Near Infrared Devices in Biomedical Applications

Elisabeth S. Papazoglou, Ph.D.

School of Biomedical Engineering

Drexel University

October 2004

Outline

- BIOMEDICAL PHOTONICS- OPTICAL PROPERTIES OF TISSUE- RADIATIVE TRANSPORT MODEL

- Diffusion approximation- NIR WINDOW- PHOTON MIGRATION SPECTROSCOPY

- Frequency Domain - ADVANTAGES / DISADVANTAGES- APPLICATIONS- ETHICAL CHALLENGES

Biomedical Photonics

• Biomedical Photonics vs. Biomedical Optics• Electromagnetic spectrum

– Gamma rays - 1019

– X-rays - 1nm to 1 Angstrom / 1018 Hz

– Ultra violet - 1016 - 1017 Hz

– Visible - 1015 Hz

– Infrared (near and far) 1 mm - 1 micron / 10 - 1012 Hz

– Microwave - 1 cm / 108 - 1012 Hz

– Radio frequency - 1 m / 108 Hz

ELECTROMAGNETIC SPECTRUM

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WHAT IS LIGHT ?

• Classical Viewpoint – Light is a oscillating EM field / E is continuous– Electromagnetic wave

• Electric / Magnetic Field - Polarization

• Quantum Viewpoint– Photons - E = h

• Both representations are used to describe light propagation in tissues

WHAT IS LIGHT ?

• Classical Viewpoint – Light is a oscillating EM field / E is continuous– Electromagnetic wave

• Electric / Magnetic Field - Phase and Polarization

• Quantum Viewpoint– Photons - E = h

• Both representations are used to describe light propagation in tissues

Fundamental Optical Properties

• Index of refraction, n ()• Scattering Cross Section, s

• Differential Scattering Cross Section• Absorption cross section, a

Index of Refraction

€

n≈

=n(λ)−iα(λ)Complex Index of Refraction

€

Re[n≈

(λ )] = n(λ )

Index of Refraction = Real Part

Phase velocity and wavelength of light in medium

€

cm (λ ) =c

n(λ )Wave Frequency - independent of n

€

m =λ

n(λ )

€

=c

λ=

cm

λ m

1

2

nn

€

2 =n1

n2

λ1

€

sinθ2 =n1

n2

sinθ1

Reflection and Refraction

• Light path redirection due to boundary– Reflection and Refraction– Snell’s Law Normal Incidence

€

sinθ2 =n1

n2

sinθ1

€

T =4n1n2

(n1 + n2)2

R =1− T =(n1 − n2)2

(n1 + n2)2

REFLECTION

TYPES OF REFLECTION

• Interface Reflection = Fresnel Reflection

• Diffuse Reflectance – Subsurface origin

Scattering

Incident Wave Scattered Wave

n1

n2

Biomedical Applications - Scattering

• Diagnostic Applications– Size, Morphology, Structure– Lipid membranes, nuclei, collagen fibers

• Therapeutic Applications– Optimal Light Dosimetry (Light treatment)

- Delivery

Scattering Cross Section

€

s(s)^

= PscattI0

S is propagation direction of wave relative to scatterer

Scattering Coefficient

Mean Free Path

€

μs = ρσ s

l =1

μ s

Absorption Cross Section

Absorption Coefficient

Absorption Mean Free Path= Absorption length

€

a =Pabs

I0

€

μa = ρσ a

€

la =1

μa

Beer Lambert Law

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dI = −μaIdz

I = I0 exp[−μaz]

€

I = I0 exp[−ελ az]

Extinction Coefficient (cm2 /mol)

Molar concentration mol/cm3

TRANSMISSION

€

T=I/I0

€

A = OD = log10(I0 /I) = −log10(T)ATTENUATIONABSORBANCE

Absorption and Emission

• Absorption Spectrum - Dependence

• Absorbed Light is dissipated

Photon emission Non radiatively /Kinetic energy transfer

Luminence Fluorescence, Phosphorescence

Coherent and Incoherent Light

• Coherence– Ability to maintain non random phase

relationship in space and time and exhibit stable interference effects

• Speckle pattern from laser (light amplification by stimulated emission of radiation)

• Incoherent light– Random spatial and temporal phase patterns– No Interference

Rayleigh Limit• Tissue structure size << Photon Wavelength

– Rayleigh Limit- Scatterer sees uniform electric field - Dipole moment can be mathematically expressed

– Elastic scattering / • Energy incident photon = Energy Scattering Photon

• INELASTIC SCATTERING - RAMAN

– LOSE ENERGY - STOKES

– GAIN ENERGY = ANTI-STOKES

1,000,000 Rayleigh photons for

1 Raman photon

Mie Theory

• Light scattering by spherical objects -

– Any size to wavelength ratioMie regime - where wavelength and scatterer are of the

same order of magnitude- Biomedical Applications = 500 to 1000 nm wavelength- Many cellular structures are of similar size

Absorption

• Energy is “extracted” from the light by molecules

• Diagnostic Applications - Energy Transitions at certain wavelengths - fingerprints

• Therapeutic Applications - Absorption of energy from a laser is the primary mechanism

- Electronic, Vibrational, Rotational Levels

€

E total (r, t) = E1(r, t) + E2(r, t)

Some concepts - Interference Contribution

Total Electric Field - Two light scatterers

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U(r) = εE total (r) ⋅E total (r) = ε[E12(r) + E2

2(r) + 2E1(r) ⋅E2(r)]

= U1(r) + U2(r) + 2εE1(r) ⋅E2(r)

Total Energy = Square of Amplitude

= medium permittivityE1

. E2 > 0 constructive interferenceE1

. E2 < 0 destructivee interference

Average Interference E1 . E2 = 0

Multiple Scattering

L

L

€

P(z)

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Pscatt = P(z)σ sρL

€

P(z + L) =

P(z)(1−σ sρL)

Mutliple Scattering - “Decoherence”Radiation Transport Model

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I0σ sρΔz = I0μ sAΔz = I0σ sN layer

Power Scattered Out of Incident Wave

Remaining power after passing through layer

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Pc (0 + Δz) = I0A − I0σ sρAΔz = I0A(1−σ sρΔz)

Meaning of

€

(1−σ sρΔz)

What is it if it is zero???

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L = ΓΔz

Pc (L) = I0A(1−σ sρΔz)Γ = I0A(1−σ sρL

Γ)Γ

Layers in length L of thickness deltaz

As increases --- exponential convergence

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I0A(1−σ sρL

Γ)Γ → I0Aexp(−σ sρL)

No absorption -

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Pscatttotal = Ic (0)A − Ic (L)A = I0A(1− exp[−σ sρL])

= I0A(1− exp[−σ sN / A])

Power Expansion

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1− exp[−σ sN / A] = −(−σ sN / A)m

m!m=1

∞

∑

€

= s

AN −

1

2

σ s2

A2N 2 +

1

6

σ s3

A3N 3 + ..

Limiting Cases

• When can we say

€

Ptotalscatt = NI0σ s

Waves Scattered only Once

Multiple versus Single Scattering

€

μsL <<1

Radiation Transport(Boltzmann Equation)

€

1

cm

∂I(r, ˆ s , t)

∂t= −ˆ s ⋅

r ∇I(r, ˆ s , t) − (μa + μ s)I(r, ˆ s , t)

+μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )I(r, ˆ ′ s , t)d ′ Ω + Q(r, ˆ s , t)

4π

∫

DYNAMICS

dA

r

€

ˆ s

d

€

dP = I(r, ˆ s , t)cosθdadΩ

Light power - Specific intensity I

Incident and Diffuse Light

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I(r, ˆ s , t) = Ic (r, ˆ s , t) + Id (r, ˆ s , t)

€

1

cm

∂Ic (r, ˆ s , t)

∂t+ ˆ s ⋅

r ∇Ic (r, ˆ s , t) = −(μa + μ s)Ic (r, ˆ s , t)

Coherent Light

Coherent and Incoherent Light

€

1

cm

∂Id (r, ˆ s , t)

∂t+ ˆ s ⋅

r ∇Id (r, ˆ s , t) = −(μa + μ s)Id (r, ˆ s , t)

+μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )Id (r, ˆ ′ s , t)d ′ Ω + Q(r, ˆ s , t)

4π

∫

+μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )Ic (r, ˆ ′ s , t)d ′ Ω

4π

∫

Incident and Diffuse Light

€

1

cm

∂Id (r, ˆ s , t)

∂t+ ˆ s ⋅

r ∇Id (r, ˆ s , t) = −(μa + μ s)Id (r, ˆ s , t)

+μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )Id (r, ˆ ′ s , t)d ′ Ω + Q(r, ˆ s , t)

4π

∫

+μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )Ic (r, ˆ ′ s , t)d ′ Ω

4π

∫

€

μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )Ic (r, ˆ ′ s , t)d ′ Ω

4 π

∫ - Single scattering

0 at steady state

0 = ignore multiple scattering

Absorption Dominant Limit

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ˆ s ⋅r

∇Id (r, ˆ s ) = −(μa + μ s)Id (r, ˆ s )

+μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )Ic (r, ˆ ′ s )d ′ Ω

4π

∫

Straight line path of length s parallel to s^ is

€

dId

ds(r, ˆ s ) = −(μa + μ s)Id (r, ˆ s ) +

μa + μ s

4πp(ˆ s ⋅ ˆ ′ s )Ic (r, ˆ ′ s )d ′ Ω

4 π

∫

€

dy

ds+ P(s)y = Q(s) ---- Remember????

Scattering Phase Function

SPF = Fraction of light scattered in s from incidence at s’

€

p(ˆ s ⋅ ˆ ′ s ) =4π

σ s + σ a

dσ s

dΩ(ˆ s ⋅ ˆ ′ s )

W0 =1

4πp(ˆ s ⋅ ˆ ′ s )d ′ Ω =

σ s

σ s + σ a4 π

∫ =μ s

μ s + μa

G= average cosine of scatter = measure of scatter retained in the forward direction

€

g =1

2W0

p(cosθ)cosθ sinθdθ4 π

∫

Limits of g

• g=0 for Rayleigh scattering – Forward and backward scattering are equally

probable

• g > 0

• g< 0

• G is an “anisotropy measure”

Scattering Dominant Limit: The Diffusion Approximation

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′ μ s = (1− g)μ s

D =cm

3(μa + (1− g)μ s)

μ t ' ≡ μa + (1− g)μ s

Reduced Scattering Coefficient

Diffusion Coefficient

Attenuation of medium

Diffusion Equation

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Id (r, ˆ s , t) ≅1

4πΦd (r, t) +

3

4πFd (r, t)ˆ s f ⋅ ˆ s

Φd (r, t) = Id (r, ˆ s , t)dΩ4 π

∫

Fd (r, t) = Fd (r, t)ˆ s f = Id (r, ˆ s , t)ˆ s dΩ4 π

∫

Total Intensity

Angular Dependence of specific intensity

Net Intensity Vector

€

1

c

∂

∂tΦd (r, t) +

r ∇ ⋅Fd (r, t) = −μaΦd (r, t) + Qc + Qs

cmFd (r, t) = −Dr

∇Φd (r, t)

∂

∂tΦd (r, t) = −D∇ 2Φd (r, t) − μacmΦd (r, t) + Qc + Qs

Fick’s Law

Discussion PointsHuman Tissue -Effective Refractive Index

Water - Index? Compare to other constituents?

Melanin - ?

Whole tissue ? Brain / Kidney?

Tooth ??

Index mismatch between lipids and cytoplasm

Scattering Properties

Size of organelles in cells = 100 nm -6 micron

Mitochondria are primary scatterers - 0.5-2 microns

Cell Nucleus = 4-6 micron in range

Melanosomes are 100 nm to 2 microns

Erythrocytes = 2 micron thick / 7-9 micron in diameter

Absorption Properties

• Therapeutic Window - 600-1300 nm

• Orange to NIR

• 600 region - hemoglobin / oxy and deoxy

• < 600 DNA, Tryptophan and Tyrosine

• 900 -1000 Water Absorption is very strong

Importance of Diffuse Light

• Diffuse reflectance

• Volume of tissue sampled

• Information about the bulk of the medium

• Limits of – Absorption Dominant Region– Scattering Dominant Region - Diffusion

Approximation

Melanosomes

for light skinned caucasians, fv = 1-3%

for well-tanned caucasions and Mediterraneans, fv = 11-16%

for darkly pigmented Africans, fv = 18-43%.

[Jacques 1996]:

Photon Migration Spectroscopy• Combine experiments with model based data analysis

• Absorption and scattering of highly scattering media• 600-1000 nm• Photons propagate randomly• Incoherent photons• Probes tissue vasculature

• BROAD MEDICAL APPLICATIONS

FREQUENCY DOMAIN INSTRUMENTS

• PHASE SHIFT • MODULATION DECREASE = RATIO OF DC/AC• FREQUENCY OF OSCILLATION REMAINS THE SAME

€

AB = Log(Io /I) = ε[C]L

AB = AbsorbanceL=Photon Path length (cm)[C]= Absorber Concentration is the molar extinction coefficient moles/liter cm-1 or cm 2/mole

€

I = I0 exp(−μaL)

μa = 2.303ε[C]

What is L???

IMPORTANT POINTS

• Absorption and scattering coefficicents• Rayleigh Limit / Mie Theory / Mie regime• Define g - g = 0, g positive, g negative• Extinction Coefficient• Diffusion and Absorption Approximation• Diffuse Reflectance Spectroscopy• Therapeutic Window• Melanin as a confounding factor• Applications of NIR - Limitations