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Transcript of Near Infrared Devices in Biomedical Applications Elisabeth S. Papazoglou, Ph.D. School of Biomedical...
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
€
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
€
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)
€
Pscatt = P(z)σ sρL
€
P(z + L) =
P(z)(1−σ sρL)
Mutliple Scattering - “Decoherence”Radiation Transport Model
€
I0σ sρΔz = I0μ sAΔz = I0σ sN layer
Power Scattered Out of Incident Wave
Remaining power after passing through layer
€
Pc (0 + Δz) = I0A − I0σ sρAΔz = I0A(1−σ sρΔz)
Meaning of
€
(1−σ sρΔz)
What is it if it is zero???
€
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
€
I0A(1−σ sρL
Γ)Γ → I0Aexp(−σ sρL)
No absorption -
€
Pscatttotal = Ic (0)A − Ic (L)A = I0A(1− exp[−σ sρL])
= I0A(1− exp[−σ sN / A])
Power Expansion
€
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
€
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
€
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
€
′ 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
€
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