Post on 30-Dec-2015
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