On one hand, this is a side effect and must be avoided or takeninto account when selecting the immersion agent; on the other hand, this makes itpossible to control tissue functioning. The behavior of microvessels of rat mesen-tery under the topical action of glycerol and glucose was described in Ref. 1645. Atopical application of 75% glycerol during the initial period of 1–3 s led to slowingof blood flow in all microvessels (arterioles, venules, and capillaries). After 20–25s, stasis appeared and vessels were dilated by 30% on average, intravascular hemol-ysis took place; 1 min after agent application, diameters of vessels were increased


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even more, to 40%. Until the sixth minute, stasis was maintained in all vessels, butthe diameters of vessels were slightly decreased. These changes in microcirculationwere exactly local within the area of glycerol application. The topical applicationof glucose also decreased blood flow velocity in microvessels. For example, underthe action of 40% glucose on a venule with a diameter of 11 μm and initial flowrate of 1075 μm·s−1, the flow rate decreased to 510 μm·s−1 at 3 s after glucoseapplication and to 202 μm·s−1 at 5 s. Similarly with action of glycerol, dilationand stasis of blood flow were observed in all vessels (arterioles, venules, capil-laries, and shunts) within 20–30 s, but no intravascular hemolysis was found andonly RBC aggregates in the lumen of microvessels were observed. The strengthof vessel dilation was greater than that for glycerol, the mean diameter increasedby 30% 30 s after glucose application, but up to the fourth minute, it rose by 2.5times, on average. From the third to fifth minutes, blood flow appeared again in afew microvessels, but the velocity of reflow was markedly slower than in control.The changes in blood flow were also local, but in a larger area than for glycerol,approximately 1 × 1 cm2, there were no disturbances in the functioning of bloodmicrovessels in the other parts of the mesentery. Evidently, a decrease in glucoseconcentration and corresponding loss of agent hyperosmotic property led to softerglucose action on blood circulation; in particular, no blood stasis was observed for20% glucose, and after 3–4 min of glucose application, blood flow in all vesselswas not significantly different from the initial flow.

The vasculature under the dura mater also became visible after the treatment ofglycerol in in vivo experiments with rabbit.1439, 1486, 1487 The reflectance decreasedas a function of time for glycerol action, which proved the visual observation. Thedura mater nearly recovered to native condition after 1 min. Velocity images of invivo cerebral blood flow (CBF) under the effect of glycerol are shown in Fig. 9.65.Glycerol was applied around the exposed area. When glycerol diffused in brain tis-sue and influenced CBF under the dura mater, CBF in exposed area also changed.Figure 9.66 illustrates the spatiotemporal characteristics of CBF changes underthe treatment of glycerol. Under the action of glycerol, blood flow first decreasedwhile the blood vessels underneath the dura mater became increasingly visible.Next, blood flow increased to near baseline; at the same time, the turbidity of thedura mater returned. Figure 9.66 displays the time course of changes in four dif-ferent vessels (Fig. 9.65), which is expressed as the ratio of the measured velocityunder conditions of treatment with glycerol to that of control condition. Vessel2 is an arteriole. Vessels 1, 3, and 4 are venules. Blood flow in vessel 2 (arte-riole) began to decrease after a 20-s application of glycerol, while that in othervessels (venules) decreased immediately after application with glycerol. The bloodflow in vessel 1 decreased more slowly than that in other vessels, which suggestedthat blood flow in the arteriole had a different response from that in the venules.Blood flow in all vessels decreased to 70%–80% of baseline after treatment withglycerol.

An example of the subdermal side of a native hamster dorsal skin flap windowpreparation is shown in Fig. 9.67(a). The main arteriole (A) is 97 ± 18 μm in diam-eter (lumen) and the main venule (V) is 188 ± 21μm in diameter. The diameters of



Figure 9.65 Blood-flow images following the epidurally applied glycerol around the exposedarea of in vivo dura mater. White-light image of the area of interest (a). Blood flow mapsexpressed as measured velocity, which is proportional to the blood flow velocity, duringtreatment with glycerol and represented by images at the time points shown in Fig. 9.66 (b)–(h): imaged blood flow before the application of glycerol (control), four vessels are indicated(b); 10 s application of glycerol, no obvious change in blood flow was observed (c); 20s application of glycerol, blood flow began to decrease (d); 30 s application of glycerol,blood vessels underneath dura mater began to be clear (e); 40 s application of glycerol,blood flow decreased and the transparency of surrounding dura mater increased (f); 50 sapplication of glycerol, more blood vessels could be seen through dura mater and the bloodflow decreased significantly (g); and 70 s application of glycerol, blood flow increased anddura mater became turbid again (h). Bar = 1 mm (see Ref. 1439). (See color plates.)

the branches, a and v, are 92 ± 18 and 181 ± 21μm, respectively. Figure 9.67(b)shows the blood vessels in the same window preparation 10 min after the applica-tion of 100% glycerol. The smallest branches of the arterioles and venules are nowclear in the image. This is likely attributable to the increased clearing of the tissue


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Figure 9.66 Time course of change in relative blood flow in vessels 1, 2, 3, and 4, whichare indicated in Fig. 9.65(b), before and after the epidural application of glycerol. After 20s, the blood flow in vessel 2 (arteriole) began to decrease, while blood flow in other vessels(venules) decreased immediately after application with glycerol. Decreases of blood flow inthese vessels were 20% to 30% of baseline. The letters b, c, d, e, f, g, and h denote the timepoints of corresponding images in Figs. 9.65 (b)−(h) (see Ref. 1439).

Figure 9.67 Images of subdermal side of in vivo hamster dorsal skin flap window prepa-ration (see Ref. 1644). Native, the main arteriole (A) is 97 ± 18 μm in diameter (lumen)and the main venule (V) is 188 ± 21μm in diameter; the diameters of the branches, a andv, are 92 ± 18 and 181 ± 21μm, respectively (a). 10 min after the application of glycerol(100%) (b); 20 min after the application of glycerol, the diameters of the main vessels are97 ± 18 μm (A), and 189 ± 20 μm (V), and the diameters of the branches are 141 ± 17 μm(a) and 259 ± 21 μm (v) (c). Scale bar: 0.25 cm.

overlying the vessels and can also occur with vasodilation. The venule branch, v,is dilated to 259 ± 19 μm. The main vessels and arteriole branch (a), however, arenot noticeably dilated. After 20 min, the main venule branch in the window prepa-ration appears very dark and is occluded [Fig. 9.67(c)]. The diameters of the mainvessels are 97 ± 18 μm (A) and 189 ± 20 μm (V), and those of the branches are141 ± 17 μm (a) and 259 ± 21 μm (v).

Another example of enhanced visibility of blood vessels and dermal bloodflow imaging through rat skin under topical treatment by a mixture of PEG-400and thiazone (a chemical skin permeability enhancer) is presented in Fig. 9.68.This figure shows white-light and speckle temporal contrast images of skin beforeand after treatment with the mixture.1781



Figure 9.68 Blood vessel visibility and dermal blood flow imaging through rat skin undertopical treatment by a mixture of PEG-400 and thiazone: images of skin before and aftertreatment with the mixture (a); white-light (top row) and speckle temporal contrast images(bottom row) of rectangle area A in (a) after treatment (b) (see Ref. 1781). (See color plates.)

Optical clearing of vascularized tissue may have certain important biomedicalapplications connected with investigation of vascular system structure and func-tion, including relation of diameters of arterioles and venules, capillary density,and bifurcation angles. These parameters can be important in physiology and ther-apy for the diagnosis and treatment of some diseases (such as vascular diseaseor cancer). On the other hand, the optical clearing effect coupled with temporaryand local cessation of blood flow in microvessels in the area of treatment maysignificantly help vascular photothermal therapy1644 due to deeper penetration oflight into tissue and reduction of the effect of cooling in the zone of coagulationcaused by blood microcirculation, the intensity of which is damped by the actionof many OCAs. All of these factors lead to significant interest of researchers in theproblem of interaction between the blood microcirculation network and lymphaticvasculature with OCAs.972, 973, 1439, 1643–1645, 1777–1781, 1784, 1860–1863

Exceptionally important advances have been made in optical clearing of skullbones,1342, 1343, 1784, 1860 which opened up the opportunity for in vivo visual obser-vation of cerebral blood flow1784 and its quantitative evaluation using full-fieldspeckle imaging (see Figs. 9.48–9.50).1784, 1860

9.8.2 Optical clearing of blood

Refractive index mismatch between erythrocyte cytoplasm and blood plasmacauses strong scattering of blood that, for example, prevents the acquisitionof high-quality images of intravascular structures through whole blood. Therefractive index of erythrocyte cytoplasm is mostly defined by hemoglobin con-centration.48 Hemoglobin oxygenation1362 and glycation may play certain rolesin refractive index mismatch (see Section 7.9).767, 1057 The scattering properties


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of blood are also dependent on the volume and shape of erythrocytes, whichare defined by blood plasma osmolarity48,1699 and aggregation or disaggregationability.1331, 1647, 1700, 1701, 1864–1866

The feasibility of index matching as a method to overcome limited penetrationthrough blood for obtaining OCT tissue images has been demonstrated for circu-lating,1646, 1701 steady-state, or sedimenting blood.1331, 1647, 1700 Glucose, low- andhigh-molecular dextrans, x-ray contrast, glycerol, and some other biocompatibleagents were used to increase the refractive index of blood plasma to closer to that oferythrocyte cytoplasm to improve the penetration depth of OCT images. OCT andother noninvasive imaging techniques, such as backreflectance spectrophotometry,and polarization-sensitive fluorescence, multiphoton, and Raman spectroscopies,which already have witnessed widespread and exciting applications in biomedi-cal diagnostics,126, 144 may have additional advantages for the early diagnostics ofvascular disease through optically clarified blood.

Normal human blood is a scattering system that consists of approximately 43vol. % of scattering particles (99% RBCs, 1% leukocytes and thrombocytes) andapproximately 57 vol. % plasma.48, 1311 Under normal physiological conditions,Hct, defined as the volume fraction of cells within whole blood, ranges from 36.8%to 49.2%.48 Propagation of light in this medium can be studied within the modelof light scattering and absorption by an individual particle, taking into account theinterparticle correlation effects and polydispersity.

As noted, blood plasma osmolarity is an important factor for changes in thescattering properties of blood.48, 1009, 1331 The effects of glucose, glycerol, trazo-graph, and PG, which are hyperosmotic agents, led to significant changes in bloodplasma osmolarity. Changes in osmolarity induce variation in RBC volume due towater exchange, which, therefore, has an impact on the hemoglobin concentrationwithin the RBC and on their refractive index. It was demonstrated that glucosesolution with concentration less than 20% led to increased blood scattering dueto the osmotic dehydration of erythrocytes.1009 Significant optical clearing wasobtained at glucose concentrations higher than 40%, but these concentrations cancause aggregation of erythrocytes.1331

The result of the OCT study is the measurement of optical backscattering orreflectance, R(z), from the RBCs versus axial ranging distance, or depth, z. Thereflectance depends on the optical properties of blood, i.e., the absorption (μa)and scattering (μs) coefficients, or total attenuation coefficient, μt = μa + μs. Therelationship between R(z) and μt is, however, highly complicated because of thehigh and anisotropic scattering of blood. However, for optical depths less than 4,reflected power can be approximately described by Eq. (9.35). Optical depth is ameasure of depth in terms of number of mean free path lengths, i.e., μsz. The valueof α(z) is linked to the local refractive index and the backscattering property of theblood sample. If α(z) is kept constant, at least a laminar blood flow for circulatingblood or measurements before the sedimentation process begins for uncirculatingblood should be provided; μt can be obtained theoretically from the reflectancemeasurements at two different depths, z1 and z2 [see Eq. (9.41)]. Optical clear-ing (enhancement of transmittance), �T, by agent application can be estimated by



using Eq. (9.42), where Ra is the reflectance from the backward surface of the ves-sel within a blood sample with an agent, and Rs is that with a control blood sample(whole blood with saline).

A 1300-nm OCT system was used for taking images of the reflector throughcirculated blood in vitro.1646 As immersion substances, dextran (group refractiveindex: 1.52) and IV contrast (group refractive index: 1.46) were used. This systemallows the blood to be circulated in vitro through transparent tubing to reproducecoronary flow. Blood with Hct ∼35% was pumped through a closed system oftubing by a perfusion pump. The flow rate was 200 ml/min, which is approxi-mately the peak flow in the coronary artery. The diameter of the tubing was 6 mm,approximately the diameter of a normal adult coronary. A reflector was placed inthe tubing; the imaged section of the reflector was approximately 2 mm below theinner surface of the tubing. Once blood was introduced into the system and circu-lated, OCT imaging was performed of the reflector. The total intensity of the signalfrom the reflector is used to represent penetration [see Eq. (9.42)]. The more lightis scattered by blood, the lower the signal from the reflector.

After baseline data were obtained with blood, test substances were added to theblood. The test substances were dextran (0.25 g/ml in normal saline), IV contrast,or normal saline.1646 Hematocrit and RBC concentrations were measured beforeand after the experiments. All added substances had a volume of 40 ml, which wasadded to a total volume of 260 ml. For the saline control, a 7 ± 3% increase insignal intensity was noted, which was not a statistically significant effect. A 69 ±12% increase in �T was noted for dextran, which was statistically different fromthe saline control (p < 0.005). For the IV contrast, a 45 ± 4% increase was noted,which was also significantly different from the control (p < 0.001).

By OCT imaging in the presence of saline, blood (Hct 35%), or lysed blood(Hct < 1%) it was directly demonstrated that RBC intracellular/extracellular mis-match, and not membranes or hemoglobin absorption, is the primary source of NIRattenuation by blood. In the presence of blood, the reflector was difficult to locate.However, when the RBCs were lysed, signal intensity returned to values not signifi-cantly different from saline. The fact that the cell membrane is not the major sourceof scattering is not surprising because it is too small relative to the wavelength tosignificantly scatter (see Figs. 6.2 and 6.3).

In the case of dextran, the effect was consistent with index matching. Withthe IV contrast, a small but significant decrease in RBC volume was noted by adecrease in hematocrit, but not the number of RBCs, relative to the saline control.Therefore, some improvement in penetration may be attributable to a reductionin cell volume. The lack of improved penetration with the addition of normalsaline (40 ml) is consistent with data of Ref. 48, which suggested that dilutionof the hematocrit to below 10% was necessary before significant improvement inpenetration could be observed.

Studies into reducing blood scattering by the immersion technique usingvarious osmotically active solutions that are biocompatible with blood, likesaline, glucose, glycerol, propylene glycol, trazograph, and dextrans, were alsodescribed.1331, 1647, 1700, 1701 The 820- and 1310-nm OCT systems were applied for


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taking images of the reflector through a layer of uncirculating fresh whole blood.The OCT system used yields 12 μm axial resolution in free space. This determinesthe imaging axial resolution, which is comparable with the dimensions of RBCs orsmall aggregates. It was shown that for uncirculating blood, the sedimentation mayplay an important role in blood clearing using the immersion technique, and thatOCT allows for precise monitoring of blood sedimentation and aggregation.

Venous blood was drawn from healthy volunteers and stabilized by 9NC coag-ulated sodium citrate 3.2% or by K2E EDTA K2. The major blood samples wereprepared immediately after taking blood by gently mixing blood and agent (foragents in liquid state) or agent–saline solution (for agents in solid state) with low-rate manual rotating for 1 min before each OCT measurement. A few sampleswere stored before measurements up to 24 h after taking blood. Four groups ofblood samples with various hematocrit values were investigated in the study.

A few different glass vessels of 0.2 to 2 mm thickness were used as blood sam-ple holders. For some holders, to enhance reflection from the bottom interface, ametal reflector was used. The sample holder was mounted on a translation stageat the sample arm and placed perpendicular to the probing beam. The amplitudeof reflected light as a function of depth at one spatial point within the sample wasobtained. The result is the measurement of optical backscattering or reflectance,R(z), from the RBCs versus axial ranging distance, or depth, z, described byEq. (9.35). The total attenuation coefficient, μt, and enhancement of transmittance(optical clearing), �T, by agent application were estimated by using Eqs. (9.41)and (9.42), respectively. Averaging for a few tenths of z-scans was employed.

The scattering, μs, and reduced scattering coefficient, μ′s, of blood depend on

mismatch of averaged refractive indices of blood plasma and erythrocyte cyto-plasm. The ratio nRBC/nbp ≡ m determines the scattering coefficient; nRBC is themean refractive index of erythrocyte cytoplasm, and nbp is the mean refractiveindex of the blood plasma. For the model of RBC ensemble as a monodispersesystem of noninteracting scattering dielectric spheres of radius a irradiated at aNIR wavelength λ, when 5 < 2πa/λ < 50, anisotropy scattering factor, g > 0.9,and 1 < m < 1.1, and μ′

s is described by Eq. (7.27).Blood plasma contains up to 91% of water, 6.5–8% (about 70 g/l) vari-

ous proteins, and approximately 2% low molecular compounds. Because of thelow concentration and relatively low refractive index of low molecular chemicalcompounds, the mean blood plasma (background) index can be estimated as theweighted average of refractive indices of water (92%), nw, and proteins (8%), np:

nbp = fwnw + (1 − fw)np, (9.46)

where f w is the volume fraction of water contained in plasma; nw = 1.329 at 800nm, and index of proteins can be assumed as np = 1.470.1360 Because approximately92% of the total plasma is water, it follows from Eq. (9.46) that nbp = 1.340. Theempirical formula, described by Eq. (7.33), can be used for the estimation of bloodplasma index in the wavelength range from 400 to 1000 nm. The refractive indexof erythrocyte cytoplasm, defined by the cell-bounded hemoglobin solution, can



be found from Eq. (7.27). It follows from Eq. (7.34) that an approximately ten-fold reduction in μ′

s is expected when the refractive index of the blood plasma ischanged from nbp = 1.340 to 1.388 and the refractive index of RBC cytoplasmis kept constant, nRBC = 1.412 (for hemoglobin concentration in cytoplasm of400 g/l).48

For slightly diluted blood (Hct ∼35%), optical clearing was found only fordextran of molecular weight M = 500,000 with concentration in a blood sample of0.325 g/dl and glycerol with volume fraction of 13%. Values of �T, characterizingoptical clearing, ranged from 20.2 to 78.4% for dextran and from 13.7 to 95% forglycerol, independent of time of blood sample storage (Table 9.10). Minimal andmaximal values have been found for blood samples that were stored after takingblood for short (1–3 h) and long (24 h) time intervals, respectively. For the timeinterval of 4–6 h of blood storage, �T = 46.5% for dextran and 74.5% for glycerol.Evidently, at high concentrations of RBC in a sample, interaction of agents withblood significantly depends on physicochemical parameters of blood, which maybe changed during prolonged storage (hemolysis). Thus, all other measurementswere completed as quickly as possible after taking the blood.

For blood diluted 56.5% by saline, the blood samples with trazograph-60, PG,and glycerol had lower total attenuation coefficients than control. Optical clearing,�T, was from 45.3% to 117.1%, as measured immediately after mixture, when sed-imentation is not critical for the optical properties of the blood layer (Table 9.10).The minimal attenuation (approximately one half that for the control) and maximalenhancement of transmittance (�T = 117.1%) were found for the application ofglycerol. PG is also a good enhancer of blood transmittance (�T = 77.2%).

Similar effects of increase in transmittance and decrease in scattering weredemonstrated by the use of dextrans of various molecular weights. Table 9.10indicates that all three dextrans (A, B, and C) reduced the amount of attenuation(scattering) coefficient in blood with respect to saline; �T was in the range from52.1% to 150.5%. The dextran with the highest molecular weight appeared to havea much stronger effect on the increase in transmittance immediately after mixing. Ablood sample mixed with an agent of higher refractive index, for example, dextranC, had higher reflectivity from the metal surface than agents such as saline (control)and dextran A with lower refractive indices. The results support the hypothesis thatthe refractive-index matching effect is important for clearing of 50% diluted blood.

Table 9.10 indicates that dextrans C and B at a concentration of 2.43 g/dlin 35% diluted blood are more effective agents to decrease the light attenuationof blood than the saline control: the total attenuation coefficient decreased from37.1 cm1 for the saline control to 31.2 cm−1 and 29.7 cm−1, respectively. In thiscase, �T was approximately 90% and 100% for dextran C and B, respectively.Interestingly dextran C, providing higher refraction, had less effect than dextranB at the same concentration. Moreover, the increase in concentration (refractionpower) did not always achieve higher optical clearance: 0.5 g/dl dextran C had astronger effect than 5 g/dl in samples with 20% blood and 80% saline.

These changes in scattering property, generated by the addition of dextran solu-tion, may first be explained by the refractive index matching hypothesis. It has


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Table 9.10 Total attenuation coefficient and enhanced transmittance, �T (%), of bloodsamples diluted by saline and added agents; pH for all solutions was approximately 7.5;dextran A (M = 10,500); dextran B (M = 65,500), and dextran C (M = 473,000).

Agent Concentration(volume % or g/dl)

Hct, % μt, cm−1 �T, % Comments

Saline 13% (control) 35 61 (3) — From 1 to 24 h after tak-ing blood; dextran sul-fate, M ≈ 500,000.1700

Glycerol 13% 35 51 (5) 13.7–95.0Dextran 0.325 g/dl 35 55 (5) 20.2–78.4Saline 35% (control) 26 37.1 (1.3) — Male volunteer,

24 yr old.1647Dextran A 2.43 g/dl 26 38.2 (2.4) 11.9 (8.3)Dextran B 2.43 g/dl 26 29.7 (3.6) 100.1 (20.2)Dextran C 2.43 g/dl 26 31.2 (1.8) 86.7 (29.1)

Saline 56.5 % (control) 17.4 42 — Female volunteer, 35 yrold.1331, 1700Trazograph-60 6.5 % + 50% saline 17.4 26 45.3

Propylene glycol 6.5% + 50% saline 17.4 26 77.2Glycerol 6.5% + 50% saline 17.4 20 117.1Glucose 1.62 g/dl 17.4 57 45.3Dextran A 1.62 g/dl 17.4 43 47Dextran B 1.62 g/dl 17.4 54 44.6Dextran C 1.62 g/dl 17.4 58 20.5

Saline 56.5% (control) 17.4 36.5 — Male volunteer,35 yr old.1331Dextran A 1.62 g/dl 17.4 29.5 52.1

Dextran B 1.62 g/dl 17.4 30.0 110.6Dextran C 1.62 g/dl 17.4 32.5 150.5Saline 56.5% (control) 17.4

17.425.6 (1.6) — Male volunteer, 23 yr

old.1647Dextran A 1.62 g/dl 22.5 (2.4) 20.5 (4.2)Dextran B 1.62 g/dl 17.4 19.0 (3.8) 44.5 (3.4)Dextran C 1.62 g/dl 17.4 14.3 (4.3) 47.0 (9.7)

Saline 80 % (control) 8 13.5 — Male volunteer, 36 yrold, hemoglobin: ini-tial, 175 g/l; diluted, 37g/l, Ref. 1647. At thebeginning of blood sed-imentation.

Dextran A 1 g/dl 8 17.5 (0.9) 11.4 (6.2)Dextran A 5 g/dl 8 14.3 (1.2) 11.3 (3.3)Dextran A 10 g/dl 8 12.2 (1.8) 49.4 (12.1)Dextran B 1 g/dl 8 14.2 (1.5) 21.1 (5.4)Dextran B 5 g/dl 8 13.0 (2.8) 49.0 (26.2)Dextran B 10 g/dl 8 11.5 (1.3) 76.8 (21.2)Dextran C 0.5 g/dl 8 10.0 (1.6) 106.3 (39)Dextran C 5 g/dl 8 13.3 (0.7) 67.0 (5.8)

Dextran A 1 g/dl 8 — 90 Male volunteer, 36 yrold, hemoglobin: ini-tial, 175 g/l; diluted,37 g/l; compared tothat of saline control onlight transmission after10 min sedimentation,(�Tdext/�Tsaline)%.1647

Dextran A 5 g/dl 8 — 61Dextran A 10 g/dl 8 — 32Dextran B 1 g/dl 8 — 144Dextran B 5 g/dl 8 — 126Dextran B 10 g/dl 8 — 18Dextran C 0.5 g/dl 8 — 285Dextran C 2 g/dl 8 — 133Dextran C 5 g/dl 8 — 15

been shown that scattering can be reduced when the refractive index of plasma isincreased. The refractive index of dextran saline solution was increased with con-centration in all molecular weight groups. The measured indices of blood sampleswith dextrans agreed well with the theoretical values, calculated according to theequation n = cbnb + (1 − cb)nsaline, where cb is the volume fraction (20%) ofwhole blood in the diluted sample and nsaline is the index of saline with or without



dextrans. As expected, the refractive index of blood with dextran increases as theconcentration of added dextran increases due to an increased index of the groundmatter of the sample.

The total attenuation coefficient for glucose and dextrans was not significantlychanged with respect to the control; nevertheless, transmittance enhancementsof 45% for glucose and of 52–150% for dextrans were found. The concurrentincreases in attenuation and transmittance by dextran B and C relative to A not onlyindicate that refractive index matching is important for blood layer optical clear-ing but also that RBC aggregation, which defines the scattering indicatrix, may besubstantial. Dextran macromolecules are neutral polymers. High molecular weightdextrans are used artificially to induce RBC aggregation by bridging surfaces ofadjacent cells after adsorption on their surfaces. The low molecular weight dextransprevent normal blood aggregation. Blood smear microscopy shows that rouleauxhave occurred in blood diluted with dextran C, but that no aggregates were pro-duced in the blood mixed with low molecular weight dextran A.1683, 1684, 1700, 1701

The lower sedimentation rate of blood with dextrans B and C and higher sedimen-tation rate with dextran A, relative to the rates for whole blood or for blood dilutedwith saline, also reflect the aggregation abilities of various dextrans.1331 The high-molecular weight dextran C has greatly changed the morphology and size of scatter(RBCs and aggregates). Normal RBCs are biconcave disks of 8-μm diameter and2-μm thickness when they are in an isotonic solution. It is known that the sizes,shapes, and orientations of RBCs contribute to the properties of blood backscatter-ing.1864, 1866 Aggregation results in a decrease in diffusing surfaces, which, in turn,leads to a decrease in the backscattered signal.1865 It can be concluded that thegreater transmittance enhancement of dextran C is governed strongly by scatteringchanges (refractive-index matching) accompanied by RBC aggregation.

Some discrepancy between μt and �T can be also explained by the fact thatdifferent algorithms are used to estimate them: μt is defined as a single scatteringparameter and �T is defined as an experimental value that accounts for multiplescattering, which is why it is more sensitive for reduction of scattering. It has beenshown that immersion initially leads to a reduction in the number of scatteringevents, and only then to the appearance of ballistic photons (see Figs. 9.4–9.6).791

For example, for the scattering system described in Ref. 791, which normally hasfor unmatched indices of scatterers, ns = 1.47 and ground material, n0 = 1.35, atotal transmittance at 800 nm is 10%, and after index matching (n0 = 1.41), thetotal transmittance rises to 45%, but the number of scattering events (as many as10–15) remains high [see Fig. 9.5(c)].

For fresh erythrocyte concentrates flowing at physiological velocity at an oxy-gen saturation of 98%, the change of Hct from 0.4 to 0.2 causes a reduction of μ′

s

from 16.8 to 8.8 cm−1 at 633 nm, measured by an integrating sphere technique.48

The corresponding changes in μs and g are: μs from 850 to 800 cm−1 and 0.980to 0.989, respectively. The total attenuation coefficient measured by OCT (seeTable 9.10) is more than 10 times less, relative to value of the scattering coefficientmeasured by an integrating sphere technique for blood samples with approximatelyequal hematocrit; this also shows the limitations of a single-scattering algorithm to


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extract a proper value of the total attenuation coefficient. Another reason for suchstrong discrepancy between μt and �T data may be caused by spatial variationsof the reflectivity of the blood sample, α(z), associated with variations of the localrefractive index and the backscattering property of the blood sample.

Sedimentation increases the transparency of a blood layer because there is lessbulk scattering as the RBCs fall. As expected, the undiluted blood sample has thelowest reflectance from the metal plate because it has a higher concentration ofscatters (RBCs) and a lower sedimentation rate.1331, 1700 For slightly diluted bloodby a saline and with the addition of low molecular weight dextran A, reflectancefrom the metal plate increases at the depth of the blood sample, because both dilu-tion by saline and addition of dextran A cause more intense sedimentation. DextranB, which has a mean molecular weight, permits higher reflectance than the control(i.e., blood diluted by saline) only during the first 4 min; this result reflects thecompetition between two processes: refractive-index matching, which is impor-tant at the beginning, especially for dextran; and sedimentation, which is moreimportant for the control sample after some time has elapsed. The high molecu-lar weight dextran C permits an increase in metal plate reflectance compared withthat of the control for only a short period at the beginning of sedimentation, whenonly the refractive index matching effect dominates. Such behavior shows that aftera certain time interval, RBC sedimentation may be more important for increasingreflectance than the refractive index matching effect, which is provided by dextranswith higher molecular weight. This result is clear from the in-depth reflectanceprofiles presented in Fig. 9.69, which show the three primary evolution peaks intime. The first peak is independent of time and induced by reflectance at the glass–blood interface; the second peak, which is broad and has some structure, is causedby reflectance at the RBC–plasma interface (within this peak, aggregates can beobserved); and the third peak is caused by the metal reflector. Qualitatively, theheight difference between the first and third peaks shows changes in the transmit-tance of the blood layer, and the second broad peak is related to the attenuationcoefficient of this layer.

To clarify the role of RBC aggregation on optical clearing and to accountingfor the time-dependence of the aggregation process, the blood sample was allowedto sediment after the addition of dextrans and before measurements. Table 9.10summarizes the effect of dextrans compared to the saline control on light transmis-sion for the sample with 20% blood and 80% saline after 10 min sedimentation.As indicated, the influence of dextran on the light transmission was different com-pared to that at the beginning of mixing dextrans in blood (corresponding upperrows). The lower concentration (0.5 g/dl) dextran C still had the strongest effecton reducing the scattering of light in blood, with a 2.8-fold stronger effect thanthat of the saline control. However, enhancement by the highest concentrations ofdextran C (5 g/dl) and dextran B (10 g/dl) was dramatically lower than that of thesaline control. At the beginning, they both had very high blood optical clearingcapability, with 67.5% and 76.8% of �T, respectively. In addition, the effect wasdecreased with the increase of dextran in blood within all three groups, contrary tothe expectation of the refractive index matching hypothesis.



Figure 9.69 OCT in-depth reflectance profiles measured for slightly diluted whole blood(13% volume fraction of saline, hematocrit ∼35%, concentration of dextran 3.25 g/dl in ablood sample) at the beginning of the sedimentation process (a, d, g); at 5 min (b, e, h); andat 10 min for (a–c) saline only, (d–f) dextran A added, and (g–i) dextran C added (c, f, i). Thefirst peak is induced by reflectance at the glass–blood interface; the second peak, which isbroad and has some structures, is caused by reflectance at RBC–plasma interface; and thethird peak is caused by the metal reflector (see Ref. 1331).

The decreased aggregation capability of dextran with concentration accuratelyexplained that light transmission decreased less with the increase of dextran forboth types (moderate and large molecular). Over a range of concentrations, dextranC and B induced RBC aggregation. However, dextrans have been known to exerta biphasic effect on RBC aggregation; they induce aggregation at low concentra-tion and disaggregation at high concentration.1867 For example, with dextran B, themaximal aggregation size is obtained at approximately 3%, above which the sizedecreases. In OCT measurements of Ref. 1647, 2 g/dl dextran C and 5 g/dl dextranB in 20% blood with 80% saline appeared to be the critical concentration to affectRBC aggregation. Their aggregation parameters became smaller than those of 0.5g/dl dextran C and 1 g/dl dextran B. When the concentration increased to 5 g/dlfor dextran C and 10 g/dl for dextran B, they played a disaggregative role. This iswhy the cells are much less packed than with the saline control, accounting for the


536 Chapter 9

reduced light transmission. Although refractive index matching suggested a higherlight transmission, the aggregation–disaggregation effects are now dominant.

The behavior of RBC in flow is dependent on the processes of aggregation–disaggregation, orientation, and deformation. For normal blood, rouleaux are easilydecomposed to their individual cell constituents as blood flow (shear) increases.In some pathological cases, however, capillary circulation is seriously affectedbecause inseparable rouleaux are formed. Increased RBC aggregability has beenobserved in various pathological states, such as diabetes and myocardial infarction,or following trauma.1868 The aggregation and disaggregation properties of humanblood can be used for characterization of the hemorheological status of patients suf-fering different diseases.1866 In this connection, optical clearing methodology forcontrolling the optical properties of blood using molecules with specific actions onthe RBC and plasma may be useful for monitoring blood parameters in flow.

It is obvious that refractive index matching is not the only factor to affect trans-mittance in these experiments. The amount of aggregation certainly has an effect,but other factors may contribute, such as the hematocrit, the manner in which RBCsare packed, the shapes and variance in size of these aggregates, and the fluctuationof all these parameters in time and space.

The osmolarity of blood plasma is also an important factor in changes in thescattering properties of blood, and therefore, in the control of blood clearing andthe improvement of the contrast of OCT images obtained within or behind a layerof blood. In discussed experiments, the osmolarity of the plasma was different foreach added agent. Variation in plasma osmolarity leads to changes in the shapesof the erythrocytes: RBCs shrink (acanthocytes) when the plasma is hyperosmoticand swell (spherocytes) when it is hypo-osmotic. For diluted blood samples (Hctof 7.5%), μs shows a slight decrease (∼10%) with increasing osmolarity in therange from 225 to 450 milliosmol/l; also, g decreases from 0.995 to 0.991, andcorrespondingly, μ′

s increases linearly with osmolarity up to 70%.48 This strongeffect on the scattering properties of blood solution is caused not only by changesin cell shape but also by the variation with osmolarity of the refractive index ofthe cell-bounded hemoglobin solution. The refractive index of the cell-boundedhemoglobin solution can be estimated from Eq. (7.34). Assuming a mean erythro-cyte volume of 90 μm3 and an inner cell hemoglobin concentration of 350 g/l forisotonic conditions, the following values of refractive indices and sphere equiva-lent diameters were calculated (see Table 9.4). This table clearly indicates that theosmolarity of the blood solution can substantially change the scattering propertiesof the blood layer. Refractive index matching is easier to achieve in conditionsof low osmolarity, but for OCT imaging of RBCs or their aggregates, hypertonicconditions are preferable.

From the preceding analysis of experimental data, it follows that to describetheoretically light transport in immersed blood, we have to consider blood asa turbid medium with multiple scattering, defined by scattering and absorptionproperties of individual particles (erythrocytes) and by concentration effects andpolydispersity of the cell suspension. The erythrocyte size and complex refractiveindices (n′ + in′′) of erythrocytes and blood plasma define μa and μs, and g. The



Table 9.11 RBC parameters found from osmolarity of the blood solution (see Ref. 48).

Osmolarity,milliosmol/l

Hct,%

RBC volume,μm3

RBC hemoglobinconcentration, g/l

Refractive indexat 589 nm

Equivalent spherediameter, μm

250 (hypotonic) 8.1 96.7 325 1.397 5.70300 (isotonic) 7.5 90.0 350 1.402 5.56400 (hypertonic) 6.6 78.6 400 1.412 5.32

size, shape, and optical parameters of blood cells, as well as optical properties ofblood suspension, are presented in Section 7.10 and Tables 7.2, 7.3, and 9.11. Theerythrocyte mean volume at isotonic medium is 94 ± 14 μm3 and volume distribu-tion is in the range from 30 to 200 μm3 (see Refs. 48, 1311, 1325, 1869, and 1870).The hemoglobin concentration in hemolyzed blood is between 134 and 173 g/l.Each erythrocyte contains approximately 29 pg of hemoglobin. The hemoglobinconcentration within an erythrocyte ranges from 300 to 360 g/l. The real part of therefractive index of the red blood cell is very close to 1.4 in the wavelength rangefrom 400 to 1200 nm.275, 1325, 1391, 1869

The phase function and scattering cross section of an individual erythrocytedepend on its orientation.225 However, light scattering characteristics of large num-bers of randomly distributed nonspherical particles are very similar to those ofa system of randomly distributed spherical particles with equal volume.48, 1871

Therefore, calculations can be conducted for a model of homogeneous sphereswith volume equal to that of real erythrocytes. Such model provides more simplecalculations than that for a rigorous theory accounting for particle nonsphericity,211

and allows one to account for particle polydispersity in the simplest way; in partic-ular, on the basis of the data presented in Ref. 1325 (see Fig. 9.70). The presence oflarge particles in the distribution can be associated with small aggregates of RBC.

Evidently, the hemoglobin concentration, CHb, in an erythrocyte correlateswith its volume, VRBC. In accordance with data of Ref. 1869, such dependenceis defined by

CHb = 0.72313 − 0.00451VRBC, (9.47)

where CHb is the hemoglobin concentration in g/ml and VRBC is the RBC volumein μm3.

The spectral dependence for the real part of RBC refractive index is presentedin Fig. 7.12225, 1325 and the spectral dependence for the imaginary part can be cal-culated using data presented in Fig. 7.11. Both refractive index components areproportional to hemoglobin concentration in RBC; the real part is defined by Eq.(7.34) with βHb = 0.001942 dl/g for 589 nm48 and βHb = 0.00284 dl/g at 640nm,225 and the imaginary part by the following expression:

n′′ = αHbCHb, (9.48)

where αHb is the spectrally dependent coefficient, equal to 1.477 × 10−6 dl/g at640 nm.225


538 Chapter 9

Figure 9.70 Size distribution function of spherical particles modeling erythrocytes in blood(see Ref. 1325). Volume fraction of erythrocytes in blood (hematocrit) is 45%, whichcorresponds to venous blood of an adult male.

Because concentrations of salts, sugars, and other organic components in RBCcytoplasm are negligible, hemoglobin can be considered to be dissolved in wateronly [see Eq. (7.34)]; thus, the spectral dependence of refractive index of themedium in which hemoglobin is dissolved is defined by water. For more precisedescription of refractive index of this medium, n0(λ), when organic componentsare accounted for, instead of nw(λ), n0(λ) = nw(λ) + 0.007 may be used.1010

The spectral dependence of the real part of the refractive index of blood plasmacan be described by the empirical Eq. (7.33), and because blood plasma containsup to 91% of water, and only 6.5–8% (approximately 70 g/l) proteins (hemoglobin,albumin, and globulin) and approximately 2% low molecular compounds, itsimaginary part is negligible and can be ignored in calculations.

For further calculation of scattering and absorption coefficients and scatteringanisotropy factor, Mie theory for a homogeneous spherical particle is used. The cor-responding equations for scattering and absorption cross sections and anisotropyfactor are given by Eqs. (3.53), (3.54), and (3.55). For a densely packed polydis-perse particle system, which is whole blood, absorption and scattering coefficientsand scattering anisotropy factor are defined by [see Eqs. (3.24) and (3.27)]222

μa =NRBC∑i=1

Niσai , (9.49)

μs = F(Hct)NRBC∑i=1

Niσsi , (9.50)



g =

NRBC∑i=1

μsigi

NRBC∑i=1

μsi

, (9.51)

where F(Hct) is the packing function of RBC [see Eqs. (3.21), (3.22), and(3.23)],275, 762, 763 which accounts for the interparticle correlation effects; Hctis the hematocrit; NRBC is the number of RBC diameters (volume fractions);Ni = fRBCi/VRBCi is the number of RBCs in a unit volume of blood; fRBCi is thevolume fraction of RBCs with volume VRBCi = (4/3)πa3

i (see Fig. 9.70), where ai

is the radius of an individual equivalent volume spherical particle.Under glucose application as an immersion agent, the spectral dependence of

the index of refraction on blood plasma corrected by the added glucose–watersolution should be accounted for [see Eqs. (6.5) and (7.39)] as

nbp+gl(λ) = nbp(λ) + 0.1515 × Cgl, (9.52)

where nbp(λ) is the refractive index of blood plasma, defined by Eq. (7.33), andCgl is the concentration of glucose in g/ml. Because glucose has no strong absorp-tion bands within the spectral range from 400 to 1000 nm, its absorption may beneglected. It can be also hypothesized that glucose molecules do not bond withproteins in blood plasma and hemoglobin in RBC during the limited time (a fewminutes maximum) of their interaction.

As we already discussed, RBCs are very sensitive to changes in blood plasmaosmolarity (see Table 9.11). When osmolarity increases due to cell dehydration,RBC volume decreases, hemoglobin concentration within the cell increases, andindex of refraction increases. Glucose injection in blood causes a linear increasein plasma osmolarity with glucose concentration, up to 6000 mOsm/l at glucoseconcentration of 1.0 g/ml in blood plasma. Indeed, for patients, such large glu-cose concentrations may only be applied locally in the vicinity of a vessel wallsite under spectroscopic study or optical imaging. Using data of Ref. 48, the fol-lowing empirical relation was suggested to describe RBC volume change withosmolarity:1009

VRBC(osm) = VRBC(300)(

0.463 + 1.19 exp{− osm

376.2

}), (9.53)

where VRBC(osm) is the RBC volume in μm3 at given osmolarity expressed inmOsm/l and VRBC(300) is the RBC volume at isotonic osmolarity, osm = 300mOsm/l. Following glucose injection, the local Hct decreases. If Hct before injec-tion of glucose was 45% at osm = 300 mOsm/l; then at Cgl = 0.05 g/ml, osm = 580mOsm/l and Hct = 32%; at Cgl = 0.1 g/ml, osm = 850 mOsm/l and Hct = 26%; andat Cgl = 0.2 g/ml, osm = 1400 mOsm/l and Hct = 22%. For further increases of glu-cose concentration (0.3–1.0 g/ml), hematocrit stays constant, Hct ∼= 21%, despitelinear increases in blood plasma osmolarity (2000–6000 mOsm/l).

Results of modeling the control of scattering properties for whole bloodupon its immersion (local intravessel injection) by a glucose solution at different


540 Chapter 9

concentrations accounting for RBC packing function in the form F(Hct) = (1 −Hct) [see Eq. (3.21)], polydispersity [150 volume fractions of volume (size) distri-bution (Fig. 9.70)], osmolarity, and hematocrit effects are presented in Fig. 9.71.The scattering coefficient and scattering anisotropy factor were calculated. Thescattering coefficient behavior with concentration and the wavelength [Fig. 9.71(a)]is defined by: (1) the change in blood plasma osmolarity [increase in scattering forall wavelengths far from Soret band, caused by RBC shrinkage and increase inrefractive index for low concentration of glucose (see Table 9.11)]; (2) reductionof blood hematocrit (plays a certain role in the scattering decrease for glucoseconcentration less than 0.3 g/ml); (3) refractive index matching—the main effect(significant reduction in scattering for glucose concentration from 0.5 to 0.7 g/mlin dependence of the wavelength); and (4) dispersion of hemoglobin absorbingbands [within a strong Soret band (415 nm), it is not possible to achieve a signifi-cant reduction of scattering, and the positions of the dip and the depth of scatteringdamping are slightly modified for other lower-absorbing hemoglobin bands at 542and 575 nm].

Maximal damping of the scattering corresponds to 900 nm, where the influenceof hemoglobin bands dispersion is minimal, but the highest glucose concentrationof 0.7 g/ml is needed in this case. The increase in scattering coefficient at higherglucose concentrations is caused by a refractive index mismatch, when refractiveindex of the RBCs becomes lower than that for blood plasma modified by the addi-tion of glucose. The same factors define the behavior of the scattering anisotropyparameter [Fig. 9.71(b)] RBC shrinkage causes a decrease of the g-factor for smallglucose concentrations, refractive index matching for the moderate concentrationscauses its increase, and further refractive index mismatch causes its reduction.For applications, especially when OCT endoscopy is used, concurrent reductionof scattering and increase of g-factor upon administration of immersion agent isimportant. The transport scattering coefficient, μ′

s = (1 − g)μs, decreases and trans-port free path length for a photon, ltr ∼= 1/μ′

s, increases dramatically, thus morephotons, which carry information about hidden objects (for example, thin-walledplaques in the coronary arteries) can be detected. From data in Fig. 9.71, it followsthat for the wavelength of 900 nm, the scattering coefficient of blood is changedfrom 1200 cm−1 to approximately 50 cm−1 and that for g-factor from 0.991 to0.994 with glucose immersion, thus, the transport free path length increases morethan 35 times. Correspondingly, the depolarization depth of blood560,583,650 whichis proportional to ltr, should be much larger under optical clearing.

The described method for immersed blood modeling is applicable for adminis-tration of any other biocompatible immersion agent, such as dextrans, glycerol, ortrazograph (Table 9.10). Under blood clearing, there also exists another possibilityof blood immersion using the local blood hemolysis, which can be provided in thevicinity of the fiber-optic endoscopic probe.1359 In this method, free hemoglobin isthe immersion agent. To model optical properties, all previously discussed effectsshould be taken into account. The local increase of hemoglobin concentration inplasma can lead to local change of plasma osmolarity:1009



Figure 9.71 Theoretical modeling of blood optical clearing at glucose intravessel injection.Calculated curves for the scattering coefficient (a) and scattering anisotropy factor (b) atglucose concentration in blood (see Ref. 1010). Initial blood hematocrit is 45% and RBChemoglobin concentration is 322 g/l; 150 volume fractions of RBC with different volume(size) in accordance with the RBC volume distribution function, presented in Fig. 9.70, wereused in modeling.

osm′ = osm + CbpHe

MHb, (9.54)

where osm is the plasma osmolarity under physiological condition (280–300mOsm/l); CbpHb is the concentration of plasma hemoglobin, g/l; MHb is the molar


542 Chapter 9

Table 9.12 Size distribution of the equivalent spherical particles modeling RBCs (see Ref.1872).

Volume fraction, % 4 14 30 32 14 6

Radius, μm 1.2 ± 0.2 1.7 ± 0.3 2.2 ± 0.2 2.7 ± 0.3 3.4 ± 0.4 4.3 ± 0.5

mass of hemoglobin (MHb = 66500 g/M). The expected change in RBC volumecalculated by using empirical Eq. (9.53) is no more than 0.1% at hemolysis below20%. For simplicity, the polydispersity of RBCs can be taken into account on thebasis of the six-fraction blood model given in Table 9.12,1872 which correlates witha more complete distribution given in Fig. 9.69.

Calculations of the absorption coefficient, scattering coefficient, and anisotropyfactor of whole blood at normal conditions and local hemolysis have been per-formed by using Eqs. (9.49)–(9.51), with the packing function F(Hct) = (1 −Hct)(1.4 − Hct). In contrast with small changes of absorption coefficient, moresignificant changes of the scattering properties of blood have been observedwith increases in free hemoglobin concentration in plasma. A rather spectrallysmooth decrease in scattering coefficient was found for all wavelengths with freehemoglobin release at hemolysis.1359 At hemolysis rate of 20%, a decrease in thescattering coefficient for both wavelengths (633 and 820 nm) was calculated to be40%, whereas the anisotropy factor increased at 633 nm from 0.9940 to 0.9952,and at 820 nm from 0.9919 to 0.9929.

The described method can be realized not only for blood hemolysis, but alsofor local free hemoglobin injection.1702 Hemoglobin administration may also serveas a clearing agent for tissue clearing, when needed in the spectral range far fromthe strong absorption bands of hemoglobin. On the other hand, the sensitivityof scattering properties of blood to RBC hemolysis may be used for designingthe effective optical technology for in vivo monitoring of blood hemolysis invessels.

Direct experimental proof of the optical immersion of a RBC in hemoglobinsolution is presented in Ref. 252. Measurements were made for individual erythro-cytes by using phase microscopy (see Fig. 8.28, panel B, image c and scan d). It wasalso demonstrated in ex vivo studies with animals using OCT that an intravenousinjection of highly concentrated hemoglobin solution enhances light transport inblood and surrounding tissues (see Figs. 9.72 and 9.73).1702 This result may havepromise for immediate clinical applications, particularly to improve blood opticalpermeability for OCT probing, which was suggested for cardiovascular imag-ing by using dextrans.1646 Actually, the efficiency and safety of the nonocclusionmethod for OCT in vivo image acquisition in humans using the low molecularweight dextran as an OCA were reported.1701 In these clinical studies, a frequency-domain OCT was performed with the continuous flushing method via a guidingcatheter. Twenty-two patients with 25 coronary stented lesions were enrolled in thestudy.



Figure 9.72 Enhancement of transmittance for various clearing agents mixed with blood.Data were obtained using the OCT system at 930 nm (see Ref. 1702). Hemoglobin of twoconcentrations dissolved in saline was used as an OCA; other OCAs, such as PEG, PG,and PPG, were used undissolved. Microscopic image of blood smears after addition ofhemoglobin dissolved in saline to blood is shown in the insertion.

9.8.3 Cell studies

The optical immersion method is a valuable technique for studying the refrac-tive and scattering properties of living cells.158, 216, 245, 264, 1360, 1383, 1619, 1620, 1699,

1715, 1716, 1799, 1800, 1873 For cellular refraction measurements, this technique has beenused since the 1950s.1360, 1383, 1619 It was successfully used in combination withphase refractometry to study the distribution of water and solids in animal cells(mechanisms of cell cornification); to examine mechanisms of animal cell motil-ity connected with water redistribution; to study cell permeability, damage, anddeath; and to examine the vitality and growth cycles of bacteria, fungi, yeasts, andspores. Some of the hematological applications of the immersion technique in cellsuspension studies were discussed earlier in Subsection 9.8.2.

In cell examination, the requirements for immersion agents should be slightlydifferent than in tissue optical clearing, in which, for many applications, only celldamage is critical and the hyperosmotic property of agents provides one of theleading mechanisms for tissue clearing. In general, an immersion substance to beused for the refractometry of living cells should fulfill the requirements discussedin the following.1360, 1383

1. The immersion substance should be nontoxic, not affecting the structure orfunction of living cell; i.e., chemically inert and affecting no chemical componentsof a cell.

2. The immersion substance should be isotonic, i.e., causes no changes incell volume. Cell shrinkage or swelling induced by water displacement from thecell into the surrounding medium, or vice versa, is accompanied by correspond-ing changes in cell refractive index; thus, the measured refractive index will not


544 Chapter 9

Figure 9.73 A-scans of the OCT images at 1300 nm for mouse tail vein in norm (a) (the onlyfront vein wall is seen at the depth ∼0.5 mm) and after intradermal injection of fructose andintravenous injection of hemoglobin with the concentration of 160 g/l (b) [both vein walls,front (∼0.5 mm) and rear (0.8 mm), are clearly shown, as are and some structures behind](see Ref. 1702).

have a true value. Isotonicity is a biological character of a cell in solution, which isconnected with such physical characteristics of a solution as its iso-osmotic prop-erty, but may not be similar. To provide iso-osmotic and isotonic conditions, theimmersion substance should exert low osmotic pressure; that is, it should consistof dissolved particles with high molecular weight and dimensions. For exam-ple, osmotic pressure of 10% water solution of bovine serum albumin (BSA) isequivalent to water solution of sodium chloride (NaCl) at pressure of 0.08%.

3. The immersion substance should not penetrate the cell when the refractiveindex of a whole cell is under study. Otherwise, upon cell immersion in a mediumwith a higher refractive index, this substance diffuses inside the cell and equalizesrefractive indices inside and outside the cell, making the measured cell refractiveindex far from the true value. Thus, for many cases, the immersion substanceshould have a macromolecular structure to prevent cell permeability. However,



for some specific cases, when intracellular organelles are under investigation,immersion agents with a controllable permeation can be used.

4. The immersion substance should be freely soluble in water so that the refrac-tive index of the solution can be equal to or exceed that of the part of the cell to bemeasured. As for animal cells, the refractive index ranges from 1.350 to 1.426 (seeTable 7.6) and for bacterial cells, from 1.360 to 1.420.1383 The immersion substancerefractive index values must be variable in these ranges with steps of 0.002–0.005.The best decision is to determine two well-mixing solutions, one with the mini-mal index and another with the maximal index of the range under study. It is veryimportant that for each mixed solution, The immersion substance maintains its iso-tonic properties. Evidently, this condition can be satisfied if both solutions havelow osmotic pressure and their mixing is not accompanied by a specific chemicalreaction, causing increase in osmotic pressure.

5. The immersion substance should be optically transparent and isotropic, i.e.,conditions of less absorption and scattering in the measuring wavelength range, aswell as less linear birefringence and chirality, should be provided.

6. The immersion substance should be stable in the range from room to phys-iological temperatures, and does not change its optical properties at prolongedstorage.

Such requirements are mostly completely fulfilled for water solutions of albu-min and water–glycerol gelatinous gels.1360, 1383 The fifth fraction of bovine orhuman serum albumin contains the total mass of serum albumin, approximately3% of α-globulin, and less than 0.5% of β-globulin,1383 and its index of refrac-tion has a linear dependence on concentration with an increment of βp = 0.00185[Eq. (7.34)]. There is some discrepancy from linearity for high concentrations thatpossibly connected with their relative high viscosity. For microbiological studies,protein solutions are usually prepared with the refractive index ranging from 1.360to 1.420 with an interval of 0.002 on the basis of 0.5−0.6% solution of NaCl indistilled water.1383

Water–glycerol gelatinous gels are applicable when cell motility does not allowone to provide precise measurements using protein solutions.1383 Such gels fixand immobilize cells, preserving their vitality; they are optically transparent withlow birefringence and high stability of optical properties, if correctly exploited,and with low osmotic pressure. Isotonic gel kits for studies are prepared by dilu-tion of concentrated salt-free and purified gelatinous gels with turbidity of 0.5 ×10−3 cm−1 in 0.2% sterile solution of glycerol in 0.5% solution of NaCl with pH7.0–7.2; other compositions with 1% glycerol, 1% glycerol and 0.5% glucose, or10% saccharose also can be used. Using protein solutions and gelatinous gels asimmersion substances and phase-contrast microscopy with effective suppressionof the background light, refractive indices of numerous bacteria of certain familieshave been measured, such as Coccaceae, Bacteriaceae, Bacillaceae, Spirillaceae,and Proactinomycetaceae.1383 On the basis of refraction measurements, the con-centration of dry materials and water in bacterial cells, their density, bacterialgrowth-cycle, and rehydration of lyophilized bacterial cells and hydration of sporeswere studied. Differentiation between vital and dead cells in lyophilized cellpreparations and percentage of vital spores were also determined.


546 Chapter 9

Figure 9.74 Effect of the extracellular fluid to cytoplasm refractive index matching onthe phase-contrast microscope image of dysentery bacteria cells. There is a sharpenhancement of the membrane brightness (Ref. 1383, p. 70).

The optical clearing effect can most easily be demonstrated by analyzing phasemicroscope images of bacterial cells containing only a cytoplasm and a mem-brane.1383 If a biological object is homogenous, matching its refractive index valuewith that of the host medium will make it optically invisible. In the case of bacte-ria containing only a cytoplasm and a membrane, matching of the refractive indexof the cytoplasm with that of the extracellular fluid will make the image of thecytoplasm disappear and sharply enhance the brightness of the optical image ofthe membrane. For a case in which the refractive index of the extracellular fluid isexternally controlled by the administration of an appropriate chemical agent, thedisappearance of the cytoplasm and the sharp enhancement of membrane bright-ness can be used as an efficient method of measuring the refractive index of thecytoplasm and monitoring cell vitality. Figure 9.74 illustrates the optical clearingeffect.

The finite-difference time-domain (FDTD) approach was recently suggestedas a promising tool for a more detailed study of the optical clearing effect in cellsand its possible applications.1716 In Ref. 1716, the 3D and 2D FDTD simulationresults of light transmission through a biological cell containing only cytoplasmand membrane are presented. The calculated 2D distributions and two cross sec-tions of a phase of the Ez component of the forward-scattered light through thebiological cell in the near field are shown in Fig. 9.75. It is clear that refractiveindex matching (graphs on the right) significantly enhances the phase contrast ofthe cell membrane, as indicated by the experimental data of Fig. 9.74. The intensityof phase microscope images is directly proportional to the phase accumulated bythe light beam after its propagation through the cell. Calculations were made fortypical parameters of a microbial cell: the diameter of the cell is 1.44 μm and thethickness of the membrane is 0.06 μm, the refractive indices of the cytoplasm andmembrane are 1.36 and 1.47, respectively. During calculations, the FDTD cell sizeof 0.02 μm was used, and extracellular fluid refractive index values were 1.36 and1.33 with and without refractive index matching conditions, respectively.



Figure 9.75 FDTD modeling of light scattering by biological cells in controlled extracellularmedia (see Refs. 1715 and 1716). Calculated 2D distributions and two cross sections ofthe phase of the Ez light component shown in the near field of a biological cell containingonly cytoplasm and membrane. It is clearly shown that refractive index matching (graphs inthe right) significantly enhances the phase contrast of the cell membrane. Cell radius: 0.72μm, membrane thickness: 0.06 μm, cytoplasm refractive index: 1.36, membrane refractiveindex: 1.47. Asymmetry is due to the z-polarization of the incident light. The simulationswere performed by FDTD Solutions software, which is commercially available by LumericalSolutions, Inc., Vancouver, BC, Canada.


548 Chapter 9

Experimentally determined ratios of scattering intensities from cells (ratfibroblast cell clone MR1; ∼105 cells/mL) immersed in media of low and highindices of refraction are presented in Ref. 216. As a medium with low index ofrefraction, n = 1.332, PBS was used in both cases. The media of higher index hadn = 1.345 (BSA in PBS) and n = 1.343 (ovalbumin in PBS). The scattered lightintensity at small angles (<20 deg) was significantly greater when the cells wereimmersed in PBS with a low refractive index than when they were immersed ina protein solution with a higher index. Thus, it may be concluded that there issignificant scattering at small angles from cell structures that are in contact with theimmersion substance. However, at larger angles (>40 deg), the effect of increasedindex of refraction of the immersion substance on light scattering is much smaller.Following the estimations of the authors of Ref. 216, the percentage of lightscattering from internal cellular structures can be determined. Considering thatthe ratio of scattering intensity from cells suspended in the immersion substancewith low and high indices for angles above 40 deg is 1.3, the fraction of scatteringintensity from particles internal to the cell can be estimated. The scattering inten-sity in the immersion substance with low refraction is given by Inc + Ic, where Inc

and Ic are the intensities of scattering from structures not in contact and in contactwith the immersion substance, respectively. In the immersion substance with highrefraction, scattering from the particles in contact with the immersion substancereduced by about a factor of 2.1 and the scattering is given by Inc + 0.48 · Ic.Thus, the relative light scattering from internal cell components when the cells areimmersed in PBS, Inc/(Inc + Ic) ≈ 0.55, because (Inc + Ic)/(Inc + 0.48 · Ic) ≈ 1.3.

9.8.4 “Self-clearing” or metabolic clearing effects

Within the human body, there are plenty of endogenous substances that can serveas OCAs. One example was already discussed, blood hemoglobin, which can beeasily and locally produced within the vessel1359 and makes the blood layer moretransparent to provide a more precise image of a vessel wall (see Figs. 9.72 and9.73).1702

Another example is fat lipolysis, which can be produced in different ways,including photodynamic or photothermal treatment through skin.1023, 1725 The finalproducts of fat lipolysis are water and glycerol. Depending on the parameters oflaser treatment, the released amount of endogenous glycerol can be controlled. InFig. 9.76, a sequence of white light transmittance images of thin adipose tissuesample stained by ICG and irradiated by a diode laser (λ = 810 nm) is shown. It isclear that, with time elapsed after irradiation from 16 to 37 min, optical immersionoccurs with smooth transmittance within the whole area of the sample. We canhypothesize that the photochemical action of ICG954 under laser irradiation hasinduced fat cell lipolysis1023,1725 with secretion of glycerol that works as an OCAand provides refractive index matching within the cell layer structure.

More precisely, the refractive index matching concept is proved by the mea-sured distribution of the cell layer transmittance, T, along the projection of theupper cell, the contours of which are clearly shown in Fig. 9.76(a). The spatial



Figure 9.76 Images of adipose tissue sample stained by ICG before (a) and after (b) irra-diation during 2 min by a diode laser. Time elapsed after irradiation: 9 min (b), 16 min (c),26 min (d), 30 min (e), 37 min (f). Temperature of the sample was kept at 34◦C. CW diodelaser (250 mW·cm−2, λ = 810 nm) (see Ref. 1725).

Figure 9.77 Distribution of transmittance, T, along the projection of the upper cell at dif-ferent moments of time: �, 0 min; •, 9 min; �, 26 min; �, 37 min (a). Dependences ofthe averaged transmittance, Tav, and its standard deviation, σ(T), on time, t, elapsed sinceirradiation: �, Tav; • and �, lower and upper boundaries of σ(T), respectively (b) (see Ref.1725).

distributions of transmittance for different time periods elapsed after laser irradia-tion are presented in Fig. 9.77. Initially, the distribution is rather nonmonotonous,with narrow spikes (bright spots) that can be associated with lensing and wave-guiding effects owing to the specific structure of fat tissue as multiple sphericalcells filled up by a homogeneous lipid matter and separated by a thin fibrous tis-sue called septa. With time after irradiation, due to refractive index matching, bothlensing and wave-guiding effects should be eliminated, which is supported by thedata presented in Fig. 9.77(a). Finally, Fig. 9.77(b) demonstrates that transmittancecan be improved only locally (see lower curve), but the averaged transmittance,Tav, is less dependent on time.

9.9 Applications of the Tissue Immersion Technique

9.9.1 Glucose sensing

Noninvasive and continuous monitoring of glucose concentration in blood and tis-sues is one of the most challenging and exciting applications of optics in medicine.


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Figure 9.78 Reduced scattering coefficient at 650 nm (dots) and blood glucose concentra-tion (solid curve) measured on a volunteer with insulin-dependent diabetes mellitus duringa double clamping experiment (see Ref. 469). Multichannel CCD-based spatially resolvedfiber-optic backreflectance spectrometer and neural network software were used to mea-sure and extract optical properties. Reflectance measurements were collected at 15-sintervals for ∼5 h, and skin and room temperature were monitored throughout the courseof the experiment; the volunteer remained as still as possible, and food and drink were notpermitted.

The major difficulty preventing the development and clinical application of a non-invasive blood glucose sensor is associated with the very low signal producedby glucose molecules. This results in low sensitivity and specificity of glucosemonitoring.105, 138, 166

The concept of noninvasive blood glucose sensing using the scatteringproperties of blood as an alternative to spectral absorption and polarizationmethods105,166,991 for monitoring of physiological glucose concentrations in bloodof diabetic patients is under intensive discussion.166, 467–469, 991–999, 1006–1008, 1191, 1192,

1387–1389, 1622, 1650, 1683, 1684, 1761, 1765, 1874–1877 Many of the effects considered inSubsection 9.8.2, such as RBC size, refractive index, packing, and aggregationchanges under glucose variation, are important for glucose monitoring in diabeticpatients. Indeed, at physiological concentrations of glucose ranging from 40 to400 mg/dl, the roles of some of these effects may be changed, and certain othereffects, such as the rate of glucose penetration inside the RBC and the followinghemoglobin glycation, may be important1387, 1389, 1650, 1681, 1878 (see Subsection 7.11and Fig. 7.14).

Noninvasive determination of glucose was attempted by using NIR lightscattering of skin tissue components measured by frequency domain 467 or spa-tially resolved diffuse reflectance techniques.469, 1875 Both approaches are basedon changes in glucose concentration, which affect the refractive index mismatchbetween the interstitial fluid and tissue fibers, and hence, μ′

s. A glucose clampexperiment (concentrations of injected glucose and insulin are manipulated toresult in a steady concentration of glucose over a period of time991) showed thatδμ′

s at 650 nm qualitatively tracked changes in blood glucose concentration for theexamined volunteer with diabetes (Fig. 9.78).469 The distances between the sourceand detector fibers were in the range rsd = 1–10 mm, which corresponds to theapproximate range of 0.5–5 mm in tissue upon which μ′

s is determined. A drift in



μ′s that was independent of glucose prevented statistical analysis and was attributed

by the authors to other physiological processes contributing to δμ′s.

469 Changes inμ′

s did not exclusively result from changes in the refractive index of the intersti-tial fluid caused by increased glucose concentration. Spatially resolved reflectancemeasurements (at 800 nm and rsd = 0.8 − 10 mm) and oral glucose tolerance testwere conducted to study five healthy volunteers and 13 volunteers with type 2 dia-betes by using a probe continuously attached to the abdomen.1875 For volunteerswithout diabetes, 80% of measurements showed tracking between δμ′

s and bloodglucose concentration, and the other 20% showed no correlation. For volunteerswithout diabetes, 73% of measurements resulted in calibration models for μ′

s versusblood glucose concentration. Poor correlation between measured δμ′

s and glucoseconcentration in these experiments may be connected with the sensitivity of theprobe, having a large probing depth, to the vascular effect of glucose, inducingtemporal variations of the blood flow in the skin and subcutaneous tissue.991

The response of a nondiabetic male subject to a glucose load of 1.75 g/kg bodyweight, as a standard glucose tolerance test, was determined by continuously moni-toring the product of nμ′

s measured on the muscle tissue of the subject’s thigh usinga portable frequency-domain spectrometer (Fig. 9.79).467 The refractive index, n,of the interstitial fluid modified by glucose is defined by Eq. (7.39). As the sub-ject’s blood glucose rose, nμ′

s decreased. Figure 9.79(b) shows the correlation plotobtained from the data of Fig. 9.79(a). The correlation plot accurately fit a simplephysical model based on the Rayleigh–Gans approximation and accounting for therefractive index matching concept. Key factors for the success of this approach arethe precision of measurements of the reduced scattering coefficient and the sep-aration of scattering changes from absorption changes, as obtained with the NIRfrequency-domain spectrometer.467 Evidently, other physiological effects related toglucose concentration could account for the observed variations of μ′

s, and as men-tioned earlier, the effect of glucose on the blood flow in tissue may be one sourceof the errors in μ′

s measurements.Occlusion spectroscopy is an approach that is based on light scattering from

RBCs.991, 1683, 1684, 1877 This method suggests a controlled occlusion of finger bloodvessels to slow blood flow for providing minimal shear forces of blood flow, andthus, allowing RBCs to aggregate. Change in light scattering upon occlusion ismeasured. Occlusion does not affect the rest of the tissue components, whereasscattering properties of aggregated RBCs differ from those of the nonaggregatedcells and from the rest of the tissue. As already discussed, a change in glucoseconcentration affects the refractive index of blood plasma, and hence, affects bloodlight scattering at occlusion owing to refractive index match/mismatch betweenaggregates and plasma. Occlusion spectroscopy differs from spatially resolvedreflectance and frequency-domain measurements in that it proposes measurementsof glucose in blood rather than in interstitial fluid. The occlusion spectroscopymethod was tested in a human study using a hyperinsulinemic–hypoglycemicclamp.1684 This technique offers the potential for directly measuring the changein the refractive index of blood plasma, but in clinical studies, many other factors


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Figure 9.79 Glucose tolerance test performed on a human subject with portable frequency-domain (120 MHz) NIR (850 nm) spectrometer (see Ref. 467). At time t = 45 min, the subjectingested a glucose load of 160 g of table sugar (1.75 g/kg body weight); the solid curve is themeasurements of nμ′

s on the thigh of the subject, n is defined by Eq. (7.39); the open circlesindicate blood glucose concentration as determined by a home blood glucose monitor; thedata acquired every 30 s were averaged in sets of five to produce the plot (a). Correlationcorresponding to (a) between the measured blood glucose and product nμ′

s averaged overa time of 2.5 min, centered on the time the finger was lanced for measurement. The error innμ′

s is the standard deviation of the five measurements, averaged to obtain a single point.The error in blood glucose concentration is estimated to be ±2.5 mg/dl. Solid line is thetheoretical result according to the Rayleigh–Gans model (b).

affecting the scattering of RBCs and their aggregates should be accounted for: (1)the complexity of the RBC aggregation phenomenon and its dependence on glu-cose concentration and other pathological conditions and diseases;991,1864,1865 (2)the effect of glucose on the shape and structure of RBCs.

OCT can be proposed for noninvasive assessment of glucose concentration intissues.991, 1006, 1008, 1874, 1876, 1879, 1880 A high-resolution OCT technique may allowsuperior sensitivity, accuracy, and specificity of glucose concentration monitoring



owing to precise measurements of glucose-induced changes in the tissue opti-cal properties from the layer of interest (dermis). Unlike the diffuse reflectancemethod, OCT allows depth-resolved qualitative and quantitative information to beprovided about tissue optical properties of the three major layers of human skin:dead keratinized layer of squames (stratum corneum of epidermis); layer of pricklecells (epidermis); and connective tissue of dermis. Dermis is the only layer of theskin containing a developed blood microvessel network. Because glucose concen-tration in the interstitial fluid is closely related to that in blood, one can expectglucose-induced changes in the OCT signal to be detected from the dermis area ofthe skin. Two methods of OCT-based measurement and monitoring of tissue glu-cose concentration were proposed: (1) monitoring of tissue scattering coefficient,μs, as a function of blood glucose concentration using standard OCT;1006−1008

and (2) measurement of glucose-induced changes in refractive index, �n, usingnovel polarization-maintaining fiber-based dual-channel phase-sensitive opticallow-coherence reflectometer (PS-OLCR).1874

The experiments were performed with a portable OCT system with centralwavelength of 1300 nm, power of 0.5 mW, and coherence length and lateral res-olution of approximately 14 and 12 μm, respectively.1006, 1008, 1879 The authorsreported results obtained from phantom (aqueous suspension of polystyrene micro-spheres and milk), animal (27 New Zealand rabbits and 13 hairless Yucatanmicropigs), and human (20 healthy volunteers in 24 experiments) studies. OCTimages were obtained from skin (ear of the rabbits, dorsal area of the micropigs,and arm of the volunteers). The slopes of the OCT signals were calculated at adepth of 150–900 μm. Glucose administration was performed using: (1) intra-venous bolus injections for rapid increase of blood glucose concentration; (2)an intravenous clamping technique for slow, controlled changes of blood glu-cose concentration in animal studies; and (3) a standard oral glucose tolerancetest (OGTT) in human studies. Blood samples were analyzed using OneTouch(Lifescan Inc., Milpitas, CA), HemoCue (Ryan Diagnostic, Inc., Naperville, IL)and Vitros 950 (Ortho-Clinical Diagnostics, Inc., Raritan, NJ) blood glucoseanalyzers.

First, an OCT image is taken of the layers of skin, and the OCT signal asa function of depth is evaluated. The slope of the portion of the plot in the der-mis layer is used to calculate μs. In an anesthetized animal skin experiment, OCTimages demonstrate that glucose affects the refractive index mismatch in skin anddecreases μs.1879 The slope of the OCT signal versus depth line is determined andcorrelated with the concentration of blood glucose (Fig. 9.80).

Typical results obtained in the clinical studies are shown in Fig. 9.81. OCTimages and blood samples were taken from left and right forearms, respectively.Satisfactory correlation between the increase of the blood glucose concentrationand decrease of the smoothed OCT signal slope has been observed at the depth of200–600 μm during OGTT. Measurements performed in layers of epidermis andupper dermis either did not show changes in the OCT signal slope at variationsof blood glucose concentration, or the changes were very weak. Most likely, thisis due to a gradient of glucose concentration from dermal blood microvessels to


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Figure 9.80 Representative OCT signals obtained from Yucatan micropig skin during glu-cose clamping experiment at low and high blood glucose concentration (top) and part of theOCT signal in the dermis area with the linear fit of OCT signals in this layer (bottom) (seeRef. 1008).

the SC. Thus, sensitivity and accuracy of the OCT measurements of blood glucoseconcentration would be maximal in the regions of developed blood microvesselnetwork (that is, dermis area).

A comparison of results obtained from the skin of the rabbit ear during bolusglucose injection experiments and the skin of the micropig during glucose clamp-ing showed that the OCT signal slope changed approximately 8%/mM during thebolus glucose injection experiment and 2%/mM during glucose clamping. Thatsuggests the possibility of a tissue physiological response to the sharp increaseof analyte concentration in the interstitial fluid during bolus glucose injectionexperiments.

The results obtained in phantoms, animals, and clinical studies demonstratedthe potential of the OCT technique to detect small glucose-induced changes in thescattering coefficient of turbid media with high accuracy and sensitivity. However,additional studies should be performed on: (1) reduction of noise associated with



Figure 9.81 Slope of OCT signal and blood glucose concentration versus time. OCTimages and blood samples were taken from a human skin of left (a) and right (b) forearmsduring OGTT (see Ref. 1007).

speckles and tissue inhomogeneity; (2) development of algorithms and methodsfor compensation of motion artifacts; and (3) approbation of the system in clini-cal studies involving diabetic patients. Although OCT-based glucose sensors mostlikely need calibration with invasive glucose sensors, they may dramatically reducethe number of invasive measurements and provide continuous monitoring of bloodglucose concentration.

A question of specificity of the OCT technique to monitor blood glucose con-centration in tissues has been addressed.1008 Experimental and theoretical analysesof the influence of several physical and physiological parameters (such as alteringthe refractive index mismatch between the interstitial fluid and scattering centersand structural modifications in tissue owing to changes in glucose concentra-tion) on the OCT signal slope were performed. Obtained results demonstrate that:


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(1) several body osmolytes may change the refractive index mismatch betweenthe interstitial fluid and scattering centers in tissue, but the effect of glucose isapproximately one to two orders of magnitude higher; (2) an increase of theglucose concentration of interstitial fluid in the physiological range (3–30 mM)may decrease the scattering coefficient by 0.22%/mM due to cell volume change;(3) stability of the OCT signal slope is dependent on tissue heterogeneity andmotion artifacts; and (4) moderate skin temperature fluctuations (±1◦C) do notdecrease accuracy or specificity of the OCT-based glucose sensor, but substan-tial skin heating or cooling (several ◦C) significantly change the OCT signalslope. These results suggest that the OCT technique may provide blood glucoseconcentration monitoring with sufficient specificity under normal physiologicalconditions.

A new differential phase contrast OCT-based method (PS-OLCR) of mon-itoring glucose-induced changes in tissue optical properties has also been pro-posed.1874 Whereas conventional OCT uses the detection and analysis of theintensity of backscattered optical radiation, phase-sensitive OCT utilizes the phaseinformation obtained by probing a sample simultaneously with two common pathlow-coherence beams. Variations in the sample refractive index will be exhibitedin the phase difference, �ϕ, between these two beams. The PS-OLCR technique iscapable of measuring Angstrom/nanometer-scale path length changes between thebeams [associated with the phase difference as (λ/4π)�ϕ] in clear and scatteringmedia. The theoretical and experimental pilot studies on application of PS-OLCRfor noninvasive, sensitive, and accurate monitoring of analyte concentration werereported by the authors of Ref. 1874. They studied concentration-dependentchanges of phase, dϕ/dC, and refractive index, dn/dC, in aqueous solutions ofglucose, CaCl2, MgCl2, NaCl, KCl, KHCO3, urea, BSA, and globulin in clear andturbid tissue-like media. Obtained results demonstrate: (1) satisfactory agreementbetween refractive indices measured with the PS-OLCR technique and the con-ventional white-light refractometer and previously reported in the literature for thevisible spectral range; (2) an effect of glucose on dn/dC at approximately one tofour orders of magnitude greater than that of the other analytes at the physiologicalconcentrations; (3) satisfactory agreement between results obtained in translucentand scattering media, suggesting that PS-OLCR can be applied for in vivo measure-ments; and (4) high sub-mM sensitivity of PS-OLCR for measurement of glucoseconcentration.

Like other scattering techniques, the detected phenomenon in OCT is the effectof glucose on the refractive index of the interstitial fluid. However, this does notallow for blood circulation and temperature changes. Unlike the spatially resolvedbackreflectance and frequency-domain methods that use larger measuring volumeand span multiple layers in tissues,467–469, 991, 1875 OCT offers certain advantages,because it limits sampling depth to the upper dermis without unwanted signals fromother layers. Precise sampling is very important for glucose monitoring in tissue,because glucose uptake is different in different tissue layers: lowest in connectivetissue and smooth muscle, and highest in adipose tissue and skeletal muscle.1881



Additionally, when blood glucose changes rapidly, there is a time lag of 10–25 min,resulting in a transient difference between the blood and subcutaneous glucoseconcentrations, which should be considered.1881

It is important that blood glucose concentrations alter thermally modulatedoptical signals from skin.991, 1661 This is attributable to certain physiologic andphysical effects induced in temperature-modulated skin. The temperature mod-ulation mostly affect cutaneous vascular circulation (physiological effect), andchanges in glucose concentration mostly affect cutaneous light scattering (phys-ical effect). A device based on the thermo-optical response of human skin wasused to collect signals from the forearms of volunteers.1271, 1661 Glucose concentra-tions were correlated with temperature-modulated localized reflectance signals atwavelengths between 590 and 935 nm. There are no known NIR glucose absorptionbands in this range, thus, μa is mostly defined by blood absorption reflecting hemo-dynamic changes in cutaneous tissue. Evidently, μ′

s is a measure of the refractiveindex mismatch between the ISF and tissue connective fibers.

Localized reflectance data were collected continuously over a 90-min periodof probe–skin contact as temperature was repetitively increased between 22◦C and38◦C for 15 temperature modulation cycles.991, 1661 Each cycle comprised the fol-lowing steps: skin was equilibrated for 2 min at a probe temperature of 22◦C, andthe temperature was raised to 38◦C over the course of 1 min, maintained for 2 min,and then lowered to 22◦C over a 1-min period. At each temperature limit (duringthe 2-min window), four optical data packets were collected and values of μa andμ′

s were determined. Temperature modulation between 22◦C and 38◦C caused aperiodic set of cutaneous refractive index and vascular changes, leading to peri-odic changes in skin reflectance.991, 1661 A four-term linear least-squares fitting ofglucose to the reflectance data was used:

[Glucose] = a0 + �iai × R′i(r, λ, T) (9.55)

The reflectance parameter R′(r, λ, T), as defined by Eq. (9.55), equals ln (mea-sured localized reflectance). Thirty-two sequences of R′ (at T22◦C) = lnR(r, λ, T22◦C)and R′ (at T38◦C) = lnR(r, λ, T38◦C) were used in the linear least-squares correlation.For each meal tolerance test (MTT) over the 2-h period, the temperature sequencesencompassed 20 data points.991, 1661 The correlation between glucose values andoptical signals in this spectral range was attributed to the effect of glucose on therefractive index and the cutaneous hemodynamic response; the correlation coef-ficient was in the range from 0.69 to 0.94 for two volunteers tested for 6 dayseach.

The thermo-optical response method offers certain compartmentalizationadvantages over localized reflectance measurements that use wide source–detectorseparations,467–469, 1875 because it limits sampling depth to the dermis by virtue ofthe probe design (short source–detector separations) and the use of temperaturecontrol.


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Figure 9.82 Atherosclerotic vascular tissue characterization using histology, OCT structuraland functional imaging (see Ref. 1769): schematic representation of aorta cross-section ofnormal (upper) and atherosclerotic plaque (lower) areas and corresponding permeabilitycoefficients of 20% glucose through atherosclerotic (diseased) compared to normal porcineaorta areas measured by functional OCT at IOC (a); histology (b, c) and correspondingOCT structural images (d, e) for normal and atherosclerotic specimens, respectively.

9.9.2 Characterization of atherosclerotic vascular tissues

The concept of IOC is the basis for quantifying the permeability rates of differentagents, drugs, and metabolic molecules in tissues using an optical method.1341, 1615

Among the optical techniques, OCT is one of the most sensitive modalities, whichadditionally has, for many cases, sufficient probing depth and spatial resolution.In particular, OCT has been employed to quantify the permeability coefficientsof glucose and different lipoproteins in vascular tissues [porcine aorta and humancarotid endarterectomy (CEA) tissue].1770, 1771 As we already discussed in Section9.6, the structural organization of cells and fibers in a tissue can significantly influ-ence the molecular permeability rate.1341, 1615, 1773–1775 Therefore, quantifying thepermeability rate in normal versus pathological tissues allows for early detectionof tissue abnormalities associated with these structural changes. For example, thepermeability rate of 20% glucose solution in normal vascular tissues was calcu-lated to be (6.80 ± 0.18) × 10−6 cm·s−1 (n = 4), which significantly increasedduring the formation of early arteriosclerotic disease: (2.69 ± 0.42) × 10−5

cm·s−1 (n = 7), as shown in Fig. 9.82(a).1769 As indicated by Figs. 9.82(d) and9.82(e), the structural OCT images do not allow one to effectively differentiatenormal from diseased tissues in this particular case, particularly in comparisonwith histological capabilities [Figs. 9.82(b) and 9.82(c)]. Instead, IOC functionalOCT images enable effective distinguishing between normal and abnormal tissues.



Table 9.13 Permeability coefficients of lipoproteins and 20% glucose in normal andatherosclerotic CEA human tissues at 20◦C and 37◦C (see Ref. 1770).

Agent Permeability coefficient, P ± SD, ×105 (cm·s−1)

20◦C Normal 37◦C Normal 20◦C Pathological 37◦C Pathological

VLDL 1.13 ± 0.26 (n = 5) 1.20 ± 0.25 (n = 6) 1.50 ± 0.21 (n = 5) 1.75 ± 0.34 (n = 5)LDL 3.16 ± 0.37 (n = 6) 4.77 ± 0.48 (n = 5) 1.97 ± 0.34 (n = 6) 2.01 ± 0.23 (n = 9)HDL 1.57 ± 0.26 (n = 10) 2.42 ± 0.24 (n = 7) 2.01 ± 0.32 (n = 6) 2.43 ± 0.31 (n = 5)20% glucose 3.51 ± 0.27 (n = 13) 3.70 ± 0.44 (n = 5) 6.31 ± 0.61 (n = 5) 5.70 ± 0.48 (n = 6)

This property could significantly increase the specificity and accuracy of tissueclassification and further the use of OCT in clinical diagnostic imaging.1615

IOC functional OCT imaging was further investigated to assess the diffusion ofother small and large biomolecules such as very low-density lipoprotein (VLDL),low-density lipoprotein (LDL), and high-density lipoprotein (HDL) in normal andatherosclerotic human CEA tissues.1770 Most interestingly, although the diffusionof glucose, VLDL, and HDL were lower in normal versus atherosclerotic vas-culature, the rate for LDL permeation through normal CEA tissue was (4.77 ±0.48) × 10−5 cm·s−1, which is significantly greater (p < 0.05) than the rates foratherosclerotic CEA tissue (2.01 ± 0.23) × 10−5 cm·s−1 (see Table 9.13). Thisrepresented direct experimental support of a hypothesis that there is a facilitateddiffusion of LDL molecules in vascular tissues. All of these results suggest thatIOC functional OCT imaging has great potential for early identification of patho-logical alternations of the tissues and can represent an additional biomarker oftissue health.

9.9.3 Optical imaging of lymph nodes

For ex vivo study, lymph nodes were excised without fat and surrounding tissuesfrom a mouse and placed in a well (8 mm in diameter and 2 mm in depth; molecularprobes) of a microscope slide to obtain optical images using high-resolution (up to300 nm) TDM at different magnifications (4×, 10×, 20×, 40×, and 100× with oilimmersion).1033 To decrease beam blurring due to light scattering in lymph nodes,different hyperosmotic OCAs were tested. The nodes were embedded for 5 min in40% glucose, 100% DMSO, or 80% glycerol. Comparison of optical images withdifferent agents and PBS (control) revealed that glycerol had a maximal opticalclearing efficiency (Fig. 9.83).

The treatment of lymph nodes with 80% glycerol allowed for the label-freeimaging of a fresh mouse node at the cellular level, including localization ofimmune related, metastatic, and other cells (e.g., lymphocytes, macrophages, den-dritic cells, and melanoma cells), as well as surrounding microstructures (e.g.,afferent lymph vessel, subcapsular, transverse, and paracortical sinuses, deepcortical unit, reticular meshwork, follicles, and venous vessels) (Fig. 9.84).


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Figure 9.83 Optical imaging of a lymph node of nude mouse ear ex vivo at topical appli-cation of PBS (control), 40% glucose, 100% DMSO, and 80% glycerol (a) and in vivo attopical application of 80% glycerol (b) for two different microscopic magnifications, ×4 and×40 (see Ref. 1033). For the in vivo case (b), left images are for native lymph node tissuesand right for glycerol-treated tissues.

9.9.4 Precision femtosecond laser surgery

Femtosecond laser pulses can generate high precision subsurface photodisrup-tion in transparent tissues, such as cornea.781, 1811 The strong optical intensitiesrequired for photodisruption can be achieved through the focus of a high peakpower laser beam. The location of optical breakdown can be controlled to occuronly at the focus of the beam where the intensity exceeds the threshold levelof breakdown. If the laser is focused beneath the surface of a tissue, subsur-face breakdown occurs only at the focus. No damage takes place in the tissuelayers through which the beam was focused. In contrast to transparent tissues,turbid tissues scatter light, spreading the pulse in both space and time, mak-ing it difficult to maintain the tight focus and short pulse duration needed forwell-confined photodisruption.781, 1811 The same problems are characteristic fornonlinear spectroscopy, including multiphoton fluorescence microscopy and SHGimaging.1123–1132, 1576–1580, 1662

The ability to focus light through turbid tissue is limited, especially at wave-lengths less than 1300 nm. Tissue optical clearing technology using an appropriateimmersion agent can be applied for temporal reduction of scattering needed forproviding an effective nonlinear study of underlying tissue photodisruption. Inparticular, femtosecond laser technology was used to demonstrate early proof



Figure 9.84 Optical imaging of microanatomy of the fresh lymph node ex vivo obtained withoptical clearing technique using 80% glycerol (see Ref. 1033). To localize these images, theschematic of a lymph node designed by Sabio is shown. It presents a midsagittal sectionof a lymph node containing three lymphoid lobules with basic anatomical and functionalunits, including superficial cortex, deep cortex, and medulla. Experimental TDM imagesof afferent lymph vessel, subcapsular, transverse, and paracortical sinuses, deep corticalunit, a reticular meshwork, follicles, and venous vessels are shown around central schemat-ics. C1 shows likely basophilic lymphocytes; C2, elongated fibroblastic reticular cells, andC3, B lymphocytes and follicular dendritic cells. Melanoma metastasis is shown in thebackreflectance image.

of concept for high-precision subsurface photodisruption in translucent humansclera.781, 1811 Approximately 5-μJ femtosecond pulses from two laser sources,1060 nm (500 fs) and 775 nm (150 fs), with a repetition rate of 1 kHz, were usedto make a subsurface incision in sclera in vitro.781 The beam was focused to a spotsize of 1.5 μm (775 nm) or 5 μm (1060 nm) and scanned below the tissue surfaceat various depths to produce incision patterns.

Tissue samples were impregnated by hypaque-76 (x-ray contrast) to make themtransparent, usually within 15 min. The measured axial transmission spectra ofnormal and treated by hypaque-76 scleral tissue (the light forward-scattered in asmall cone angle around the incident beam was detected), as well as saline andhypaque-76 spectra, are presented in Fig. 9.85. As shown, transmission of nor-mal sclera is never greater than 10%, with a broad maximum at 1600–1800 nm.For sclera treated by hypaque-76, the transmittance greatly increases across theentire spectrum, especially for wavelengths in the NIR from 800 to 1350 nm. A


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Figure 9.85 Transmission spectra of normal human scleral samples and those treatedby hypaque-76 along with saline and hypaque-76 (see Ref. 781). All samples wereapproximately 0.5 mm thick.

transparent window is also created between two strong water absorption bands,from 1500 to 1800 nm. Transmission at 775 and 1060 nm is above 60%.

The difference in transmission is not expected to affect the results of photodis-ruption itself because photodisruption depends on the intensity of the pulse andnot the linear absorption. Thus, spectral windows with less scattering and absorp-tion allow for a focused beam to penetrate into a tissue with less attenuation anddistortion, and do not influence the efficiency of photodisruption.

As expected, at 775 nm, the size of the intensity distribution emerging fromthe normal sclera did not change on the position of the focusing lens because scat-tering is very strong. The emergent beam is many times larger than the unscatteredspot and is strongly speckle-modulated (see Fig. 9.8).555 At a longer wavelength,1060 nm, because of less scattering, the distribution is smaller but still heavilyscattered. Therefore, focusing to the backsurface of the tissue is not possible whenusing these wavelengths, so for normal scleral tissue, breakdown was initially onlypossible at the front surface.781 After treating the tissue with hypaque-76, the spotsize decreased to almost that of the unscattered beam for both wavelengths; thus,the strong focusing of the beam should permit controlled backsurface photodis-ruption. Several types of intrascleral incisions were experimentally demonstratedby using optical clearing technology: partial thickness channel creation, which canbe used to perform transscleral procedures analogous to deep sclerotomy, wherea block of inner surface sclera is removed with minimal disruption to overlyinglayers; or alteration of the mechanical properties of the sclera for the treatment ofpresbyopia; full thickness channel creation, which that may be useful for drainingaqueous for the treatment of glaucoma; creation of a grid of tissue pores that may



be useful in changing the bulk properties of tissue, including its hydraulic conduc-tivity; scleral pocket creation, which may be useful for inserting implants to treatpresbyopia.781, 1811

OCAs are used in laser surgery of vessels to treat skin vascular pathologies,1808

as well as for noninvasive laser coagulation of the canine vas deferens.1809 IOC isalso promising for accompanying laser and any other surgery when fluorescent orreflection optical imaging is used to support the operation.1787

9.9.5 Skin tattoo imaging and laser removal

Another good example of IOC application is tattoo removal by laser thermoly-sis, which can be optimized to use lesser power density, and therefore, to induceless pain and irradiation in the surrounding tissues.200, 1341, 1613, 1615, 1724, 1738, 1802, 1810

This optimization is based on the selection of laser wavelength and application ofimmersion optical clearing to enhance laser light absorption by tattoo pigments orany other localized absorbing substance (for example, malignant neoplasm) lyingat some depth in the skin.

Nanosized pigmented ink particles used for tattoos are located within dermisfibroblasts and mast cells, predominantly in a perivascular region. Red and NIRlaser radiation penetrates deeply into skin and is absorbed more or less stronglyby blue, green, and black tattoo pigments included in the composition of most tat-toos.1724 Although short-wavelength radiation is well absorbed by tattoo pigments,the use of visible lasers is limited by strong light scattering in skin and hemoglobinabsorption.

IOC can improve laser tattoo removal due to reduction of light scattering inthe upper tissue layers, and correspondingly, to more effective laser beam deliveryto the embedded ink particles.1724, 1738, 1802, 1810 As was already shown, a numberof laser diagnostic, surgery, and therapy technologies may have a significant bene-fit at a reversible skin optical clearing. However, slow diffusion of OCAs throughthe human skin barrier hinders the practical application of IOC. To overcome thebarrier function of skin epidermis, a number of different chemical and physicalmethods have been proposed, such as skin stripping, microdermabrasion, laserfractional ablation of skin surface, iontophoresis, US, laser-induced photomechan-ical waves, and needle-free injection.200, 1341, 1613, 1615 The FLMA technique is arelatively safe and minimally invasive method used to administer not only OCAsand drugs, but also micro- and nanoparticles into the skin. Figure 9.86 illustrateshow the FLMA technique combined with IOC works for in vitro testing of a humanskin sample with a modeled black-ink tattoo at fractional ablation of SC and glyc-erol application during 24 h.1802 The tattoo is poorly shown on the left image andclear on the right image; dotted areas of ablated skin via which glycerol penetratesare also clear. Evidently, this demonstration is valid for imaging of any in-depthabsorbing pathology of the skin.

Figure 9.87 illustrates the possibility of in vivo enhancement of tattoo imag-ing using skin surface preprocessing by the cyanoacrylate glue-stripping techniquefor rapid and complete SC removal and glycerol delivery under pressure.1738


564 Chapter 9

Figure 9.86 In vitro mages of skin sample surface with black ink tattoo model: before pro-cessing (a) and after skin fractional ablation (lamp/transparent appliqué with many blackdots) and glycerol application during 24 h (b) (see Ref. 1802). Tattoo is clearly shown onthe right image (b) and dotted areas of ablated skin are also clear. Image (b) is generatedwith polarization filtering.

Unadjusted preglycerol [Fig. 9.87(a)] and postglycerol [Fig. 9.87(b)] photographsof the treated skin region are shown. Figures 9.87(c) and 9.87(d) are close-ups of the areas indicated in Figs. 9.87(a) and 9.87(b), respectively. Enhancedvisualization of the vasculature of the skin is also provided.

The efficiency of laser radiation delivery to the skin sites where tattoo pigmentis localized can be evaluated on the basis of MC simulations for variable opticalproperties of skin layers due to tissue clearing potency. In accordance with theoptical and structural–morphological properties of skin, the six-layer skin modelwas used1802,1810 with the primary parameters presented in Table 9.14.1824

In the visible and NIR spectral ranges, the absorption coefficient of each skinlayer is defined as1802,1810

μak = BkCkμbla (λ) + (1 − Bk − Wk)μ

bga + Mkμ

mela (λ) + Wkμ

wa (λ) , (9.56)

where k = 1,. . . ,6 is a layer number; Bk and Wk are the volume fractions of bloodand water in each layer; for the melanin containing layers (epidermis and basalmembrane), Mk = 1, for the other skin layers, Mk = 0; μbl

a , μmela , μw

a , and μbga are the

absorption coefficients of blood, melanin, water, and background matter (collagen)of tissue, respectively (μbg

a is assumed to be wavelength independent and equal to0.15 cm1)1824; Ck is a dimensionless correction factor. The correction factor is anumber from 0 to 1 and takes into account the fact that blood is localized in vesselsrather than distributed homogeneously in the skin dermis. If the blood vessel diam-eter is sufficiently large, and light does not penetrate to the inner part of the vessel,then hemoglobin of the interior part would not take part in the absorbing process; inthis case, the correction factor will be considerably smaller than unity. Otherwise,for thin vessels, the correction factor is close to unity. Taking into account that thecorrection factor depends on the vessel diameter, we used the following empiricalexpression in the model:1802,1810



Figure 9.87 In vivo raw images pre-glycerol application (a, c) and post glycerol applica-tion (b, d) for a patient with preprocessed skin by cyanoacrylate glue-stripping techniqueallowed for rapid and complete SC removal. 100% glycerol was used as an OCA, whichwas delivered into skin under pressure. Fluid pressure was maintained through continuousaddition of glycerol from a dispenser using regulated compressed air over a separate glyc-erol to maintain a pressure of 30–70 mmHg for 30–60 min. After the bandage was drainedthrough the fluid access port and removed, any remaining glycerol was wiped away with apaper towel. The intensification of the ink vision and the ability to visualize vasculature isseen in the post-glycerol treatment (b, d) (see Ref. 1738).

Ck = 1

1 + a(0.5μbl

a dvesk

)b , (9.57)

where dvesk is the blood vessel diameter in centimeters and μbl

a should be expressedin inverse centimeters. If blood vessels lying parallel to the skin surface are illu-minated by a collimated light beam, a = 1.007 and b = 1.228, while for thediffuse illumination of the vessels, a = 1.482 and b = 1.151. The blood opticalproperties (i.e., anisotropy factor and both absorption and scattering coefficients)were calculated on the basis of the algorithm described in detail in Ref. 1010. Inthe framework of the modeling, it was assumed that the degree of hemoglobinoxygenation is 0.8 (oxygenation for arterial blood is 0.9 and that for venous bloodis 0.7) and the value of blood hematocrit is 0.4.


566 Chapter 9

Table 9.14 Parameters of skin layers used in the MC simulations; μs is the scatteringcoefficient of a bloodless tissue at 577 nm (see Ref. 1824).

Skin layer Thickness,μm

Refractiveindex

Watercontent, %

Bloodcontent, %

μs, cm−1 Mean vesseldiameter, μm

Epidermis andSC

100 1.45 60 0 300 —

Basalmembrane

15 1.40 60 0 300 —

Dermis andupper bloodplexus

200 1.38 75 1.7 120 6

Reticulardermis

1500 1.35 75 1.4 120 15

Dermis andlower bloodplexus

200 1.38 75 1.7 120 6

Subcutaneousadipose tissue

3000 1.44 5 0 130 —

The scattering coefficient of skin layers is defined as

μsk (λ) = BkCkμbls (λ) + (1 − Bk)μ

bgsk (λ) . (9.58)

Here,

μbgsk (λ) = μ0

sk

(577

/λ)

is the scattering coefficient of bloodless tissue,1824 μ0sk is the scattering coefficient

of bloodless tissue at the wavelength of 577 nm (see Table 9.14), λ is expressed innanometers.

The anisotropy scattering factor is expressed in the following form:

gk (λ) = BkCkμbls (λ) gbl + (1 − Bk)μ

bgsk (λ) gbg (λ)

μsk (λ), (9.59)

where

gbg (λ) = 0.7645 + 0.2355

[1 − exp

(−λ − 500

729.1

)]

is the scattering anisotropy factor of bloodless tissue.1824 The absorption coefficientof melanin is described by the following empirical expression:1824

μmela (λ) = A exp

(−λ − 800

182

), (9.60)

where A is the ratio of the optical density of pigmented skin layers (epidermis andbasal membrane) to their thickness. In the model, A was taken as 0.87 cm−1 forepidermis and 13.5 cm−1 for basal membrane.1824



The optical clearing of different skin layers was simulated by using Mie scat-tering theory,214 which requires knowledge about the refractive indices of skinscatterers and surrounding ISF, and also the sizes of the scatterers. Calculationsfor epidermis and basal membrane were performed using the model of sphericalparticles, because cell mitochondria are the main scatterers for epithelial tissues,while for dermis, the model of cylindrical particles was used, because of the fibrousstructure of the dermis. Because the particle size distribution and the correspond-ing packing factor of the scatterers are unknown, monodisperse Mie-equivalentparticles were used for the simulation.

The scattering coefficients of the epithelial skin layers were calculated in theform214

μs(λ) = 3

4

ϕ

πa3sph

πa3sphQs

(asph, ns, nI

)F(λ) , (9.61)

where asph is the radius of a spherical particle; Qs(asph, ns, nI

)is the scattering effi-

ciency factor; F(λ) is the packing factor of the particles; ns is the refractive indexof the particles; nI is the refractive index of the ISF; ϕ is the volume fraction ofparticles for each layer. For dermal layers, the scattering coefficient was calculatedas214

μs(λ) = ϕ

πa2c

2acQs (ac, ns, nI) F(λ) , (9.62)

where ac is the radius of cylindrical particles. Both the effective size of the particlesand their packing factor were calculated by the minimization of the target function

TF [a(λ) , F(λ)] = (μmod

s − μMies

)2 + (gmod − gMie

)2, (9.63)

where μmods and gmod correspond to the data calculated according to Eqs. (9.58) and

(9.59) for each layer; μMies and gMie are the scattering coefficient [Eqs. (9.61) and

(9.62)] and anisotropy factor calculated for each layer on the basis of Mie theory.To minimize the target function, the Nelder and Mead simplex method was used.

The influence of clearing agent on the optical properties of skin was simplymodeled by increasing the ISF index of refraction up to 1.45. It was assumed thateffective size, packing factor, and index of refraction of the scatterers were notchanged during immersion optical clearing.

For modeling a tattoo, an absorbing layer in the form of a cross with 50 μmthickness and 1 × 1 cm size was added to the skin model. The total area of themodeled skin sample was 3 × 3 cm. Absorption coefficient of the cross was equalto absorption coefficients of ink, i.e., 11.8 × 103, 10.8 × 103, 8.7 × 103, 7.9 ×103, 6.1 × 103, and 5.2 × 103 cm−1 at wavelengths of 470, 532, 650, 694, 850,and 1064 nm, respectively. Scattering properties of this layer were assumed to besimilar to those of reticular dermis. The depth of ink location in the model waschosen as 0.5 or 1 mm.

MC simulation was performed on the basis of the algorithm presented inRef. 327. For the calculation of the photon fraction absorbed in the tattoo area,


568 Chapter 9

the following procedure was used: when a photon trajectory passed through thetattoo area, parameter At (photon fraction absorbed in tattoo area) increased onwμa

/(μa + μs) at each act of interaction,327 where w is the current weight of the

photon packet, and μa and μs are the coefficients of absorption and scattering inthe given point, respectively. After the detection of all photon packets, the value ofAt was summed over all packets and normalized to the total weight of the packets,which were used for simulation. A new propagation direction of the scattered pho-ton packet was determined according to the Henyey–Greenstein scattering phasefunction, dependent on the polar scattering angle, θ, only with the assumption thatthe distribution of photon propagation direction over the azimuthal scattering angleis uniform [see Eq. (1.15)].

For the simulation of skin images with a tattoo, 25 × 106 photon packets wereused. Photons normally incident on the skin surface were uniformly distributedover the 3 × 3 cm2 area. For the detection of backscattered photons, this area(3 × 3 cm2) was separated on the grid with a 0.01 mm2 area of grid cells. Whena backscattered photon exited, its weight was recorded to the array cell, whichcorresponded to the coordinates of the exit point, then was summed over all pack-ets. After the simulation finished, it was normalized to the average weight of theincident packets upon the corresponding area.

The thicknesses and refractive indices of skin layers used in the MC simula-tions are presented in Table 9.14. Without optical clearing for each wavelength andskin layer, the absorption coefficient, scattering coefficient, and anisotropy factorwere calculated by using Eqs. (9.56), (9.58), and (9.59), respectively. For immer-sion skin optical clearing, the scattering coefficient and anisotropy factor of eachskin layer were calculated by using Eqs. (9.58)–(9.62).

MC simulations of reflectance spectra and images of human skin with a blacktattoo localized in reticular dermis at depths of 0.5 and 1.0 mm are presented inFigs. 9.88 and 9.89.1802, 1810 In Fig. 9.88, curve 1 shows the reflection spectrumof the intact skin without tattoo, as well as curve 2, showing the tattoo located atthe depth of 0.5 [Fig. 9.88(a)] and 1.0 mm [Fig. 9.88(b)]; curves 3 and 4 showimmersed skin layers over or under the tattoo, respectively; and curves 5 and 6show totally immersed skin without/with tattoo, respectively. In all cases, the sub-cutaneous adipose tissue layer was not immersed. The shape of the intact skinreflectance spectrum is determined by light scattering of tissue components andabsorption of melanin; blood hemoglobin with bands at 416, 542, and 575 nm;and water at 980 nm. The presence of the tattoo reduces the skin reflectance dueto light absorption by the ink pigment. For a smaller pigment location depth, theskin reflectance decreases more significantly. The modeling demonstrates that opti-cal clearing of different skin layers, above and below the tattoo location, allows forcontrolling skin reflectivity in a rather wide range within the visible and NIR wave-lengths. However, to use IOC effects in practice to image and/or ablate absorbinginhomogeneity such as a tattoo or tumor, we are able to introduce and calculatetwo more parameters, such as image contrast, K, and fraction of light absorbed bythis inhomogeneity, A.1802,1810



Figure 9.88 MC simulated human skin reflectance spectra with a black color tattoo atdepths of 0.5 (a) and 1.0 mm (b): (1) normal skin; (2) skin with tattoo; (3) skin layers abovetattoo are immersed by an OCA (model of topical OCA administration); (4) skin layers undertattoo (between tattoo and subcutaneous adipose tissue) are immersed by an OCA (modelof intradermal injection of an OCA); (5) and (6) all skin layers from the surface up to subcu-taneous adipose tissue are immersed by an OCA (model of combined OCA administration:topical and via injection): (5) normal skin, (6) skin with tattoo (see Ref. 1802).

Figure 9.89 Three sets of MC simulated skin tattoo images at wavelengths 532, 650, and1064 nm: the depth of the tattoo is 0.5 mm (a, b) and 1.0 mm (c, d); size of the tattoo is 1 ×1 cm; no clearing (a, c); skin layers above the tattoo are optically cleared (model of topicallyapplied immersion agent) (b, d) (see Ref. 1810).


570 Chapter 9

Table 9.15 MC simulation results of image contrast of 1-mm-deep skin tattoo pre- and post-OCA topical application (seeRef. 1810).

Wavelength, nm Immersed skin,KPOST

Native skin,KPRE

KPOST/KPRE

470 0.070 0.022 3.182532 0.100 0.028 3.571650 0.284 0.113 2.513694 0.382 0.166 2.301850 0.380 0.172 2.2091064 0.371 0.181 2.050

The images presented in Fig. 9.89 were simulated by using optical propertiesof skin at λ = 532, 650, and 1064 nm. The left images of each set correspond to theskin with tattoo, and the right images to the same skin but with optically clearedskin layers above the tattoo, in accordance with the model of a topically adminis-tered immersion agent.1810 The tattoo image boundaries without IOC look ratherblurred owing to high light scattering by the upper tissue layers. The simulation ofphoton migration in skin has shown that the immersion of the upper skin layers ismore efficient for improving image contrast and increasing the number of photonsabsorbed by the tattoo.

As it follows from Fig. 9.89, the optical clearing of the upper skin layers signif-icantly enhances the image contrast, which improves the localization and imagingof the tattoo. The image contrast can be estimated as

K = (R1 − R2)/(R1 + R2), (9.64)

where R1 and R2 are the skin reflectance outside and inside the tattoo area,respectively.

Results of tattoo image contrast calculations for normal and optically clearedskin are also presented in Table 9.15 and Fig. 9.90. It is clear that contrast of thetattoo images increases with the wavelength of illuminating light and some satura-tion in the NIR spectral range. At the same time, clearing efficiency, expressed asa ratio of the image contrast of tattoo in immersed skin to that of tattoo in nativeskin, slightly decreases with the wavelength. However, contrast is still very high,especially for deeper tattoo localization, and less dependent on the wavelength inthe range above 700 nm (Fig. 9.90).

Figure 9.91 presents the spectral dependences of the fraction of photonsabsorbed by the skin layer with tattoo, A, at depths of 0.5 and 1 mm. Curves 1and 5, which describe intact and totally immersed skin without tattoo, are verysimilar and close to zero due to small absorption of native skin in this range andthis particular localization—this is a baseline for modeling the fraction absorbedby the tattoo. The presence of the tattoo changes the spectral dependence of thefraction of absorbed photons in accordance with the absorption spectrum of the inkor dye. The immersion of layers under the tattoo reduces the number of photons



Figure 9.90 Wavelength dependences of contrast ratio KPOST/KPRE for tattoo images[“POST” and “PRE” are after and before optical clearing (model of OCA topical application),respectively] (see Ref. 1810).

Figure 9.91 Results of MC simulation of absorbed photon fraction in the black tattooed areaof skin at depths of 0.5 (a) or 1.0 mm (b) under different conditions: (1) normal skin; (2) skinwith tattoo; (3) skin layers above tattoo are immersed by an OCA (model of topical OCAadministration); (4) skin layers under tattoo (between tattoo and subcutaneous adiposetissue) are immersed by an OCA (model of intradermal injection of an OCA); (5) and (6) allskin layers from the surface up to subcutaneous adipose tissue are immersed by an OCA(model of combined OCA administration: topical and via injection): (5) normal skin, (6) skinwith tattoo (see Ref. 1802).

absorbed in the given area, which is clearly shown in Fig. 9.91, curve 4. At thesame time, if only upper layers over the tattoo are cleared, a significant numberof photons propagate through the upper layers almost without scattering and areabsorbed in the tattoo area. Photons that have passed through the absorbing layerto lower skin layers, which are not cleared, can be effectively backscattered andalso absorbed by the tattoo. The fraction of photons absorbed in the wavelengthrange from 600 to 1000 nm increases upon clearing of upper skin layers, on aver-age, by 30% and 40% for tattoos at depths of 0.5 and 1 mm, respectively. Thus, fora deeply located tattoo, this method of clearing is more efficient.


572 Chapter 9

Table 9.16 MC simulation of light absorbed fraction, A, by tat-too located 1.0 mm deep: APRE is for normal skin; APOST is forupper skin layers immersed by an OCA (see Ref. 1810).

Wavelength, nm APRE APOST APOST/APRE

470 0.017 0.027 1.588532 0.021 0.036 1.714650 0.045 0.068 1.511694 0.056 0.077 1.375850 0.066 0.086 1.3031064 0.071 0.085 1.197

Figure 9.92 Wavelength dependences of the ratio of light absorbed fractions by tattoo,APOST/APRE (“POST” and “PRE” are after and before optical clearing, respectively) (seeRef. 1810).

Table 9.16 summarizes data of IOC efficiency for a 1-mm-deep tattoo. Thistable indicates that the absorbed fraction increases with the increased wavelength,similar to the image contrast behavior (see Table 9.15), and the ratio of the lightfraction absorbed in the tattoo embedded in immersed skin to the fraction for thatembedded in the native skin decreases with the wavelength (see Fig. 9.92). Theratio decreases from 1.588 (λ = 470 nm) to 1.197 (λ = 1064 nm) for a tattoo locatedat the depth of 1.0 mm and from 1.633 (λ = 470 nm) to 1.082 (λ = 1064 nm) fora tattoo located at the depth of 0.5 mm. This is related to general decrease in skinscattering for longer wavelengths; so fewer overall photons circulate within theabsorbing layer and are absorbed by the tattoo.

However, the efficiency of IOC is still sufficient to provide laser thermoly-sis of tattoos or other skin-absorbing abnormalities for a number of wavelengths.Based on literature data for different laser systems, it was estimated1810 that to



achieve similar tattoo damage with optical clearing, the density of laser energy canbe reduced with dependence on the tattoo localization depth up to 50–60% for theblue-green spectral range, 30–40% for the red, and 10–20% for the NIR.

9.10 Other Techniques for Controlling Tissue OpticalProperties

9.10.1 Tissue compression and stretching

As was already mentioned in Section 9.1, squeezing (compressing) or stretch-ing of a soft tissue produces a significant increase in its optical transmission.1617

The major reasons for this are as follows: (1) increased optical tissue homo-geneity due to removal of blood and interstitial fluid from the compressed site[see Eq.(7.27)]; (2) closer packing of tissue components, causing less light scat-tering due to cooperative (interference) effects (see Chapter 3);654,1616 and (3)thinner tissue. Mechanisms underlying the effects of optical clearing and chang-ing of light reflection by soft tissues at compression and stretching were proposedin a number of theoretical and experimental studies.61, 62, 495, 654, 768, 769, 1059, 1068,

1257, 1341, 1616, 1628, 1629, 1657, 1670, 1678, 1803–1807

Askar’yan1617 was the first to study the propagation of a laser beam throughsoft tissue phantoms and human palm under mechanical compression, and Ivanovet al.1616 described this phenomenon theoretically by using a comprehensive tissuemodel. The reduction of extinction coefficient after tissue compression and pro-longation of clearing effect after removing pressure for a certain time interval wassuccessfully demonstrated experimentally.1617

It should be emphasized, however, that squeezing-induced effects in tissuescontaining little blood, such as sclera, are characterized by marked inertia (a fewminutes) because of the relatively slow diffusion of water from the compressedregion.769 It was suggested that the compression of sclera may displace water fromthe interspace of collagen fibrils, increasing the protein and mucopolysaccharideconcentrations. Because these proteins and sugars have a refractive index similarto that of collagen fibrils, a more index-matched environment can be created. Onthe other hand, compression reduces specimen thickness, d, which might increasethe effective scatterer concentration inside the tissue.1257 Therefore, compressionmay also generate an increase in μs. However, the total effect on change in opticalproperties, which is proportional to the product of μsd, is characterized by lessscattered light.

Sometimes the increase in scatterer concentration is likely to be more dominantthan the reduction in index mismatch.1257 In addition, reduction of tissue thicknesscauses an increase in local chromophore concentration (for bloodless tissue, ortissue specimens having aggregated and/or coagulated blood), i.e., the absorptioncoefficient increases.

The authors of Ref. 1257 observed that compression caused leaking aroundthe specimen. Some of the extracellular fluids along the edge of the tissue sam-ple were forced out upon compression. Unless sufficient pressure was applied torupture the cell walls, the intracellular fluids would be retained by the cells in


574 Chapter 9

the bulk of the sample. When compressed, tissue thickness was reduced so thatthe volumetric water concentration was increased. This may explain the increaseof absorption coefficient at the wavelengths of water bands with compression.1257

Optical properties of in vitro samples of human skin, bovine aorta, bovine sclera,and porcine sclera in the spectral range from 400 to 1800 nm were measured byusing the integrating sphere technique. The IAD method was applied for convolu-tion of absorption and reduced scattering coefficients from the measured data. Thediffuse reflectance and transmittance of tissue samples with an area of 2 × 2 cm2

were measured at zero pressure and at external pressures of 0.1, 1, and 2 kg/cm2

uniformly distributed over the sample surface. The authors generally observed adecrease in reflectance, whereas transmittance, absorption, and scattering coeffi-cients increased owing to compression. Some of these data for human skin arepresented in Table 7.1. As explained earlier, the amount of scattering dependson refractive index mismatch, as well as on scatterer concentration and spacing.Along the load direction, the spacing between tissue components is reduced, anddue to water escaping from the compression site, refractive index matching shouldoccur; both effects lead to decreasing of the average light scattering, which is whytransmittance increases and reflectance decreases. On the other hand, compres-sion reduces specimen thickness, which might increase the effective concentrationof scatterers and chromophores inside the tissue, causing a certain increase inscattering and absorption coefficients. In experiments with uniformly distributedcompression, the increased concentration of scatterers was likely more dominantthan the reduction in index mismatch and scatterer packing effect with resultingelevation of scattering (μs) and absorption (μa) coefficients. However, the inten-sity of transmitted light should be increased because certain elevations of thesecoefficients do not strongly affect this product (μs + μa) × d because compres-sion thickness can be changed significantly (up to 50–70%).1803, 1807 Cooperativeeffects also may have a great influence on the reduction of the overall scattering(see Chapter 3).

The relative balance of the contributions of these listed mechanisms is expectedto be changed if pointwise compression is applied.392, 393, 769 To understand the opti-cal properties of compressed tissue, time-resolved studies in the range of minutesare important.769

Spectral properties of skin can be effectively controlled by applying externallocalized pressure in in vivo experiments when UV-induced erythema (skin red-ness) is developed.1059, 1068, 1656 The pain threshold stress (force per unit area) isthought to be ∼1.1 MPa.1803 Figure 9.93 shows apparent optical density (OD) eval-uated from the in vivo measured backreflectance spectra of erythematous humanskin for different values of external localized mechanical pressure. To the thirdday after UV irradiation, the developed erythema is seen as increased absorbance(OD) in the 520–580 nm spectral range due to increased blood volume in the skin.Blood hemoglobin blocks the backscattered intensity from the deep skin layers.For longer wavelengths from 600 to 700 nm, increased blood volume increaseslight scattering from tissue, which is viewed as the increase of apparent OD. Atpressures of (8.4–14) × 105 Pa, blood leaves the compressed area of the skin, so



Figure 9.93 Apparent OD spectral distributions of erythematous human skin (three daysafter UV irradiation) for different values of external mechanical pressure: (1) withoutpressure; (2) 5.6 × 104 Pa; (3) 8.4 × 104 Pa; (4) 1.4 × 105 Pa (see Refs. 1059 and 1656).

OD spectral dependence becomes smoother owing to less absorption in the range520–580 nm and less scattering in the range 600–700 nm.

Similar technology with a lesser amount of external pressure, 3 × 105 Pa,was used for in vivo determination of carotenoids in human skin based on detec-tion of its absorbing band, which was clarified after compression in the region of467–515 nm of the skin reflection spectrum.1319 Schematics of a device for skinreflectivity measurements at compression are shown in Fig. 9.94(a). It consists of alight source (white LED or tungsten halogen lamp); a light delivery and collectionmodule that is placed in contact with the tissue site of interest via measuring lens;a spectrograph or two-wavelength detection scheme; and data acquisition, process-ing, and display electronics. The measuring lens is pressed against the tissue siteof interest for approximately 10–15 s to obtain the desirable spectrum. Extractionof carotenoid levels from measured absorption spectra is based on the strength ofthe carotenoid absorption band between 467 and 515 nm relative to a straight-lineconnection between the two spectral points [Fig. 9.94(b)]. The dermal carotenoidabsorption spectrum, shown as a shaded area, is very similar in this wavelengthregion to the corresponding absorption of β-carotene in solution.

An FTIR spectrometer (Matrix-F, BRUKER Corporation) with a fiber-opticprobe and a pressure transducer to monitor the contact pressure between thefiber probe and tissue was used for in vitro (porcine skin) and in vivo (humanskin) studies evaluating the spectral alterations associated with bulk (free) andbound water.1629 Figure 9.95 shows variations in the second derivation of appar-ent absorbance log(1/R) for skin with fiber probe pressure or time elapsed at fixedpressure.1629 In vitro spectra measured at different pressure variations for inclusionof bulk (absorption band at 1160 nm) and bound (absorption band at 1220 nm)water with pressure elevation are accurately indicated [Fig. 9.95(a)]. For the invitro case, as the fiber-optic probe was fixed on the tissue site, the absorption peak


576 Chapter 9

Figure 9.94 Dermal carotenoid measurements via pressure mediated skin reflection spec-troscopy (see Ref. 1319): schematics of skin reflectivity device (a); schematics of extractionof carotenoid level from the measured apparent absorption spectrum (b). Carotenoidabsorption between 467 and 515 nm is shown as a shaded area, the correspondingabsorption band of β-carotene in solution is shown in insertion.

of bulk (free) water within the tissue decreased with pressure duration while theabsorption peak of bound water increased, as shown in Fig. 9.95(b). According tothe mechanical properties of biological tissue, the nonlinear relationship betweenthe strain variation ratio and pressure duration time is primarily caused by themigration of bulk water within the tissue. In the early stages of tissue deformationunder a certain pressure, the bulk (free) water moved out of the compressed regionwith high migration rate due to its high permeability and low viscosity and the large



Figure 9.95 Variation of second derivation of apparent absorbance, log(1/R), for skin withpressure change or time elapsed at fixed pressure (see Ref. 1629): in vitro spectra (porcineskin) at different pressures (a); variation of bulk (free) water (absorption band at 1160 nm)and bound water (absorption band at 1220 nm) with pressure duration for in vitro (porcineskin) (b) and in vivo (human skin) (c) measurements.

strain within the tissue. Because of the stress relaxation of tissue, the deformationand bulk (free) water migration rate gradually slows down. After approximately 6min, the deformation of tissue and transportation of bulk water are constant.1629

When the pressure is applied to in vivo skin, the volume of free water withinskin is first decreased, then increased as the pressure becomes larger than 250 kPa.The bound water performs in the opposite way. The experimental results indicatedthat as the free water is squeezed out of the pressure region, part of the bound watermight change into free water to ensure normal tissue metabolic activity. Therefore,compared with the in vitro porcine skin, the thickness and bulk water of human skinin vivo was less changeable with pressure and time elapsed at fixed pressure, but thebound water within the tissue decreased continuously, as shown in Fig. 9.95(c).1629

Light propagation in human skin at mechanical tension was studied in vivousing steady-state diffuse reflectometry with a variable source–detector separation,rsd.495 To examine the effect of skin tension on the optical properties, the skinwas maintained in a stretched position by pulling it mechanically in a defined


578 Chapter 9

direction, then fixing it to the aluminum ring with double-sided adhesive tape.For medium and far distances from the detector to the light source (rsd = 2 and7 mm), it was found that anisotropy of light propagation followed the stretchingdirection. The direction of stretching complies with that of the maximal reflectancesignal for a given distance greater than approximately 2 mm. Thus, the scatteringcoefficient is minimal when measured along the direction of stretching, becauseintensity is maximal for the distant detector. MC modeling was also conducted,accounting for the anisotropy of the scattering coefficient, caused by different pho-ton interactions with the medium when traveling along and across tissue fibers anddescribed by Eq. (7.16) with the fraction of scatterers (cylinders) oriented in thepreferential direction, f = 0.35.495 It follows from Eq. (7.16) that the scatteringcross section varies with the direction cosine of the incident photon with respect tothe axis of the cylinder. It is maximal and minimal for perpendicular and parallelincidences. MC modeling has demonstrated that for short source–detector separa-tions, the detected signal is much higher (scattering coefficients are also higher)for the perpendicular direction regarding the preferential direction of the collagenfibers. For farther detectors, the signal is higher in the parallel direction (scatteringcoefficient is lower). These correlated or anticorrelated dependences between theintensity backreflectance and the scattering coefficient, respectively, for short andlong source–detector separations are also indicated by data in Fig. 9.33.

From this analysis, it follows that under skin stretching, the scattering coeffi-cient and corresponding light backreflectance and transmittance can be effectivelycontrolled. On the other hand, intact skin has its own anisotropy, which is believedto be caused by the preferential orientation of collagen fibers in the dermis, asdescribed by Langer’s skin tension lines.495 Thus, the reduced scattering coeffi-cient of human skin varies by up to a factor of two between different directions oflight propagation in the same position (see Table 7.1). At external forced tension,more significant damping of scattering along the direction of mechanical stress isexpected.

The measurements of deformations and applied loads and estimation of thebiomechanical properties of tissue are critical to many areas of the health sci-ences, including monitoring of the tension in wound closures, skin flaps, andtissue expanders.1678 Such measurements, which can be provided by detection ofthe polarized light reflectivity, will allow surgeons to treat wounds more success-fully by minimizing scar tissue and maximizing the speed of treatment, by lettingthem know how much the skin can be stretched at each treatment step. In vivohuman experiments showed that the specular reflection from skin changes with thestretch.1678 For small values of stretch, the specular reflectivity measured for a He-Ne laser (λ = 633 nm) beam with a 45-deg angle of incidence increases linearlywith strain. The linear relationship between applied stretch and polarized reflectiv-ity can be understood if the skin surface is approximated by a sinusoidal profile inthe resting stage. Stretching reduces amplitude and increases the spatial scale ofthe skin profile, thereby making it smoother and flatter, resulting in a correspond-ing increase of reflectivity. For 10 tested subjects with various skin complexions,the slope of the dependence—the reflectivity (normalized to maximal value)—on



Table 9.17 Comparative results for ex vivo porcine skin at air dehydration andmechanical compression (see Ref. 1803). Errors shown as ±1 SD.

Air dehydration Mechanical compression

Before After Before After

Thickness, μm 1700 ± 140 680 ± 220 1300 ± 100 540 ± 150Strain = �d/d0, % — −59.8 ± −9.6 — −58.5 ± −8.3Refractive index 1.36 ± 0.02 1.49 ± 0.03 1.39 ± 0.02 1.5 ± 0.05Water volume fraction 0.68 ± 0.09 0.35 ± 0.12 0.66 ± 0.02 0.20 ± 0.05Water weight fraction 0.57 ± 0.01 0.37 ± 0.01 — —

strain (expressed in percent) is in the range from 0.0074 to 0.0391 (1/%) with thelinear correlation coefficient, R2, from 0.88 to 0.99. For larger stretches [for strainsabove 8.8% (5-mm stretch)] of the tested human subject, the dependence is satu-rated and even decreases. The stretches in two perpendicular directions (paralleland perpendicular to the long axis of the forearm) yield satisfactory correlationbetween stretch and reflected light intensity and show that skin has anisotropicproperties that can be detected by light reflection. For example, the slope measuredin the parallel direction to the long axis of the forearm was 0.0095 ± 0.0002 (1/%),and that in the perpendicular direction was 0.0065 ± 0.0008 (1/%).1678

Local tissue compression combined with an optical probe of an OCT imagingsystem provides significant additional information about the study of pathology,both in depth sensing and kinetics of the response to compression of the tis-sue.1803–1807 The early studies of tissue compression have stimulated the applicationof this technology to OCT, where concerns about penetration depth and image con-trast are critical. In Ref. 1803, a hemispherically tipped glass rod (borosilicate,nglass = 1.474), 20 mm long with a 3-mm tip diameter, was used as a probe forlocalized skin compression and concurrent OCT imaging at a mean wavelength of1310 nm (swept source OCT system) (Fig. 9.96). The glass rod did not add any per-ceivable distortions to the OCT signal. The stepwise loading protocol, allowing forremoval of the transient viscoelastic response of the tissue, and thus capturing thequasi-static mechanical deformation response, was used for ex vivo and in vivo skinimaging. To measure changes in skin thickness and refractive index attributable tocompression, OCT images were obtained at each indentation step. The authors ofRef. 1803 demonstrated that, for similar effective tissue strain, air dehydration andmechanical compression produce similar changes in refractive index and water vol-ume fraction. These data directly prove the concept that mechanical compressionmay cause local water removal within compressed regions of the tissue. This watermay then be transported laterally along interstitial pressure gradients, increasinglocal protein concentration.

Table 9.17 summarizes results from ex vivo air immersion (dehydration) andcompression experiments. Dehydration of porcine skin specimens over 5 h causedthe mean thickness to decrease from 1700 μm to 680 μm. To compare watercontent changes between air-immersed and compressed skin samples, effective


580 Chapter 9

Figure 9.96 OCT glass rod probe for tissue compression measurements (see Ref. 1803).

strain, describing the relative thickness change caused by dehydration, was definedanalogously to mechanical strain as �d/d0, where �d is change in thickness andd0 is original thickness. Dehydrated samples underwent −59.8% mean effectivestrain.

Skin mean refractive index, nskin, increased from 1.36 to 1.49. The calculatedwater mean volume fraction decreased from 0.68 to 0.35 over the dehydrationperiod. A positive correlation was found (R = 0.95, P < 0.001) between calcu-lated water volume fraction, f w, and independently measured water weight fraction(weight loss). This supports the assumptions made in Refs. 1267 and 1803 thatskin can be represented as a biphasic mixture of water and protein [see Eq. (7.29)],and permits the use of the Lorentz–Lorenz equation for dynamic water contentcalculation from refractive index measurements [see Eq. (7.34)]:1803

(nskin)2 − 1

(nskin)2 + 2= (nw)2 − 1

(nw)2 + 2fw + (np)2 − 1

(np)2 + 2× (1 − fw), (9.65)

where fw + fp = 1, and nw and np are refractive indices of water and proteins,respectively.

Mechanically compressed ex vivo skin specimens underwent mean thicknessreduction from 1300 to 540 μm and effective mean strain of −58.5%. Figure 9.97shows refractive index and water content versus compressive displacement. Duringthe initial 100 μm of probe displacement, thickness and refractive index remainedunchanged. Tissue mean refractive index was initially 1.39 and contained approx-imately 66% water. Compression to maximum displacement increased the skin



Figure 9.97 OCT measured thickness, refractive index, and water volume fraction of exvivo porcine skin during mechanical compression (see Ref. 1803).

Table 9.18 In vivo human skin OCT measurements of SC optical thickness andincreased OCT backreflectance intensity of postcompression images at 1 mm opticaldepth (dB) for different skin sites (see Ref. 1803).

Ventral forearm Dorsal hand Palm Finger

SC thickness(optical), μm

Before compression 40 ± 10 40 ± 10 210 ± 130 220 ± 160After compression 20 ± 10 30 ± 10 150 ± 50 110 ± 80

OCT intensity increase (dB) 0.8 ± 0.2 0.5 ± 0.2 1.1 ± 0.5 1.5 ± 0.8

mean refractive index to 1.50 and correspondingly decreased water content to awater volume fraction of 20%.

In in vivo studies, an average OCT A-scan profile was generated for eachanatomical site on each volunteer by averaging across the 200 μm lateral scan,as schematically shown in Fig. 9.96. The SC thickness for each site of a vol-unteer represented an average of three measurements. OCT signal intensity at adepth of ∼1 mm (in the reticular dermis) was also evaluated by using this tech-nique. Table 9.18 summarizes the results of in vivo human skin experiments. Itwas found that SC thickness in the fingertip (mean optical thickness of 220 μm)was reduced by approximately 50% owing to compression, and postcompressionimages showed a 1.5 dB increase of the average light intensity at 1 mm depth in thepapillary dermis. Each anatomical site has a different mechanical and correspond-ing optical response caused by differences in skin structure, thickness, and watercontent.

Age-dependent in vivo OCT skin studies with continuous mechanical com-pression have also been reported.1807 OCT images were obtained for three malevolunteers of different ages at low and high mechanical pressures. The OCT probewas placed in a special holder, allowing for control of the force of pressure on theskin and keeping it constant. The probe was pressed onto the human skin with theforce varying from 0.4N (pressure of 0.07 N/mm2) to 2N (pressure of 0.35 N/mm2)


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Figure 9.98 In vivo OCT measured temporal dependencies of epidermis–dermis junctioncontrast at thin skin compression for three age groups of volunteers [23 years (n = 3),29 years (n = 2), and 49 years (n = 4)] at low-pressure compression (0.07 N·mm−2) (a);and for high-pressure compression (0.35 N·mm−2) (b). Contrast values are averaged for anumber of experiments with the experimental error (±SD) (see Ref. 1807).

and was held in this position for 10–15 min while the OCT images of the skin wereacquired continuously at a rate of 1 image every 5 s. The effect of mechanicalcompression was characterized by image contrast, introduced as the ratio of OCTsignals for neighboring layers indicated in dB. The temporal dependences of OCTimage contrast for the epidermis–dermis junction measured at low and high pres-sures are presented in Fig. 9.98. For the 23-year-old volunteer, the image contrastincreased monotonically with time for both the low- and high-pressure protocols.For the 29-year-old volunteer, maximal contrast was reached much faster for thehigh pressure than for lower; less than 1 min was sufficient to reach the contrastfor which more than 3 min was needed at low pressure. The skin of the oldervolunteer (49 years old) demonstrates an increase in junction contrast, especiallyfor the high-pressure protocol, that reaches similar maximum as for younger skinat the sixth minute. Evidently, these changes could be associated with different



dynamics of water inflow, particularly connected with the different balance of freeand bound water for the young and aged skin and different elasticity of the skinof the various age groups.1807 It is well known that skin water content decreaseswith age because the amount of glycosaminoglycans declines with age, as dothe amounts of hyaluronic acid produced by fibroblasts and interstitial fluid. Atlow pressure [Fig. 9.98(a)], water inflow from the dermis of young volunteers isexpressed more in contrast to that of an older volunteer as a result of less hydrationin the aged skin dermis and more rigidity in the dermis due to loss of hyaluronicacid production. However, in the case of high pressure, the dermis of an oldervolunteer has more significant deformation, so the measured contrast increasessimilarly to the young skin.

As discussed, mechanical compression results in higher OCT signal intensity,i.e., higher contrast, and thus, better imaging capability. The localized mechani-cal compression of skin decreases tissue thickness and water content and increasesrefractive index and OCT signal intensity. Mechanical loading may also decreaseabsorption and scattering in the compressed region, particularly at 1310 nm, nearthe 1450 nm absorption peak of water (low concentration of water due to itsdisplacement). The effect of mechanical compression on the contrast betweenepithelial and stromal layers of human rectum ex vivo in OCT images was studiedin Ref. 1806. Owing to different mechanical properties and water content of theselayers, the changes in scattering properties induced by compression are different,which leads to better contrasting of these layers in OCT images.

The intensity of skin autofluorescence (AF) is also well-controlled atexternal localized pressure applied to the skin site.1059, 1068 As indicated byFig. 9.99, the external localized pressure in the range from 0 to 1.4 × 105

Pa considerably changes the fluorescence output with wavelength of 460 nmunder induced erythema. Owing to more effective fluorescence light attenu-ation by blood hemoglobin at more intensive erythema (14 days after UVirradiation), skin compression more effectively controls (increased) fluorescenceoutput.

It was also shown that application of a pressure cuff to the upper arm ofhealthy volunteers at levels of 0, 20, 30, 40, and 60 mm Hg did not signifi-cantly alter the levels of oxyhemoglobin or melanin of preliminary UV-irradiatedvolar forearm skin (induced erythema and melanin pigmentation).1670 In contrast,deoxyhemoglobin significantly contributes to the skin color appearance. Bloodpooling, expressed as increased deoxyhemoglobin, can contribute to what is visu-ally perceived as pigmentation. Oxyhemoglobin values increased to a maximumon day 1 after UV irradiation, correlating well with the clinical evaluation of ery-thema, then decreased exponentially to the baseline. Melanin contents showeda significant increase on day 7 and remained relatively constant for the next 3weeks, correlating well with the clinical evaluation of pigmentation (tanning).Deoxyhemoglobin increased slightly on day 1 and remained elevated for the next2 weeks. Thus, it correlated moderately with clinical erythema scoring on day 1only, but contributed significantly to that clinically perceived as skin tanning on


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Figure 9.99 AF intensity of erythematous human skin (λf = 460 nm) dependent on externalmechanical pressure: (�) seven days after UV irradiation (less developed erythema); (•) 14days after UV irradiation (more developed erythema). AF intensity of human skin withouterythema and compression (dotted line) is marked as a reference value (see Refs. 1059and 1068).

days 7 and 14. Application of pressure below the diastolic level increased deoxy-hemoglobin concentration, as measured by diffuse reflectance spectroscopy. Thisincrease corresponded to the decrease of a pigmentation parameter in a similarfashion that has been documented for increases in melanin concentration. Topicalapplication of H2O2 reduced deoxyhemoglobin levels, as measured by reflectancespectroscopy. This reduction coincided kinetically with visible skin blanching.

9.10.2 Temperature effects and tissue coagulation

A reproducible effect of temperature between 25 and 40◦C on the reduced scat-tering coefficient of human dermis and subdermis was found in an ex vivo studyin the NIR.333, 334 For dermis, the relative change in the reduced scattering coeffi-cient showed an increase [(4.7 ± 0.5) × 10−3◦C−1], and for subdermis, a decrease[(−1.4 ± 0.28) × 10−3◦C−1]. The absolute values of the coefficients are presentedin Table 7.1. It was hypothesized that the observed positive and negative tem-perature coefficients of scattering for dermis and subdermis are connected withdifferences in their structural components. The primary scattering components ofsubdermis were assumed to be lipids in membranes and vacuoles. It is known thatlipids undergo phase changes at certain temperatures, which alter their orientation,mobility, and packing order.1361, 1819, 1820 Glycolipids found in human cell mem-branes undergo phase transitions in the temperature range from 25◦C to 45◦C;namely, a transition from a gel phase through a stable crystalline phase to a liquid-crystalline phase with increasing temperature. Therefore, the decrease in scatteringcoefficient, experimentally modeled with increasing temperature, is consistent with



the increase in fluidity known to occur in lipids with increasing temperature.Modifications to the collagen fiber structure of dermis caused by increasing tem-perature, possibly through changes in hydration, are the most plausible explanationfor the increased scattering properties.333, 334 As claimed by the authors of Refs.333 and 334, the finding that a tissue that is largely protein has a positive tem-perature coefficient and a tissue that is largely lipid has a negative temperaturecoefficient leads to interesting possibilities for tissues in which the protein/lipidratio is intermediate, such as brain tissue.

The temperature changes of μa, and μ′s of human forearm skin have been also

determined in the course of in vivo studies for two skin surface temperatures: 22◦Cand 38◦C1271 (see data in Table 7.1). A rather high increase in coefficient valuesof 16–21% for μa and much smaller increase of 2.7–4.6% for μ′

s were found withtemperature change from 22◦C to 38◦C for the wavelengths 950–590 nm.

Low-intensity laser radiation, when used for spectroscopy (diagnostics) or ther-apy, may heat tissue and distort results of tissue optical property measurements, ormay induce uncontrolled change in a photobiological response of a tissue causedby a local heating. An increase in human skin temperature under CW laser irradia-tion can be estimated on the basis of experimental and theoretical studies presentedin Refs. 323–325 and 1660. It was found experimentally that for NIR laser radi-ation (789 nm) guided to the skin surface of the forearm of a conscious humanvolunteer by a 1-mm optical fiber, the temperature increased linearly with powerlevel as (0.101 ± 0.001)◦C/mW at the depth of 0.5 mm: (0.038 ± 0.001)◦C/mWat the depth of 1 mm, and (0.029 ± 0.0005)◦C/mW at the depth of 1.5 mm in therange of illuminating power up to 10 mW.1660

The combination of the MC technique to calculate the fluence rate distributionof light and an adaptive finite-element method to solve the heat transfer equationwas applied to investigate the process of hyperthermia induced by transskin irra-diation with a He-Ne laser (633 nm).323–325 It was shown that overheated tissuevolume, heating depth, and temperature can be effectively controlled by changingthe free convention boundary conditions on the tissue surface and varying power,radius, and shape of the incident laser beam. A four-layer model of human skin(epidermis, upper dermis, blood plexus, and lower dermis) with optical and ther-mal properties of the tissue layers taken from the literature was used for modeling(see Tables 1.1, 4.1, and 7.1). Modeling was conducted for Gaussian and rectan-gular incident light beams at noncoagulating intensities. By variations in value ofthe heat transfer coefficient, A, corresponding to free convection at an initial skinsurface temperature equal to 34◦C, A = 0.009 W/cm2K, to weak isolation, A =0.004 W/cm2K, and strong, A = 0.0005 W/cm2K, the effect of thermal insulationon tissue temperature distributions was studied. For a 25-mW Gaussian incidentbeam of 1 mm in diameter, the subsurface temperature maxima at the depths of0.20, 0.18, and 0.10 mm and equal to 36.7◦C, 41.3◦C, and 42.8◦C, were foundas isolation increased. At the depth of 1 mm, the calculated temperatures were37.7◦C, 38.1◦C, and 38.5◦C as the degree of isolation increased. The previouslymentioned experimental data1660 are accurately fit to the modeled data for freeconvention boundary conditions on the skin surface. From experiments, it follows


586 Chapter 9

that for light power of 25 mW, a temperature increase at the depth of 1 mm isexpected as (0.038◦C/mW) × 25 mW = 0.95◦C. In turn, calculations showed thattemperature increased from the initial value without radiation of 36.4◦C to 37.7◦Cwith laser action, i.e., at 1.1◦C. Slightly higher temperature increase in theory thanthat expected from the experimental estimation may be explained by the shorterwavelength of light, which is more effectively absorbed by tissue chromophores.

The loss of water by tissue owing to temperature effects (freezing in a refrig-erator or noncoagulating heating) seriously influences its optical properties. Forinstance, in in vitro study of human aorta, the absorption coefficient increased by20–50%, especially in the visible range, when on average, 46.4% of total tissueweight was lost as a result of dehydration with prolonged freezing of the tissuesample in a refregirator.764, 765 The weight loss was accompanied with an averageshrinkage in thickness of 19.5%. Primarily because of shrinkage (denser packing oftissue components), the absorption coefficient was increased in the spectral range400–1300 nm. There was only a slight increase of 2–15% in the reduced scatteringcoefficient in the visible range, again owing to closer packing of tissue components.

The slope of the wavelength dependence of the μ′s, which is proportional to

λ−h [see Eq. (3.29)], is a good test for the alteration of tissue morphology underheating or freezing. Data summarized in Table 3.2 demonstrate experimental val-ues of parameter h for normal, dehydrated, and coagulated human aorta receivedduring an in vitro study in the spectral range 400–1300 nm.764, 765 Tissue dehy-dration (by slow freezing) increases slope (h) from 1.15 (control) to 1.22, whichreflects more dense packing of scatterers at tissue shrinkage. Sample heating during5 min in a saline bath at temperatures in the vicinity of tissue coagulation thresholdmay increase h; for instance, for 60◦C from 1.21 (control) to 1.28 (possibly due tolocal protein coagulation); or decrease h, for instance, for 70◦C from 1.30 (control)to 1.10 (possibly due to more extensive protein coagulation). This result reflectsthat collagen denaturation begins dominating tissue behavior between 55◦C and70◦C.764 Because of the heterogeneity of aorta tissue, its components may havereached different end points at the end of the 5-min heating period. At 100◦C heat-ing of the samples in a saline bath, h was reduced from 1.38 for the normal tissuesamples to 1.06 for the heated samples, and for the samples preliminarily wrappedin aluminum foil, h was reduced from 1.26 to 1.03.

Under tissue heating in a bath absorption coefficients may increase up to 28%(60◦C) or decrease up to 22% (70◦C) on selected wavelengths. At the same time,values of the reduced scattering coefficient were increased for all heating temper-atures in a wide range from 1.1% to 76%, dependent on the wavelength, in therange from 350 to 1320 nm and heating temperature. At temperature of 60◦C,the increase was rather smooth: 16–19% in this wavelength range. At 70◦C, theincrease of μ′

s was not as smooth, being changed from 1.1% to 24.8%. Heatingup to 100◦C increased the reduced scattering coefficient 22–76%, but tissue wrap-ping decreased these values to 15–54%. Such complex behavior of scattering andabsorption properties of precoagulated and coagulated tissues reflects tissue hetero-geneity; the specificity of protein denaturation process, leading to the appearance



Table 9.19 Possible mechanisms responsible for inducing reversible changes in tissueoptical response on laser long-pulsed irradiation (see Ref. 765).

Mechanism Description Optical response

Thermal lensing, n(T) = n(273K) +� T(r, z, t) (dn/dT)

Gradient in index of refractioncaused by nonuniform heating

Decrease in T t and increase in Rd

Temperature dependence of reducedscattering coefficient: μ′

s(T) =μs(T)[1 − g(T)]

Change in size and/or shape of scat-terers due to temperature rise

Increase in T t and decrease in Rd(as μ′

s decreases)

Water transport Temporary local dehydration duringlaser heating

Increase in T t and decrease in Rd

Thermal expansion Decrease in tissue density andincrease in tissue thickness causedby thermal expansion of tissue

Decrease in T t and increase in Rd

of coarse and small thermally coagulated granular cellular proteins and some dam-age to tissue chromophores; and interactions of heated saline with tissue, resultingin diffusion of saline and chromophores.764

Following Ref. 764,∗ it may be verified that tissue progresses from normal todenaturated states between 60◦C and 70◦C, and that at ∼60◦C, certain changes inthe optical properties caused by thermal damage are still reversible even thoughthe thermal threshold for protein coagulation is exceeded. In general, the com-plex behavior of tissue optical properties at heating can be explained by particularchanges in tissue morphology. To model the optical properties of heated tissues,the modified morphology should be expressed in such terms as scatterer size dis-tribution, refractive index mismatch between particle and interstitial fluid, particlepacking, and chromophore concentrations.

Long-pulsed laser heating may induce reversible and irreversible changes inthe optical properties of tissue.765, 1662 The total transmittance decreases and the dif-fuse reflectance increases in both fresh and precoagulated human skin and canineaorta samples, when irradiated by a 0.2-ms pulsed Nd-YAG laser emitting at 1064nm with a repetition rate of 10 Hz (20 pulses of 0.9 J/pulse) and a 1.5-mm lightspot.765 The existence of nonlinear behavior in the optics of biological media wasindicated. Possible mechanisms responsible for this nonlinear optical response arelisted in Table 9.19. The in vitro skin-equivalent raft tissue irradiated with one pulsefrom a perovskite laser (λ = 1341 nm) with fluence of 20 J/cm2 and pulse durationof 20 ms showed thermal injury areas characterized by less scattering, as shown onthe OCT images, and losing of the SHG signal.1662 Such behavior was interpretedby the authors of Ref. 1662 as disintegration of collagen fibers at thermal tissueprotein denaturation, which can be rejuvenated upon tissue healing.

Laser ablation or coagulation is usually accompanied by a change in the nor-mal optical properties of the tissue.765, 1712 For example, ablation of aortal tissueusing an excimer laser (308 nm) results in a 2.3–3.7-fold increase in its optical

∗Errata for the paper are presented in Ref. 3, p. 379


588 Chapter 9

density compared with the untreated material.1712 Published results on optical prop-erties of coagulated tissues are presented in Table 7.1. Despite some variationsin dependence on tissue type, wavelength studied, and sample preparationtechnique, the general tendency is the increase in both the absorption and scatteringcoefficients from a few dozen to 200–300% at tissue coagulation.

Low temperatures (+12◦C) sometimes result in a cold cataract, i.e., a sharpincrease in the scattering coefficient due to protein aggregation.1470, 1681 Thisprocess is reversed with an increase in temperature.

Cryogenic temperatures used in cryosurgery may also change the scatteringproperties of tissues due to local variations in refractive index, such as the bound-ary between liquid and frozen water in tissue.1669 The corresponding subsurfacemorphological changes were evident during freezing (–80◦C) of in vivo hamsterskin.

Tissue dehydration by heat treatment (drying in air or in a stream of hotair)178, 1386, 1752 or lyophilization by freezing1857 were used to identify mechanismsof optical clearing and structural characteristics of tissues.

9.10.3 Tissue whitening

Sometimes, to provide more contrast images of intracellular components of theepithelial tissues, instead of optical clearing, the usage of induced tissue turbidity(whitening) is more preferable.1663, 1671, 1679, 1812, 1814 For example, a fundamentalpart of the colposcopic exam is the use of acetic acid, which, when applied tothe cervix, induces transient whitening changes in the epithelial tissues.1668 Thespatial and temporal changes of aceto-whitening are the major visual diagnosticindicators in the determination of the most severe dysplastic regions. The aceto-whitening effect causes a differential brightening of dysplastic tissue relative tonormal tissue, and in addition to cervical disorders, is used to screen for skin andother epithelial diseases.

The brightening of nuclei enhances the contrast and significantly improves thedetectability of nuclear morphology in basal cell cancers.1671 Under normal con-ditions, the nucleus contains a diffuse network of thin chromatin filaments thatare typically 30–100 nm in diameter and occupy a small volume within. Becauseof the small dimensions and insignificant difference between the refractive indexof chromatin, which can be estimated as 1.39, and that of the surrounding tis-sue components (cell cytoplasm and interstitial fluid), which is about 1.35, thebackscattering in the nucleus is low. Acetic acid causes the chromatin to assembleinto thick fibers that are 1–5 μm in diameter; the compacted chromatin fills a largefraction of the intranuclear volume1671 and some increase in its refractive index isalso expected;1668 thus, the backscattering signal from nuclei is increased and theyappear bright. After washing ex vivo samples of human epidermis with 5% aceticacid for 3 min, the epidermal cell nuclei appear bright, as shown in the confocalreflectance images.1671

The temporal kinetics of the aceto-whitening process, as measured by thereflected light, maximizes during the first 1–2 min and decays over several minutes



(5–10 min) thereafter, allowing high-grade cervical intraepithelial neoplasia (CIN2/3) to be clearly distinguished from normal cervical epithelium when the ratioof green to red light intensities of the backscattered light was analyzed.1668

Normalizing the green by the red light preserves kinetics in the reflected signal,indicating that the reflected light has a spectral change. Rough aceto-whiteningin the CIN 2/3 cervical tissue in vivo causes a 20–80% increase in the origi-nal reflectance. By contrast, mature squamous epithelium appears to increase inreflectance only by approximately 5%; moreover, reflectance is constant in timeafter the application of acetic acid.

9.11 Conclusion

This chapter shows that optical immersion technology allows one to effectivelycontrol the optical properties of tissues and blood. This control leads to an essentialreduction of scattering, and therefore, causes much higher transmittance (opti-cal clearing) and the appearance of a large amount of least scattered (shake)and ballistic photons, allowing for successful application of coherent-domain andpolarization imaging techniques. The kinetics of tissue optical clearing, defined bythe kinetics of refractive index matching and dehydration, is characterized by atime response of approximately 5–30 min, which, in turn, depends on diffusivityof the immersion agent in a tissue layer, water diffusion rate, and thickness of tis-sue layers. Tissue and cell swelling or shrinkage may play an important role in thetissue clearing process upon the application of hyperosmotic agents.

In vivo reflectance spectrophotometry and frequency domain measurementsfor immersed tissues show that the refractive index matching technique providedby the appropriate chemical agent, in combination with a permeability enhancercan successfully be used in tissue spectroscopy and imaging, when radical reduc-tion of scattering properties is needed. Hyperdermal injection of glucose causes theessential clearing of human skin. For such tissues as sclera or cornea, a few dropsof glucose are sufficient to ensure very high and rather prolonged tissue clearing.In in vivo experiments, the impregnation of a tissue by an agent is more effectivethan in in vitro studies owing to the higher diffusivity of an agent at physiologicaltemperature and by the involvement of blood and lymph microvessels into the pro-cess of agent distribution. However, certain physiological reactions of living tissueon hyperosmotic solutions may influence the measured spectra.

Kinetic optical characteristics can be used for the determination of diffusioncoefficient and concentration of endogenous (metabolic) and exogenous (chemicalagent) fluids in the human sclera, skin, and other tissues. This is particularly impor-tant for the differentiation of healthy from pathological tissues, for which kineticsare significantly different.

The immersion technique has great potential for noninvasive medical diag-nostics using OCT owing to the rather small thickness of tissue layers usuallyexamined by OCT, which allows for fast impregnation of a target tissue withthe topical application of an immersion liquid. It has been demonstrated that thebody’s interior tissues, such as blood vessel wall, esophagus, stomach, cervix, and


590 Chapter 9

colon can usually be imaged at a depth of approximately 1–2 mm. For more effec-tive diagnosis using OCT, a higher penetration depth can be provided by applyingimmersion substances.

The method for clearing tissue is convenient, cheap, and simple for diagnosticpurposes; in particular, it can be applied for in vivo monitoring of microcirculation.It may be useful for studying the structure and function of blood microvessels—diameters of arterioles and venules, capillary density, and bifurcation angles.

Optical clearing might be a fruitful technique for various methods of tissuespectroscopy, microscopy, and imaging (Raman, confocal, fluorescence, laser scan-ning, near-field, multiphoton, and SHG), in which scattering is a serious limitation.Encouraging results have already been received for the enhancement of fluores-cence signal under tissue optical immersion. The reduction of light scattering mayassist in the differentiation of various fluorophores in the depth of a tissue, such asskin.

The concept of index matching may improve the optical penetration depthof whole blood, which is proven experimentally in in vitro studies. It should beconsidered that blood optical clearing is defined not only by the refractive indexmatching effect, but also by changes in the size and shape of red blood cells andtheir aggregation ability when chemicals are added.

Many of the tested agents and methods of delivery have certain advantages anddisadvantages. The primary disadvantages include osmotic stress, which occursat high concentrations of hyperosmotic agent, and low permeability of tissue cellstructures for the clearing agents. Therefore, the finding of new agents and deliverytechniques is appreciated.

The concept and technology of immersion optical clearing is applicablenot only to soft tissues and blood, but also to hard tissues. At present, ten-dons,621, 622, 1578 cranial bones,1342, 1343, 1784, 1860 teeth,750, 751, 1341, 1705 and nails1235

have been tested.In conclusion, in addition to immersion and compression optical clearing, more

sophisticated methods can be used for the suppression of optical scattering andimprovement of the image quality of biological tissues, such as the optical phaseconjugation method,1612, 1882, 1883 which has intensively been under developmentover the past decades for technical applications.1884


Part II: Light-ScatteringMethods and Instruments for

Medical Diagnosis


Chapter 10

Continuous WaveSpectrophotometry andImaging

The specificity of optical spectral diffusion techniques and scattering spectroscopyis discussed. Two types of instruments and measuring techniques are presented:spectroscopic, used for monitoring local parameters of tissue, and tomographic,used for tissue pathology imaging using structural and functional information.Some of these techniques are based on CW light source tissue probing. A fewexamples of CW measuring and imaging instruments and results of clinical studiesare presented.

10.1 Techniques and Instruments for in vivo Spectroscopy andImaging of Tissues

For in vivo study of thick tissue (for example, female breast), collimated light trans-mittance can be described by an exponential law, such as Eq. (1.1), taking intoaccount that because of multiple scattering, the effective migration path of a pho-ton before it is absorbed should be larger than the thickness of the tissue.414 Fora slab of thickness d, the diffusion equation can be used to calculate a mean pathlength L of the photons:398

L = μeff

2μaμ′s

·(μ′

sd − 1)

exp(

2µeffµ′

s

)− (

μ′sd + 1

)exp

(2µeffµ′

s

)− 1

, (10.1)

where μeff is defined by Eq. (1.18). Using Eq. (1.1) for the matched boundaries(n = 1), the collimated transmittance can be written in the form414

Tc (λ) = x1 exp [−μa (λ) L (λ) x2] , (10.2)

593


594 Chapter 10

where L(λ) reflects the wavelength dependence of μa(λ) and μ′s(λ); x1 takes into

account the measurement geometry and multiply scattered but not absorbed pho-tons, which do not arrive at the detector; and x2 compensates for measurementerrors in d and inaccuracies in the reduced scattering coefficient, μ′

s.Semiempirical Eq. (10.2) was successfully used for fitting of the in vivo

measurement spectra of female breast and estimation of the concentrations ofthe absorbers water (H2O), fat (f), deoxyhemoglobin (Hb), and oxyhemoglobin(HbO2), as follows:414

μa = cH2OσH2O + cfσf + cHbσHb + cHbO2σHbO2, (10.3)

where σi is the cross section of the absorption of the ith component.By varying the concentrations of the four tissue components, the measurement

spectra were accurately fitted by Eq. (10.2); the correlation coefficients were betterthan 0.99 in all cases.414 Figure 10.1 shows the spectrometer for in vivo measure-ment of the collimated transmittance spectra of a female breast and some examplesof measured and fitted spectra for normal and pathological (cancer tumor) tissues.Typically, most carcinoma spectra exhibit a lower transmittance than the refer-ence spectrum (for the same breast thickness). The fits show that this is generallyattributable to increased blood perfusion (higher Hb/HbO2 values of the carcinomacurve). In the wavelength region between approximately 900 and 1000 nm, spectraare rather different; this is clearly due to the altered water and fat content of carci-nomas compared with that of the healthy breast. The majority of mastopathies andcarcinomas show higher water concentration and blood volume at the lesion site. Acomparison of healthy and cancerous sites yields a slightly lower concentration of

Figure 10.1 Schematic setup of the spectrophotometer system used for in vivo measure-ments of breast tissue spectra (see Ref. 414) (a). Spectra and respective fits of a breastcancer patient (56 years, breast thickness of 60 mm) within the area of carcinoma and fora healthy breast and similar localization to the carcinoma (b).


Continuous Wave Spectrophotometry and Imaging 595

oxyhemoglobin for the tumor. Unfortunately, the specificity is insufficient becauseit is not possible to discriminate between benign mastopathies and malignant carci-nomas by means of water content, blood volume, and oxygenation.414 More recentstudies indicate that the optical method is one possible way to differentiate malig-nant from benign tumors. This approach can be used to precisely determine thewater content as well as the relative content between free and bound waters intissue. For example, in a study for breast cancer, it was experimentally found thatthe ratio of bound water content relative to free water is inversely proportional tothe histological grading of tumor growth.1885 One spectroscopic method for thedetermination of free and bound water in the skin is described in Subsection 9.4.3.In Subsection 9.6.1, another approach is discussed for differentiation between freeand bound water based on immersion optical clearing.

Transmittance NIR spectrometry for measuring oxygenation has had the mostsuccess to date in newborn infant heads, largely because of the small size of thehead, the thin overlying surface tissues and skull, and the lower scattering coef-ficient of the infant brain.55, 511, 542 The development of cooled CCD, time- andspatial-resolved techniques, and instruments has proceeded rapidly and the rangeof NIR spectroscopy investigations and applications is increasing. At present, thereare more than 500 commercial clinical NIR spectroscopy instruments for monitor-ing and imaging the degree of oxygenation in tissues, the concentration of oxidizedcytochrome, and tissue hemodynamics.

For many tissues, in vivo measurements are possible only in the geometry ofbackscattering. The corresponding relations can be written on the basis of a diffu-sion approximation. For a semi-infinite medium and source and detector probesseparated by a distance, rsd, normal to the sample surface (see Fig. 10.2), andoptically matched (so that specular reflectance at the surface can be neglected),the reflecting flux is given by Eq. (7.13).1275 A more general expression, valid forrefractive index mismatch conditions on the boundary, is given by Eq. (1.33).297, 298

For backscattering optical spectroscopy and tomography, in addition to themeasured coefficient of reflection defined by Eqs. (1.33) and (7.13), it is necessaryto know the depth from which the optical signal originates. This depth is definedby the photon-path-distribution function for the photons migrating from a source toa detector.1886, 1887 This spatial distribution function for a homogeneous scattering

Figure 10.2 Geometry of a fiber backscattering experiment for investigation of a semi-infinite medium (a), and a “banana” shaped region of photon path distribution (b) (see Refs.1886 and 1887).


596 Chapter 10

medium has a “banana” shape [see Fig. 10.2(b)]. In the weak absorption limit, themodal line of the banana region (the curve of the most probable direction of aphoton migration) is given by1886, 1887

z ≈[

1

8

({[x2 + (rsd − x)2

]2 + 32x2(rsd − x)2} 1

2 − x2 − (rsd − x)2

)] 12

, (10.4)

0 ≤ x ≤ rsd. At x = rsd/2, the modal line of the banana region reaches maximumdepth:

zmax ≈ rsd

2√

2. (10.5)

Instead of Eq. (10.2), used for in vivo study in a transillumination experiment, usingEqs. (7.13) and (10.4), we can write a modified Beer–Lambert law to describe theoptical attenuation in the following form:1886, 1887

I

I0= exp (−εabcabrsdDPF − Gs) , (10.6)

where I0 is the intensity of the incident light; I is the intensity of detected light; εab

is the absorption coefficient measured in μmol−1·cm−1; cab is the concentration ofabsorber in μmol; rsd is the distance between the light source and detector; DPFis the differential path length factor accounting for the increase in the migrationpaths of photons due to scattering; and Gs is the attenuation factor accounting forscattering and geometry of the tissue.

When rsd, DPF, and G are kept constant (for example, during the estimationof the total hemoglobin or degree of oxygenation), then the changes in the absorb-ing medium concentration can be calculated by measuring the changes in the OD,�(OD) = �[log(I0/I)]:

�cab = �(OD)

εabrsdDPF. (10.7)

In optical imaging, the changes in OD are measured as follows:499, 1886, 1887

�(OD) = log

(I0

Itest

)− log

(I0

Irest

)= log(Irest) − log(Itest), (10.8)

where Irest and Itest represent the light intensity detected when the object is at rest(brain tissue or skeletal muscle) and during testing (induced brain activity, coldor visual test, or training). For example, based on the OD changes at wavelengthsof 760 and 850 nm, one can determine either the absorption images for these twowavelengths or functional images [oxygenation (oxy) and blood volume – totalhemoglobin (total)] within the detection region of study:

�(OD)oxy = �(OD)850 − �(OD)760, (10.9)

�(OD)total = �(OD)850 + kbvo�(OD)760, (10.10)



Figure 10.3 NIR attenuation [log10] for 1-cm depth deoxyhemoglobin (DeoxyHb), oxyhe-moglobin (OxyHb), and water; hemoglobin concentration 210 μM in water (see Ref. 4).

where (OD)850 and (OD)760 are the optical densities measured at the wavelengths850 and 760 nm, and kbvo is the modification factor for reducing the cross talkbetween changes in blood volume and oxygenation. This factor is determined bycalibration on a blood model.

NIR absorption spectra of HbO2, Hb, and water are presented in Fig. 10.3.4

The water band at approximately 980 nm can be used as an internal standard forevaluating the absolute concentrations of the blood components in tissue in vivo,because the content of water in tissues varies relatively slowly and can be deter-mined independently by other noninvasive techniques or by using material frombiopsy after advanced in vivo study of blood dynamics466, 1888, 1889

10.2 Example of the Spectroscopic System

A typical experimental system for in vivo backscattering spectroscopy andthe corresponding spectra for normal and pathological tissues are shown inFig. 10.4.47, 94, 95 Figure 10.4(b) is an example of spectra taken from the colon ofone patient. The absorption bands are of oxyhemoglobin (the Soret and Q-bandsare clearly evident). The 400−440-nm segment encloses the hemoglobin Soretband, but also encompasses some absorption from compounds such as flavinmononucleotide, beta-carotene, bilirubin, and cytochrome. The 540−580-nm seg-ment covers the hemoglobin Q-band, with minor absorption from cytochrome andother components. On the basis of measuring the spectral differences between nor-mal and pathological tissues, the corresponding spectral signature “identifiers” canbe created. These spectral identifiers for in vivo medical diagnostics usually usethe ratios of the reflection coefficients integrated within selected spectral bands ormeasurement of the spectrum slope for the selected spectral bands.

In the literature, many different systems are described for diffusion spec-troscopy or optical biopsy of various pathologies of tissues and organs based on


598 Chapter 10

Figure 10.4 Schematic diagram of the experimental system for in vivo measurements ofspectral reflectance of internal organs (see Ref. 47) (a). Typical tissue spectra, shown asexamples, for two measurements made in the colon of one patient (the spectra have beennormalized to the same total integrated signal between 350 and 700 nm); normal mucosaand partial villous adenoma (b).

CW light sources.1, 3, 5, 6, 10, 14, 16, 23, 32, 33, 47, 50, 55, 88, 89, 91, 100, 129, 130, 134, 169, 174, 183, 196, 197,

206, 369, 466, 499, 511, 539, 1313, 1315, 1889–1899 Modern trends in multimodality medical diag-nostic technologies and devices are embodied in diffusion optical spectroscopy,which is used in combination with magnetic resonance imaging (MRI),1895 Ramanspectroscopy,1897 or time-resolved fluorescence imaging.1892 Noninvasive oxime-try,466, 511, 1889, 1890, 1894, 1898 regional monitoring of the total hemoglobin1896 orcarotenoid content in the skin,1319, 1897 diagnosis of breast cancer1891 and skincancer,1892 and monitoring of atherosclerotic plaques1898 represent the focus ofclinical studies. In addition to diffusion reflectance spectroscopy, fluorescencespectroscopy at excitation of endogenous or exogenous fluorophores is widely used(see, for example, Refs. 129, 130, 134, 147, 206, 466, 511, 1058, and 1059).

10.3 Example of the Imaging System

The whole-spectrum NIR spectroscopy system described in Ref. 1899 uses illumi-nation of a subject’s head with light from a halogen lamp emitting a continuousspectrum [see Fig. 10.5(a)]. The backreflected light is detected and spectrallyanalyzed by a commercial grating spectrograph equipped with a liquid nitrogen–cooled CCD detector. The system provides a spectral resolution of 5 nm in therange of 700−1000 nm; spectra were collected every 100 ms. Figure 10.5(b)illustrates the image received by using this optical instrument and the testing algo-rithm described [see Eqs. (10.9) and (10.10)]. It shows a focal increase in totalHb in response to stimulation with a stationary multicolored dodecahedron. Thearea of the peak response is clearly focused and approximately 0.5 × 0.5 cmin size.



Figure 10.5 CCD-NIR spectroscopy system (see Ref. 1899). Scheme (a). Functionalimage, changes in blood volume (total hemoglobin) [see Eqs. (10.9) and (10.10)] duringvisual simulation (stationary dodecahedron) as detected over the occipital cortex (b).

In the literature, many robust CW schemes are presented for opticalreflectance diffusion imaging of various pathologies of tissues.1, 3, 6, 14, 23, 32,

33, 55, 88, 89, 129, 130, 139, 183, 196, 197, 206, 466, 511, 532, 1900–1903 Additionally, fluorescence dif-fusion imaging with the excitation of endogenous or exogenous fluorophores iswidely used (e.g., Refs. 129, 130, 134, 147, 206, 466, 511, 954, 1058, 1059, 1900,1901, and 1904).

10.4 Light Scattering Spectroscopy

Light scattering spectroscopy (LSS) provides structural and functional infor-mation about a tissue. This information, in turn, can be used to diagnoseand monitor disease. This technique is capable of identifying and character-izing pathological changes in human tissues at the cellular and subcellularlevels.47, 61, 94, 95, 129, 130, 216, 236, 272, 662, 791, 809, 825, 1163, 1326–1330, 1905, 1906 One importantapplication of biomedical spectroscopy is the noninvasive detection of earlycancerous human epithelium.272, 825, 1163, 1327–1329, 1905, 1906 The enlarging, crowd-ing, and hyperchromaticity of epithelium cell nuclei are common features to alltypes of precancerous and early cancerous conditions. LSS can be used for thedetection of early cancerous changes and other diseases in a variety of organs,such as esophagus, colon, uterine cervix, oral cavity, lungs, and urinary blad-der.825, 1163, 1328, 1329, 1905, 1906 Eye lens cataract and other ophthalmic diseases canalso be diagnosed by using LSS.809

Cells and tissues have complex structures with a very broad range of the scat-terer sizes: from a few nanometers, the size of a macromolecule, to 7–10 μm,the size of a nucleus, and 20–50 μm, a size of a cell itself. Most subcellularorganelles are not uniform and have complex shapes and structures; nevertheless,they can be referred to as scattering particles (see Chapter 1). A great variety ofcell organelle structures are small compared to the wavelength. Light scatteringby such particles is known as Rayleigh scattering and is characterized by a broadangular distribution and the dependence of the scattering cross section on lineardimension of the particle, a, as a6 and on light wavelength, λ, as λ−4. When theparticle is insufficiently small, the coupled dipole theory or another approach such


600 Chapter 10

as Rayleigh–Gans approximation (RGA) can be used. RGA is particularly appli-cable to particles with size comparable to the wavelength and may be useful tostudy light scattering by small organelles such as mitochondria or lysosomes. ForRGA, the scattering prevails in the forward direction, the total scattering intensityincreases with the increase of the particle relative refractive index m as (m − 1)2

and with its size as a6.Scattering by a particle with dimensions much larger than the wavelength,

such as a cell nucleus, can be described within the framework of van de Hulstapproximation, which enables scattering amplitudes in the near forward directionto be obtained [see. Eq. (7.28)]. For large particles, the scattered intensity is highlyforward-directed: the width of the first scattering lobe is approximately λ/a; thelarger the particle, the stronger and narrower the first lobe. The intensity of for-ward scattering exhibits oscillations with changes in the wavelength. The origin ofthese oscillations is interference between the light rays, one passing through thecenter of the particle and one not interacting with the particles. The frequency ofthese oscillations is proportional to a(m − 1), so it increases with particle size andrefractive index. The intensity of scattered light also peaks in the near backwarddirection, but this peak is significantly smaller than the forward-scattering peak.

These results agree well with the rigorous scattering theory developed forspherical particles (Mie theory).214 To discriminate the peculiarities of cell struc-tures originated by the pathology, the difference in light scattering can be used.The structures with large dimensions and high refractive index produce a scatteredfield that peaks in the forward and near backward directions, in contrast to smallerand more optically “soft” structures, which scatter light more uniformly. Perelmanet al.216, 272, 1163, 1327 studied elastic light scattering from densely packed layers ofnormal and T84 tumor human intestinal cells, affixed to glass slides in buffer solu-tion (see Fig. 1.2). The diameters of the normal cell nuclei ranged from 5 to 7 μm,and those of the tumor cells from 7 to 16 μm. The reflectance from the samplesexhibits distinct spectral features. The predictions of Mie theory were fit to theobserved spectra. The fitting procedure used three parameters: average size of thenucleus, standard deviation in size (a Gaussian size distribution was assumed), andrelative refractive index. The solid line in Fig. 10.6 is the distribution extracted fromthe data, and the dashed line shows the corresponding size distributions measuredby light microscopy. The extracted and measured distributions for both normal andT84 cell samples corresponded well, indicating the validity of the above physicalimage and the accuracy of the method for extracting information.

In tissues, the photons returned after single scattering in the backward ornear-backward directions produce a so-called single-scattering component. Thephotons returned after multiple scattering events produce diffuse reflectance. Thespectra of both single-scattering and diffusive signals contain valuable informa-tion about tissue properties. However, the type of information is different. Thesingle-scattering component is sensitive to morphology of the upper tissue layer,which, in the case of any mucosal tissue, almost always includes or is limitedby the epithelium. Its spectroscopic features are related to the microarchitectureof the epithelial cells; sizes, shapes, and refractive indices of their organelles,



Figure 10.6 Nuclear size distributions of the samples, presented in Fig. 1.2. Normal intesti-nal cells (a); T84 cells (b). In each case, the solid line is the distribution extracted fromthe data using Mie theory, and the dashed line is the distribution measured using lightmicroscopy (from Ref. 272).

inclusions, and suborganellar components and inhomogeneities. Thus, analysis ofthis component might be useful in diagnosing diseases limited to the epithelium,such as preinvasive stages of epithelial cancers, dysplasias, and carcinomas in situ(CIS).825, 1163, 1328, 1329, 1905, 1906 The diffusive component contains information abouttissue scatterers and absorbers, and its diagnostic possibilities and instrumentationare discussed early in this chapter.

The single-scattering component is more important in diagnosing the initialstages of epithelial precancerous lesions, whereas the diffusive component carriesvaluable information about more advanced stages of the disease. However, single-scattering events cannot be directly observed in in vivo tissues, because only a smallportion of the light incident on the tissue is directly backscattered.

Several methods have been proposed to distinguish single scattering. Field-based LSS1330 and spectral OCT142 were developed for performing cross-sectionaltomographic and spectroscopic imaging. In these extensions of conventional OCT,information about the spectral content of backscattered light is obtained by detect-ing and processing the interferometric OCT signal. These methods allow thespectrum of backscattered light be measured either for several discreet wave-lengths,1329 or simultaneously over the entire available optical bandwidth from 650to 1000 nm in a single measurement.142

A much more simple polarization-sensitive technique is also available.216 It isbased on the fact that initially polarized light loses its polarization when traversinga turbid tissue. A conventional spatially resolved backscattering technique withsufficiently small source–detector separation can additionally be used.272 In thiscase, the single-scattering component (2–5%) should be subtracted from the totalreflectance spectra, which can be done by using the diffusion approximation–basedmodel by fitting to the coarse features of the diffusive component.


602 Chapter 10

Figure 10.7 Diffuse reflectance analysis: measured reflectance spectra (noisy lines), andmodeled fits (smooth lines) (a); scattering spectra obtained from the reflectance mea-surements (noisy curves) and corresponding Mie theory spectra (smooth curves) (b). Theeffective scatterer sizes, ds, are indicated (from Refs. 1327 and 1330).

Zonios et al. studied the capability of diffuse reflectance spectroscopy to diag-nose colonic precancerous lesions, adenomatous polyps, in vivo.1330 Figure 10.7shows typical diffuse reflectance spectra from one adenomatous polyp site andone normal mucosa site. Significant spectral differences are readily observed, par-ticularly in the short-wavelength region of the spectrum, where the hemoglobinabsorption valley around 420 nm stands out as the prominent spectral feature.This valley is much more prominent in the spectrum of the adenomatous polyp.This feature, as well as more prominent dips around 542 and 577 nm, which arealso characteristic to hemoglobin absorption, are all indicative of the increasedhemoglobin presence in the adenomatous tissue.



Apparently, the differences between these spectra are attributable to changes inthe scattering and absorption properties of the tissues. Both the absorption dips andslopes of the spectra are sensitive functions of the absorption and scattering coef-ficients, providing a natural way to introduce an inverse algorithm that is sensitiveto such features. The authors quantified the absorption and scattering properties byusing the diffusion-based model discussed in Subsection 1.1.2. The equation1330

analog to Eq. (1.33) was fit to the data by using the Levenberg–Marquardt mini-mization method. Thus, the total hemoglobin concentration, cHb, and hemoglobinoxygen saturation, α, were obtained. Also, the optimal reduced scattering coeffi-cient, μ′

s(λ), was found for each wavelength, λ, ranging from 360 to 685 nm. It wasfound that μ′

s(λ) has a spectral dependence that resembles a straight line decliningwith λ. The slope of μ′

s(λ) decreases with an increasing effective size of the scat-terers, ds [Fig. 10.7(b)]. This allows the effective scatterer size to be determinedfrom known μ′

s(λ). The model fits shown in Fig. 10.7(a) agree very well with theexperimental data.

The promise of LSS for the diagnoses of dysplasia and CIS was tested in in vivohuman studies in four different organs and in three different types of epithelium:columnar epithelia of the colon and Barrett’s esophagus, transitional epithelium ofthe urinary bladder, and stratified squamous epithelium of the oral cavity.1328 Allclinical studies were performed during routine endoscopic screening or surveil-lance procedures. In all of these studies an optical fiber probe delivered white lightfrom a xenon arc lamp to the tissue surface and collected the returned light. Theprobe tip was brought into gentle contact with the tissue to be studied. Immediatelyafter measurement, a biopsy was taken from the same tissue site. The spectrum ofthe reflected light was analyzed and the nuclear size distribution determined. Bothdysplasia and CIS have a higher percentage of enlarged nuclei, and on average, ahigher population density, which can be used as the basis for spectroscopic tissuediagnosis.


Chapter 11

Time-Resolved and SpatiallyModulated Spectroscopy andTomography of Tissues

Time-resolved and spatially modulated optical diffusion techniques and instru-ments are discussed. A promising technique and device for accurate in vivomeasurement are analyzed. In accordance with the basic principles discussed inChapter 1, four types of time and spatially resolved techniques and instrumentsare considered: the time domain, which uses ultrashort laser pulses; the frequency-domain, which exploits an intensity modulated light and narrow band heterodynedetection; the phased array technique, which utilizes an interference of photon dif-fusion density waves; and a technique for tissue probing by a spatially modulatedlight beam.

11.1 Time-Domain Techniques and Instruments

One of the time-resolved laser systems designed for in vivo measurements of opti-cal properties of the human breast is presented in Fig. 11.1.414 This system consistsof a mode-locked Ti-sapphire laser at a wavelength of 800 nm with a pulse durationof 80 fs and a repetition frequency of 82 MHz. The probe laser beam transillu-minates the female breast and the forward-scattered light reaches the detectionside of the Synchroscan streak camera (S1 photocathode, Hamamatsu C3681).For the enhancement of tissue transmittance, making it more homogeneous, andfor the sake of providing stable boundary conditions, the breast was slightly com-pressed between two transparent plates. Such compression was much less thanthat in conventional x-ray mammography to avoid any influence from changedblood perfusion on the absorption properties. The scattered light was imaged ontothe slit of the streak camera with 1:1 magnification. The dimensions of the slitare 50 μm × 6 mm and the numerical aperture of the camera optics is 0.22. Toprovide a temporal reference, the reference laser beam was optically delayed andimaged on the streak camera slit; a trigger beam synchronized the streak camera.

605


606 Chapter 11

Figure 11.1 Schematic setup for time-resolved transillumination of female breast tissuein vivo (see Ref. 414).

The working principles of a streak camera and other instrumentation used in time-resolved techniques are described in detail in Refs. 427–429, 511, 538, and 540.

The temporal profile of the light intensity incident on the camera was recordedwith a time resolution of approximately 10 ps and displayed as a spatial profile.Precise shading correction and dark count subtraction were performed for eachmeasurement of the dispersion curve. For in vivo measurements, the probe laserbeam, with total power of 100 to 150 mW, was expanded to a diameter of 10 mm tokeep the power density below the maximum permissible exposure of 200 mW/cm2.

Normalized dispersion curves for three volunteers, T1, T2, and T3, and the cor-responding results of the theoretical fit according to the diffusion model [see Eq.(1.42)] are shown in Fig. 11.2. The dispersion curves range over a typical periodof 6 ns with a mean time-of-flight of more than 2 ns. Owing to the strong scat-tering and low absorption, most photons travel 10 times the geometrical distancethrough the compressed breast. The signals T1 and T2 (d = 45 mm) overcome thebackground noise for a time of flight of approximately 510 ps, which is more thantwice the minimum time of flight of a ballistic photon (refractive index of tissue:1.4). For a thicker tissue layer, T3 (d = 59 mm), this time shifts to 830 ps, whichis about three times longer than for ballistic photons.

Measurement at different positions of the breast reflects the influence of phys-iological alterations within different areas of the organ (different types of tissue;different blood volumes and oxygenation) and serves as a basis for diffuse opticalmammography [see Fig. 11.2(b)].538 The slightly different boundary conditionsand degree of compression, as well as the inhomogeneity of superficial tissue pig-mentation, can be critical for obtaining reliable mammograms. Table 7.1 presentsthe results of in vitro, ex vivo, and in vivo measurements of optical parameters ofthe human female breast and certain other thick tissues, conducted by the discussedmethods as well as some other optical techniques.


Time-Resolved and Spatially Modulated Spectroscopy and Tomography of Tissues 607

Figure 11.2 Normalized in vivo dispersion curves of the breasts of three volunteers (T1, T2,and T3; thickness d) and corresponding theoretical fit curves: Three breasts in one position(a); one breast in three positions (b) (see Ref. 414).

Algorithms for solving the inverse problem on the determination of μa andμ′

s by using Eqs. (1.41) and (1.42) can be successfully used not only for tissuespectroscopy but also for tomography. For tomography purposes, we are not ableto provide measurements of the absolute concentrations of absorbers and absolutevalues of the scattering coefficients (although this is desirable), which allow one toimplement these algorithms faster. Generally, the imaging is aimed at the detectionof pathology or at localization of lesions. The detection of a lesion is achieved byrecording a 2D image with sufficient contrast, while localization requires opticalslicing and tomographic reconstruction to obtain 3D images by which the size,shape, and position of the hidden object can be determined.413

Imaging systems usually use 2D or 3D scanning of a narrow laser beam or atranslation optical stage with the object attached. Nonscanning systems are morerobust, and correspondingly, fit medical applications much better. Such nonscan-ning systems use a multichannel fiber-optical arrangement with fixed positionsof light sources and detectors, or low noise, high sensitivity, and fast CCD cam-eras with multichannel plate optical amplification.1, 6, 511, 518, 538, 540 In any case, themeasurement procedure is completed by sampling the intensity of each pixel as afunction of time to obtain time–space intensity mapping. The image is numericallyreconstructed by attributing to each pixel the intensity measured over the selectedintegration time.413

A multichannel NIR imager/spectrometer based on the time-correlated single-photon counting technique was designed for breast imaging in clinics [seeFig. 11.3(a)].1907 The instrument uses two NIR wavelengths 780 and 830 nm, themean power of each laser diode is approximately 40 μW, and they pulse at 5 MHzwith a pulse width of approximately 50 ps. A highly sensitive R5600U-50 GaAsphotomultiplier was chosen for breast examination. For enhancement of the con-trast of carcinoma images, intravenous administration of Infracyanine 25 (IC25),


608 Chapter 11

Figure 11.3 Multichannel, time-correlated single-photon counting NIR imager/spectrometer: 1, two laser diodes; 2, a wavelength coupler; 3, 19:1 signal splitter;4, the reference branch; 5, 1 × 24 optical DiCon fiber-optics switch; 6, graded index,10-m-long optical fibers; 7, compression plates; 8, 8-step-index, 10-m long fiber bundles;9, PMT; 10, amplification unit; 11, router; 12, attenuator; 13, SPC-300 photon countingsystem using an SRT-8 8-channel multiplexer; 14, Intel Pentium PC; CFD, constant-fractiondiscriminator; MCA, multichannel analyzer; TAC, time-to-amplitude converter (a). Relativedisplacement of the light sources and detectors, positions of the projection plane, andpathology (carcinoma, black sphere) (b) (see Ref. 1907).

an NIR contrast agent, was used. Optical absorption changes were calculated byusing the following relation:

�μa = − 2

c�t2

t2∫t1

lnJ2(r, t)

J1(r, t)d t, (11.1)

where c is the speed of light in the medium; �t is the time resolution of thepulse-height analysis (PHA, Hamamatsu, Inc.) of the multichannel analyzer (MCA,Hamamatsu, Inc.); J1, J2 is the photon current measurement preinjection andpostinjection of IC25, respectively; and t1, t2 is the width of the J1 time-resolvedcurve. Equation (11.1) provides accurate values of �μa for small absorptionchanges.

The relative displacement of the light sources and detectors, and the posi-tions of the projection plane and pathology (carcinoma, black sphere) are shown inFig. 11.3(b). The calculation of absorption coefficient differences along the straightlines connecting those source–detector pairs in space that have comparable sep-arations [shown as diamonds in Fig. 11.3(b)] allows for the estimation of IC25distribution in tissue. Tests with patients were simultaneously conducted with thestandard MRI examination protocol.

Figure 11.4 illustrates the possibilities of time-resolved optical diffusionmammography in comparison with MRI. Measurements were conducted for apatient (70-year-old Caucasian) diagnosed with an infiltrating ductal carcinomaapproximately 10 mm in diameter. For the presented image, six sources and eight



Figure 11.4 MRI and NIR image coregistration. Sagittal fast spin echo (FSE) MRI slicefrom a 70-year-old patient with infiltrating ductal carcinoma (a). Spin echo (SE) MRI axialimage of the same patient (b). NIR projection image at 780 nm (c). NIR projection image at830 nm (d) (see Ref. 1907).

Figure 11.5 Schematic diagram of the MONSTIR imaging system: FS, fiber switch; VOA,variable optical attenuator; PF, polymer fiber; LPF, long-pass filter; MCP-PMT, multichan-nel plate-photomultiplier tube; PA, preamplifier; CFD, constant fraction discriminator; PTA,picosecond time analyzer; PD, photodiode; PTD, picotiming discriminator (see Ref. 524).


610 Chapter 11

detectors were employed. Satisfactory correspondence was observed between theMRI and NIR images. In the 780-nm light image, two objects were resolved, eitherdue to measurement noise or the actual physiology of the tissue. Owing to moreabsorption (12%) of IC25 at 780 than at 830 nm, expected differences should befurther enhanced.

A much more comprehensive time-resolved optical tomography systememploying 32 channels and designed for imaging of the neonatal brain and thehuman breast is shown in Fig. 11.5.524 This is the multichannel optoelectronic near-infrared system for time-resolved image reconstruction (MONSTIR). Light froma pulsed high-power picosecond laser source is switched sequentially into one of32 fibers, which are attached to the surface of an object under study. The detec-tion system is used to record the temporal distribution of light exiting the tissueat certain positions around the object with a temporal resolution of approximately80 ps and a rate of photon counting up to a few 105 per second per channel. Thisis accomplished by utilizing 32 fully simplex ultrafast photon-counting detectors.The scattered photons are collected by 32 low-dispersion, large-diameter (2.5-mm)fiber bundles, which are coupled to 32 stepper motor–driven variable optical atten-uators (VOAs). Because of the large dynamic range of light intensities around theobject, the VOAs are required to ensure that the detectors are not saturated or dam-aged and that the system operates within the single-photon counting mode. Lighttransmitted via VOA is collected by a short 3.0-mm-diameter single polymer fiber,and is then transmitted via a visible blocking filter to the photocathodes of fourultrafast eight-anode multichannel plate-photomultiplier tubes (MCP-PMT). Theresulting electronic pulse is preamplified and converted into a logic pulse, and a his-togram of photon flight times is recorded and transferred to the control computer. Adedicated image reconstruction software package, TOAST (Time-Resolved OpticalAbsorption and Scattering Tomography), is used for reconstruction of tomographicimages of the absorption and scattering profiles.543

A portable three-wavelength NIR time-resolved spectroscopic (TRS) system(TRS-10, Hamamatsu Photonics K.K., Japan) is available on the market.1908 Inthe TRS system, a time-correlated single-photon-counting technique is used fordetection. The system is controlled by a computer through a digital I/O interfaceconsisting of a three-wavelength (761, 795, and 835 nm) picosecond (about100 ps) pulsed light source, a photon-counting head for single photon detection,and signal-processing circuits for time-resolved measurement. The averagepower of the light source is at least 150 μW at each wavelength at a repetitionrate of 5 MHz. The instrumental response of the TRS system, which includes3-m-long light source fiber (graded index type single fiber with a core diameter of200 μm) and 3-m-long light detector fiber (a bundle fiber of 3-mm in diameter),is approximately 150 ps FWHM at each wavelength. This system was used forestimating the absorption and reduced scattering coefficients of the head in a piglethypoxia model.1908 Measurements of absolute values of absorption coefficientat three wavelengths enable the estimation of hemoglobin concentration and itsoxygen saturation in the head.



x

y

flaser synthesizer

synthesizerf + 100 Hz

synch

reference PMT

detector PMT

attenuator scatterer reference

absorbertissue

fiber measur. computer

100 Hz A/D100 Hz

Figure 11.6 Typical scheme of a frequency-domain light-scattering spectrometer or photondensity waves imaging system (if 2D scanning of irradiating and receiving fibers is provided)(see Refs. 1 and 3).

11.2 Frequency-Domain Techniques and Instruments

Considerable progress in investigation tissues and molecules of biological impor-tance with the use of the modulation technique has provided the foundationfor the development and commercial production of spectrometers of a newtype (for example, ISS Fluorescence & Analytical Instrumentation). A typi-cal scheme of the frequency-domain spectrometer for tissue study is shown inFig. 11.6.1–4, 6, 427–429, 437, 438, 511, 538, 540 Such systems for phase measurements use aheterodyning principle (two photomultipliers with heterodyning in one of the firstdynodes) to transfer a measuring signal to a low-frequency range (100 Hz for theshown system), where phase measurement can be conducted much more precisely.

We should also mention models of compact and comparatively cheapdevices—modulation spectrometers—for noninvasive quantitative determinationof oxygen saturation of blood hemoglobin, monitoring of optical parameters oftissues, and localization of absorbing or scattering inhomogeneities inside a tis-sue. Such spectrometers include diode lasers as radiation sources at one or twowavelengths and a photomultiplier with heterodyning in one of the first dynodes ora fast semiconductor photodetector with a high-frequency amplifier.429, 453, 454, 511

Specifically, NIM Incorporated produced a PMD 3000b two-wavelength spectrom-eter (with λ = 760 and 810 nm and a fixed modulation frequency of 200 MHz) fornoninvasive quantitative determination of oxygen saturation of hemoglobin.1909

Carl Zeiss Jena was the manufacturer of a more sophisticated and universal sys-tem, which operates at the wavelength of 685 nm with two fixed modulationfrequencies equal to 110 and 220 MHz. This system also includes a computer-controlled optical table, which ensures the regime of tissue transillumination.453, 454

A much simpler and more universal research system has been developed andmanufactured in Saratov University.547 This system includes quantum-well lasers


612 Chapter 11

(λ = 790 and 840 nm), which ensure a highly efficient low-noise modulationof laser radiation within the range of 100–1000 MHz; a set of optical fibers;and a computer-controlled optical table, which allows one to implement differ-ent geometric schemes in the experiment. The detection unit employs an avalanchephotodiode with a high-frequency amplifier (20 dB). The total dynamic range ofthe detection unit, along with a spectrum analyzer or network analyzer, is 70 dB.

Regarding medical devices, the requirements of a phase measuring systemare very high (better than 0.03 deg in a 2 Hz bandwidth) and similar to thoserequired by multifrequency, multi-wavelength optical fiber communication sys-tems [time division multiplex (TDM) and wavelength division multiplex (WDM)].4

Communication systems work at much higher modulation frequencies than med-ical systems, are well developed in their usage of digital equipment, and havea high degree of multiplexing. The last two features should be very useful fordesigning a new generation of medical equipment. Although the requirements formedical systems are currently quite modest (three wavelengths and two modula-tion frequencies), the appearance of the first generation of optical tomographs witha spatial resolution of approximately 1 cm−3 increases the need for multiplexingup to 16/32 channels. In the near future, for providing a resolution much less than1 cm−3, the use of 103 source–detection combinations is expected.4

Phase systems are divided into homodyne and heterodyne systems, whichmeans that they do not and do down-convert the radio frequency (RF), respec-tively, prior to phase measurements. Heterodyne systems have been termedcross-correlation or phase delay measurement devices (PDMDs). These devicesare intended to measure tissue optical properties (μa and μ′

s) to an accuracy of5% and hemoglobin saturation of 3% in the 40–80% range, requiring phase andamplitude precision as follows:4

• Phase and amplitude noise in a 2-Hz bandwidth should be less than 0.03 deg and0.1% of the total signal at a carrier frequency of 50−200 MHz.

• Source-to-detector attenuation may be more than 100 dB, with RF couplingcausing less than 0.03 deg phase error.

• Amplitude-phase crosstalk should be limited on the following level: a signalattenuation of 10 dB should not cause more than a 0.03 deg phase error.

• Multifrequency operation should not cause more than 0.03 deg phase interchan-nel crosstalk (at 50 dB attenuation).

• Optical multiplexing employing light sources of different wavelengths shouldcause less than 0.03 deg phase interchannel crosstalk.

• Bandwidth signal output should be variable from 0.2 to 2 Hz, or 40 Hz in specialcases of brain study.

• Sufficient information from multiple RF or multiwavelength operation shouldbe available.

Four types of PDMDs adapted to study tissue optical characteristics are pre-sented in Fig. 11.7.4 Two are homodyne [Figs. 11.7(a) and 11.7(b)] and two are



Figure 11.7 Four types of optical propagation delay measurement devices for tissue study:Homodyne systems (a, b); (a) has IQ demodulation, (b) a zero-crossing phase detector.Heterodyne systems (c, d); (c) is amplitude modulated and (d) is single sideband (SSB) withF1 as the RF oscillator and F2 as the local oscillator (audio); the upper sideband f1 + f2is used (see Ref. 4). LD, laser diode.

heterodyne [Figs. 11.7(c) and 11.7(d)]. The system in Fig. 11.7(a) uses an in-phase quadrature (IQ) demodulator; that in Fig. 11.7(b) uses a zero-crossing phasedetector. The system in Fig. 11.7(c) uses amplitude modulation at two close RF,f 1 and f 2, and that in Fig. 11.7(d) uses single sideband (SSB) modulation; f 1 is anRF and f 2 is an audio frequency; both systems have zero-crossing phase detectors.

A number of phase measurement systems are described in Refs. 1 and 4. Theamplitude measurements are relatively simple, but they do not always providethe required accuracy because, for example, of the influence of stray light. Phasemeasurements are amplitude independent and can be conducted with acceptableaccuracy. Moreover, multiwavelength phase measurements alone are sufficient toestimate such important quantities as hemoglobin concentration and its degree ofoxygenation. Simultaneous amplitude and phase measurements are used for thedetermination of absolute values of absorption coefficients.

The basic form of a homodyne system with an IQ demodulator is presentedin Fig. 11.7(a). Determining the phase shift path (the phase difference betweenthe reference oscillator and the signal pathway) involves a laser diode, an opti-cal detector, an amplifier, and a narrow band filter. The working principle of anIQ demodulator is shown in Fig. 11.8. It includes a 90-deg splitter (hybrid), twodouble-balanced mixers (DBMs) and a 0-deg splitter. In the demodulator, the car-rier (as reference signal) is recovered from an incoming modulated signal and fedto the 90-deg hybrid and the modulated signal (as the signal under test) to the 0-deghybrids.


614 Chapter 11

Figure 11.8 Diagram of IQ demodulator as a phase and amplitude detector (see Ref. 1910).

Functioning as a multiplier, the in-phase mixer produces an output:4, 1910

I(t) = sin(ωt) × 2A sin(ωt + ��) = A cos �� − A cos(2ωt + ��), (11.2)

where sin(ωt) is the carrier signal, 2Asin(ωt + ��) is the modulated signal, andthe phase delay, ��, is caused by the scattering medium.

The quadrature mixer produces an output:

Q(t) = cos(ωt) × 2A sin(ωt + ��) = A sin �� + A sin(2ωt + ��). (11.3)

In Eqs. (11.2) and (11.3), Asin�� and Acos�� are dc signals that carry infor-mation about amplitude (A) and phase (��) caused by light interaction with thescattering medium. Asin(2ωt +��) and Acos(2ωt + ��) are high-frequencycomponents that are blocked by using low-pass filters (LPFs); therefore, after fil-tration, such signals as Idc and Qdc are registered. The phase and amplitude causedby a medium can be found from equations:

�� = tan−1

(Qdc

Idc

), A = (

Q2dc + I2

dc

)1/2. (11.4)

For the backscattering geometry, such as that presented in Fig. 10.2, theanalytical expressions for �� and A in diffusion approximation are defined asfollows:4, 453, 454

�� = rsd

⎧⎨⎩

[(μac)

2 + ω2] 1

2 − μac

D

⎫⎬⎭

12

+ ��0, (11.5)

A =(

A0

4πDrsd

)exp

⎧⎪⎨⎪⎩−rsd

⎡⎣

[(μac)

2 + ω2] 1

2 + μac

2D

⎤⎦

12

⎫⎪⎬⎪⎭ , (11.6)



where rsd is the source–detector separation; ��0 is the initial phase due to theinstrumental response; A0 is the initial amplitude due to the instrumental response,D ≈ c/(3μ′

s); and c is the speed of light in the medium.For relatively small modulation frequencies, when ω < μac, the phase shift is

a linear function of frequency:

�� = rsdω

2 (Dμac)1/2 + ��0 ≈ rsdω

2c

(3μ′

s

μa

)1/2

+ ��0. (11.7)

For relatively large frequencies, when ω > μac (ω/2π ≤ 500 MHz),

�� = rsd

( ω

2D

)1/2 + ��0 ≈ rsd

(3ωμ′

s

2c

)1/2

+ ��0. (11.8)

A0 and ��0 can be calibrated by using a standard model (phantom) with known μ′s

and μa. Then, after calibration of the experimental setup, optical parameters of thetissue under study can be calculated from the measured amplitude and phase shifton the basis of Eqs. (11.5) and (11.6) using the following iteration formulas:

μa = r4sdω

2 − 4D2 (�� − ��0)4

4cD (�� − ��0)2 r2

sd

,

μ′ = c

3D− μa, (11.9)

D = − r2sdω

2 (�� − ��0)[ln (A) + ln

(4πDrsd

A0

)] .

Therefore, the homodyne system measures the phase difference betweenthe reference oscillator and the signal pathway. The analogue IQ detector (seeFig. 11.8) allows one to reach an accuracy of ∼0.2 deg in phase and ∼0.5 dBin amplitude, with carrier frequencies of 140 MHz.4, 1910

The heterodyne principle is characteristic for many communication systems.Because the error of the phase measurements decreases when oscillator frequencyslows and the bandwidth of a detector is constant, instruments designed for a low-frequency range may be more accurate. The nonlinear mixing of two signals withdifferent frequencies, f 1 and f 2, gives signals with sum and difference frequen-cies, one of which, namely ( f1 − f2), is selected, amplified, filtered, and coupledto a phase detector as a reference signal [see Fig. 11.7(c)]. Propagation of modu-lation signal f 1 through the optical system, biological tissue, optical detector, andamplifier/filter leads to phase and amplitude changes. The signal on intermediatefrequency [( f1 − f2), 1−100 kHz] is obtained from a second mixer and serves asthe measuring signal for the phase detector. The intermediate frequency should besufficiently high to avoid the 1/f noise problem and sufficiently low to excludehigh-frequency errors in zero-crossing phase detection. The drawback of the het-erodyne system is that the oscillators F1 and F2 must have phase coherence equalto the required system accuracy.


616 Chapter 11

The SSB system [see Fig. 11.7(d)] provides both efficient light modulationand efficient signal detection. It has important advantages: (1) the carrier modula-tion and the laser diode modulation are present only when the local oscillator (F2)activates the selected sideband (thus, convenient control of RF light modulation isavailable); (2) the local oscillator frequency can be in a convenient audio range; and(3) all RF power is in a single narrow band of frequencies set by the low-frequencyoscillation.

As an example, let us consider in more detail the functioning of a two-wavelength heterodyne IQ detection system, presented in Fig. 11.9.4, 1910 The two-wavelength NIR systems are usually used to detect hemoglobin saturation of livingtissue. Two RF signal sources are used and operate at slightly different frequen-cies, namely 140.00 and 140.01 MHz, which provide the driving signals for twolaser diodes with different wavelengths. The two laser beams are combined anddirected simultaneously with the fiber coupler to the tissue under study. The opti-cal signals collected from the tissue are fiber coupled to the PMT (or to severalPMTs). After passing an amplifier, two-wavelength optical signals simultane-ously enter each IQ demodulator (the signal differentiation is due to different RFfrequencies).

If channel 1 is characterized by the RF signal sin(ω1t) and the detected signalby 2A1 sin(ω1t + ��1), and channel 2 by sin(ω2t) and 2A2 sin(ω2t + ��2), thenIQ signals for each channel can be expressed as the following:1910

I1(t) = [2A1 sin (ω1t + ��1) + 2A2 sin (ω2t + ��2)] × sin (ω1t)

= A1 cos ��1 − A1 cos (2ω1t + ��1) + A2 cos [(ω1 − ω2) t + ��2]

− A2 cos [(ω1 + ω2) t + ��2] ,

Q1(t) = [2A1 sin (ω1t + ��1) + 2A2 sin (ω2t + ��2)] × cos (ω1t)

= A1 sin ��1 + A1 sin (2ω1t + ��1) + A2 sin [(ω1 − ω2) t + ��2]

+ A2 sin [(ω1 + ω2) t + ��2] ,

I2(t) = [2A1 sin (ω1t + ��1) + 2A2 sin (ω2t + ��2)] × sin (ω2t)

= A2 cos ��2 − A2 cos (2ω2t + ��2) + A1 cos [(ω1 − ω2) t + ��1]

− A1 cos [(ω1 + ω2) t + ��1] ,

Q2(t) = [2A1 sin (ω1t + ��1) + 2A2 sin (ω2t + ��2)] × cos (ω2t)

= A2 sin ��2 + A2 sin (2ω2t + ��2) + A1 sin [(ω1 − ω2) t + ��1]

+ A1 sin [(ω1 + ω2) t + ��1] .

(11.10)

This system uses two LPFs: one is a dc–1.9-MHz band to reject the high-frequency components (2ω1, 2ω2, ω1 + ω2) in each channel; the other is a dc–10-kHz band to block the low-frequency component (ω1 − ω2 = 10 kHz). Accordingto Eq. (11.10), such filtration allows one to separate the combined signal into twosignals for each wavelength, and each channel itself contains only I- and Q-signals[see underlined terms in Eqs. (11.10)]. However, it was shown experimentally that



Figure 11.9 Two-wavelength phase-modulated spectroscopy system operating at 140 MHzand using analogue IQ demodulation (see text for details and Ref. 4).

the third-order mixing effects influence low-frequency cross-correlation betweenchannels. The interchannel cross talk for a phase is less than 1.4 deg/dB and foramplitude is less than 3.8 mV/dB (phase or amplitude changes in one channelcaused by changes of amplitude in another).

For more effective separation of signals, an FFT analysis can be used. Amuch simpler solution is to use time-share control of the system. The computer-controlled time share ensures that at one time, only one wavelength of the opticalsignal passes through the whole system. In this way the interchannel cross talk canbe reduced for phases up to 0.1 deg/dB and for amplitudes up to 0.5 mV/dB.4

11.3 Phased-Array Technique

In NIR, the wavelengths of diffusive photon-density waves in tissues are equal to5–14 cm for modulation frequencies from 500 to 100 MHz [see Eqs. (1.53) and(1.54)]. This means that imaging resolution is low with the usual source and detec-tion combination, despite the high accuracy of phase and amplitude measurements.The photon-density wave interference method initially described in Ref. 459 (phaseand amplitude cancellation method, or phased-array method) is very promising forimproving the spatial resolution of the modulation technique.4, 53, 470

The concept of this method is illustrated in Fig. 11.10. It is based on the useof either duplicate sources and a single detector, or duplicate detectors and a singlesource, so that the amplitude and phase characteristics can be nulled and the systembecomes differential. If equal amplitudes at 0- and 180-deg phases are used as


618 Chapter 11

Figure 11.10 Geometry of amplitude and phase cancellation technique; two sources (S1and S2) and a single detector (D1), or two detectors (D2 and D3) and a single source (S3)(see Ref. 1913).

sources, appropriate positioning of the detector can lead to null in the amplitudesignal and crossover between 0- and 180-deg phase shifts, i.e., at 90 deg:

A sin(ωt + 0) + A sin(ωt + 180) = 2A cos(90) × sin(ωt + 90), (11.11)

where ω is the light modulation frequency.In a heterogeneous medium, the apparent null of the amplitude and crossover

of the phase may be displaced from the geometric midline (see Fig. 11.11). Thismethod is extremely sensitive to perturbation by an absorber or scatterer. A spatialresolution of approximately 1 mm for the inspection of an absorbing inhomo-geneity has been achieved and similar resolution is expected for the scatteringinhomogeneity. Another good feature of the technique is that at null condition,the measuring system is relatively insensitive to amplitude fluctuations common toboth light sources. On the other hand, inhomogeneities, which affect a large tissuevolume common to the two optical paths, cannot be detected. The amplitude sig-nal is less useful in imaging because the indication of the position is ambiguous

Figure 11.11 Demonstration of the existence of amplitude null and phase crossover fora phased-array measuring system used to study an adult human brain. The detector isscanned between two sources placed 4 cm apart and excited by 0 and 180 deg phase-shifted RF signals at 200 MHz (see Ref. 1911).



Figure 11.12 Single-wavelength (780 nm), 50-MHz phased-array, single sideband (SSB)phase modulation imaging system (see Ref. 1911).

(see Fig. 11.11). Although this can be compensated by further encoding, the phasesignal is robust and phase noise less than 0.1 deg (signal-to-noise ratio more than400) for a 1-Hz bandwidth can be obtained.4

The phase modulation system requires, for optimal results, SSB measuringtechnology [see Fig. 11.7(d)]. Nine sources and four detectors are used in the50-MHz single-wavelength (780 nm) phased-array imaging system presented inFig. 11.12.1911 The number of sources and detectors can readily be increased; fur-thermore, the number of source and detector combinations can be increased by sim-ply moving the source detector pad in two dimensions with respect to its originalposition by half the minimal distance between source and detector, equal to 2.5 cm.The image pad dimensions are 9 × 4 cm (see the upper left part of Fig. 11.12).

A local oscillator at 1 kHz modulates a 50-MHz SSB transmitter, the RFoutput of which is connected to a 0 deg/180 deg phase splitter/inverter, and thento nine switches appropriate to the nine light sources, which are sequenced at 0-and 180-deg phases by 1-Hz switches. The four PMTs are sequentially connectedto the 50 MHz SSB receiver (0.5 mV sensitivity), and the audio output at 1kHz is coupled to a zero-crossing phase detector to provide the phase signals insequence. The phase detector is coupled via a controlling computer to a computerfor image computation and display (not shown). The transmitter and receiver


620 Chapter 11

Figure 11.13 Image test for adult human brain (blonde hair) using the 50-MHz phased-array system presented in Fig. 11.12. Parietal stimulation for 48 s by touching a contralateralfinger was provided (see Refs. 1911 and 1913).

are phase-locked by RF coupling. The phase noise of the system is less than0.1 deg (1-Hz bandwidth). A complete set of data from 16 source and detectorcombinations is obtained every 16 s.

Figure 11.13 illustrates a single-wavelength (780 nm), 50-MHz phased arrayimage test of neurovascular coupling in a human brain. The image represents theincrements in phase shift caused by touching the contralateral finger. Calibrationwith models verifies that this signal is attributable to an increase in hemoglobinconcentration.1911

A more universal and comprehensive phased-array imaging system that can beused for testing the brain function of neonates is described in Ref. 1912. Single-wavelength laser diode light sources were replaced by a set of two laser diodes(750 and 830 nm, total of 18 lasers) with a 20-mW power source. The wavelengthof 780 nm was shifted to 750 nm because at 750 nm, the signal gain is more thandouble, owing to the respective extinction coefficients. Detection of the opticalsignals was provided by four PMTs (TO8, Hamamatsu). Two independent phasemeters and two SSB radio transmitters/receivers were used with 50- and 52-MHzfrequencies. The size of the optical probe is slightly larger (10 × 5 cm) becausetwo lasers are located in a point, but the source–detection separation was the same:2.5 cm (see Fig. 11.12). A dual-wavelength phased-array imaging system can beused for testing the brain function of neonates and its relationship with certain neu-rological disorders by monitoring metabolic activity, which is indicated by oxygenconcentration or glucose intake to the brain cells.

Another dual-wavelength imaging system (750 and 830 nm) that uses a sim-ple amplitude cancellation technique (see Fig. 11.11) was used to image a humanbreast.1913 The optical probe of the imager consists of nine laser diode light sourcesand 21 silicon photodetectors. The imager sequences through all sources and detec-tors in a millisecond and provides high-quality breast tumor images every 8 s. Asan example, in Fig. 11.14, four in vivo images of diseased and healthy breasts



Figure 11.14 Four in vivo images of diseased (with tumor) right breast with reference tothe contralateral breast (left, healthy) at 750 and 830 nm, and two calculated images:750–830 nm (deoxygenation image) and 0.3 × 750 + 830 nm (blood volume image) (seeRef. 1913).

are presented. Because different images are obtained between the right and leftbreast, many of the background signals are eliminated and strong signals congru-ent with the expected position of the tumor are displayed (no evidence of the nippleis presented and two shapes for blood volume and deoxygenation are clear).

The detection limit in localizing of macroinhomogeneities hidden in a highlyscattering tissue by using phased-array imaging systems is discussed in Ref. 430.

11.4 In vivo Measurements, Detection Limits, and Examples ofClinical Study

Let us briefly consider a few spectroscopy and imaging frequency-domain systemsthat demonstrate the achievements in the field of optical in vivo diagnostics andhave been applied for clinical studies. It was shown previously that for accurateevaluation of the absolute absorption and reduced scattering coefficients for asingle source–detection position, frequency-dependent measurements of the ampli-tude and phase of photon density waves should be provided. Therefore, to obtainquantitative measurements of the absolute optical parameters of various types oftissue, a portable, high-bandwidth (0.3–1000 MHz), multiwavelength (674, 811,849, and 956 nm) frequency-domain photon migration (FDPM) instrument wasdesigned432, 434 (see Fig. 11.15). The key component of an FDPM system is a net-work analyzer (8753C, Hewlett Packard) that is used to produce modulation sweepin the range 0.3–1000 MHz. The RF from the network analyzer is superimposedon the direct current of four different diode lasers using individual bias-tees andan RF switch. Four 100-μm diameter gradient-index fibers are used to couple each


622 Chapter 11

Figure 11.15 Multiwavelength, multifrequency, and multichannel frequency-domain spec-trometer (see Refs. 432 and 434).

light source to an 8 × 8 optical multiplexer (GP700, DiCon Instruments). Dynamicphase reference and real-time compensation for source fluctuations were providedby an optical tap, which diverts a portion of the source output (5%) to a 1-GHz PINdiode coupled to network analyzer channel B.

Light is launched onto the tissue under study using up to eight source fibers,corresponding to eight source positions. An APD (C5658, Hamamatsu) is used todetect the diffuse optical signal. Both the APD and probe end of the source opti-cal fiber are in direct contact with the patient’s skin surface. The optical powercoupled into the tissue averages approximately 10–30 mW, roughly a factor of 10below thermal damage threshold levels for these fibers and wavelengths. Up toeight separate sources can be directed onto up to eight unique measurement posi-tions by using the 8 × 8 optical multiplexer. Measurement time depends on therequired precision, the number of sweeps performed, and the RF/optical switchtime. For studies in human subjects, approximately 0.5 s is used to sweep overthe entire 1-GHz range of modulation frequencies. However, total elapsed time forfour laser diodes (two sweeps per laser), data transfer, display, and source switch-ing is approximately 40 s. The source–detector separation used for human subjectmeasurements was fixed and equal to 1.7, 2.2, or 2.7 cm.

The results of experimental study for three patients using the developed FDspectrometer are presented in Tables 7.1 and 11.1. Table 11.1 also lists the calcu-lated physiological parameters of living tissue, such as absolute concentrations ofdeoxy- and oxyhemoglobin, total hemoglobin, and water. It was assumed that thechromophores contributing to the absorption coefficient, μa, in the human subjectare principally oxy- and deoxyhemoglobin, and water. Therefore, the concentration


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624 Chapter 11

of each component in the tissue is determined from the FDPM measurements ofμa at three different wavelengths (674, 811, and 956 nm) in accordance with thefollowing system of three equations:432, 434

εHb(λi)cHb + εHbO2(λi)cHbO2 + εH2O(λi)cH2O = μa(λi), (11.12)

where εchrom. (λi) is the extinction coefficient, in units of cm−1mol−1, of a givenchromophore at wavelength λi,⎡

⎣ 6578300 740100 0.07481833100 2153900 0.4271500600 3048600 7.24

⎤⎦ ×

⎡⎣ cHb

cHbO2

cH2O

⎤⎦ =

⎡⎣μa(674)μa(811)μa(956)

⎤⎦ . (11.13)

Each column of this matrix contains values of extinction coefficients for each of thechromophores considered at three chosen wavelengths. The values of absorptioncoefficient at each wavelength are defined from experimental study.

This spectroscopy system can additionally be used as an imaging system. ManyFD imaging systems are described in the literature (see Refs. 1, 3, 4, 6, 427–429,466, 510, 538–540, 543, and 1914–1919). One was designed by the University ofPennsylvania and NIM, Inc., for regional imaging of brain tissue.1914 The systemcan operate at selectable RFs ranging from 50 to 400 MHz. A dual-wavelengthlight source (two laser diodes at 779 and 834 nm), APD photodetection, and SSBmodulation/demodulation electronics are the primary features of the imager. Itwas successfully used for a preliminary clinical study, i.e., the positions of theshunt components were defined on the basis of reconstructed images (at a depth of1.2 cm) of brain tissue of a patient with hydrocephalus (abnormal increase in theamount of CSF) who was undergoing surgery to have a shunt replaced.

A very stable and fast scanning imaging system that uses the diffraction ofdiffuse photon density waves is described in Ref. 447. The system consists of anRF-modulated (100 MHz), low-power (about 3 mW) diode laser (786 nm). Thesource light is fiber-guided to the tissue. A detection fiber couples the detected dif-fuse wave to a fast APD. SSB IQ demodulation electronics are used. The dynamicrange of the system is approximately 2500. The source position was fixed, a singledetection fiber was scanned over a square region 9.3 × 9.3 cm2, and the ampli-tude and phase of the photon density wave were recorded at each position for atotal of 1024 points. To obtain projection images of hidden macroinhomogeneitiesin a highly scattering tissue, imaging algorithms based on K-space spectral andFFT analysis were developed and clinically tested. The FFT approach has yieldedclinical projection images with processing times much smaller than current col-lection times. It was shown that boundary effects present important problems.Matching substances might be used to reduce the boundary effects; nevertheless,the boundary effects may be incorporated in the reconstruction algorithm.

A schematic diagram of an FD optical mammography apparatus (LIMA),developed at Carl Zeiss, is shown in Fig. 11.16.453, 454 It uses two diode lasers at 690and 810 nm. The intensities of these lasers are sinusoidally modulated at 110.0010and 110.008 MHz, respectively. The average power is approximately 10 mW. Both



Figure 11.16 Schematic diagram of a frequency-domain mammograph (LIMA) (see Refs.455 and 454).

laser beams (2 mm in diameter) are collimated, made collinear, and directed tothe object. An optical fiber (5 mm in diameter) located on the opposite side ofthe breast delivers light to the detector. A PMT with modulated gain at 110 MHzis used as a detector. The differences in frequencies of light and gain modulationare �f1 = 1 kHz (relative to the signal at 690 nm) and �f2 = 0.8 kHz (relativeto the signal at 810 nm), and are called cross-correlation frequencies. Appropriateelectronic filtering allows separation of signals at these frequencies, i.e., at the twowavelengths.

The breast is slightly compressed between two parallel glass plates. The dual-wavelength laser beam and detector fiber are scanned in tandem along the upperand lower plane, respectively, so that source–detection separation is fixed. Theentire compression assembly with the two glass plates can be rotated by 90 degto allow data to be acquired in craniocaudal and mediolateral projections. Theextension of the scanning step (image pixel size) can be established by software,but is generally defined by the spatial resolution required, the total acquisition time,and the signal-to-noise ratio. For this system, a scanning step of 1.5 mm in bothdirections requires a total acquisition time of approximately 3 min for a wholemammogram and experiences noise of approximately 0.2 deg for phase and 0.1%for amplitude measurements. The boundary effects were overcome by using anappropriate algorithm [N(x, y) function] based on the idea to explore the phaseinformation in a given pixel (x, y) for obtaining an estimate of the breast thickness


626 Chapter 11

in that pixel. As a second step, the dependence of the amplitude signal on tissuethickness was modeled by using the empirically determined dependence on thick-ness in the optically homogeneous case. The LIMA system was clinically tested on15 patients affected by breast cancer.

Two mammograms, x-ray and optical (810 nm), for a female left breast witha tumor are presented in Fig. 11.17. A comparison of these mammograms clearlyshows that this optical technique has good contrast and tumor detectability, ratherthan high spatial resolution, which is intrinsically limited by the diffusive natureof light propagation in tissue. The promise of optical imaging methods lies in theirhigh contrast, detectability, and specificity, which provide diagnostic capabilities.

Figure 11.17 X-ray (a) and optical craniocaudal (b) mammograms of a female left breastwith a tumor [55-year-old Caucasian woman with an invasive ductal breast cancer (laterallower quadrant; the major tumor is 3.0 cm in diameter]. X-ray and optical images can-not be compared point by point because the degree of compression and the compressiongeometry are different in the x-ray and optical measurements (see Refs. 453 and 454).



Further enhancement in contrast can be achieved by introducing additional lightsources, wavelengths, modulation frequencies, and/or multiple detectors (see abovediscussion). In addition to contrast enhancement, FD and TD methods have thepotential to provide an in situ optical biopsy by measuring localized opticalproperties.432, 433

One of the first phase imaging systems for in vivo studies was designed at theUniversity of Illinois at Urbana-Champaign.456 The optical signal at 760 nm fromthe mode-locked titanium-sapphire laser (Mira 900, Coherent) was modulated at160 MHz. Heterodyne mixing at the dynode chain of the PMT produces a cross-correlation signal (1.25 kHz) carrying the same phase and amplitude information asthe original signal. The imaging system provides subsecond data integration timesper pixel (104 total pixels, 8 × 8 cm2 grid in a gradation of 101 steps of 0.8 mmeach), resulting in a total measurement time of approximately 10 min. To partiallycompensate for limits on the detector’s dynamic range and reduce the influence ofboundary effects, the human hand under investigation was immersed in a highlyscattering aqueous solution of Liposyn III (20%) (an intravenous fat emulsion)with the scattering and absorption properties approximately matched to those ofthe hand by diluting the emulsion with water and serial additions of black India ink.

An FD tissue spectrometer, described in Ref. 431, uses an arc lamp as a lightsource that is intensity modulated at 135 MHz by a Pockels cell and heterodynemixing at the dynode chain of the PMT with a cross-correlation signal at 100 Hz.For typical signal levels, the noise in this system is dominated by photon shot noise.The effects of the noise can be minimized by using a phased-array configurationwith two detectors. For best results, signals from the two detectors should be equal-ized so that noise in the weaker signal is not dominant. The system can provide, atbest, approximately 4% uncertainty in μa and μ′

s if the signals at the two detectorsare equalized. Increasing the modulation depth and frequency allows for randomerrors to be further reduced up to approximately 1%.

Systematic errors caused by finite tissue volumes and curved surfaces can bemuch larger than random errors induced by shot noise. As discussed previously,these systematic errors can presumably be reduced if appropriate scattering andabsorbing immersion surrounding a substance is applied or sufficient informationabout the tissue geometry is available to justify the use of a more corrected algo-rithm.453, 454, 456 In vivo measurements made of the femoral biceps muscle of rabbitsshow that it is difficult to achieve shot noise limits in practice. The rms values forμa and μ′

s are typically 20% for a 15-s measurement time because the shot noisecontribution is estimated to be about 8% in μa and 4% in μ′

s. This means that othersources of variation (tissue blood content or oxygenation, tissue inhomogeneityduring scanning, finite source and detection size, or uncertainty in their relativepositions) with time were more important than the inherent instrument noise whendetermining the precision of the μa and μ′

s estimates.The results of measurements of absorption and reduced scattering coefficients

through the forehead on 30 adult volunteers using a multidistance FD NIR-spectrometer (Imagent, ISS, Champaign, IL) were reported.1916 The spectrometeremploys laser diodes modulated at the frequency of 110 MHz and PMTs whose


628 Chapter 11

gain is modulated at a slightly offset frequency of 110.005 MHz to heterodynethe high frequency down to the frequency of 5 kHz. In studies described in Ref.1916, 33 laser diodes (16 at 758 nm and 16 at 830 nm) and four PMTs were used.The laser diodes were multiplexed so that two lasers with the same wavelengthand at the same location were simultaneously activated. The light from the laserswas guided by optical fibers with a core diameter of 400 μm to the tissue surfaceand the photons reemitted from the tissue were collected simultaneously by thefiber bundles with a diameter of 5.6 mm, placed several centimeters apart fromthe source fiber. The collected light was carried to the PMTs, and then the signalsfrom the PMTs were digitally processed to yield the average intensity, modulationamplitude, and phase difference. These data were used for accurate estimation ofthe absolute absorption and reduced scattering coefficients of the adult brain. Itwas found that the adult head can reasonably be described by a two-layer modeland that the nonlinear regression for this model can be used to accurately retrievethe absolute absorption and reduced scattering coefficients of both layers if thethickness of the scalp/skull is known. For example, optical coefficients of the brainwere estimated at 830 nm as μa = 0.145 ± 0.005 cm−1 and μ′

s = 4.1 ± 0.1 cm−1.The hemoglobin concentration and oxygen saturation of the adult brain werealso calculated with sufficient accuracy to provide monitoring of cerebral oxygensaturation and hemodynamics to assess cerebral health related to tissue oxygenperfusion.

A portable, multiwavelength, FD, NIR spectroscopy instrument, similar to thatshown in Fig. 11.9, was used for investigating the optical properties of the brainin 23 neonates in vivo.1917 It was found that the absorption coefficients of theinfant forehead are lower than the values reported for adults; being averaged for23 infants, these coefficients were equal to μa = 0.078 ± 0.014 cm−1 at 788 nmand μa = 0.089 ± 0.019 cm−1 at 832 nm. A large intersubject variation in μ′

s wasalso demonstrated: μ′

s = 9.16 ± 1.22 cm−1 at 788 nm and μ′s = 8.42 ± 1.23 cm−1

at 832 nm. Physiological parameters derived from the absorption coefficients attwo wavelengths were determined as the following: the mean total hemoglobinconcentration was 39.7 ± 9.8 μM and the mean cerebral blood oxygen saturationwas 58.7 ± 11.2%. Therefore, it was shown that the bedside FD NIR spectroscopyprovided quantitative optical measurement of the infant brain.

Description of clinical and related research for pulsed imaging systems, includ-ing optical mammography and stroke monitoring, can be found in Refs. 527–531,1114, and 1920–1922.

11.5 Spatially Modulated Method

The background description of the spatially modulated imaging (SMI) method formeasuring tissue optical properties and imaging is given in Subsection 1.4.3. As aclinical trial to proof the method, in vivo measurements of the human forearm in thefield of view 72 × 48 mm were conducted.479 The measurements were performedfor four spatial modulation frequencies uniformly distributed over the intervalbetween 0 and 0.15 mm−1. The setup for SMI measurements is shown in Fig. 11.18.



Figure 11.18 SMI setup for studying tissues at different spatial frequencies by generationof a grayscale illumination pattern using a light source in combination with an SLM andCCD camera as a detector: NEC HT1000 is a commercially available digital projector, con-taining a digital micromirror-based DLP (Texas Instruments) and a UHP mercury lamp withremoved color filter wheel; bandpass filter is an interference filter for detection of a narrowwavelength band (λ = 640, 660, or 800 nm; ±10 nm FWHM); CCD camera (Roper Cascade512F, 16-bit, up to 30 fps for 512 × 512 pixels) (see Ref. 479).

Grayscale illumination patterns are generated using a light source in combinationwith a spatial light modulator (SLM). As shown in Ref. 479, a simple digital pro-jector, based on a digital micromirror-based digital light processing (DLP) lightengine and an ultrahigh-performance (UHP) mercury lamp can be used.

The projector’s color filter wheel should be removed for producing broadbandwhite light illumination of the sample, allowing one to use interference filters fordetection of a narrow wavelength band. To create the illumination patterns, 8-bitgrayscale bitmap images can be generated using MATLAB (Mathworks, Inc.), thenplaced in a PowerPoint (Microsoft, Inc.) presentation file for automatic sequenc-ing using the Microsoft Office ActiveX controls through an external LabVIEW(National Instruments, Inc.) program. The intensity of diffusely reflected light wascaptured by a 16-bit frame-transfer CCD camera (Roper Cascade 512F) capableof imaging up to 30 fps at full resolution of 512 × 512 pixels. As usual, specu-lar reflection is avoided by illuminating at a small angle to normal incidence. Formore precise filtering, including the selection of diffuse reflectance, crossed linearpolarizers can be added. This is especially useful for rough surfaces (such as skin),where specular light can be reflected at all angles.

The modular principle of the SMI system makes it very flexible and inexpen-sive. The field of view of the system is limited only by the magnification of theillumination and collection optics (with fundamental resolution limits establishedby the physics of light transport). Its spectral range can be chosen by appropriateselection of light source, SLM, and imaging sensor. For many applications, an SMIsystem has the potential to be very inexpensive by using widespread consumer-grade digital cameras and projection systems. The authors of Ref. 479 used a


630 Chapter 11

Figure 11.19 SMI technique: planar diffuse reflectance of the human forearm (a), maps ofreconstructed optical absorption (b) and reduced scattering (c) coefficients at λ = 640 nm;average multifrequency diffuse reflectance data and least-squares fit to Eq. (1.69) (d); andpixel histograms of absorption (e) and reduced scattering (f) maps (see Ref. 479).

research-grade 16-bit CCD system, but the required dynamic range for many appli-cations can be as low as 8 bits, depending on the required reflectance intensity (andthus, optical property) resolution.

For in vivo measurements of the diffuse reflection from a human forearm, abandpass detection interferential filter working at a wavelength of 640 ± 10 nmand crossed linear polarizers, which reject specular reflection from skin rough sur-face and maximize the sensitivity to the diffuse component of the light, were used(Fig. 11.19).

To demonstrate the sensitivity of the SMI system to physiological perturba-tions, a standard venous occlusion study was conducted on a 29 × 40 mm areaof the volar forearm (Fig. 11.20). The wavelength of 800 ± 10 nm was selectedfor measurements. Because it is close to the isosbestic point of the hemoglobinspectrum, 805 nm, hemoglobin oxygenation had little effect on the absorption,which was primarily determined by the blood volume. Diffuse reflection for 0 and0.135 mm−1 spatial modulation frequencies was measured every 4 s over intervalsof 13 min. After 2.5 min of baseline registration, an arm cuff was filled up with airto a pressure of 100 mm Hg for 6.5 min, then subsequently released at the ninthminute.

In Fig. 1.28 (middle), diffuse reflectance images (Rd) versus spatial frequency( f x) (maps) measured for the in vivo human forearm are presented. The increaseof differential contrast in diffuse reflectance as illumination frequency increases



Figure 11.20 SMI technique applied to venous occlusion data collection for the humanvolar forearm at 800 nm: diffuse reflectance map (left) and optical absorption coefficientmap (right) measured at the baseline (a), dotted lines in the reflectance map indicate theregions of interest for time-course analysis; region-wise average changes in optical absorp-tion (top) and reduced scattering (bottom) coefficients are shown for the whole imagefield (gray lines) and a region absent of any obvious large vessels (black lines) (b). Largeincrease in absorption observed in the microvascular region may be explained by the factthat the microvasculature is more susceptible to pooling, while the larger vessels are lessreactive (see Ref. 479). (See color plates.)

is clearly shown. This forms the basis for separate evaluation of absorption andscattering properties of tissue. In addition, modulation at high frequencies allowsfor sampling a more superficial region of the tissue; therefore, a lower contributionfrom deeper vascular features during probing on these frequencies is expected. InFig. 11.19, the recovered optical property maps, calibration, and statistics for mul-tifrequency MTF fitting at each pixel are shown, including the calibrated diffusereflectance at planar illumination, f x = 0 mm−1 [Fig. 11.19(a)]; spatial maps ofthe absorption [Fig. 11.19(b)] and reduced scattering [Fig. 11.19(c)] coefficients;averaged data for the diffuse reflectance at the four spatial frequencies and theresults of processing by the least-squares method using Eq. (1.69) of multifre-quency experimental data for each pixel [see Section 1.4; Fig. 11.19(d)]; and thecorresponding pixel histograms for absorption [Fig. 11.19(e)] and reduced scatter-ing [Fig. 11.19(f)] coefficients. Absorption contrast from the underlying veins is thedominant feature in the optical property maps. A vertical feature of lowered scatter-ing appears in the middle of the image that can be associated with a large superficial


632 Chapter 11

tendon, which may be acting effectively as a light guide owing to its generallyhigher index of refraction compared to soft tissue.169 Based on these experimentaland fitting data, it can be concluded that 1/e sampling depth ranges from 2 to 3.3mm for low (∼0 mm−1) and high (0.15 mm−1) spatial frequencies, respectively.

On the absorption map, a region containing a clearly visible vein is marked(dashed lines). In this region, there is 100% absorption contrast over the vein(0.46 mm−1) compared with the background (0.23 mm−1). At the same time, scat-tering within this area produces small contrast, only 10% spatial variations. Themeasurements of the diffuse reflection of the volar forearm at venous occlusionshown in Fig. 11.20 demonstrate the kinetics of changes in tissue blood volumethrough the measured values of the absorption coefficient at 800 nm. For the analy-sis, two spatial domains were selected: one for demonstration of global change overthe entire image, and the second only for a small area with no visible blood vessels,but where, as elsewhere, microvasculature is presented. Averaged over these areas,temporal changes in optical properties are shown in Fig. 11.20(b), where changesin the absorption (upper curves) and the reduced scattering (lower curves) coeffi-cients with respect to the baselines are shown. As expected, absorption increasesfor both regions at the beginning of occlusion (2.5 min), and then after removalof the occlusion at the ninth minute, there is a decay of the absorption that occursover the next ∼2 min. The maximal increase of absorption is ∼0.012 mm−1 for thewhole area, and 0.017 mm−1 to a region containing only the microvessels, whichcorresponds to increases of approximately 15% and 28% relative to the baseline.Greater increase in absorption observed in microvessel region can be explainedby the fact that the microvasculature is more susceptible to filling by the venousblood, while large vessels are less reactive. In the occlusion, slight fluctuations inthe scattering were also observed, which was <5% over the whole image and <2%in a small area without visible blood vessels.

Thus, the spatial modulation measurement platform for tissue studies allowsone to obtain quantitative full-field data for optical properties with submillimeterspatial resolution, and dynamic images of physiological disturbances, includ-ing hemodynamic response, at ischemic stroke.478, 479 For practical applicationsin medicine, the SMI method can be extended on the basis of multifrequencyimaging494 to quantify the functional mapping of endogenous and exogenouschromophores in tissues,476, 481, 482, 493 and to obtain images with depth resolution,including multilayer and tomographic approaches.494

In addition, Figs. 11.21 and 11.22 present further illustration of the effective-ness of the SMI method for in vivo fluorescence imaging following the quantitativedistribution of the photodynamic agent Protoporphyrin IX (PpIX) induced by ALAat application to the skin (volar forearm).493 The device optimally takes advantageof widely available digital projection technology and modular assembly principle.A LED-based digital micromirror device (DMD) (Texas Instruments) projectionsystem providing both structured illumination at discrete wavelengths (630, 730,and 850 nm) for the determination of optical properties and planar illumination forfluorescence over a 30 × 40 mm field of view was used. Reflectance and fluores-cence signals from the tissue were captured by a 12-bit CCD camera (Lumenera).



Figure 11.21 DMD (Texas Instruments) projection system for structured LED illuminationat discrete wavelengths (630, 730, and 850 nm) and planar illumination for fluorescence(over a 30 × 40 mm field of view) and a 12-bit CCD camera (Lumenera) for detection ofreflected light and fluorescence (see Ref. 493).

A cross-polarization scheme blocked specular reflections at spatial frequency-domain imaging (SFDI). For fluorescence, the analyzer should be replaced with along-pass filter with a cutoff at 650 nm. The image plane of the CCD was matchedto the same field of view as the projection. For SFDI measurements, six spatialfrequencies (0 to 0.5 mm−1) were projected at three spatially shifted phases (0,120, and 240 deg) per wavelength. Total acquisition times took ∼4 s, but wereallowed to vary to utilize the full dynamic range of the camera. An exposure of2 s was used to acquire fluorescence images as a practical measure.493 Quantitativedetermination of the optical parameters of the skin on the basis of SMI and anempirical model using the MC method allowed the authors493 to eliminate effectsof absorption and scattering on the detected fluorescence signal, and accordingly,to determine the concentration of PpIX with accuracy of ∼0.2 μg/ml. The methodwas applied for determination of the concentration of PpIX in normal human skinin vivo, for which a model-weighted concentration was found to be ∼1.6 μg/ml,which is in agreement with literature data.

As any method with spatial resolution,495 the SMI method is sensitive to thespatial anisotropy of the optical properties of tissues, which is especially importantfor the skin, muscle, tendon, and cartilage, which have a fibrous structure well-modeled as a set of infinite cylinders (see Chapters 2 and 3). The interaction of lightwith an infinite dielectric cylinder can be precisely described by electromagnetictheory,214 in the framework of which the direction cosine with respect to the axis ofthe cylinder does not change as a result of the scattering event, and the scatteringcross section varies with the direction cosine of the incident photon with respectto the axis of the cylinder.495 The cross section is maximal for perpendicular inci-dence and zero for parallel incidence. Its functional dependence with directionalcosine is defined by the collagen fiber diameter, the wavelength of light and rel-ative refractive index of the collagen, and the interstitial fluid. In tissues, there is


634 Chapter 11

Figure 11.22 Application of SMI technique for in vivo imaging of spatial distribution of ALA-induced PpIX in human volar forearm skin: image of skin tissue prior to topical applicationof ALA (a); raw fluorescence image (b); 7 h after application of ALA (scale bar: arbitraryunits); correction map (1/X1D) based on measured optical properties (c); and correctedfluorescence image (scale bar units: μg/ml) (d) (see Ref. 493). (See color plates.)

a distribution of fiber sizes and orientations; therefore, the functional dependenceshould be averaged over fiber sizes and orientations.

The authors of Ref. 483, based on a spatial Fourier domain solution to ananisotropic diffusion model that predicts the effects of bulk scattering orienta-tion on the amplitude and phase of the projected patterns, have introduced anew contrast function using a scattering orientation index (SOI). This index issensitive to the degree to which light scattering is directionally dependent. Usingtissue-simulating phantoms and ex vivo samples of muscle and brain, the authorsshowed that SOI is independent of the overall amount of bulk light scatteringand absorption, and that isotropic versus oriented scattering structures can beclearly distinguished. The orientation of subsurface microscopic scattering struc-tures located up to 600 μm beneath highly scattering tissue (μ′

s = 1.5 mm−1) canbe recognized.


Chapter 12

Polarization-SensitiveTechniques

In this chapter, polarization-sensitive techniques for imaging and functional diag-nosis of biological tissue are considered. Methods are described based on polariza-tion discrimination of a probe polarized light that is scattered by, or transmittedthrough, a tissue or a cell structure. The advantages of polarization methodsfor tissue imaging and functional diagnostics are discussed. It is shown thatpolarization-spectral selection of scattered radiation and polarization-fluorescencemethod significantly improve the diagnostic potential of the method.

12.1 Polarization Imaging

12.1.1 Transillumination polarization technique

The polarization discrimination of a light transmitted through a multiply scatter-ing medium may provide high-quality images of inhomogeneities embedded inthe scattering medium. Principles are described of transillumination polarizationdiaphanography of a heterogeneous scattering object.1923 This technique makesit possible to locate and image absorbing objects hidden in a strongly scatteringmedium. The method uses modulation of the polarization azimuth of a linearlypolarized laser beam and lock-in detection of the polarization properties of lighttransmitted through the object. The scattering sample was probed by an Ar-ionlaser beam. The orientation of the polarization plane of the probe beam wasmodulated by a Pockels cell as follows: during the first half-period of the mod-ulating signal, it was not changed, and during the second half-period, it was rotatedby 90 deg. Transmitted (depolarized) and forward-scattered (polarized) compo-nents of the probe light were collimated by two diaphragms and divided into twochannels by a polarizing beam-splitter. It was found that, in comparison with con-ventional diaphanography, polarization diaphanography allows shadow images tobe obtained of a hidden object in a scattering medium that is characterized by upto approximately 30 scattering events, on average.1923

635


636 Chapter 12

Figure 12.1 Scheme of the experimental setup for transillumination polarization imaging(see Ref. 196). 1, Linearly polarized beam of He-Ne laser (633 nm); 2, detector; 3, glass tankfilled by scattering medium (diluted milk); 4, absorbing half-plane; 5, polarizer; 6, analyzer;7, collimating diaphragms or light-collecting optical fiber; 8, chopper.

Polarization and conventional transillumination imaging were compared inRefs. 565–567 and 1853. The absorbing inhomogeneity, such as the absorb-ing plate placed in a scattering slab, was probed by a linearly polarized laserbeam (Fig. 12.1). The shadow images were reconstructed from the profiles of theintensity and degree of polarization, P, of the transmitted light (Fig. 12.2). Thedependencies of the degree of linear polarization on the edge position exhibit anincrease in P in the vicinity of the edge. The explanation for this peculiarity issimilar to that proposed by Jacques et al.595 for the polarization-sensitive detec-tion of backscattered light (see Subsection 12.1.2) and is connected with that nearthe absorber edge. The degree of polarization may be approximately doubled invalue (for a highly scattering media) because no I⊥ photons are scattered into theshadow-edge pixels by the shadow region, while I|| photons are directly scatteredinto these pixels. Better quality shadow images of the object are obtained withthe use of the polarization imaging technique in comparison with conventionaltransillumination.

12.1.2 Backscattering polarization imaging

The principle of polarization discrimination of multiply scattered light has beenfruitfully explored by many research groups in morphological analysis and visual-ization of subsurface layers in strongly scattering tissues.129, 135, 136, 138, 196, 588,590,

591, 594, 595, 669, 671,672, 676, 731, 1445,1527, 1544, 1565, 1853, 1924–1928 One of the most popularapproaches to polarization imaging in heterogeneous tissues is based on the use oflinearly polarized light to irradiate the object (the chosen area of the tissue surface)and to reject the backscattered light with the same polarization state (copolarizedradiation) by the imaging system. Typically, such polarization discrimination is


Polarization-Sensitive Techniques 637

Figure 12.2 Experimental dependencies of normalized intensity (a) and degree of linearpolarization (b) of transmitted light on the absorbing half-plane edge position at differentconcentrations of the background scattering medium (diluted milk) (see Ref. 196).

achieved simply by placing a polarizer between the imaging lens and the object.The optical axis of the polarizer is oriented perpendicularly to the polarizationplane of the incident light. Thus, only the cross-polarized component of the scat-tered light contributes to the formation of the object image. Despite its simplicity,this technique has been demonstrated to be an adequately effective tool for func-tional diagnostics and for the imaging of subcutaneous tissue layers. Moreover, theseparate imaging of an object with copolarized and cross-polarized light permitsthe separation of the structural features of the shallow tissue layers (such as skinwrinkles or the papillary net) and deep layers (such as the capillaries in derma).The elegant simplicity of this approach has stimulated its widespread applicationin both laboratory and clinical medical diagnostics.

A typical scheme of instrumentation for polarization imaging using the above-discussed approach is presented in Fig. 12.3. In the imaging system developed


638 Chapter 12

Figure 12.3 Instrument for selective polarization or spectral imaging of subsurface tissuelayers (a); copolarized (b) and cross-polarized (c) images of the human palm at 580 nmpolarized laser light illumination (see Ref. 1925).

by Demos et al.,1925 a dye laser with Nd-YAG laser pumping is used as theillumination source. The probe beam diameter is 10 cm and the average inten-sity is approximately equal to 5 mW/cm2. A cooled CCD camera with a 50-mmfocal length lens is used to detect backreflected light and capture the image. Thefirst polarizer, placed after the beam expander, is used to ensure illumination withlinearly polarized light. A second polarizer is positioned in front of the CCDcamera with its polarization orientation perpendicular or parallel to that of theillumination.

The efficiency of selective polarization imaging is illustrated in Fig. 12.3,where the co- and cross-polarized images of the human palm are presented.Fig. 12.3(b) illustrates a surface image (copolarized), where superficial skin papil-lary pattern is clearly shown. Additionally, Fig. 12.3(c) demonstrates a subsurfaceskin image (cross-polarized image).



A similar camera system, but one that uses an incoherent white light sourcesuch as xenon lamp, is described in Refs. 36, 595, and 1928, which present theresults of a pilot clinical study of various skin pathologies using polarized light(see Fig. 12.4). The image processing algorithm used is based on evaluation of thedegree of polarization, which is then considered as the imaging parameter. Twoimages are acquired: one parallel, I||, and one perpendicular, I⊥. These images arealgebraically combined to yield the polarization image:

PI = III − I⊥III + I⊥

(12.1)

In the polarization image, the numerator rejects randomly polarized dif-fuse reflectance, therefore, PI may be used to monitor tissue birefringence.Normalization by the denominator cancels the common tendency of PI to separatethe attenuation of polarization components due to tissue absorption, i.e., melaninpigmentation for skin.

The polarization images of pigmented skin sites (freckles, tattoos, or pig-mented nevi) and unpigmented skin sites (normalization by the denominatorcancels in the PI attenuation, which is common in individual polarization com-ponents due to tissue absorption, i.e., melanin pigmentation for skin) are analyzedto find the differences caused by various skin pathologies (see some examples inFig. 12.5).595 Additionally, the point-spread function of the backscattered polarizedlight is analyzed for images of a shadow cast from a razor blade onto a forearm skinsite. This function describes the behavior of the degree of polarization at the imag-ing parameter near the shadow edge. It was discovered that near the shadow edge,the degree of polarization approximately doubles in value because no I⊥ photonsare superficially scattered into the shadow-edge pixels by the shadow region, whileI|| photons are directly backscattered from the superficial layer of these pixels.

Figure 12.4 Prototype of polarization camera for skin examination (see Ref. 595). Incidentlight is linearly polarized in parallel to the scattering plane. An optical flat enforces a uniformskin/glass interface for reflection of glare away from the camera. Polarized and diffuselyscattered light reach the camera after passing through a linear polarizer that can be orientedparallel or perpendicular to the scattering plane.


640 Chapter 12

Figure 12.5 Comparison of white light (WLI) versus polarization (PI) images (see Ref.595). Freckle: polarization image removes the melanin from a freckle (a). Benign pigmentednevus: polarization image removes the melanin and shows apparent scatter, showing thedrop of polarized light reflectance from epidermis lining the hair follicles (b). Tattoo: polar-ization image lightens the “blackness” of the tattoo, and specular reflectance of polarizedlight off the carbon particles yields a strong image (c). Malignant basal cell carcinoma: whitelight image underestimates the extent of the skin cancer (d).

This result suggests that the point-spread function in skin for cross talk betweenpixels of the polarization image has an HWHM of approximately 390 μm.

Comparative analysis of polarization images of normal and diseased humanskin has shown the ability of the preceding approach to emphasize image con-trast based on light scattering in the superficial layers of the skin. The polarizationimages can visualize disruption of the normal texture of the papillary and upperreticular layers caused by skin pathology. Polarization imaging can be consid-ered as an adequately effective tool for identifying skin cancer margins and forguiding surgical excision of skin cancer [see Fig. 12.5(d)]. Various modalities ofpolarization imaging are also considered in Ref. 1929.

The evaluation of the quality of polarization images is based on the presenta-tion of multiply scattered light as a superposition of partial contributions charac-terized by different values of the optical paths, s, in the scattering medium.135, 1927

The statistical properties of the ensemble of partial contributions are described bythe PDF of the optical paths, ρ(s), whereas the statistical moments of the scatteredlight are represented by the integral transforms of ρ(s) with properly chosen ker-nels. The degree of polarization of multiply scattered radiation with initial linearpolarization can be approximately represented in the form of the Laplace transformof ρ(s):

PL = III − I⊥III + I⊥

≈ 3

2

∞∫0

exp

(− s

ξL

)ρ(s) ds, (12.2)



where III and I⊥ are the intensities of the co- and cross-polarized components ofthe scattered light, respectively. The parameter ξL is the depolarization length forlinearly polarized light.

By considering the polarization visualization of the absorbing macrohetero-geneity, with the degree of polarization of backscattered light as the visualizationparameter, the contrast of the polarization image can be defined as135

VP = PinL − Pback

L

PinL + Pback

L

, (12.3)

where PinL is the degree of residual linear polarization of the backscattered light

detected in the region of localization of the heterogeneity and PbackL is the analo-

gous quantity determined far from the region of localization. The contrast, VP, ofthe reconstructed polarization image can be represented as a function of the scat-tering layer thickness, l, the depth of inhomogeneity position, h, the transport meanfree path, ltr, of the scattering medium, the scattering anisotropy factor, g, and thedepolarization length, ξL.135 The PDF of the optical paths, ρ(s), can be obtained bya MC simulation.

To compare the efficiency of the various polarization imaging modalities, theexperimental setup shown in Fig. 12.6 was used.1853 The total normalized intensity(the intensity of the copolarized and cross-polarized components) or the degree ofresidual linear polarization of the backscattered light were used as the visualizationparameters. A scattering medium (a water–milk emulsion) in a rectangular glasstank (18 × 26 × 26 cm3) was used as a tissue model. The side and rear walls ofthe tank were blackened. The absorbing object (a rectangular plate with blackenedrough surfaces) was positioned in the central part of the tank at different h (1 to4 cm) from the transparent front wall. The probe white light was linearly polarizedperpendicular to the plane of incidence. To avoid specular reflection from the frontwall of the tank, the illuminating beam was directed at an angle of 30 deg relativeto the normal to the wall.

The object images for each of three chromatic coordinates (R, G, and B) werecaptured by using a color CCD camera (Panasonic NV-RX70EN) and a Miro DC20frame grabber (MiroVideo, Germany). The color 8-bit images of the object werecaptured with 647 × 485 resolution with the use of copolarized and cross-polarizedbackscattered light. The brightness distributions for each of the R, G, and B imagecomponents along an arbitrarily chosen line of the image [Fig. 12.6(b)] are appliedto reconstruct the images of the absorbing heterogeneity with different visualiza-tion parameters [Fig. 12.6(c)]. In the absence of a scattering medium, and hence,backscattered radiation, the image contrast is equal to zero. Increase in the milkconcentration first results in a sharp increase in the image contrast up to the max-imum value, with the subsequent monotonic decrease caused by the increase ofscattering multiplicity.

Comparison of the experimental data and MC simulations135, 1853, 1927 allowsone to conclude that maximal contrast in the polarization image is obtained atthe depth of an inhomogeneity position on the order of (0.25–0.6) ξL (depending


642 Chapter 12

Figure 12.6 Polarization imaging experiment (see Ref. 196). Schematic diagram: 1, cellwith a scattering medium; 2, absorbing plate; 3, white marker; 4, black markers; 5, polarizer;6, analyzer; 7, halogen lamp; 8, CCD camera; and 9, PC (a). Distributions of backscat-tered radiation intensity along an arbitrarily chosen line of the image for different volumeconcentrations of milk emulsion: 1, 0%; 2, 0.66%; 3, 1.96%; and 4, 5.51% (R-componentof the color image) (b). Dependencies of the polarization image contrast on the volumeconcentration of milk emulsion when the normalized intensity of the (1) unpolarized light,(2) copolarized, and (3) cross-polarized components, and (4) degree of polarization ofbackscattered radiation are used as the visualization parameters (c).

on the degree of residual polarization in the backscattered background compo-nent detected outside the region of the inhomogeneity localization). In particular,this conclusion agrees with data on polarization imaging of skin, which highlightsthe efficiency of polarization imaging for epidermis and upper layers of papillaryderma (100–150 μm).1928

12.2 Polarized Reflectance Spectroscopy of Tissues

12.2.1 In-depth polarization spectroscopy

Imaging and monitoring of the morphological and functional state of biologicaltissues may be provided on the basis of spectral analysis of polarization propertiesof the backscattering light.1930 Tissue probing by a linear polarized white light and



measuring of the spectral response of co- and cross polarized components of thebackscattered light allow one to not only quantify chromophore tissue content, butalso to estimate in-depth chromophore distribution.

In the visible wavelength range, skin may have a reduced scattering coefficientμ′

s ∼ 30–90 cm−1 and absorption coefficient μa ∼ 0.2–5 cm−1 (see Table 7.1), soexpected transport mean free path of a photon ltr = (μa + μ′

s)−1 [see Eq. (1.23)] is

in the range 100–300 μm. Because of the domination of scatterers with size, char-acterized by diffraction parameter ka > 1 [see Eqs. (2.54) and (2.55), Fig. 2.7 and2.8], the depolarization length, ξL, in skin is comparable with the transport scatter-ing length, ltr, and exceeds the thickness of skin epidermis. On the other hand, suchabsorbers as melanin in epidermis and hemoglobin in dermis must increase thedegree of residual polarization of the backscattered light in the spectral ranges cor-responding to absorbing bands of dominating chromophores. Moreover, these chro-mophores are placed on different depths, thus their localization may be estimatedowing to characteristic absorbing bands on differential polarization spectra.135, 1930

Figure 12.7 shows the experimental setup for the spectral measurements ofbackscattering polarization. Light from a white light source (halogen lamp of200 W) is guided to the object by a fiber bundle with the attached wideband lin-ear polarization filter. The diameter of the irradiated skin surface is approximately8 mm. The backscattered light from the skin is collected by another fiber bundle,to which a polarized filter is attached. This filter is variable and may change its ori-entation parallel or perpendicular to the optical axis of the first polarization filter.Fiber bundles are used to exclude some polarization sensitivity that may take placewith the use of monofibers. To exclude specular reflection from the skin surface,the detecting fiber bundle was placed under the angle of ∼20 deg with respectto normal to the skin surface. A distal end of the fiber was connected with thespectrometer.

This instrument is able to measure reflectance spectra at parallel and perpen-dicular orientations of filters, RII(λ) and R⊥(λ), respectively. From these spectra,differential residual polarization spectra, Pr(λ), or residual polarization degreespectra, Pr

L(λ), are calculated:

Figure 12.7 Scheme of the experimental setup for the backscattering polarization spectralmeasurements (see Ref. 1930): 1, white light source (halogen lamp, 200 W); 2 and 3, fiberbundles; 4 and 5, polarization filters; 6, object under study; 7, photodiode-array gratingspectrometer; 8, PC.


644 Chapter 12

�Rr (λ) = RII (λ) − R⊥ (λ) , (12.4)

PrL (λ) = RII (λ) − R⊥ (λ)

RII (λ) + R⊥ (λ). (12.5)

Two examples of in vivo human skin studies using polarization spectroscopy arepresented in Figs. 12.8 and 12.9.1930 Figure 12.8 demonstrates spectral distributionsof Pr

L(λ) of the backscattered light for different values of the index of erythemainduced by UV light. For a higher erythema index (EI) or skin redness (increasedblood volume), Pr

L(λ) is improved within the absorption Q-bands of the blood.

Figure 12.8 In vivo measured residual polarization degree spectra for a volunteer with UVinduced erythema of different degrees: 1, EI = 157; 2, EI = 223; 3, EI = 249; 4, EI = 275;and 5, EI = 290 (see Ref. 1930). Erythema index was measured using the erythema-melaninmeter described in Ref. 680.

Figure 12.9 In vivo measured differential residual polarization spectra for a volunteer atepidermal stripping of different thickness:1930 1, normal skin; 2, thickness of the removedskin layer is 40 μm; 3, 50 μm; 4, 60 μm; and 5, 70 μm.



This occurs owing to a reduction in the multiplicity of scattering for the photonswith wavelengths within absorption bands because of the more intensive absorp-tion of the photons with longer trajectories, which are initially responsible fordepolarization of light propagating in tissue.

Figure 12.9 presents differential polarization spectra, which are also sensitiveto absorption properties of skin that was controlled using a tape stripping technol-ogy. Less epidermal thickness is corresponding to a higher blood volume withinthe measuring volume (higher hemoglobin absorption). Therefore, despite the[RII(λ) − R⊥(λ)] value reduction within the blood absorption band central wave-lenghts (545 and 575 nm), due to attenuation of the both polarization components,its difference from the values measured far from the blood absorption bands, i.e.,in the range 650–750 nm, is significant to provide in-depth profiling of epidermalthickness and blood vessels in the skin.

As a criteria of epidermal thickness the following parameters can be used:1930

V545 = �Rr(650−700) − �Rr

545

�Rr(650−700) − �Rr

545

or V575 = �Rr(650−700) − �Rr

575

�Rr(650−700) − �Rr

575

. (12.6)

In these equations, indices 545 and 575 denote the differential residual polariza-tion backscattering coefficient at the wavelengths of hemoglobin absorption bandcenters (λ = 545 and 575 nm) and at the wavelength range, where hemoglobinabsorption is small (λ = 650–700 nm).

This method is still simple, and through gaining spectral information, it mayprovide more valuable information about living tissue than nonspectral polariza-tion methods described in Subsection 12.1.2. The experimental system is shownin Fig. 12.10. Monochrome images of the skin are captured by a VS-CTT 60-075video system (Videoscan Ltd., Russia). To achieve smoother white light irradiationof the skin surface and to avoid specular light detection, four 50-W halogen lampsdirected irradiation from four different sides at the angle ∼30 deg with respect tonormal to the skin surface. The output of each light source was filtered by identicallinear polarized filters, and in front of the monochrome CCD camera, a rotat-able polarization filter-analyzer is placed. Figure 12.11 shows an example of skin

Figure 12.10 Experimental setup for polarization-spectral imaging of in vivo tissues:1930

1, Tissue; 2, polarization filters; 4, polarization and interferential filters; 3, light sources;5, monochrome CCD camera; 6, PC.


646 Chapter 12

Figure 12.11 Polarization-spectral (λ = 550 nm) images of skin burn lesion of the volun-teer:1930 (a) a co-polarized image; (b) a crossed-polarized image; (c) degree of polarizationimage, Pr

L.

burn lesion polarization-spectral imaging at the wavelength of hemoglobin absorp-tion (∼550 nm). It is clearly shown that the maximal image contrast of ∼0.49 isprovided as a visualization parameter for polarization degree.

12.2.2 Superficial epithelial layer polarization spectroscopy

One promising approach to early cancer diagnosis is based on the analysis of a sin-gle scattered component of light perturbed by tissue structure (see Section 10.4).The wavelength dependence of the intensity of the light elastically scattered by thetissue structure appears sensitive to changes in tissue morphology that are typicalof precancerous lesions. In particular, it has been established that specific featuresof malignant cells, such as increased nuclear size, increased nuclear/cytoplasmicratio, and pleomorphism, are markedly manifested in the elastic light scatteringspectra of probed tissue. A specific fine periodic structure in the wavelength ofbackscattered light has been observed for mucosal tissue.272 This oscillatory com-ponent of light scattering spectra is attributable to single scattering from surfaceepithelial cell nuclei and can be interpreted within the framework of Mie the-ory. Analysis of the amplitude and frequency of the fine structure of the intensityspectrum allows one to estimate the density and size distributions of these nuclei.However, the extraction of a single scattered component from the masking multi-ple scattering background is a problem. Also, as discussed in Subsection 12.2.1,absorption of stroma related to hemoglobin distorts the single scattering spectrumof the epithelial cells. Both of these factors should be taken into account wheninterpreting the measured spectral dependencies of the backscattered light.

The negative effects of a diffuse background and hemoglobin absorption can besignificantly reduced by the application of a polarization discrimination techniquein the form of illuminating the probed tissue with linearly polarized light, followedby separate detection of the elastic scattered light at parallel and perpendicularpolarization states (i.e., the copolarized and cross-polarized components of thebackscattered light).216, 229 This approach, called polarized elastic light scattering



spectroscopy, or polarized reflectance spectroscopy (PRS), will potentially providea quantitative estimate not only of the size distributions of cell nuclei but also ofthe relative refractive index of the nucleus. These potentialities, which have beendemonstrated in a series of experimental works with tissue phantoms and in vivoepithelial tissues,135, 216, 229, 232, 272, 680, 1906 allow one to classify the PRS techniqueas a new step in the development of noninvasive optical devices for real-time diag-nostics of tissue morphology, and consequently, for improved early detection ofprecancers in vivo. An important step in the further development of the PRS methodwill be the design of portable and flexible instrumentation applicable to in situ tis-sue diagnostics. In particular, fiber-optic probes1931 with skin-related probing depthand high spatial resolution are prospective for clinical applications of polarizedreflectance spectroscopy for early skin cancer diagnostics.

12.3 Polarization Microscopy

Polarized light microscopy has been used in biomedicine for more than a cen-tury to study optically anisotropic biological structures that may be difficult, oreven impossible, to observe by using a conventional light microscope. Manycommercial microscopes are available on the market, and numerous investi-gations of biological objects have been made using polarization microscopy.However, modern approaches in polarization microscopy have the potentialto enable the acquisition of new and more detailed information about bio-logical cells and tissue structures. At present, it is possible to detect opticalpath differences of even less than 0.1 nm.234, 244, 249–270, 600, 1373, 1389, 1529, 1932–1934

Such sensitivity, as well as the capability to examine scattering samples, areattributable to recent achievements in video, interferential, and multispectralpolarization microscopy. Full Mueller matrix measurements and other com-bined techniques, such as polarization/confocal and polarization/OCT microscopy,promise new capabilities for polarization microscopy including in vivo measure-ments.135, 216, 229, 232, 362, 367, 602, 624,625, 628–634, 666–749, 1929–1940

In addition to Chapter 2 and Subsections 3.6.3 and 9.6.1, this section will dis-cuss only a few of the recent studies and novel techniques that have the potentialto examine the anisotropic properties of scattering samples. One example is themultispectral imaging micropolarimeter (MIM), which can detect birefringence ofthe peripapillary retinal nerve fiber layer (RNFL) in glaucoma diagnosis.234, 600 Theoptical scheme of MIM is presented in Fig. 12.12. Light from a tungsten-halogenlamp, followed by an interference filter (band of 10 nm), provides monochromaticillumination to an integrating sphere (IS). Lens L1 (F = 56 mm) collimates thebeam incident onto a polarizer (P). The use of an integrating sphere assures that theoutput intensity of the polarizer varies less than 0.2% as it rotates 360 deg. Lens L2

(F = 40.5 mm, NA = 0.13) focuses the image of the exit aperture of the integratingsphere onto a specimen (SP) in a chamber (CB) with flat entrance and exit win-dows. Lens L3 (F = 60 mm, NA = 0.07) focuses the specimen image onto a cooledCCD camera that provides a pixel size of approximately 4 μm on a specimen inan aqueous medium (magnification ≈5.8). Although the lenses are achromatic, the


648 Chapter 12

Figure 12.12 Optical scheme of the multispectral imaging micropolarimeter used in trans-mission mode (see Ref. 600). LS, light source; IF, interference filter; IS, integrating sphere;P, linear polarizer; SP, specimen; CB, chamber; L1, L2, and L3, lenses; C′, linear retarder;A, linear analyzer; CCD, charge-coupled device.

wide spectral range (440–830 nm) requires only small changes in the position ofdetection optics (moving the lens L3 and CCD together within a 0.5 mm range)to adjust the focus for each wavelength. A liquid crystal linear retarder (C′), fol-lowed by a linear analyzer (A), is used to measure the output Stokes vector ofthe specimen. Both polarizer and analyzer are Glan–Taylor polarization prisms.The azimuth and retardance of the retarder are set for a few discrete values, andthe azimuth of the analyzer is always fixed at 45 deg. Each setting of the retarder[respectively, azimuth and retardance: (1) 0, 90 deg; (2) 0, 200 deg; (3) 22.5, 207deg; (4) –22.5, 207 deg] is characterized by a 1 × 4 measurement vector. Together,the four retarder/analyzer settings are characterized by a 4 × 4 matrix, D, with eachrow corresponding to one measured vector.

A Stokes vector, S, can be calculated as

S = D−1R, (12.7)

where D−1 is the inverse of the measurement matrix and R is a 4 × 1 responsevector corresponding to the four retarder/analyzer settings.821 To evaluate the lin-ear retardance of a specimen, the Mueller matrix, M, should be found from themeasurements of the incident, Sinc, and output, S, Stokes vectors (see Chapter 2):

S = KM(ρ, δ)Sinc, (12.8)

where the factor K accounts for the losses of intensity in transmission and ρ andδ are the azimuth and retardance of the specimen, respectively. This expressionincludes four equations for the three unknowns, K, ρ, and δ. In most cases, it isuseful to overdetermine the system of equations in Eq. (12.8) by using more thanone Sinc.

The retardance and azimuth of RNFLs of living and fixed rat were measuredover a wide spectral range.600 It is found that the RNFL behaves as a linear retarderand that the retardance is approximately constant at a wavelength range from 440to 830 nm. The average birefringence measured for a few unfixed rat RNFLs,with an average thickness of 13.9 ± 0.4 μm, is 0.23 ± 0.01 (nm/μm) ≡ 2.3 ×10−4. The influence of the polarization properties of the retina on the measured



Figure 12.13 Estimated retardances (arrow length) and slow axes (arrow direction) of thebundle and gap areas of rat RNFLs (see Ref. 600). Images are at the wavelength of 440 nm.Image sizes: 222 × 199 μm (a); 187 × 177 μm (b). Nerve fiber bundles appear as brighterbands. Each arrow starts in the center of the measured area. Calibration bar is 1 nm ofretardance. White arrows represent measurements that are not corrected for retinal polar-ization ability and black arrows are corrected ones (a). Black arrows are corrected bundleretardances; white, small arrows in the gaps show the variation of residual retardances,also after correction (b).

anisotropic properties of RNFLs was found. Images presented in Fig. 12.13 illus-trate the importance of correcting for the polarization properties of the retina andfor the distributions of retardance and azimuth within the sample.

Another technique, which is related to quantitative polarized light microscopy,is based on a video microscopy technique applied to measure variations in theorientations of the collagenous fibers arranged in lamellae within eye corneal tis-sue.1932 The lamellar structure of the cornea and sclera is very visible in Figs. 3.3,3.4, and 3.5. Within a lamella, the fibrils are parallel, but the fibrils of adjacentlamellae do not generally run in the same direction. They may have a relativeorientation at any angle between 0 and 180 deg.

As was discussed in Section 3.6, in the corneal stroma, the fibrils have a diam-eter of 25–39 nm, while the mean diameter of scleral fibrils is equal to 100 nm.Therefore, the individual fibrils can not be resolved with ordinary light microscopy,but owing to the intrinsic birefringence of collagen fibrils and its dependence on theangle of their orientation from lamella to lamella, they can be recognized. Alongits fiber axis, collagen is highly birefringent, so the lamellae that are cut parallel tothe fiber axes [θ = 0 deg, see Fig. 12.14(a)] appear brighter under polarized lightwhen the polarizer and analyzer are crossed and the length of the tissue section isoriented at 45 deg to the polarizer/analyzer axis [see Fig. 12.14(b)]. Collagen is notbirefringent perpendicular to its fiber axis [θ = 90 deg, see Fig. 12.14(a)], so thoselamellae that are cut perpendicular to their fibril direction appear completely darkin this section [see Fig. 12.14(b)]. The variation in intensity along the X–Y tran-sect across the cornea section [see Fig. 12.14(b)] is caused by the different angularorientations of the particular lamella (in total, about 15 lamellae are visible) andpresented in Fig. 12.14(c).

Because of the regular arrangement of the lamellae, only angle θ is necessary todefine the 3D orientation of the fibrils in sections of normal cornea. Nevertheless,to determine this angle distribution for a specific tissue section, it is necessary


650 Chapter 12

Figure 12.14 Polarization microscopy of a collagenous tissue structure (see Ref. 1932).Schematic diagram of a tissue section containing three lamellae (the number of fibrils isgreatly reduced and the relative fibril diameter greatly exaggerated; an actual electronicmicrograph is shown in Fig. 3.4); angle θ is the angle of inclination of the fibrils relative tothe plane of sectioning (a). Digital photomicrograph of a section through part of a rabbitcornea viewed under polarized light (×500) (b). Variation in intensity along the x–y transectacross the cornea section of the photomicrograph in Fig. 12.14(b) (c).

to account for the lamellar birefringence of form that contributes approximately67% to the total birefringence.1932 For sections of disrupted pathological corneaand those of sclera and limbus (the region at which the cornea and sclera fuse),the situation is more complicated because the lamellae have a much less ordered,“wavy” arrangement [see Fig. 3.6(b) for sclera].

Many tissues possess very complex patterns of alignment of the structure-forming elements. Some promising polarization-microscopic methods for generat-ing alignment maps for such tissues have been developed (see, for example, Refs.1935–1937). The method presented in Refs. 1935 and 1936, as well as that used inRef. 1932, is a useful tool for cases in which the tissue structure along the direc-tion of probing light propagation can be considered to be uniform. In Refs. 1935and 1936, a microscopic polarimetry method for generating fiber alignment maps,which can be used for characterizing the structure of fibrous tissues, tissue phan-toms, and other fibrillar materials, is considered. This method is based on probingthe sample with elliptically polarized light from a rotated quarter-wave plate andan effective circular analyzer. Nonlinear regression techniques are implementedfor estimating the optical parameters of the optic train and the sample. Processingthe sequence of images obtained with different mutual orientations of the rotatedquarter-wave plate and the analyzer, which is based on the fast harmonic analy-sis, permits the recovery of an alignment direction map and a retardation map.These maps describe spatial distribution of a sample’s local linear birefringence,and therefore, can be used for morphological analysis of tissues with an expressed



structural anisotropy that have linear birefringence as their dominant optical prop-erty. The potential of this method for accurately generating alignment maps forsamples that act as linear retarders to within a few degrees of retardation, has beendemonstrated in experiments with an in vitro sample of a porcine heart valve leaflet.

The method proposed in Ref. 1937 can also be used in more general situationswhen the orientation of the structure-forming elements (for instance, the colla-gen fibers) varies along the probing direction. These variations should be takeninto account when thick (>50 μm) tissue layers (e.g. dermis) are analyzed. In thediscussed method,1937 a standard polarization microscope arranged with a CCDcamera can be used. The measurements are usually conducted with wide-spectral-range color filters and without a quarter-wave plate. The following expressiondescribes the dependence of the detected signal at any detection point on the anglesof orientation of the polarizer (ϑ) and the analyzer (ϑ′) of the microscope:

iC ≈ B0 + B1 cos η + B2 cosσ + B3 sin η + B4 sinσ,

η = 2(ϑ − ϑ′), σ = 2

(ϑ + ϑ′), (12.9)

where Bi (i = 0, 1, 2, 3, and 4) are the coefficients that depend on the local opticalproperties of the sample in the probed region and the spectral properties of incidentlight. As shown in Ref. 1937, the measured values of Bi are capable of providingimportant information about the sample structure. They can also be used for thecharacterization of specific features of light propagation in the sample; in particu-lar, they allow us to recognize the so-called adiabatic regime of light propagationin the studied medium. This means that in the adiabatic regime, the orientationof the local optical axis changes smoothly in the probed region of the tissue. Forfibrous tissues, the direction of the local optical axis typically coincides with thelocal preferred direction of fiber orientation. If the adiabatic regime is realized,then the angles υ and φ, which are calculated from the obtained values of Bi

as υ = (1/4)tan−1(B2/B4) and φ = (1/2)tan−1(B1/B3), provide information aboutthe structure of the sample. Angle φ is equal to the angle between the azimuthalprojections of the local optical axes of the medium at the upper and lower bound-aries of the sample, and angle υ defines the orientation of the bisector of the anglebetween these projections. Analysis of the experimentally obtained “Bi-maps,” aswell as the spatial distributions of υ and φ, can be proposed as an effective tool fortissue structure characterization.1937 In particular, the B0-map (this coefficient char-acterizes the local transmittance of the sample for nonpolarized light), the υ-map,and the φ-map for the in vitro sample of human epidermis (stratum corneum) arepresented in Ref. 1937.

The study of collagen structure and function is important for understandinga wide range of pathophysiological conditions, including aging. One prospectivelaser technique, which can provide in vivo microscopic monitoring of colla-gen structure, is polarized SHG microscopy (see Section 8.7 and Subsection9.6.5).1570, 1575 The backscattered SHG signal induced by a 100 fs titanium-sapphirelaser, with a mean wavelength of 800 nm, a maximum energy of 10 nJ, and apulse repetition rate of 82 MHz, was measured by a polarized SHG scanning


652 Chapter 12

confocal microscope.1575 The microscope objective has a transverse resolution ofapproximately 1.5 μm and an axial resolution of approximately 10 μm. Inside thescattering media, both numbers increase. The maximum intensity in the sample wasapproximately 4 × 1011W/cm2. To avoid sample damage, a continuous scanningtechnique was used. A systematic analysis of type I collagen in a rat-tail tendon fas-cicle was conducted by using this microscope. Type I collagen from the fasciclesprovides one of the strongest SHG signals of all of the various tissues analyzedby the authors in Ref. 1575. They hypothesize that such high SHG efficiency isattributable to the collagen’s highly ordered architecture. The polarization prop-erties of collagen are also defined by its ordering. It was shown experimentallythat the second harmonic signal intensity varies by about a factor of 2 across asingle cross-section of the rat-tail tendon fascicle.1575 The signal intensity dependsboth on the collagen organization and the backscattering efficiency. To characterizecollagen structure, both intensity and polarization dependent SHG signals shouldbe detected. Actually, axial and transverse scans for different linear polarizationangles of the input beam show that SHG in the rat-tail tendon depends strongly onthe polarization of the input laser beam. In contrast to SHG signal intensity, thefunctional form of the polarization dependence does not change significantly overa single cross-section of the sample and is not affected by backscattering efficiency.

The measured data agreed well with an analytical model developed for an SHGsignal at linear polarized excitation and were used to determine the fibril orien-tation and the ratio between the only two nonzero, independent elements in thesecond-order nonlinear susceptibility tensor, γ ≈ – (0.7−0.8).1575 The small rangeof values observed for γ in a tendon fascicle suggests that there is structural homo-geneity. This parameter might, therefore, be useful in noninvasively characterizingdifferent collagen structures.

The primary problem encountered in the in situ microscopy of tissues is multi-ple scattering, which randomizes the direction, coherence, and polarization state ofincident light. Many optical gating methods have been proposed to filtrate ballisticand least-scattering photons, which carry information about the object structure.One of these is the polarization gating method and its modifications, which aredescribed in this chapter, Chapter 2, and Subsections 3.6.3 and 9.6.1. The funda-mental limitation of all optical gating methods, including the polarization method,is that only a small number of ballistic and least-scattering photons take part inthe formation of an object image. Therefore, polarization-gating techniques incombination with image reconstruction methods can be useful for improving theimage resolution in the case of a highly scattering object.1238, 1239 Both reflection-mode and transmission-mode polarization gating scanning microscopes have beenanalyzed.1238, 1239

An optical immersion technique, based on matching the refractive index of thetissue scatterers with the surrounding ground (interstitial) medium, allows one toessentially control the scattering properties of a tissue (see Chapter 9). Usually,the refractive index of the ground medium is controlled. This is accomplished



by impregnating the tissue with a biocompatible agent, such as glucose, glycerol,propylene glycol, or x-ray contrasting agents. Because the refractive index of theapplied agent is higher than that of the tissue ground substance, which is similarto the index of water, the refractive index of the ground increases and scatteringdecreases. Most of the applied agents are hyperosmotic; therefore, they can pro-duce temporal and local dehydration of the tissue, which also leads to an increasein the refractive index of the interstitial space. Figures 9.35 to 9.38 show experi-mental results on the temporal transmittance of linear polarized light through tissuesections, measured by a white-light video-digital polarization microscope or polar-ization spectrometer on the application of an immersion agent (x-ray contrastingagent, trazograph-60, or glycerol).621, 622, 654, 1578, 1697, 1726

Reduction of scattering at optical immersion makes it possible to more eas-ily detect the polarization anisotropy of a tissue and to separate the effects oflight scattering and intrinsic birefringence on tissue polarization properties. It isalso possible to study birefringence of form with optical immersion, but whenthe immersion is strong and the refractive index of tissue birefringent structureis similar to the index of the ground media, the birefringence of form may betoo small to be detected (see Fig. 9.38, showing that complete refractive indexmatching at the edge region causes tissue to lose not only scattering, but alsobirefringence). The kinetics of tissue optical clearing and the manifestation of tis-sue anisotropy upon the reduction of scattering are characteristic features, whichcorrelate with clinical data.555, 621, 622 Figure 9.10 illustrates the reversibility ofthe optical immersion effect in controlling the polarization properties of a turbidtissue.555 Practically all healthy connective and vascular tissues show the strongor weak optical anisotropy typical of either uniaxial or biaxial crystals.621, 622

Pathological tissues show isotropic optical properties.Polarization microscopy is also helpful for investigating individual cells, par-

ticularly for evaluating the amount of glycated hemoglobin in erythrocytes thatcan be an early diagnostic marker of hyperglycemia in diabetic patients.1389

Hemoglobin glycation causes changes in the cell’s refractive index. By usingpolarizing-interference microscopy, it is possible to measure the light refractiveindex in an individual erythrocyte. The refractive index of hemoglobin or anRBC, containing approximately 95% hemoglobin, varies approximately linearlywith a change in glucose concentration—it saturates only under strong hyper-glycemic conditions.1387, 1388 A Nomarsky polarizing-interference microscope,MPI-5 (Poland), was used for measurements of light phase retardation.1389 Usinga Wollaston prism mounted on an object, erythrocyte images for ordinary andextraordinary light beams were completely separated. In the thickest erythrocyteregion, the first interference maxima were visually adjusted to an eye-sensitive pur-ple color for ordinary and extraordinary images by shifting the second Wollastonprism placed in the rear focus of the object. For each erythrocyte measured, theWollaston prism displacement rendered a second value. From the whole interfer-ence bandwidth, h, and the measured Wollaston prism displacement, 2d, the phaseretardation, �, and the refractive index, n, were calculated for each erythrocyte:1389


654 Chapter 12

n = nv + �

t= nv + dλ

ht, (12.10)

where nv = 1.5133 ± 0.0001 is the refractive index of the embedding media; tis the thickness of the erythrocyte; λ = 550 nm. Separate measurements of theerythrocyte thickness using two embedded media with different refractive indicesgives t = 0.89 μm. Using this value, the refractive index is calculated with astandard deviation of ±0.0005.

A robust z-polarized confocal microscope employing only one or two binaryphase plates with a polarizer has been suggested by Huse et al.1940 The majoradvantage of a microscope having a significant longitudinal field component is thatit is possible to image the z-polarized features in randomly oriented agglomerationsof molecules of biomedical interest.

12.4 Digital Photoelasticity Measurements

Photoelasticity is an established experimental technique that has been applied tostudy the biomechanics of hard tissues like bone and tooth.1941, 1942 The photoe-lastic measuring technique is based on the stress-induced optical birefringenceeffect, which for plane stress analysis is described by the following stress-opticlaw:1941, 1942

σ1 − σ2 = θ

2π

fσh

= Nfσh

, (12.11)

where (σ1 – σ2) is the difference in the in-plane principle stress; θ is the resultantoptical phase generated due to stress-induced birefringence in the sample; fσ is thematerial fringe value; and h is the thickness of the specimen. Because the values offσ and h are constants for the mechanical stresses, recording the optical phase (θ)or fringe order (N = θ/2π) at every point of interest on the fringe pattern allows foranalysis of the stress distribution.

As an example, we will consider the results of photomechanical studies ofpost-endodontically rehabilitated teeth, using a conventional circular polariscopeand an image processing system, which were the basis for the digital phase shiftphotoelastic technique described in Refs. 1941 and 1942. A special loading devicethat applies loads along the long axis (0 deg) and 60 deg lingual to the long axisof the tooth was employed. Using the polariscope, four phase-stepped images wereobtained for the sample at each load by rotating the analyzer at 0, 45, 90, and 135deg angles with respect to the polarizer. The fringe patterns obtained were acquiredusing a CCD camera, stored, and processed by a computer. The four images wereevaluated using a phase stepping algorithm to obtain a wrapped phase map.1941

Phase unwrapping was conducted on selected lines to make the fringe modulationcontinuous and to gather information on the nature of the stress distribution.

Figure 12.15 shows a phase wrapped image of the rehabilitated tooth model,loaded at 125 N at an angle of 60 deg in the direction of the long axis of the tooth.It was found that there is a significant (up to threefold) increase in the magnitude ofthe stress within the rehabilitated tooth model in comparison with the model of the



Figure 12.15 Phase-wrapped image obtained from four-phase shifted images in a rehabil-itated tooth model, loaded at 125 N, 60 deg lingual to the long axis of the tooth (see Ref.1942).

intact tooth. Increased bending stress is identified in the cervical region and in themiddle region of the root. This results in higher compressive stress in the cervicalregion (facial side) and higher tensile stress in the middle region (lingual side).The designed digital phase shift photoelastic technique is of importance for theinvestigation of hard tissue elasticity distributions; here, for instance, it highlightedthe behavior of a postcore rehabilitated tooth to functional forces.

12.5 Fluorescence Polarization Measurements

Fluorescence polarization measurements are used to estimate various parametersof the fluorophore environment;1057 therefore, they have a potential role to playin biomedical diagnosis, particularly in discriminating between normal and malig-nant tissues.602, 1527, 1528, 1943–1950 At polarized light excitation, the emission from afluorophore in a nonscattering media becomes depolarized because of the randomorientation of the fluorophore molecules and the angular displacement between theabsorption and emission dipoles of the molecules.1057 These intrinsic molecular


656 Chapter 12

processes that result in additional angular displacement of the emission dipolesare sensitive to the local environment of the fluorophore. As already discussed inpreceding chapters, light depolarization in tissues is determined by multiple scat-tering; therefore, both excitation and emission radiations should be depolarizedin scattering media.602, 1057, 1943–1950 Polarization state transformation in scatteringmedia depends on the optical parameters of the medium: the absorption coeffi-cient, μa, the scattering coefficient, μs, and the scattering anisotropy factor, g. Dueto the different structural and functional properties of normal and malignant tis-sues, the contribution of multiple scattering to depolarization may be different forthese tissues. The reduced (transport) scattering coefficient, μ′

s, or the TMFP, ltr, inparticular, determines the characteristic depolarization depth for different tissues.Thus, fluorescence polarization measurements may be sensitive to tissue struc-tural or functional changes, which are caused, for instance, by tissue malignancyat the molecular level (the sensitivity of excited molecules to the environmentalmolecules) or at the macrostructural level (the sensitivity of propagating radiationto tissue scattering properties).

Mohanty et al.1945 considered a fluorophore located at distance z from the sur-face of a turbid medium. The homogeneous distribution of the fluorophores and thevalidity of the diffusion approximation for light transport in a scattering mediumwere assumed. The average number of scattering events experienced by the excita-tion light before it reached the fluorophore, and by the emitted light before it exitedthe medium, are described, respectively, as

N1(z) = z × μexs , (12.12)

N2(z) = z × μems . (12.13)

The fluorescence polarization ability is characterized by polarization anisotropy, r,which is a dimensionless quantity independent of the total fluorescence intensityof the object:1057

r = I|| − I⊥I|| + 2I⊥

. (12.14)

It is defined as the ratio of the polarized component to the total intensity and isconnected with the light polarization value, P:

r = 2P

3 − P. (12.15)

The polarization, measured as

P = I|| − I⊥I|| + I⊥

, (12.16)

is an appropriate parameter for describing a light source when a light ray is directedalong a particular axis. The polarization of this light is defined as the fraction oflight that is linearly polarized. In contrast, the radiation emitted by a fluorophore



is symmetrically distributed around this axis, and the total intensity is not given byI|| + I⊥, but rather by I|| + 2I⊥ (see Section 10.4 of Ref. 1057).

Assuming that each scattering event reduces the fluorescence polarizationanisotropy, r, by a factor of A (A = 0–1), the anisotropy of fluorescence that isattributable to a fluorophore embedded at a depth z can be written as

r(z) = r0 × A[N1(z)+N2(z)], (12.17)

where r0 is the value of fluorescence anisotropy with no scattering. For a homoge-neous distribution of fluorophores in a tissue of thickness d, the observed value ofthe fluorescence anisotropy is defined by each ith tissue layer:

robs =∑

i

(Ifi ri)

/ ∑i

Ifi , (12.18)

where Ifi is the contribution to the observed fluorescence intensity from the ith layer

of thickness dz at a depth, z, and ri is the value of the fluorescence anisotropy forthis layer.

For the broad-beam illumination of a flat tissue surface, the propagation ofexcitation (ex) light beyond a few MFPs [MFP ≡ lph = μt

−1, μt = μa + μs, seeEq. (1.8)] is well described by one-dimensional diffusion theory. In this approx-imation, and taking into account μex

t >> μexeff [see Eq. (1.18)], which is valid for

many tissues, the excitation intensity reaching depth, z, is expressed as

I(z) ∼= Cex exp(−μexeffz), (12.19)

where Cex is proportional to the excitation intensity and is a function of the tissueoptical parameters at the wavelength of the excitation light.

Therefore, the fluorescence from the fluorophores, embedded at depth z fromthe tissue surface, reaching the same surface will be

If(z) ≈ [Cex exp(−μexeffz)] ×ϕ[Cem exp(−μem

eff z)], (12.20)

where Cem and μemeff for the emission wavelength are defined similarly as Cex and

μexeff for the excitation wavelength, and ϕ is the fluorescence yield.

By substituting the values of Ifi from Eq. (12.20) and ri from Eq. (12.17) in

Eq. (12.18), the observed fluorescence anisotropy is expressed as

robs = r0

∫ d0 exp(−μtot

eff z) × A[N1(z)+N2(z)]dz∫ d0 exp(−μtot

eff z)dz, (12.21)

where

μtoteff = μex

eff + μemeff , (12.22)

μtots = μex

s + μems . (12.23)

Integration of Eq. (12.21) gives

robs = r0μtot

eff

μtoteff − ln(A) × (μtot

s )× 1 − exp(−μtot

effd) × (A)μtots d

1 − exp(−μtoteffd)

. (12.24)


658 Chapter 12

Fluorescence anisotropy measurements are usually provided by commerciallyavailable spectrometers, the sensitivity of which is different for two orthogo-nal polarization states. Therefore, all measured fluorescence spectra should becorrected for the system response:1057

r = I|| − GI⊥I|| + 2GI⊥

, (12.25)

where G is the ratio of the sensitivity of the instrument to the vertically and thehorizontally polarized light.

Typical G-corrected polarized fluorescence spectra at 340-nm excitationfrom malignant and normal breast tissue with thickness ≈2 mm are shownin Fig. 12.16.1945 Collagen, elastin, coenzymes (NADH/NADPH), and flavinscontribute to these spectra and to those received at a longer wavelength of460 nm.1945, 1946 The contribution of NADH dominates with excitation at 340 nmand different forms of flavins dominate with excitation at 460 nm. In Fig. 12.16,a blue shift in the polarized fluorescence spectra maximum is clearly shown inthe malignant, as compared to the normal, tissue. A similar shift of 5–10 nm

Figure 12.16 Typical polarized fluorescence spectra at 340-nm excitation of human breasttissue samples 2 mm thick (see Ref. 1945). Solid curves, spectra with excitation and emis-sion polarizers oriented vertically (I||); dashed curves, spectra with crossed excitation andemission polarizers (I⊥). Malignant tissue (a); normal tissue (b).



Figure 12.17 Polarized fluorescence anisotropy measured at 440 nm for excitation at340 nm for malignant (open circles) and normal (solid circles) human breast tissues asa function of tissue thickness (see Ref. 1945). Error bars represent standard deviation.Solid and dashed curves show theoretical fits for normal and malignant tissues, respectively[Eq. (12.24)].

was observed also for 460-nm excited fluorescence. This shift is associated withthe accumulation of positively charged ions in the intracellular environment ofthe malignant cell.1943 Some differences, particularly a spectral shift of the max-imum, between the parallel and cross-polarized fluorescence spectra observed forrather thick tissue layers (≈2 mm), may be associated with wavelength-dependentscattering and the absorption properties of the tissue.

The mean fluorescence anisotropy values for normal and malignant humanbreast samples of tissue varying from 10 μm to 2 mm in thickness, determinedwith 440 nm emission and 340 nm excitation, are presented in Fig. 12.17.1946

The theoretical fit to experimental data using Eq. (12.24) and the parameterof single scattering anisotropy reduction, A = 0.7, generates the following datafor the anisotropy and optical parameters: r0 = 0.34; μtot

s = 590 cm−1; μtoteff =

53.5 cm−1 for malignant tissue and r0 ≈ 0.25; μtots = 470 cm−1; μtot

eff = 34.5cm−1 for normal tissue. The anisotropy values are higher for malignant tissuesthan normal for very thin tissue sections, d ≤ 30 μm. By contrast, in thicker sec-tions, the malignant tissue shows smaller fluorescence anisotropy than the normaltissues.

The fact that fluorescence anisotropy varies with tissue thickness is associ-ated with the manifestation of various mechanisms of fluorescence depolarization,which are caused by energy transfer and rotational diffusion in the fluorophoresand by the scattering of excitation and emission light. Energy transfer and/or rota-tional diffusion of the fluorophores dominate in thin tissue sections, and these


660 Chapter 12

processes are faster in normal tissues than in malignant ones. In thicker sections,light scattering dominates with a greater contribution to depolarization during lighttransport within the malignant tissues.

As already mentioned in the beginning of this section, g, and correspondingly,μ′

s or ltr determine the characteristic depolarization depth in a scattering medium.Parameter A, characterizing the reduction of the fluorescence anisotropy per scat-tering event in the described model, depends on the value of the g-factor.1945 Thetheoretical analysis by the authors of Ref. 1945 has shown that, for g rangingbetween 0.7 and 0.9, the value for A varies between 0.7 and 0.8. These resultssuggest that fluorescence anisotropy measurements may be used for discriminat-ing malignant from normal sites, and may be especially useful for epithelial cancerdiagnostics, in which superficial tissue layers are typically examined.1946

A variety of multimodal methods and measuring systems, includingfluorescence-polarization measurements for the demarcation of melanoma andother types of skin cancer, are presented in Refs. 602, 1527, 1528, 1947–1950.

12.6 Conclusion

As it follows from the presented analysis, polarization-sensitive methods arepromising tools for optical medical diagnostics and imaging, particularly for in vivoand in situ morphological analysis of living tissue. Polarization discrimination ofscattered probe light, which may easily be integrated in traditional optical diag-nostic techniques, such as diffuse reflectance spectroscopy and imaging, offersthe possibility for improving the diagnostic potential of these techniques. Anothernovel contribution to optical medical diagnostics should emerge from the morpho-logical study of tissues with expressed structural anisotropy. Typically, almost allof the polarization-sensitive techniques that we considered in this chapter can berealized with inexpensive, commercially available instrumentation. Neither do theyrequire sophisticated data processing algorithms. In other words, these methods arecompletely suitable for widespread implementation in clinical diagnostic practice.Fluorescence polarization measurements that can provide additional information atthe molecular level may be useful for discriminating malignant from normal sites.


Chapter 13

Coherence-Domain Methodsand Instruments

In this chapter, we discuss coherent optical methods that hold much promisefor applications in biomedicine, such as photon-correlation and diffusion wavespectroscopies; speckle interferometry; full-field speckle imaging; coherent topog-raphy and tomography; phase, confocal, and Doppler microscopy, as well asinterferentially structured light measurements of retinal visual acuity and bloodsedimentation.

13.1 Photon-Correlation Spectroscopy of TransparentTissues and Cell Flows

13.1.1 Introduction

The physical fundamentals of photon-correlation spectroscopy were discussed inChapter 8. Descriptions of the principles and characteristics of the primary mod-ifications of homodyne and heterodyne photon-correlation spectrometers, laserDoppler anemometers (LDAs), differential LDA schemes, and laser Dopplermicroscopes (LDMs) can be found in Refs. 5, 6, 22, 76–79, 82, 555, 1433–1435,1437, 1438, 1442, 1443, 1460, 1464, 1468, and 1469. A review of medical applica-tions, primarily limited to the investigation of eye tissues (crystalline lens, cataractdiagnosis), hemodynamics in isolated vessels (vessels of eye fundus or any othervessels) with the use of fiber-optic catheters, and blood microcirculation in tissues,is provided in Refs. 5, 6, 22, 67, 76–79, 82, 83, 557, 1433–1435, 1437, 1438,1442, 1443, 1445, 1447, 1460–1464, 1468–1470, 1473, 1479, and 1951–1986.In this section, we will discuss the application of the photon-correlation tech-nique to early cataract diagnostics and measurement of blood and lymph flow inmicrovessels.

661


662 Chapter 13

13.1.2 Cataract diagnostics

Photon correlation spectroscopy or QELS was originally developed to studysmall colloidal particles in fluids.1957 More than three decades ago, Tanaka andBenedek1958, 1959 proposed this technique to study the onset of cataract in theocular lens; however, it did not find extensive commercial acceptance in oph-thalmology. Owing to innovations in the field of optoelectronics, QELS is nowemerging as a potential ophthalmic tool, making possible the study of virtuallyevery tissue and fluid comprising the eye.1469 The capability of QELS in theearly detection of molecular morphology has the potential to help develop newdrugs to combat not just diseases of the eye, such as cataract, but to diagnose andstudy those of the body, such as diabetes and possibly Alzheimer’s, as claimed byAnsari.1469, 1956

Coherent fiber-optic photon-correlation spectrometers were designed for thestudy of cataractogenesis, and are potentially useful for early diagnosis ofcataract.1470, 1960 The instrument described in Ref. 1470 includes two optical fibers.The first, single-mode fiber, transmits a Gaussian beam of an He-Ne or diodelaser to an object. The second multi- or single-mode fiber is employed to collectbackscattered radiation at a certain angle and to transmit this radiation to a pho-todetector [see Fig. 13.1(a)]. The power of the He-Ne laser radiation (at 633 nm) ison the order of 1 mW. The size of the laser beam on the crystalline lens is approxi-mately 150 μm. Scattered radiation is detected at angles of 155 deg (detector 1) and143 deg (detector 2). Figure 13.1(b) shows typical autocorrelation functions (AFs)measured for a bovine crystalline lens under conditions of temperature-inducedcataract (reversible cold cataract). The results of the solution of the relevant inverseproblem (determination of the sizes of scatterers in human crystalline lenses asfunctions of human age) while taking into account Eqs. (8.28), (8.30), and (8.31)are presented in Fig. 13.1(c). These data demonstrate that the method under consid-eration is sufficiently sensitive for the monitoring of age changes in the structure ofthe crystalline lens caused by growth in the sizes of aggregated protein components.

In Ref. 1470, a clinical modification of the measuring system for early diagno-sis of cataract is presented. According to the estimates, the expected power densityincident on a retina that is sufficient to measure the AF of intensity fluctuationswithin a time interval of approximately 2 min is no higher than 0.05 mW/mm2,which is almost three orders of magnitude lower than the threshold of retinaldamage.

The fiber-optic QELS probe, shown in Fig. 13.2, combines the uniqueattributes of small size, low laser power, and high sensitivity.1469, 1956 The sys-tem is easy to use because it requires no sensitive optical alignment or vibrationisolation devices. A low power (50–100 μW) light from a semiconductor laser,interfaced with a monomode optical fiber, is tightly focused in a 20-μm diame-ter focal point in the tissue of interest via a gradient index (GRIN) lens. On thedetection side, the scattered light is collected through another GRIN lens andguided onto an APD detector built into a photon-counting module. APD processedsignals are then passed on to a digital correlator for analysis. The probe provides


Coherence-Domain Methods and Instruments 663

Figure 13.1 Photon-correlation spectrometer for early diagnosis of cataract (see Ref.1470). Diagram of the spectrometer (a). Autocorrelation functions for temperature-dependent cataract of bovine eye (b). Age-dependent changes in scatterer diameters for thehuman lens (c). Two fractions, finely dispersed (α-crystallin, hollow symbols) and coarselydispersed (protein conglomerates, solid symbols) are excluded from empirical autocorrela-tion functions [see Eq. (8.31)]. Triangles and squares represent measurements made withdifferent types of coherent fiber probes.

quantitative measurements of the pathologies of cornea, aqueous, lens, vitreous,and the retina. By choosing suitable optical filters, it can be converted into a devicefor spectral measurements (autofluoresence and Raman spectroscopy) and laser-Doppler flowmetry/velocimetry, providing measurements of oxidative stress andblood flow in the ocular tissues. The device can also be easily integrated into manyconventional ophthalmic instruments such as slit-lamps, Scheimpflug cameras,videokeratoscopes, and fluorometers.


664 Chapter 13

Figure 13.2 Schematic diagram of the sensitive, vibration protected, universal, and easy touse QELS fiber-optic probe (see Ref. 1956). This probe was originally developed at NASAto conduct fluid physics experiments in the absence of gravity onboard a space shuttle orspace station orbiter.

This compact probe (Fig. 13.2) was used for monitoring of cataractogenesisin mice in vivo by examination of the measured AF profiles [see Eqs. (8.28) and(8.30)] at different timelines.1469, 1956 As an example, Philly mice were studied.This animal develops cataract spontaneously between day 26 and 33 after birth.The data include a 45-day-old normal mouse of the control FVB/N strain, whichdoes not develop a cataract, and two Philly mice roughly 26–29 days old. Eachmeasurement took 5 s at a laser power of 100 μW. The changing AF slope is anindication of cataractogenesis as the lens crystallins aggregate to form high molec-ular weight clumps and complexes. The QELS autocorrelation data are convertedinto particle size distribution by using an exponential sampling program and areshown in Fig. 13.3. Although conversion of the QELS data into particle size dis-tributions requires certain assumptions regarding the viscosity of the lens fluid,these size values do indicate a trend as the cataract progress. These measurementssuggest that a developing cataract can be quantitatively monitored with reasonablereliability, reproducibility (5–10%), and accuracy.

In addition to cataract monitoring, the QELS probe has been proposed andexperimentally tested for early, noninvasive, and quantitative detection and mon-itoring of such diseases and abnormalities as vitreopathy, pigmentary glaucoma,diabetic retinopathy, and corneal evaluation of wound healing after laser refractivesurgery.1469, 1956

A portable fiber-optic photon-correlation spectrometer based on an He-Nelaser (633 nm), single-mode fibers, a photomultiplier operating in the regime of



Figure 13.3 In vivo cataract measurements in Philly mice (see Ref. 1956). Autocorrelationprofiles (a). Particle size distribution for the normal eye, control mouse (b). Particle sizedistribution for a mouse with trace cataract (c). Particle size distribution for a mouse withmild cataract (d).

a photon counter, and a 288-channel real-time correlator with a sampling time of200 ns is described in Ref. 1471. This spectrometer allows for in vivo studies ofthe crystalline lenses of patients. These investigations also confirmed the bimodalcharacter of the distribution of scatterers in the tissue of a human crystalline lens.Specifically, for healthy eyes of patients aged between 39 and 43 (six eyes, threefemale patients), the finely dispersed fraction has a mean radius of 4.25 (±1.7) nm,whereas the mean radius of the coarsely dispersed fraction is 497 (±142) nm. Forcataractous crystalline lenses, the mean radius of the finely dispersed fraction tendsto 160 nm, whereas the mean radius of the coarsely dispersed fraction tends to 1000nm. The spectrometer permits one to determine the size distribution of species forvarious localizations of the volume of measurements. The bimodal size distribu-tions of scatterers measured under conditions when the volume of measurementsis shifted along the axis of a cataractous crystalline lens are presented in Fig. 13.4.

13.1.3 Blood and lymph flow monitoring in microvessels

Parameters of blood or lymph flows in individual vessels can be measured with theuse of a technique based on the diffraction of a focused laser beam from movingscatterers (see Subsection 8.4.2).77, 555, 1434, 1442, 1473, 1474 A diagram of the relevantspeckle microscope is presented in Fig. 13.5. Laser radiation focused into a spot of


666 Chapter 13

Figure 13.4 Bimodal distribution of the radii of scattering particles for a cataractous crys-talline lens (female patient, aged 76, in vivo measurements) with different localizations ofthe volume of measurements along the axis of the crystalline lens: front part of the corticallayer, middle part of the cortical layer, nucleus, middle part of the rear cortical layer, and rearpart of the cortical layer (see Ref. 1471).

Figure 13.5 Diagram of a speckle microscope for the investigation of blood and lymph flowsin microvessels (see Refs. 1473 and 1474).

a small diameter on the order of 4.6 λ is projected onto a segment of the microvesselunder study. A photodetector whose entrance aperture is much smaller than themean speckle size registers intensity fluctuations in the scattered light. The detectedintensity fluctuations are analyzed with a low-frequency digital spectrum analyzeror converted into a digital signal for subsequent computer analysis. The typicalspectra for blood and lymph flows in superficial vessels of rat mesentery averagedover 128 realizations of a random signal are displayed in Fig. 13.6.



Figure 13.6 Spectra of intensity fluctuations in the scattered light (averaged over 128 real-izations) for the diffraction of a focused laser beam on the rat mesentery: 1, blood vessel(12 μm in diameter); 2–12, lymphatic vessels of various diameters for different rats; mea-surements were performed within the frequency range of 30–1500 Hz (see Refs. 1473 and1474).

For a blood microvessel, the spectrum of intensity fluctuations in the scatteredfield has a nearly Gaussian shape in the low frequency range. The spectra of inten-sity fluctuations for lymphatic vessels are rather complicated, which indicates thatthe motion of lymph in microvessels is much more complex than that of blood. Forexample, lymph may be involved in a characteristic shuttle-like motion, remainunmovable near the vessel wall, or move in a direction opposite of the flow in thecentral part of a vessel. This behavior of lymph is associated with complex contrac-tion dynamics of smooth-muscle cells in vessel walls, governed by a local rhythmdriver (pacemaker) and the behavior of the valves of lymphatic vessels.

To estimate parameters of blood and lymph flows in microvessels, we introducethe following quantities:1473, 1474

VV = � F

DV,∑

V=

�F∫0

|S(f ) − G(f )|4 df

[�F∫0

|S(f ) − G(f )|2 df

]2

/�F

. (13.1)

Here, �F is the width of the averaged spectrum, DV is the diameter of a microves-sel, S(f ) is the power spectrum of intensity fluctuations for the speckle field studied,and G(f ) is the spectrum with a Gaussian envelope. The S(f ) and G(f ) spectrahave equal bandwidths and powers. Parameter VV is directly proportional to theflow velocity, and �V provides information concerning the spatial and temporalvariations of the flow rate in the studied area of a vessel.

The characteristics given above have been employed to analyze the influenceof a lymphotropic agent (Staphylococcus toxin, ST) on the dynamics of lymph flowin mesentery microvessels of experimental animals (rats).1473, 1474 It was found that


668 Chapter 13

even at the fifth minute of ST action, all examined vessels showed variations inthe spectra of intensity fluctuations in scattered light, which indicates the veloc-ity characteristics of the flow change: 59% of the 17 vessels studied displayed adecrease in the mean velocity, VV, of lymph flow by (41 ± 8)% and a growth in the�V parameter by (33 ± 7)%. The remaining 41% of vessels displayed an increasein the mean rate of lymph flow by (63 ± 22)% and a decrease in the �V parameterby (35 ± 9)%. In later stages (between the fifth and twentieth minutes), vasocon-striction progresses, and the number of vessels contracting in phase decreases,which leads to changes in lymph dynamics. After the twentieth minute, lymphflow stopped in all vessels.

The optical scheme of the setup providing detection of cell flow direction andvelocities in the range from 10 μm/s to 10 mm/s with temporal resolution up to50 ms is shown in Fig. 13.7.1442, 1443, 1478 Radiation from a uniphase He-Ne laser(633 nm) is delivered through the illuminator channel and focused by the objectiveof the microscope into a spot of diameter approximately 2 μm in a plane apart adistance z = 100 μm from the axis of the microvessel. The radius of curvature ofthe wavefront of the beam illuminating the microvessel is quite small to ensure theacceptable translation length of biospeckles. The measuring volume is formed bythe intersection of the diverging laser beam with the microvessel and has the shapeof a truncated cone (whose elements have a 10 deg slope and a mean diameter onthe order of 30 μm). The laser radiation scattered by the cell flow is directed withthe help of the beam splitter to the photodetector placed at a distance of 300 mmfrom the objective plane of the microscope. The diameter of each photodetector is3 mm, which corresponds to the mean speckle diameter in the observation plane.The distance between the centers of the photodetectors is approximately 7 mm.Signals from the photodetectors are amplified by the photocurrent transducers anddigitized with the help of a two-channel 16-bit analogue-to-digital converter witha sampling frequency of 44.1 kHz. A PC is used to determine the cross-correlationfunction of the photodetector signals as well as the position of its peak.

Depending on the time resolution, the processing of photodetector signals ofduration 60 s takes between 90 and 300 s. A digital video camera combined witha transmission microscope is used for real-time analysis of microvessels’ functionin vivo: estimate the mean flow velocity and its direction, measure the diameter of amicrovessel, register the appearance of phasic contraction in the investigated lym-phatics. Dynamic digital images were processed with specially developed software.The cell velocity was determined as the ratio of the difference in cell coordinatesin two consecutive frames to the time interval between two frames. The mean flowvelocity was calculated by averaging the velocities of four to six cells. The dynamicdigital microscopy allows one to record cell flow velocity in the range from 25 μm/sto 2–2.5 mm/s with a time resolution of 40 ms.

The described setup was tested for in vivo measurements of lymph flow veloc-ity in the mesentery vessels of narcotized white rat. Animals were placed on athermostabilized stage (37.7◦C) of the microscope (see Fig. 13.7) and the mesen-tery and intestine was kept moist with Ringer’s solution at 37◦C (pH ∼ 7.4). Theimages of microvessels were simultaneously evaluated by transmission microscopy



Figure 13.7 Scheme of the experimental setup of laser speckle velocimeter integrated withdynamic digital microscopy providing measurements of absolute values of cell flow velocityand its direction:1478 1, digital video camera; 2, micro-objective; 3, He-Ne laser (633 nm);4, beam-splitter; 5, photodiodes; 6, red light filter; 7, photocurrent converters; 8, PC; 9,green light filters; 10, mirror; 11, illuminator; 12, thermally stabilized table; 13, lymphmicrovessel of mesentery. Inset shows the illumination of a lymphatic vessel by a focusedGaussian laser beam (a is the length of the laser beam waist and z is the separationbetween the flow axis and the waist plane of the laser beam).

Figure 13.8 Time dependence of the lymph flow velocity in the lymphatic vessel of meandiameter 170 ±5 μm of white rat mesentery (see Ref. 1478): 1, recorded with a specklevelocimeter; and 2, with a dynamic digital microscopy (see Fig. 13.7).

and laser speckle velocimeter. Figure 13.8 shows the temporal dependences of theflow velocity in the investigated microlymphatic with mean diameter 170 ± 5 μmand mean lymph flow velocity 169 ± 4.6 μm/s.1442, 1443, 1478 These dependences


670 Chapter 13

were obtained concurrently by a laser speckle velocimeter and processing of thevideo images. A laser speckle velocimeter allows one to measure the lymphocytevelocity in relative units only. The proportionality coefficient between the data oflaser speckle velocimetry and the mean flow velocity, measured by dynamic digitalmicroscopy, was determined from the slope of the line of linear regression betweenthe velocities (measured by these two methods). The correlation coefficient of lin-ear regression equaled 0.723 for measurements in the lymph vessel and 0.966 forcalibration measurements in the glass capillary.

13.2 Diffusion-Wave Spectroscopy and Interferometry:Measurement of Blood Microcirculation

Experimental implementation of diffusion-wave spectroscopy is very simple: ameasuring system should irradiate the scattering object under investigation with alight beam produced by a continuous-wave laser and measure intensity fluctuationsin scattered radiation within a single speckle with the use of a photomultiplier andan electronic correlator. A typical setup employed for model experiments is pre-sented in Fig. 13.9.80, 81, 1499, 1961, 1962 Radiation (with wavelength of 514 nm anda power on the order of 2 W) produced by an argon laser with an intracavityetalon passes through a multimode fiber-optic cable and irradiates the surface ofa solid-state bulk sample (finely dispersed TiO2 powder suspended in resin). Thesizes of the sample are 15× 15 × 8 cm3. A spherical cavity 2.5 cm in diameter,filled with a 0.2% aqueous suspension of polystyrene spheres 0.296 μm in diame-ter at the temperature of 25◦C, is placed at the center of the sample 1.8 cm belowits upper surface. The TMFP lengths of photons for the suspension and the sam-ple are equal to ltr = 0.15 and 0.22 cm, respectively. Absorption coefficients ofthese media are equal to each other, μa = 0.002 cm−1. The diffusion coefficient ofBrownian motion in suspension is DB = 1.5× 10−8 cm2/s. The single-mode fibercollects light emerging from a certain area of the object and transmits it to thephotomultiplier. The output signal of the photomultiplier is fed to a digital autocor-relator, which reconstructs the time-domain AF of intensity fluctuations. This AFis related to that of the field by the Siegert formula [see Eq. (8.28)]. Optical fiberswere designed to pick up radiation from any area at the surface of the sample.

Figure 13.9 Typical experimental setup for diffusion-wave (correlation) spectroscopy ofscattering media (see Ref. 1962).



Figure 13.10 Experimental and theoretical normalized autocorrelation functions of inten-sity fluctuations in light scattered from a TiO2 sample with a spherical cavity filled with asuspension of polystyrene spheres (see the text for the details and Ref. 1962).

Figure 13.10 displays the experimental results for the normalized time-domainAF of the field for three different arrangements of optical fibers connected to asource of radiation and the detector and compares these experimental data withtheoretical predictions. Because the origin of the x–y coordinate frame lies on thesurface of the sample above the center of the dynamic cavity, the source of radiationand the detector were placed along the y-axis in such a manner that the coordinateof the source was y = 1.0 cm, and the coordinate of the detector was y = −0.75 cm.Measurements were performed for x = 0.0, 1.0, and 2.0 cm. The distance betweenthe source and the detector remained constant. The error of these measurementswas estimated as 3%. The primary source of errors was associated with uncertain-ties in the positioning of optical fibers. Theoretical curves represent the results ofsimulations based on the diffusion theory of autocorrelation, with allowance for theexperimental data.1499, 1961, 1962 It is clear that the AF decays faster when the sourceof radiation and the detector are located close to the dynamic sphere, which gen-erates fluctuations in the time domain. In this area, most of the detected photonspass through the dynamic volume. This behavior of AFs allows one to employ thevariation in their slopes (decay rates) as a parameter for the imaging of dynamicinhomogeneities in a medium. This model corresponds to a situation when themicrocirculation rate of blood locally increases near, for example, a growing tumor.Using a similar approach, one can model a directed blood flow. For this purpose, athrough-hole should be drilled in a solid sample at a certain depth, and scatteringfluid (e.g., Intralipid) should be circulated through this hole with a definite flowrate.1961, 1962


672 Chapter 13

To determine the AF of the field on nanosecond and subnanosecond timescales, we should replace an electronic correlator with a Michelson interferometerwith a large difference in arm lengths, which should be on the order of 3 m.80, 1963

In this case, the intensity, 〈I(τ)〉, averaged in time depends on the delay time, τ,between the interfering fields in the interferometer, the carrier frequency, ω, ofthe optical signal, the average intensity, Iave, of speckles, and the time-domain AF,g1(τ), of the field:

〈I(τ)〉 = 1

2Iave

[1 + g1(τ) cos(ωτ)

]. (13.2)

A diagram of the experimental setup and the results of model experiments are pre-sented in Fig. 13.11. Radiation of a CW laser scattered in the forward directionby an object within a single speckle is coupled into a long Michelson interferom-eter. The difference between arm lengths of this interferometer can be smoothlyadjusted by variations of air pressure in the short arm. Effects arising due to a finitecorrelation length of laser radiation and geometric factors were excluded throughthe calibration of the measuring system with the use of diluted samples whose AFsdo not decay on the time scales under examination.

The possibilities of the DWS technique for medical applications have beendemonstrated in Ref. 1964. The experimental setup employed in this study isshown in Fig. 13.12(a). The experimental system was based on a titanium-sapphire

Figure 13.11 Diffusion-wave interferometry (see Ref. 1963): Experimental setup (a).Normalized output signal (interference fringes) for (dots) τ = 0 and (squares) 20 ns fortwo-phase aqueous suspensions of polystyrene spheres, 0.0385 and 0.299 μm in diameter(b). Relevant autocorrelation function of the field g1(τ) (c).



Figure 13.12 In vivo measurements of the blood flow velocity by means of the DWS tech-nique (see Ref. 1964): Experimental setup (a). Experimental AFs of field fluctuations inbackward scattering for different pressures applied to an arm (pressure increases from1 to 4) (b). Dynamics of the relative slope of the AF for various pressures applied to an arm,P is the tonometer pressure (c). Arrows indicate the moments of time corresponding to thenarrowing (ischemia) and broadening (hyperemia) of vessels.

laser with power of approximately 100 mW and a wavelength of 800 nm. Laserradiation was transmitted onto an object through a multimode optical fiber witha core 200 μm in diameter. Radiation was detected within a single speckle withthe use of a single-mode fiber 5 μm in diameter. The distance between the opticalfibers on the surface of an object remained constant and was equal to 6 mm. Therate of blood flow in the bulk of tissue from a human forearm was adjusted withthe use of a medical tonometer. A digital autocorrelator coupled with a photomul-tiplier in the regime of a photon counter was used to measure the time-domain AFof intensity fluctuations and the dependence of the AF shape on the pressure, P,


674 Chapter 13

produced by the tonometer. These dependencies for the AF of the field, which isrelated to the intensity AF by the Siegert formula, are presented in the logarithmicscale in Fig. 13.12(b). These dependencies show sufficiently high sensitivity of theAF slope to variations in the applied pressure, i.e., changes in the rate of volumeblood flow. In accordance with Eqs. (8.30) and (8.43), the normalized AF of fieldfluctuations can be represented in terms of two components related to the Brownianand directed motion of scatterers:1964

g1(τ) =∞∫

0

p(s) exp

{−2

[τ

τB+

(τ

τS

)2]

s

ltr

}ds, (13.3)

where τ−1B ≡ �T is defined in Eq. (8.30), τ−1

S∼= 0.18 GV|q|ltr characterizes the

directed flow, and GV is the gradient of the flow rate. The other quantities involvedin Eq. (13.3) are defined in (8.26) and (8.43). The preceding relationship allows oneto express the slope of the AF in terms of the diffusion coefficient and the gradientof the directed velocity of scatterers. When shear flow is significantly dominantunder the Brownian motion, the consideration of a semilogarithmic plot of g1(τ)versus τ1/2 gives a straight line with a slope proportional to the velocity of the flowof scattering particles.

Figure 13.12(c) displays the measured velocity of blood flow as a functionof the applied pressure. If we neglect the Brownian component, this dependenceis characterized by the variation in the AF slope [see Eq. (13.3)]. Because mea-surements were performed at a wavelength close to the isobestic point (805 nm),changes in the degree of oxygenation of blood due to the variation in the appliedpressure only slightly influenced the AF slope (the velocity of blood flow). Thiscircumstance allows us to find the correlation between the velocity of blood flowand variations in the diameter of vessels by means of simultaneous and indepen-dent measurements of the oxygenation degree and the volume of blood in a tissuewith the use of a two-frequency RunMan spectrometer (NIM Inc., Philadelphia).These measurements provide a pictorial illustration of the high efficiency of theDWS technique for in vivo studies of blood flow in the bulk of tissues.

Additionally, if the parameters of blood flow remain constant, the measuredAFs provide information concerning the static optical parameters of a multiplyscattering medium, i.e., ltr or μ′

s, μa, and g [see Eq. (8.43)]. Indeed, as shown inRef. 1965, the half-width of the spectrum of time-domain intensity fluctuationsunder conditions of multiple scattering depends not only on dynamic and geometricparameters of scattering particles, but also on the absorptivity of erythrocytes inblood, which allows us to estimate the degree of blood oxygenation from the resultsof measurements performed far from the isobestic wavelength.

The hybrid instrument and measuring protocol based on diffuse correlationspectroscopy (blood flow information) and diffuse reflectance spectroscopy (bloodoxygenation information), described in Ref. 1966, allow the evaluation of micro-circulation and muscle metabolism in patients with vascular diseases. A CWlaser (800 nm) with a long coherence length and APD were used for correlationmeasurements, source–detector separations ranged from 0.5 to 3 cm, and sampling



time was 1.5 s. A complete frame of data, cycling through all source–detectorpairs, was acquired in 2.5 s. Ten healthy subjects and one patient with peripheralarterial disease were studied during both 3-min arterial cuff occlusion of arm andleg, and 1-min plantar flexion exercise. Signals from different layers (cutaneoustissues and muscles) during cuff occlusion were differentiated, revealing stronghemodynamic responses from muscle layers. During exercise in healthy legs, theobserved ∼4.7-fold increase in relative blood flow was significantly lower thanthe corresponding increase in relative muscle oxygen consumption, which was ofapproximately sevenfold. In the diseased patient, during exercise, the magnitudesof both physiological parameters were ∼1/2 those of the healthy controls, and theoxygen saturation recovery time was twice that of the controls.

In Ref. 1495, a similar NIRS/DWS hybrid system was used in clinical studiesof infants with congenital heart disease (n = 33) under conditions of hypercapnia(excessive accumulation of carbon dioxide in the respiratory and cardiovascularsystems). In these studies, concentrations of oxyhemoglobin, deoxyhemoglobin,and total hemoglobin (using NIRS) were measured together with cerebral flowvelocity (DWS), and on the basis of a simple model, the metabolic rate of oxygenwas calculated. Simultaneous measurement using spin-labeled magnetic resonancearterial imaging showed satisfactory correlation (R = 0.7, p = 0.01) with the DWSmeasurement of microcirculation. Studies have shown that optical technologieshold significant promise for clinical monitoring of infants with this disorder.

13.3 Blood Flow Imaging

It can easily be shown that the methods of Doppler flowmetry, which have beenextensively developed within the past few decades, are generally identical to cur-rent intensively developing speckle methods in their applications to the analysis ofparameters of blood microcirculation. This is because these two approaches pro-vide an opportunity to determine the velocity of blood flow at a certain point.82 Thereview of Doppler methods for monitoring of blood microcirculation in tissues canbe found in Refs. 5, 22, 101, 112, 205, 672, 1434, 1435, 1439, 1442–1445, 1460,1463, 1464, 1483, and 1967–1969 and in several original papers; e.g., Refs. 67,1461, 1462, 1490, 1491, and 1970–1978. The extension of the Doppler methodto the investigation of blood microcirculation in thick tissues has stimulated thedevelopment of the theory of Doppler signals and the methods of simulationsand detection of such signals in multiply scattering media.344, 1561, 1974–1977 Specklemethods of investigating blood microcirculation are described in Refs. 3, 5, 76,82, 83, 112, 1424, 1435, 1437–1445, 1451–1459, 1473–1480, 1484–1488, 1777,1860–1862, 1951, 1952, 1973, and 1979–2019.

The diagnosis of many diseases associated with blood microcirculation dis-orders requires the monitoring of microcirculation within large areas of a tissue,i.e., imaging of the field of blood flow velocity. Because the methods under studyare characterized by high spatial locality, one ensures mechanical scanning orsequential analysis of intensity fluctuations within a separate pixel of a CCDcamera or implements both mechanical scanning and sequential analysis. Such


676 Chapter 13

Figure 13.13 Diagram of a scanning Doppler system for the imaging of blood microcircu-lation in tissues (see Ref. 1482).

scanning systems for the imaging of blood circulation have been implementedand developed up to the stage of commercial production.1481, 1482 One such sys-tem is shown in Fig. 13.13.1482 A system for imaging of blood circulation shouldbe useful for diagnosis and therapy support in cases associated with diseases ofthe peripheral vascular system and for the medical treatment of wounds and burns.However, mechanical scanning of a laser beam or the necessity to collect and pro-cess large data arrays in systems involving CCD cameras have prevented designersfrom creating simple and high-performance imaging systems. Apparently, the onlyexception was a speckle system based on a 100 × 100-pixel matrix photodetector,which was designed specifically for the analysis of retinal blood flow. The totaltime of data analysis in this system for a 0.42 × 0.42-mm field was 15 s.1480

The potential to build a robust blood flow imager in tissue with multiple scat-tering has led to a method based on focused laser beam probing and detectionof spatial cross-correlation of the scattered field using a CCD camera.1981 Themethod is based on the concept that the region of single scattering within the tis-sue (volume occupied by a focused laser beam) will produce large correlated areas(speckles) in transverse dimension, whereas the comparably large halo of multi-ple scattered photons produced by this beam will generate small speckles. Thus,the cross-correlation function of the intensity fluctuations in two spatial points(CCD camera pixels) with the separation, �x, larger than the size of multiscat-tered speckles will reflect the form of single scattered AF. The profile of a singlescattered AF will provide information about blood or lymph flow in a volume occu-pied by a focused laser beam. The attractiveness of this approach is defined by itsapplicability to intermediate scattering regimes, whereas QELS provides accurateinformation only for a single scattering regime and DWS can be applied only for acase of diffusive photon propagation.

A typical approach to improve the performance of blood flow imagers, par-ticularly to increase the imaging speed, is to parallelize measurements by using



one-dimensional (1D) or 2D arrays of photodetectors. A new generation of high-speed instruments for full-field blood flow laser Doppler imaging (LDI) wasrecently developed on the basis of CMOS image sensors.1490, 1491, 1978 The LDIsystem employing an integrating CMOS image sensor delivers high-resolutionblood flow images every 0.7 to 11 s, depending on the number of points in theacquired time-domain signal (32–512 points) and the image resolution (256 × 256or 512 × 512 pixels). For the integrating imager, a digital CMOS camera based onthe VCA1281 monochrome CMOS image sensor from Symagery (Canada) wasutilized. This sensor operates in rolling shutter mode; it has 1280H × 1024V res-olution, 7 × 7 μm2 pixel size, 40 MHz sampling rate, and an 8-bit ADC. Thesensor has a specified flat spectral response in the range between 500 and 750nm. The camera was connected to the host PC via a fast low-voltage differentialsignaling (LVDS) interface, providing for a high-speed transfer of the obtainedframes.

For the object illumination, a solid-state, diode-pumped laser of 250 mW opti-cal power output emitting at 671 nm was used. The laser beam was coupled to a1.5-mm plastic optical fiber. A GRIN lens of 1.8 mm was placed at the distalend of the fiber. This configuration produced uniform illumination of the object.The illuminated area was up to 170 mm. The backscattered light, collected withan objective ( f = 6 mm) with a low f -number [= 1/(2NA) = 1.2], provided the sys-tem with the superior photon collection efficiency that becomes critical for shortintegration times (in the range of a few tens of milliseconds). Typically, the imagerhead was placed at a distance of 150–250 mm from the investigated tissue surface(see Fig. 13.14).

The specially developed software allows for changing the sensor parame-ters, controlling the data acquisition mode, acquiring the data, and displaying theflow-related (perfusion, concentration, speed) maps. A photographic image of the

Figure 13.14 Schematic of the high-speed full-field laser Doppler imaging system on thebasis of CMOS image sensor (see Ref. 1978).


678 Chapter 13

sample and flow related maps displayed on the monitor are obtained with the sameimage sensor; therefore, the obtained flow-maps can easily be associated with anarea of interest on the sample. The signal sampling frequency is inversely pro-portional to the time to acquire one subframe. The subframe sampling rate of thesensor depends on its size and the pixel clock frequency. The clock frequency wasfixed at 40 MHz for optimum performance speed/quality. The size of the sam-pled subframe finally defines the signal sampling frequency of the imager. For asubframe of 256 × 4 pixels, the frame sampling frequency was 30 kHz; that for256 × 6 pixels was 20 kHz, and that for 256 × 8 pixels was 14 kHz.

To obtain one flow map over a region of interest (ROI), which was 256 × 256or 512 × 512 pixels, the ROI must be subdivided in smaller regions (e.g., into32 subframes of 256 × 8 pixels) and scanned electronically. Between 32 and 512sampled points were obtained for the acquired time-domain signal for each pixelof the subframe; thus, the intensity fluctuation history was recorded for each pixelof the ROI.

The signal processing comprises the calculation of the zero-moment (M0) andfirst-moment (M1) of the power density spectrum, S(ν), of the intensity fluctua-tions, I(t), for each pixel. The zero-moment is related to the average concentration,〈C〉, of moving particles in the sampling volume. The first moment (flux or perfu-sion) is proportional to the rms speed of moving particles, Vrms, times the averageconcentration. The governing expressions are1990

Concentration = 〈C〉 ∝ M0 =∞∫

0

S(ν)dν, (13.4)

Perfusion = 〈C〉 Vrms ∝ M1 =∞∫

0

νS(ν)dν, (13.5)

S (ν) =∣∣∣∣∣∣

∞∫0

I(t) exp(−i2πνt)dt

∣∣∣∣∣∣2

. (13.6)

Here, the variable ν is the frequency of the intensity fluctuations induced by theDoppler-shifted photons.

To calculate the power density spectrum, an FFT algorithm, optimized for rapidperformance, was applied to recorded signal variations at each sampled pixel of theROI.1490, 1491, 1978 Noise subtraction was performed upon the calculated spectra bysetting a threshold level on the amplitude of the spectral components. This filteringis applied to reduce the white noise (e.g., thermal and readout noises) contribu-tion to the signal. Thereafter, the perfusion, concentration, and speed maps werecalculated and displayed on the computer monitor. The total imaging time (includ-ing data acquisition, processing, and display) depends on the number of samplesobtained for each pixel and the size of the ROI. For a 256 × 256-pixel ROI, theimaging times are 0.9 s for 64 samples, 1.2 s for 128 samples, 1.7 s for 256 samples,and 2.9 s for 512 samples.



In Figure 13.15(a), flow-related maps obtained for the finger skin of a healthyvolunteer are shown.1978 The images were obtained for imager settings for thebandwidth from dc to 4000 Hz with 66 Hz resolution; the integration time was130 μs. The total imaging time was approximately 5 s. A smoothing filter wasapplied to the row images: the value of each pixel shown was obtained by averagingthe row-values of eight neighboring pixels. The flow maps (perfusion, concen-tration, speed) are false-coded with nine colors. The images clearly show thedifference in speed and RBC concentration distributions measured in the fingerskin. The lower value for the concentration signal measured on the nail is causedby the higher amount of non-Doppler-shifted photons reemitted from the relativelythick, statically scattering nail tissue, compared to the thin, statically scatteringepidermis of the skin. The signal measured on the nail shows a higher speed of themoving RBC in the under-nail tissue. However, it could not be precisely predictedwhether this is because the blood speed was really higher under the nail, or becausethe measured values were obtained due to the influence of multiple scattering (seeAF presented in Fig. 13.28). This ambiguity is a common problem for all laserDoppler or laser speckle imagers. The black and white photographic image of theobject of interest is obtained with the same CMOS camera. This image is usefulfor determining the anatomical boundaries associated with the perfusion regionspresented in the blood flow maps.

The sequence of images [Fig. 13.15(b)] and the corresponding graph[Fig. 13.15(c)] for the averaged blood perfusion measured in real time at occlu-sion (ROI = 256 × 256 pixels; 5.5 × 5.5 cm2; the capture time of each image is1.2 s) accurately demonstrate the behavior of finger skin blood perfusion beforemechanical external arm-cuff occlusion (1–4); during occlusion (5–13); immedi-ately after removal of occlusion with visible postocclusive hyperemia (14–17); andduring restoration of the perfusion baseline (18–26).1978

The imaging time of this high-speed LDI system approaches that of the laserspeckle imaging (LSI) systems82, 83, 112, 145, 1439, 1484–1488, 1982–2019 currently acceptedas the fastest.1985 The LSI systems obtain flow-related information by measuringthe contrast of the image speckles (see Subsection 8.4.3). Effectively, the contrastvalues measured by LSI are directly proportional to the normalized M0 value thatis measured by laser Doppler with integrating photodetectors. The images shownin Fig. 13.15 demonstrate a difference between perfusion (M1) and concentration(M0) maps. It appears that LDI provides more objective information than the LSImethod because with the LDI technique, the concentration and speed signals canbe measured independently. In LSI, these two signals are typically mixed, and thus,it can be hard to attribute an exact cause for the changes in the contrast signal.1989

However, a satisfactory correlation (R2 = 0.98) between LDI and LSI measure-ments of the same area of regional CBF for different animals (male Wistar rats)was found.1982 A detailed comparison of the laser-Doppler and speckle contrastmethods of blood flow imaging can be found in Ref. 1984. It follows from thisanalysis that the speckle contrast technique can provide an image of tissue vas-cular structure with the relative distribution of blood velocity [correspondingly toa nonlinear response, described by Eq. (8.34)], but it does not provide a linearmeasurement of perfusion in comparison with LDI.


680 Chapter 13

Figure 13.15 Flow-related maps obtained with the CMOS integrated imager for finger skin(ROI = 512 × 512 pixels, imaging area is 11 × 11 cm2) (a): image of the object (intensityimage); perfusion map (lower is 200 a.u. and higher is 700 a.u.); blood concentration map(lower is 140 a.u. and higher is 310 a.u.); flow speed map (lower is 400 a.u. and higheris 1500 a.u.); capture time of each image is 5 s total. Sequence of images (b) and corre-sponding graph (c) of the averaged blood perfusion measured in real time at occlusion(ROI = 256 × 256 pixels; 5.5 × 5.5 cm2); 0: normal finger image; 1–4: before occlu-sion; 5–13: during occlusion; 14–17: removal of occlusion, visible postocclusive hyperemia;18–26: restoration of perfusion baseline; capture time of each image is 1.2 s. Increase ofblood flow parameters displayed color from blue to red (see Ref. 1978). (See color plates.)



However, the speckle-contrast technique (LASCA), fundamentals of whichare discussed in Subsection 8.4.3, is a conceptually simple high-performancetechnique for blood flow imaging.82, 83, 112, 1424, 1435, 1437–1439, 1484–1488, 1979–2019 Themeasuring system employs a CCD camera, a frame grabber, and dedicated softwarefor the computation of the local contrast of a speckle pattern and conversion of thecontrast into a color map (which provides a map of flow velocities). The resultingimage represents the contrast of the speckle field averaged in time. However, thisaveraging is performed rather quickly (the averaging time is usually equal to 5–30ms) to permit real-time measurements.

Equation (8.34) gives an expression for the speckle contrast in the time-averaged speckle pattern as a function of the exposure time, T, and the correlationtime

τc = 1/(ak0v), (13.7)

where v is the mean velocity of scatterers, k0 is the light wave number, and a isa factor that depends on the Lorentzian width and scattering properties of the tis-sue.1990 As in LDI, it is theoretically possible to relate the correlation times, τc,to the absolute velocities of the RBCs, but this is difficult in practice, inasmuchas the number of moving particles that interacted with light and their orientationsare unknown.1990 However, relative spatial and temporal measurements of velocitycan be obtained from the ratios of 2T/τc, which is proportional to the velocity anddefined as measured velocity.1439, 1486, 1487

A schematic diagram of the experimental setup is shown in Fig. 8.14. A He-Nelaser beam (λ = 633 nm, 3 mW) was coupled into an 8-mm diameter fiber bundle,which was adjusted to evenly illuminate the area of interest.1439, 1486, 1487 The illumi-nated area was imaged through a zoom stereo microscope (SZ6045TR, Olympus,Japan) onto a CCD camera (PIXELFLY, PCO Computer Optics, Germany) with480 × 640 pixels, yielding an image of 0.8 to 7 mm, depending on the magnifica-tion. The T of the CCD was 20 ms. Images were acquired through Easy-Controlsoftware (PCO Computer Optics, Germany) at 40 Hz.

The raw speckle images were acquired to compute the speckle contrast image.The number of pixels used to compute the local speckle contrast can be selected bythe user: lower numbers reduce the validity of the statistics, whereas higher num-bers limit the spatial resolution of the technique. To ensure proper sampling of thespeckle pattern, the size of a single speckle should be approximately equal to thesize of a single pixel in the image, which is equal to the width of the diffraction-limited spot size and is given by 2.44 λf /D, where λ is the wavelength and f /D isthe f -number of the system. In the system, the pixel size was 9.9 μm. With a mag-nification of unity, the required f /D is 6.4 at a wavelength of 633 nm. Squares of5 × 5 pixels were used according the theoretical studies.83 The software calculatedthe speckle contrast for any given square of 5 × 5 pixels and assigned this valueto the central pixel of the square. This process was repeated to obtain a specklecontrast map. For each pixel in the speckle contrast map, the measured velocity(2T/τc) was obtained through Eq. (8.34), which describes the relationship betweenthe correlation time and velocity, and therefore measures the velocity map.


682 Chapter 13

To compute the relative blood flows in vessels of interest, first, a threshold wasestablished in a ROI from the measured velocity image, and then, the vessels ofinterest were identified by the pixels with values above this threshold. The meanvalues of the measured velocity in those pixels were computed at each time-point.The relative velocity in the vessel of interest was expressed as the ratio of themeasured velocity in the condition of stimuli to that of control condition.

LSI is a noninvasive full-field optical imaging method with high spatial andtemporal resolution, and is a convenient technique in measuring the dynamics ofCBF. In particular, in Ref. 1439, the LSI method was used to monitor the dynam-ics of CBF in several animal models during sciatic stimulation. Stimulation of thesciatic nerve was similar to that used in conventional physiological studies. Bloodflow was monitored in the somatosensory cortex in a total of 16 rats under electri-cal stimulation of the sciatic nerve, and the activated blood flow distribution wasobtained at different levels of arteries/veins, along with the change of activatedareas. One example of the results is shown in Fig. 13.16, in which the brighter areascorrespond to the area of increased blood flow. In comparison with LDI, an area of1 mm2 ROI in Fig. 13.16(a) was chosen to evaluate its mean velocity (Fig. 13.17):the evoked CBF started to increase (0.7 ± 0.1) s, peaked at (3.1 ± 0.2) s, and thenreturned to the baseline level. This is coherent with the conclusions obtained fromthe LDI technique.1993, 1994 To differentiate the response patterns of artery/veinunder the same stimulus, six distinct levels of vessels were labeled in Fig. 13.16(a)and their changes of blood flow displayed. The results clearly showed that the

Figure 13.16 Blood flow change in contralateral somatosensory cortex of rats under unilat-eral sciatic nerve stimulation (see Ref. 1992). Vascular topography illuminated with greenlight (540 ± 20 nm) (a); blood activation map at prestimulus (b); 1 s (c) and 3 s (d) after theonset of stimulation. Relative blood flow images are shown and converted from speckle-contrast images, in which the brighter areas correspond to the areas of increased bloodflow. A-1, A-2, A-3, and V-1, V-2, V-3 represent the arbitrarily selected ROIs for monitoringchanges in blood flow. A-I, A-II, and V-I, V-II represent the selected loci on the vessel whosediameters are measured in the experiment.



Figure 13.17 Relative changes of blood flow in six areas indicated in Fig. 8.16(a) (dividedby the values of prestimulus) (see Ref. 1992).

response patterns of arteries and veins in the somatosensory cortex were totallydifferent: vein 1 (V-1, ∼140 μm in diameter) almost remained unaffected, andarteriole 1 (A-1, ∼35 μm in diameter) responded slowly; arteriole 2 (A-2, ∼35μmin diameter) peaked at (3.5 ± 0.5) s after the onset of stimulation, and then reacheda steady-state plateau, and vein 2 (V-2, ∼70 μm in diameter) presented a delayand mild response; blood flow in the capillaries (A-3 and V-3, ∼10 μm in diam-eter) surged readily and increased significantly. The changes in arteries and veinswith different diameters were also measured.1439 The activation pattern of cerebralblood flow was discrete in spatial distribution and highly localized in the evokedcortex with the temporal evolution. This is consistent with the hypothesis of Royand Sherrington.1992–1994

The influence of epidurally applied hyperosmotic glycerol on in vivo restingCBF was also investigated by using the LSI technique (see Subsection 9.7.1).1439

The skull was removed, and intact dura mater was exposed. To study the influ-ence of glycerol on in vivo CBF, a small area of dura mater was removed. Warm,dehydrated glycerol was administrated near the exposed area. Velocity images ofCBF under the effect of glycerol are shown in Fig. 9.45. When glycerol diffused inbrain tissue and influenced CBF under the dura mater, CBF in exposed area alsochanged. Figure 9.46 shows the time course of changes in four different vessels.

As described above, LSI is based on the first-order spatial statistics of time-integrated speckles. The primary disadvantage of LASCA is the loss of resolutioncaused by the need to average over a block of pixels to produce the spatial


684 Chapter 13

statistics used in the analysis, although it actually has higher resolution than othertechniques, such as scanning laser Doppler. Accordingly, a modified LSI methodutilizing the temporal statistics of time-integrated speckles was suggested.1997 Inthis method, each pixel in the speckle image can be viewed as the single point area.Then, the signal processing consists of calculating the temporal statistics of theintensity of each pixel in the image:

Ni,j =⟨I2i,j,t

⟩t− ⟨

Ii,j,t⟩2t⟨

Ii,j,t⟩2t

(13.8)

i = 1/480, j = 1/640, t = 1/m,

where Ii,j,t is the instantaneous intensity of the ith and jth pixels at the tth frame ofraw speckle images, and

⟨Ii,j,t

⟩t is the average intensity of the ith and jth pixels over

the consecutive m frames; Ni,j is inversely proportional to the velocity of scatteringparticles. The Ni,j value of each pixel in the consecutive m frames (Ii,j,t) of rawspeckle pattern is computed according to Eq. (13.8). The process is then repeatedfor the next group of m frames. The results are given as 2D grayscale (65,536shades) or false color (65,536 colors) coded maps that describe the spatial variationof the velocity distribution in the examined area.

A modified LSI technique1439, 1444, 1453, 1860, 1997 is the optimal method for study-ing RBC motion in vessels.2016 In fact, this method is simple and capable ofimaging the full field of RBC motion or blood flow inside small blood vessels with-out scanning. To obtain a 2D velocity map of RBC, which represents blood vesselsunder flow and no-flow conditions, the temporal statistics of time integrated speck-les are utilized. The value of the temporal contrast of intensity fluctuations of laserscattered light, Kt, at pixel (x, y) can be calculated as2016

Kt(x, y) = σx,y/⟨Ix,y

⟩n,

where σx,y is the standard deviation of the CCD intensity counts at pixel (x, y)during n frames; n is the number of frames acquired (n = 30), and

⟨Ix,y

⟩is the mean

value of CCD intensity counts at pixel (x, y) over the n frames.The experimental setup for this technique that was used for the imaging of

clot formation is presented in Fig. 13.18(a). The red diode laser (670 nm,10 mW)was coupled with a diffuser, which was adjusted to illuminate the area of a mouseear. The illuminated area was imaged through a zoom stereo microscope SZX12(Olympus, Japan) and a CCD camera Pixelfly (PCO, Germany). The green diodepumped solid state (DPSS) laser (Laser-Glow, Canada, 532 nm, 100 mW) was usedfor inducing vessel microinjury. The bandpass filter 700/150 nm was saturated dur-ing the green laser irradiation. The exposure time of the CCD was 50 ms. Imageswere acquired through Easy-Control software at 20 Hz. Analysis of acquired imagesequences was performed on ImageJ with a specifically designed software packagefor the analysis.

The typical image of a mouse ear captured after complete occlusion of majorear blood vessels is shown in Fig. 13.18(b). In this image, the large blood vessels



Figure 13.18 Modified dynamic light scattering (DLS) imaging technique based on full-fieldanalysis of laser speckle pattern and used for imaging of clot formation (see Ref. 2016).Experimental setup (a) and image of a mouse ear (b) captured after complete occlusion ofmajor ear blood vessels. Intensity scale on the right is the value of laser speckle temporalcontrast (0–1). Scale bar is 1 mm.

appear as white wires. White and fuzzy backgrounds correspond with the signalproduced by RBC movements in capillaries.

Other approaches for improving the LASCA technique, particularly noisereduction, are also described, based on an active speckle averaging scheme thatensures perfect ensemble averaging.1984, 1987 These approaches can use variousmethods to generate speckle images with reduced processing time, such as theuse of secondary low-coherence light sources (illumination with a dispersed laserbeam that has passed a rotating diffuser) or vibration techniques.

A few examples are presented of the application of the LSI technique to exper-imental and clinical studies. It has been successfully used to provide dynamicimages of regional blood flow in rat mesentery influenced by noradrenalin,1998

to quantify the spatial-temporal response of cerebral blood flow,1982, 1992–1994, 1999,

2000, 2003–2005, 2009, 2014 including that with functional activation of the somatosensorycortex in rats1982, 1999, 2003 and acute hyperglycemia,2000 and for studying oxy-gen metabolism in cerebral ischemia.1982, 2004, 2005 Some papers are devoted to theimaging of blood flow in the retina.2007, 2008

The method is used to image blood flow in real time while providing feedbackduring laser therapy of port wine stain birthmarks;2002 monitor laser coagulationof blood vessels,2015, 2016 as well as the status characteristics of tumor vascula-ture;2017 and image lymphatic vessels.2019 Often, the speckle method, as a channelof information about an object, is included in multimodal diagnostic or therapeuticsystems.2002, 2006, 2015–2018

New image processing approaches and corresponding hardware to monitormicrocirculation using the speckle method are under development.2009–2013 Theseinclude imaging of blood flow with a high spatial and temporal resolution obtainedfor the analysis of laser speckle data using a graphics processing unit,2010, 2013

a portable laser speckle perfusion imaging system,2011 and a system-on-chip forreal-time laser speckle imaging.2012


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13.4 Interferometric and Speckle-Interferometric Methodsfor the Measurement of Biovibrations

A large number of optical methods have been proposed for the monitoring of biovi-brations. Specifically, a fiber-optic sensor based on a single-mode X-coupler wassuccessfully employed for the monitoring of heartbeats of patients examined withthe use of a magnetic resonance tomograph.2020 Contactless biovibrometers withultrahigh sensitivity based on heterodyne laser interferometers with a high degreeof automation and well-developed software were described in detail by Khannaet al.2021, 2022 Their investigations have been devoted to the measurement of vibra-tions of different components in inner ears of animals. The confocal scheme ofa heterodyne interference microscope employed in these studies made it possibleto investigate the vibrations of various layers of the tissue. This approach pro-vided record sensitivity with respect to small displacements of objects with lowreflectivities (on the order of 10−4–10−5). The sensitivity achieved in these experi-ments within the range of vibration frequencies from 50 to 2000 Hz was 10−11 m.A conceptually similar, but much simpler, laser system for the investigation ofbiovibrations was described in Ref. 2023. This system also employs a heterodyneinterferometer and is referred to as a laser Doppler vibrometer. This instrument,which operates within a frequency range up to 10 kHz, was used to monitor vibra-tion spectra of a tympanic membrane under various disorders of the inner ear.Holographic analysis of vibrations of a tympanic membrane is also described inthe literature (e.g., see Ref. 2024). An optical system for remote monitoring ofcardiovibrations is presented in Ref. 1489. An optical interferometer with a 633-nm He-Ne laser was utilized to detect micrometer displacements (sensitivity of366.2 μm/s) of the skin surface.2025 The detected velocity of skin movement isrelated to the time derivative of the blood pressure. Motion velocity profiles of theskin surface near each superficial artery and auscultation points on a chest for twoheart valve sounds exhibited distinctive profiles. The designed optical cardiovas-cular vibrometer has the potential to become a simple, noninvasive approach tocardiovascular screening.

A laser Doppler technique based on the self-mixing effect in the diodelaser1462, 1463 was used for cardiovascular pulse measurements above the radialartery in the wrist.2026, 2027 The developed self-mixing interferometer was usedto measure the skin displacement, which was induced by a cardiovascular pulse.The reconstructed Doppler spectrograms followed the first derivative of the cor-responding blood pressure pulse for both normal and abnormal pulse conditions.The correlation coefficient between the shapes of the Doppler spectrograms andthe first derivative of the blood pressure pulse for 10 volunteers (738 cardiovascularpulsegrams) was found as 0.95 with standard deviation of 0.05. A self-mixing inter-ferometer was also used to measure the baroreflex effect and the elastic modulusof the arterial wall.

The fact that the interaction of laser radiation with tissues induces the forma-tion of speckle structures did not receive adequate consideration in biovibrometry.Interference between speckle-modulated (reflected from a tissue) and reference



fields has many specific features in this case. In designing biovibrometers, oneshould take into account these specific features and sometimes even make use ofthem76, 1448, 2028–2031 (see Chapter 8). The development of coherent optical contact-less biovibrometers for the purposes of medical diagnostics is closely related to thesolution of the problem of diffraction of laser beams propagating in nonstationary,randomly nonuniform media.76 Several speckle techniques have been developedthus far for medical applications.76, 1448, 2028–2031 A diagnostic probe based on aminiature speckle–electronic interference system, including a fiber-optic speckleinterferometer and a matrix photodetector, was described in Ref. 2030. Sequentialframe-by-frame analysis of the distribution of electron speckles makes it possibleto image vibrations in three dimensions with high quality. The probe was designedfor the quantitative analysis of vibrations of the tympanic membrane and vocalchords.

The possibility of applying a Michelson speckle interferometer to the inves-tigation of cardiovibrations and the detection of pulse waves was substantiated inRefs. 1448, 2028, and 2029. Here, we briefly consider the primary results of thesestudies and present some results on the detection of pulse waves with the use of thespeckle technique based on the diffraction of focused laser beams. Medical diag-nostics requires simple and noise-resistant optical systems. The homodyne speckleinterferometer shown in Fig. 13.19 meets these requirements. The output signal ofthis interferometer reaches its maximum when the speckle fields are matched (seeSection 8.2). For focused laser beams, such matching can easily be achieved by the

Figure 13.19 Diagram of a homodyne speckle interferometer for the investigation ofbiovibrations (see Ref. 1448).


688 Chapter 13

equalization of the arms of the interferometer. The speckle vibrometer can operatein two regimes: with comparatively large vibration amplitudes (l0 > λ/4, the regimeof fringe counting) and with small vibration amplitudes (l0 < λ/4), when the ran-dom amplitude of the output signal displays additional dependence on the initialphase. If the number of speckles within the receiving aperture satisfies the condi-tion Nsp > 4, then the output signal of the interferometer has Gaussian statistics ofthe first order, i.e., the amplitude of this signal is characterized by Rayleigh distri-bution.1448 The relevant experimental and theoretical dependencies of the averagedamplitude, 〈U〉, and variance, σ2

U, of the output signal on the number of speckleswithin the aperture of the photodetector suggest a way to improve the signal-to-noise ratio in homodyne interferometers (see Fig. 13.20). It can be demonstratedthat in the case of vibrations with large amplitudes, we have

〈U〉 ∼= d2av(Nsp)0.5, σ2

U ≈ Nsp, (13.9)

where dav is the mean transverse size of a speckle and Nsp = (2Ra/dav)2 for a circularaperture with a diameter 2Ra. In writing Eq. (13.9), we assume that variations inspeckle sizes not change the intensities of interfering beams.

Thus, to increase the amplitude of the output signal of a speckle interferome-ter, one should choose schemes that will ensure the detection of a large number ofspeckles with maximum mean size, i.e., employ focused beams and a photodetectorwith a wide aperture. Considerable longitudinal displacements are usually accom-panied by transverse and angular shifts of an object’s surface. As demonstratedin Ref. 1448, these shifts generate low-frequency modulation of the output sig-nal of an interferometer. The depth of this modulation varies within a broad rangefrom 0 to 100%, depending on specific realizations of the signal and referencespeckle fields. Because it was demonstrated that such a modulation is caused byintensity fluctuations in a group of closely located speckles, one can considerablyweaken spurious modulation by blocking the relevant group of speckles with asmall opaque screen.

Figure 13.20 Experimental and theoretical dependencies of averaged amplitude, 〈U〉, ofthe output signal of a speckle interferometer (a) and its variance, σ2

U (b), on the number ofspeckles, Nsp, within the receiving aperture (rough surface is characterized by a consider-able amplitude of vibrations, l0 ∼ λ; sizes of speckles remain unchanged, and averaging isperformed over 300 realizations of the reference speckle field) (see Ref. 1448).



For vibrations with small amplitudes, the output signal of an interferometerhas substantially different statistics. The modulus of the output signal in this casehas an exponential distribution function with a maximum probable value equal tozero. However, the mean value of the modulus of the signal and its variance arecharacterized by the same dependencies on Nsp as in the case of vibrations withlarge amplitudes1448 [see Eq. (13.9)].

Taking this into account and using Eqs. (8.22) and (8.23), we can represent theoutput signal of a homodyne interferometer in the following form:

Ui(t) = Ai sin [ϕ i + ALH(t)] , (13.10)

where H(t) is the normalized signal with a variance equal to unity that describesthe waveform of vibrations on the surface of a bio-object, Ai and ϕi are randomquantities determined by the conditions of detection of speckle interferograms andthe chosen realization of the surface with an index i, and AL is the amplitude ofvibrations. Equation (13.10) also holds true for a differential interferometer if AL isdefined as the difference between vibration amplitudes at two points. A laser differ-ential speckle interferometer with two beams focused onto the surface of an objecthas been successfully employed for the detection of a human pulse at various pointsof the skin surface in the wrist area.1448 As demonstrated in Ref. 2031, the inves-tigation of pulse waves through the analysis of phase portraits of the output signalof a differential speckle interferometer holds much promise for cardiodiagnostics.However, appropriate filtration of the signal should be conducted to efficientlyeliminate the influence of lateral shifts of skin surface caused by the pulse wave.

Based on the developed speckle technology, a robust vibrometer for medi-cal applications can be designed.2029 However, the simplicity of the instrumentis achieved at the cost of a nontrivial description of the response function of thevibrometer. Intensity fluctuations in scattered light in the case of diffraction ofa focused Gaussian beam are related to vibrations of an object by some nonlin-ear random function. Nevertheless, owing to regular variations in the speckle field(displacement and decorrelation of speckles) caused by vibrations of the scatteringsurface, the signal at the output of the photodetector contains spectral componentscorresponding to vibrations of the surface. The complex motion of the surface givesrise to additional nonlinearities in the response function. For example, a periodicmotion of skin surface caused by a pulse wave can be considered as a superposi-tion of at least three displacements: displacement normal to the surface, angulardisplacement, and transverse displacement (along the surface). For the measuringsystem described in Ref. 2029, normal vibrations do not contribute to the outputsignal. Comparatively small angular vibrations are responsible for transverse oscil-lations of speckles in the observation plane (without decorrelation of speckles),whereas small transverse surface shifts lead to partial decorrelation of the specklefield. Thus, time-domain intensity fluctuations of the scattered field in the caseof periodic vibrations of a surface also involve a periodic component. In such asituation, the nonlinear random operator relating intensity fluctuations to the dis-placement of the scattering surface depends on the sizes of the irradiated surfacearea, conditions of speckle observation, and the specific realization of the surface


690 Chapter 13

under study. However, numerical analysis of the diffraction of a focused Gaussianbeam from a moving rough surface with Gaussian statistics within the frame-work of the Kirchhoff approximation shows that when the amplitudes of transverseshifts are lower than the surface correlation length (for example, for human skin,Lc ∼ 60–80μm) and the amplitudes of angular vibrations are less than one degree,statistical and nonlinear properties of the signal do not exert a considerable influ-ence on the detection of the motion law of a rough surface.2029 A fiber-optic sensorbased on these principles transforms skin vibrations caused by a pulse wave intothe corresponding motion of speckles, which is detected in the observation plane.To standardize the reflective properties of the surface and exclude bulk scatteringin tissues, the device employs a thin rubber membrane, which is attached to the sur-face of skin in such a manner that it does not perturb the motion of the skin surface.Various thin backscattering films produced by the spraying of a substance on a skinsurface can also be employed as standard reflectors. That this method also providessufficient efficiency in the case of an open skin surface, because the contributionof bulk scattering is suppressed to a considerable extent owing to sharp focusingof radiation onto the skin surface, and the skin surface itself can be satisfactorilydescribed in terms of Gaussian statistics.

13.5 Optical Speckle Topography and Tomography of Tissues

Extensive attention has been paid to the development of methods for speckletopography and tomography.76, 135, 136, 138, 139, 221, 472, 555, 607, 608, 761, 792, 1433, 1435–1441,

1444–1447, 1449, 1465–1467, 1973, 1981, 1987, 2032–2048 Local statistical and correlation analy-sis offers promise as a method for topographic mapping and structure monitoringof scattering objects. Local estimates of correlation characteristics [correlation orstructure functions or their parameters, see Eqs. (8.20) and (8.21), and Figs. 8.5and 8.6] and normalized statistical moments [the contrast, VI, and asymmetrycoefficient, Qa, are usually employed, see Eqs. (8.5)–(8.7)] are highly sensitiveto structural parameters of an object, such as the correlation length, Lc, and thestandard deviation, σL, of optical altitudes (thicknesses) of inhomogeneities; or therelevant correlation length, Lφ, and the standard deviation, σφ, of phase fluctua-tions of the boundary field (see Section 8.1) in the case of diffraction of focusedlaser beams.76, 155, 555, 1433, 1435, 1437, 1438, 1446, 1447, 2033–2042 An object under study canbe considered as an irregular system of lenslets with definite statistical character-istics that display intensity fluctuations similar to those observed when a focusedlaser beam is scanned over the surface of an object.1447

Intensity fluctuations include two components (see Fig. 13.21). The first com-ponent is a background with a relatively small and comparatively smoothly varyingamplitude. The second component is represented by infrequent high-intensitypulses related to matched inhomogeneities (the distances between the plane ofthe waist of the incident laser beam and the object, and between the object andthe photodetector, are matched with the effective focal length of the inhomogene-ity, which ensures effective reimaging of the waist of the laser beam into theobservation plane).



Figure 13.21 Realizations of speckle intensity fluctuations obtained with a focused laserbeam scanned over an epidermis sample of psoriatic human skin (epidermal stripping) (seeRef. 555). Upper and lower realizations were obtained with a laser beam focused in frontof and behind the sample surface, respectively. Middle realization corresponds to a laserbeam focused precisely on the surface.

We can classify inhomogeneities by analyzing the contrast, VI, and the asym-metry coefficient, Qa, as functions of the distance between the waist plane of thelaser beam and the surface of an object. Using this approach, we can reconstructstatistical distributions of fluctuations of the refractive index of a medium.77 Thefact that VI and Qa abruptly increase when the ratio of the radius of the laserbeam to the correlation length satisfies the condition w/Lφ ∼ 1 is a direct mani-festation of the microfocusing effect in the far-field diffraction zone1447, 2038 (seeFig. 13.22 for VI, �z = ±0.4 mm). The growth in the ratio w/Lφ (|z| > 0.4 mm) isaccompanied by a decrease in the quantities VI and Qa, which reach values corre-sponding to completely developed speckles. These effects can occur in the case ofweakly scattering objects, such as thin tissue layers or cellular monolayers, whenLc ∼ Lφ ∼ d (where d is the thickness of the sample), Lc � λ, and σφ relatedto phase fluctuations of the field is completely determined by fluctuations of therefractive index, δn.

Multiple scattering is characteristic of optically thick tissue layers. In this case,the spatial distribution of scattered light has a broad angular spectrum, and depo-larization effects play an important role. The spatial distribution of correlationproperties of the scattered field, which is related to the structure of an object, canbe considered in a manner similar to diffusion-wave spectroscopy [see Eq. (8.43)],with allowance for the fact that an object has a static structure, and a laser beam(or the object itself) is scanned over the surface of the object at a definite rate.Along with the chosen beam radius and the character of optical inhomogeneities


692 Chapter 13

Figure 13.22 Correspondence between the contrast values (a) and the shape of the distri-bution (b) of speckle intensity fluctuations (PDFs) as functions of the position of the waistof a focused laser beam with respect to the sample surface (epidermal stripping of psoriatichuman skin), �z (mm); �z = 0 corresponds to the case when the beam waist lies on thesurface of the sample (see Ref. 1447).

of the medium, the rate of scanning determines fluctuations of the scattered fieldin the time domain. In such a situation, the normalized autocorrelation function ofintensity fluctuations is generally defined by Eq. (8.20) with ξ ≡ t and �ξ ≡ τ.The behavior of the structure function [see Eq. (8.21)] near the zero value of itsargument, which corresponds to the highest efficiency of high-frequency spatialintensity fluctuations, can be conveniently characterized in this case in terms of theexponential factor, νI:1447, 2033

νI = ln[DI(�τ2)/DI(�τ1)

]ln(|�τ2|/|�τ1|) . (13.11)

To analyze polarization properties of speckle fields, we can employ the fol-lowing time-domain first- and second-order statistical characteristics of intensityfluctuations of scattered light in the paraxial region, which should be measuredfor two orthogonal linear polarizations (relative to the polarization of the probingbeam):555

1. Mean intensity of speckles,

⟨Isp

⟩ = ⟨I||

⟩ + 〈I⊥〉 (13.12)



Figure 13.23 Optical scheme of a scanning polarization-sensitive spatial speckle cor-relometer (see Ref. 221). ADC, amplitude-digital convertor; MO, micro-objective.

2. Cross-correlation function (correlation coefficient) for two polarizationstates,

r⊥||(τ) = ⟨[I||(t) − ⟨

I||⟩] · [I⊥(t + τ) − 〈I⊥〉]⟩ , (13.13)

where the indices (⊥, ||) denote combinations of polarization states and averagingis performed over the trajectory of scanning.

Figure 13.23 presents the optical scheme of a spatial speckle correlometerintended for the topography or tomography of comparatively thin samples of tis-sues. This device employs a focused laser beam approximately 5 μm in diameterproduced by a single-mode uniphase He-Ne laser. Structure patterns of an objectwere usually reconstructed through the 2D scanning of the object and an appropri-ate analysis of statistical and correlation properties of scattered light. The scanningstep in both coordinates was 5 μm. A photodetector was placed along the directionof the axis of the incident laser beam (scattering exactly in the forward direction).The diameter of the entrance pinhole was approximately 25 μm, which is muchless than the mean diameter of a speckle. The maximum rate of scanning wasabout 5 mm/s. The electronic units employed made it possible to obtain at least20 equidistant counts per single step of scanning. An object was usually placedin the waist of the incident laser beam. The position of an object relative to thebeam waist and the orientation of a polarization analyzer mounted in front of thephotodetector were adjusted manually.

As discussed above, the estimation of structural parameters of a tissue,such as the characteristic size of local inhomogeneities and spatial fluctuationsof the refractive index, generally requires certain assumptions concerningthe scattering model. One of the simplest models of scattering is themodel of a random phase screen with Gaussian statistics of inhomogeneities


694 Chapter 13

(see Section 8.1).223, 1425, 1427, 1447, 2039 In many cases, statistical models for livingstructures are much more complicated. In particular, some of these models arenonlinear and may take into account multiple scattering. Despite the lack of well-developed models for the structure of many tissues, any empirical informationconcerning statistical properties of scattered light is useful for the analysis of struc-ture images of tissues. Such information may also be useful for the development ofstructure models themselves.

Human skin is one of the most natural objects for the application of opticalspeckle correlometry.76, 1446, 1447, 2033, 2034 All structure-specific features of the skinsurface are manifested in statistical and correlation properties of the speckle fieldproduced in the far-field diffraction zone when skin samples or skin replicas areprobed with a focused laser beam. The technology that permits one to obtain thinslices (strippings) of epidermis with the use of medical glues and quartz substrates(or glass, or metal) is very convenient for in vitro structure studies of epidermisby means of speckle-correlation optics.1446, 1447 The thickness of slices in this caseusually ranges from 30 to 50 μm. This technology allows one to obtain five to sevensequential strippings from the same place. As an example, Fig. 13.21 presents threerealizations for intensity fluctuations obtained by scanning a skin epidermis samplefrom an area of psoriasis focus of a patient for three different positions of the waistof the laser beam. These thin layers of normal and psoriatic epidermis demonstratedthat such samples can be described within the framework of a model of single orlow-step multiple scattering, because only insignificant depolarization effects wereobserved in the far-field zone.

The contrast, VI, and the asymmetry coefficient, Qa, of intensity fluctuations inthe far-field zone as functions of the variation in the defocusing parameter, �z, fornormal and psoriatic epidermis display two maxima near the area of exact focusing(�z = 0).1447 Figure 13.24 shows such a dependence for a sample of psoriatic epi-dermis, along with the relevant PDFs for intensity fluctuations. The behavior of thefirst-order statistical characteristics confirms the validity of the lenslet approachfor the description of scattering properties of epidermis. Normal epidermis (inwhich scatterers have smaller sizes and more uniform distribution) is characterizedby a partial overlapping of the maxima mentioned above. The symmetry in thearrangement of VI and Qa peaks with respect to the plane of the beam waist allowsus to assume that the statistical weights of negative and positive lenslets in anensemble of scatterers are equal to each other.

The differences between the curves VI(�z) and Qa (�z) for samples of normaland psoriatic epidermis are attributable to the changes in the structure of a tissuecaused by the disease. These changes are associated with the appearance of parak-eratotic foci (the structure of cells near such a focus is substantially disordered)and the saturation of surrounding tissues with interstitial fluids (which decreasethe efficiency of scattering, similar to immersion fluids). Later stages of the dis-ease are characterized by the appearance of microspaces filled with air and scalingin the formation of inhomogeneities, which increases scattering and changes itscharacter.1447, 2040 For small �z, VI is greater than 1, reaching the values of 1.6–1.7



Figure 13.24 Statistical dependencies lnQa and lnVI for normal and psoriatic skin samples(strippings of human epidermis); + indicates the values of Qa and VI for developed speckles(see Ref. 2040).

for certain samples. As a rule, samples of normal skin display higher contrast thansamples of psoriatic skin. Parametric dependencies for lnQa and lnVI plotted forvarious �z illustrate the differences in statistical properties of samples of normaland psoriatic skin (see Fig. 13.24). For normal skin, the first derivative of the func-tion lnQa = f (lnVI) is greater than that for psoriatic skin. This derivative has anegative slope in the case of normal skin and a positive slope for pathological skin.For developed speckle fields with VI = 1 and a negative exponential PDF of inten-sity fluctuations [see Eq. (8.9)], we have Qa = 2 (these points are indicated by aplus sign in Fig. 13.24).

Thus, the first-order statistics can be used as a simple and efficient criterion forthe recognition of structurally specific features of tissue samples. Investigationsof special skin replicas demonstrated that this technique is also efficient for thesemiquantitative determination of the dryness and fatness of skin.2036, 2041

Second-order statistical characteristics of intensity fluctuations are also highlysensitive to structural changes in tissues.1446 For normal skin, normalized 1D auto-correlation functions of intensity fluctuations are characterized by comparativelysmall values of the correlation length, LI ∼ 60–80 μm, and the absence of consid-erable fluctuations of the correlation coefficient on large scales (see Fig. 8.5). As a


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psoriatic plaque arises, the AFs display a nearly twofold increase in the correlationlength, LI ∼ 95–180 μm, and the appearance of large-scale aperiodic oscillationswith a comparatively large amplitude. Effective sizes of structural inhomogeneitiesgenerating such oscillations correlate with the sizes characteristic of an ensembleof parakeratotic foci. Detailed analysis of oscillatory components of the AF shouldallow one to estimate the surface density of parakeratotic foci and their mean sizes.

In the range of high spatial frequencies of approximately 1 μm−1 and higher,the structure function or its exponential factor, νI [see Eqs. (8.21) and (13.11)],are preferable for the description of intensity fluctuations. Local estimates of theexponential factor permit one to determine the contribution of high-frequencystructure components of a tissue and to find their spatial distribution in the formof topograms. Figure 13.25 presents topograms obtained with the use of this tech-nique for samples of normal and psoriatic epidermis.221, 2035, 2042 The topograms andthe corresponding distributions of the exponential factor (see Fig. 13.26) displaystructure changes related to different stages of pathology development. The valuesof νI were averaged along the direction of the x-axis with an averaging gate con-taining no less than 103 counts. Epidermis of normal skin with comparativelysmall-scale inhomogeneities is characterized by a slightly smaller mean value and agreater variance of parameter νI than the early and middle stages of the formationof a psoriatic plaque (see Figs. 13.25 and 13.26). Large-scale structure features,such as fragments of a skin pattern, are clearly shown in the topogram of normal

Figure 13.25 Topograms of the exponential factor, νI, obtained for samples of epidermalstrippings of human skin: normal skin (a) and psoriatic skin (the middle stage of the disease)(b) (see Ref. 221).



Figure 13.26 Evolution of the distributions of the exponential factor, νI , in the progressof psoriasis (see Ref. 221): normal skin [corresponding to Fig. 13.25(a)], early stage ofpsoriasis, middle stage of psoriasis [corresponding to Fig. 13.25(b)], and late stage ofpsoriasis.

skin. The middle stage of pathology is characterized by a small variance and a rela-tively large mean value of the parameter under consideration. In the late stage of theprocess, the variance grows, the mean value of the parameter νI slightly decreases,and the symmetry of the distribution function lowers. The stages of the formationof a psoriatic plaque, clearly distinguished by means of correlation spectroscopy,are consistent with the results of clinical observations.

The control of optical properties of tissues, particularly the possibility of con-siderably decreasing the scattering coefficient, may become a key point in theoptical tomography of tissues in the process of searching for small tumors atearly stages of their formation (see Chapter 9). Figure 9.8 presents two recordedfragments corresponding to the early and later stages of tissue optical clearing.Characteristic changes in speckle structures in the far-field zone were visuallyobserved on a screen located in the plane of a photodetector and recorded inreflected light by means of a CCD camera.221, 238 The evolution of typical nor-malized AFs of intensity fluctuations for sclera in the process of sclera clearingmeasured with the use of a speckle correlometer (see Fig. 13.23) is shown inFig. 13.27. Within small time intervals (1–2 min), the time evolution of the shapeof the autocorrelation peak, which is associated with the transition of a tissue fromone scattering regime to another, can be approximated by an exponential curve,whereas for large time intervals, this process can be approximately described by aGaussian curve. The initial stage of the process is characterized by the existenceof many scales of intensity fluctuations (the AF displays at least three distinguish-able values of its slope). At later stages of clearing, the half-width of the AF peak


698 Chapter 13

Figure 13.27 Evolution of the normalized autocorrelation function of intensity fluctuations inthe speckle field produced by light scattered from a sample of human sclera in the processof scleral enhanced translucence in trazograph-60; the thickness of the sample is 0.6 mm;the measurements were performed with a sample processed in the solution during 120,220, 420, and 820 s (see Ref. 221).

Figure 13.28 Typical time dependencies of the exponential factor, νI, and the normalizedmean intensity, 〈Is〉/I0, measured at the observation point for a scleral sample placed intrazograph-60; λ = 633 nm (see Ref. 221).

tends to a value of (0.3–0.4) × 10−3 s, which is similar to the ratio w/v of the waistradius of the incident beam to the scanning rate. This effect can be employed as acriterion of the completion of the transition from multiple to single scattering. Thetime evolution of νI [see Eq. (13.11) and Fig. 13.28] characterizes the behavior ofhigh-frequency components of intensity fluctuations.

The exponential factor and relative fluctuations of the mean intensity oftransmitted light have substantially different rates of response to the action ofhyperosmotic OCAs: νI is especially sensitive to the action of OCAs at early stagesof clearing (within ∼1.5 min for trazograph-60), whereas transmission reachesits maximum only by the tenth minute. This difference in response rates can beaccounted for by the fact that the correlation properties of the field, characterized bytransition from uniform to nonuniform speckle distributions, substantially changeat initial stages of matching the refractive indices. By contrast, maximum colli-mated transmission is achieved only when the refractive indices are completelymatched.

Straightforward modeling of the transport of initially collimated photons witha wavelength of 600 nm through a fibrous tissue consisting of collagen fibers witha mean diameter of 100 nm and a refractive index nc = 1.474, surrounded by a



ground substance whose refractive index varies within the range n0 = 1.345–1.474,shows that, even with partial matching of refractive indices, n0 = 1.450, non-scattered (∼67%) and singly scattered (∼24%) photons dominate in transmittedlight (see Fig. 9.6).791 This prediction agrees well with the measured transmis-sion and reflection spectra of sclera and the data on correlation measurements (seeSection 9.3).791, 792

Another specific feature of scleral clearing is the appearance of quasi-periodicoscillations of mean-intensity transmission, which are also manifested in correla-tion characteristics. These oscillations have small amplitude and are clearly visibleat later stages of translucence, when the primary dynamic processes associated withthe directed diffusion of the substance from the solution into the tissue and of waterfrom the tissue to the solution are close to completion. The characteristic oscilla-tion time is ∼1.5–2.0 min. Apparently, a process with such a characteristic timecan be attributed to the nonuniformity of the diffusion of substances inside a tissuein space and time. This effect may be accounted for by the multistage character ofthe diffusion process. At the first stage, diffusion of OCA into a tissue and the flowof water out of the tissue partially equalize the refractive indices of hydrated colla-gen and the intercollagen substance. Under these conditions, optical transmissionof a tissue grows until the dependence under study saturates. However, at the sec-ond stage, a relatively weak process of the interaction of the new ground substancewith collagen is manifested. The ground substance slightly lowers its refractiveindex through the dehydration of collagen, whereas the refractive index of col-lagen increases. The resulting mismatch of refractive indices slightly decreasesoptical transmission. At the next stage, a certain violation of the balance betweenthe pressures of water and OCA in the solution and tissue generates the diffusionof water from the tissue and OCA into the tissue, which leads to the more exactequalization of the refractive indices, and transmission grows again. Then, the pro-cess described above is repeated and transmission oscillates in the time domain.Such oscillations are observed within the entire period of time when a hyperos-motic agent acts on a tissue, up to the fortieth to fiftieth minute in this particularexperiment.221, 238, 555 Probably, oscillations of a similar nature with the time periodof ∼2.5–3.5 min were registered for in vivo hamster skin following the topicalapplication of glycerol as an OCA using an OCT system as a detector.1721

As discussed earlier (see Subsection 9.6.1), transition of a scattering objectfrom the regime of multiple scattering to that of single scattering should change thepolarization properties of scattered radiation, which can be described in terms ofthe first- and second-order statistical characteristics [see Eqs. (13.12) and (13.13)].At the early stage of sclera optical clearing, both polarization components oftransmitted light have approximately equal intensities. However, in the processof clearing, the component polarized along the polarization of the incident beambegins to dominate over the other component (see Fig. 9.10).555 These experi-mental data demonstrate the reversibility of the optical clearing process, whichis important for living systems, and reveal the high sensitivity of polarizationcharacteristics to structural changes in a tissue.


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Figure 13.29 Evolution of the cross-correlation coefficient for two orthogonal polarizationsof intensity fluctuations in the speckle field produced in the observation plane by a laserbeam scanned over a scleral sample processed in trazograph-60 during (1) 200 s and (2)400 s. Scanning rate was 5 mm/s (see Ref. 221).

Translucent sclera features large-scale spatial inhomogeneities of scatteringand polarization properties in the form of a domain structure, with domain areason the order of 0.1–1 mm2. This structure is associated with a spatially nonuniformdistribution of the diffusion rate of substances and is clearly manifested in bothtime-domain realizations of intensity fluctuations for separate polarization compo-nents and the behavior of the cross-correlation function for these components (seeFig. 13.29) measured with a laser beam scanned over a sample.221 It is obvious that,similar to the correlation characteristics of speckle fields, polarization and cross-correlation characteristics can be employed for imaging the structure of tissues, aswell as for tissue topography and tomography.

13.6 Methods of Coherent Microscopy

Modern methods of microscopy are developing toward in vivo structural inves-tigations of individual cells without fixation of these cells, with simultane-ous monitoring of intracellular dynamic processes caused by the vital activ-ity of the cell. The above-mentioned laser Doppler microscope5, 24, 1463, 1970

and a high-performance phase microscope with ultrahigh spatial resolution245,

252–259, 265–270, 1368–1373, 1873, 2049–2051 are examples of such devices. Another ten-dency in the development of microscopy is in vivo layer-by-layer analy-sis of tissues with high spatial resolution. Confocal microscopy1, 3, 28, 76, 120, 122,

351, 1128, 1502–1527, 1567, 1667, 1671, 1679, 1854, 1940, 1949, 2052 is a prominent example of thisdirection in microscopy (see Section 8.5 and Subsection 9.6.2). Holographicmicroscopy249–251, 260–264, 2053–2056 also offers much promise for numerous applica-tions (see Section 8.7).

A phase microscope described in Refs. 245, 267–270, 1873, and 2051 is aLinnik–Tolansky interferometer with a computer-controlled piezodriver of a mir-ror in the reference channel and a dissector (coordinate-sensitive detector) that



Figure 13.30 Diagram of a phase microscope (see Ref. 2049).

registers an interference pattern (see Fig. 13.30 and Section 8.7). In fact, sucha microscope is a microprofilometer with a spatial resolution up to 10 nm at awavelength of 633 nm. The temporal resolution provided by this microscope inthe investigation of dynamic processes is on the order of 1 ms. The resolutionin height for this device is 0.5 nm; the imaging area includes from 64 × 64 to256 × 256 pixels; the total gain is 105–106; the minimum pixel size is 5 nm; andthe time of data processing is 4–20 s. The information concerning the structureof an object is represented in the form of altitude (optical path length) topograms,cross sections, and 3D images. When dynamic processes are studied at an arbitrar-ily chosen point of an object, the results of investigations are represented in theform of time-domain realizations, Fourier spectra, or histograms. A phase micro-scope was employed for structural investigations of living and dried fibroblast cells(L 929) and mitochondria extracted from cells of rat liver in the normal and con-densed states.245, 1873 The phase images of L 929 cells obtained in these studiesare characterized by mean optical path lengths of light on the order of 600 nmfor a living cell and approximately 50 nm for a dried cell. These findings indicatethe possibility of efficient monitoring of this type of cell metabolism. Analogousimages of mitochondria demonstrate that the optical length of a normal mitochon-drion with respect to the environment is approximately 15 nm. For the condensedstate, the optical length is 3 nm. A microscope of this type was also successfullyemployed for structural investigations of the walls of fungi cells and erythrocyteswith high spatial resolution, for the study of intracellular motility with high tempo-ral resolution,2049 and for human carcinoma cells in different physiological statesinduced by hyperosmotic agents.2051

In more recent studies by Tychinskii et al.,267–270 the analysis of the generalaspects of phase microscopy and its prospective developments can be found (seealso Section 8.7). Some specific research results are discussed, for example, on cellrefraction due to its metabolic activity;268 on tumor model for breast cancer;269 andon the reaction of the nucleoli of the cell nucleus to toxic effects.270

Basic research and a wide spectrum of elegant applications of quantitativephase microscopy for imaging of cells and tissues conducted by the researchgroups of Feld and Popescu are presented in Refs. 252–259 and 1368–1373


702 Chapter 13

(see also Section 8.7). For cells, these studies include quantifying erythrocytestructures, dynamics, and mechanics by phase microscopy,252, 256, 259 combineddiffraction phase and fluorescence microscopy,253 live cell refractometry usingphase/confocal microscopy258, 1370 and microfluidic devices,254 tomographic phasemicroscopy,255 quantitative phase imaging of cell structure and dynamics innanoscale;257 for tissues: Fourier transform light scattering of inhomogeneousand dynamic tissue structures,1368, 1369 tissue refractometry using Hilbert phasemicroscopy,1370 measuring tissue optical properties from quantitative phase imag-ing of thin slices,1369, 1371 and tissue refractive index evaluation as a marker ofdisease.1372

Confocal laser scanning microscopy, the principles of which are discussedin Section 8.5, is a well-developed imaging technique for biomedical investi-gations.1, 3, 28, 76, 351, 1128, 1502–1527, 1567, 1667, 1671, 1679, 1854, 1940, 1949, 2052 For example, inin vivo morphometry using real-time confocal microscopy of human epidermis,spatial resolution better than 1 μm and depth profiling up to 150–250 μm, depend-ing on the anatomical site and skin optical characteristics (color, transparency),were achieved.2052 Some of these results on the estimation of nuclear size andnumber of keratinocytes for different layers of the living human epidermis are pre-sented in Table 13.1. The resolution achieved in structural studies of tooth dentineis comparable with the characteristic resolution of scanning electron microscopy,and additional subsurface tissue imaging with resolution of 1 μm for depths up to30–50 μm is provided.1507

Three-dimensional imaging of cells in different layers of corneal epithe-lium made it possible to reveal the character of mitosis in such cells.1515, 1516

Figure 13.31 displays a typical scheme of a confocal microscope where scanning is

Figure 13.31 Diagram of a confocal microscope with optically conjugate slits and scanningalong the z-axis (see Refs. 1 and 1503). F1, F2, and F3, filters.



Table 13.1 Estimation of nuclear size and number of keratinocytes in horizontal opticalsections of the living epidermis (see Ref. 2052).

Epidermal nuclei Diameter, µm Density, number/mm2

Stratum granulosum 12–15 1500Stratum spinosum 9–12 4000Stratum basale 6–8 7000

performed along the z-axis (along the light beam) (see Ref. 1, pp. 555–575). Sucha microscope is intended for layer-by-layer analysis of eye structure. Radiation isdelivered to the microscope by means of an optical fiber. The microscope is basedon two optically conjugate slits. One of these slits is imaged onto an object, whereasthe second slit is placed in front of a photodetector. An objective is scanned alongthe z-axis by a computer-controlled piezodriver. Immersion liquid provides opticalmatching between the objective and the eye under study.

Figure 13.32 shows another type of slit-scanning confocal microscope.Such a microscope allows one to obtain images of an object at differentdepths.1508, 1509, 1513–1516 This microscope operates in real time and can be employedfor in vivo studies of eye tissues. The primary element of the microscope is a two-sided mirror, which implements transverse scanning without shifting the axis of thereflected beam (this scheme was initially proposed by Svishchev in 1969 for theinvestigation of transparent scattering objects, including living nerve tissues). Thediminished image quality due to the motion of a patient’s eyes was excluded withthe use of an electronic scheme, which ensured the required scanning frequencyand phase synchronization between all elements of the system. As an example,Fig. 13.33 presents an image of endothelium cells of human cornea obtained withthe use of the confocal microscope shown in Fig. 13.32.1513 High-quality layer-by-layer images of cellular structures of eye tissues and skin in the normal andpathological states, as well as the dentin structure of human teeth, are presentedin Refs. 1, 3, 76, 120, 122, 351, 1128, 1502–1527, 1567, 1667, 1671, 1679, 1854,1940, 1949, and 2052.

Figure 13.32 Diagram of a slit-scanning confocal microscope operating in real time (seeRef. 1508). M, mirrors; L, lenses; S1 and S2, conjugate slits; and M–M, scanning two-sidedmirror.


704 Chapter 13

Figure 13.33 Optical map of human cornea in vivo. Image shows endothelial cells on therear surface of cornea. Optical mapping is performed at the depth of 500 μm with respect tothe cornea surface. Dark areas in the image correspond to pathological endothelium (seeRef. 1513).

Depending on the source of light employed, the detecting system, and the typeof tissue under investigation, averaging over several expositions (frames) may benecessary to achieve a satisfactory signal-to-noise ratio. For example, for weaklyreflecting eye tissues (usually, less than 1%), four to eight frames may be neces-sary. However, if a highly sensitive video camera in combination with a broadbandvideo tape recorder is employed as a detector, averaging over frames is not nec-essary, and real-time in vivo measurements can be conducted.1508, 1509 Althoughconfocal microscopes can operate with mercury or xenon arc or halogen lamps,monochromatic laser radiation provides images with higher quality owing to theabsence of chromatic aberrations introduced by the optical system. However, thetype of a laser should be chosen with allowance for the depth of penetration of laserradiation into a tissue and the transmission of the optical system of a microscope.

Comparative analysis of confocal and heterodyne scanning microscopes andtheir applications for the investigation of scattering objects have demonstrated that,in many cases, limitations of the confocal technique are primarily associated withthe small level of the signal rather than the degradation of an image due to scat-tered light.1519, 1520 Indeed, a satisfactory resolution in depth (selection of photonsreflected from a definite layer and elimination of the influence of scattered light)can be achieved when a confocal system has conjugate pinholes with a radius (inoptical units)

νp ≤ 2,

νp = 2πrpa1

λf1, (13.14)

where rp is the radius of the pinhole and al and fl are the radius and the focallength of a lens that focuses light on the pinhole. Such pinholes do not transmitmuch light. For example, with νp = 2, a pinhole transmits only 40% of radiation



incident on this pinhole within the limits of its aperture. At the same time, theheterodyne (interference) scheme involving a narrow-band light source eliminates,to a considerable extent, this restriction due to optical amplification. Eventually,the interference scheme allows one to obtain images of an object with the samesignal-to-noise ratio as in confocal microscopy, within time intervals shorter thanthose required in confocal microscopy. Additional advantages of the interferencescheme, which stem from the coherence of light and the use of the amplituderesponse of an object under study, are associated with the appearance of a newmechanism for suppressing scattered light and the possibility of detecting smallerdifferences in the reflectivities of various tissue layers. It is expected that the inte-gration of the previously considered approaches in one microscope and the useof broadband (low-coherence) sources of light (see Chapter 14) may considerablyimprove the selectivity of the system, which is important for the investigation ofnearly uniform tissues.1519, 1520

Speckle interferometry using sharply focused laser beams and spatial averag-ing of optical signals also has advantages in depth profiling of scattering objects.Using a speckle interferometer (see Fig. 8.7), glue-strippings of human skinattached to metal plates were investigated. Depth profiling of thin tissue layers witha subcellular resolution was obtained (see Fig. 13.34). This method allows one toestimate the thickness of tissue layers and the depth distribution of the refractiveindex. Appropriate transverse scanning of the object will produce tomograms witha spatial resolution of approximately 3 × 3 × 3 (μm).3 The optical gain of thisscheme and the possibility of using powerful lasers may allow one to obtain highvalues of signal-to-noise ratio.

Technical developments in the different fields of optical microscopy areincreasingly focusing on in vivo and in situ imaging of metabolic functions anddysfunctions. Observation of the dynamics of biological processes on micro-and nanoscales is required for a more detailed understanding of both cellularphysiology and pathology.

Figure 13.34 Depth profiling for glue-stripped human skin attached to a metal plate(dependence of the normalized modulation factor of the photoelectric signal, β/β0, on thelongitudinal displacement of the sample) (see Ref. 1449).


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13.7 Interferential Retinometry and Blood Sedimentation Study

Laser interferential retinometers used for monitoring of human retinal visual acu-ity are based on an optical dual-beam interferometer, which forms two coherentbeams that are focused to the nodal plane, N, of the eye and form a spatiallymodulated laser beam (SMLB) with parallel interferential fringes on retina (seeFigs. 8.9 and 13.35).5, 473, 1441, 2057 Period L of fringes and their orientation dependon corresponding parameters of the incident SMLB:5

L = Dλ

2l, (13.15)

where D is the mean distance between eye nodal plane and retina, λ is the wave-length, and 2l is the separation between two point light sources formed in the nodalplane.

Normal retinal visual acuity is defined as angular resolving power of the eyeand is characterized by the density of interferential fringes per degree of the viewangle:5

Nint =[

arcsin

(λ

2l

)]−1

. (13.16)

For the ideal conditions of front media of the eyes, the fringe pattern contrast atretina is very high, practically equal to unity, because of the high degree of mutualcoherence of the laser beams.

The procedure for estimating retinal visual acuity is simple.2057 First, a fringepattern with a large period is formed at the patient’s retina. The patient informs thedoctor when they are able to see a fringe pattern. Next, the period of the fringes isdecreased and the patient must indicate their ability to see the pattern. This proce-dure is repeated until the patient is unable to see the pattern. To avoid false patientresponses, fringes can be rotated on an arbitrary angle [see Fig. 13.35(b)].

For patients with cataractous (turbid) lens, scattering of an SMLB by a turbidmedia prevents creation of the fringe pattern [see Fig. 13.36(c) and 13.36(e)].2057

However, averaging the interferential pattern may improve the visibility of the ini-tial fringes (see Section 8.3), and therefore, this technique, with certain limits, maybe applicable for retinal visual acuity (RVA) estimations of eyes with cataract. Theoptical scheme presented in Fig. 13.36(a), in which SMLB is moved periodicallyby a deflector but fringes on the retina remain unmovable, provides such averaging.Certain other averaging schemes are also available.1441 Clinical data presented inTable 13.2 illustrate the applicability of laser RVA measurements for the predictionof RVA in patients with cataract.

Another example of SMLB application in medicine is monitoring of the ery-throcyte sedimentation rate (ESR). Usually, this test uses the measurement of thedistance over which the erythrocytes have fallen after one hour in a vertical col-umn of anticoagulated blood under the influence of gravity. The test is helpful inthe specific diagnosis of a several cases, including diabetes mellitus and myocar-dial infarction. The SMLB technique allows one to detect the temporal changes in


Tissue optics : light scattering methods and instruments for medical diagnosis

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