Download Near Infared Devices in Biomedical Applications

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 = hn
• 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 = hn
• Both representations are used to describe
light propagation in tissues
Fundamental Optical Properties
•
•
•
•
Index of refraction, n (l)
Scattering Cross Section, ss
Differential Scattering Cross Section
Absorption cross section, sa

Index of Refraction
n  n(l)  i (l)
Complex Index of Refraction

Index of Refraction = Real Part

Re[n(l)]  n(l)
Phase velocity and wavelength of light in medium
l
lm 
n( l )
c
c m ( l) 
n( l )
Wave Frequency - independent of n
n

c
l

cm
lm
n1
sin q2  sin q1
n2
q2
n1
l2  l1
n2
q1
1
n2
n1

2

Reflection and Refraction
• Light path redirection due to boundary
– Reflection and Refraction
– Snell’s Law
Normal Incidence
n1
sin q2  sin q1
n2
4n1n 2
T
(n1  n 2 ) 2
(n1  n 2 )
R  1 T 
(n1  n 2 ) 2
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
^
P
s s (s)  scatt I
0
S is propagation direction of wave relative to scatterer
s  s s
l
Scattering Coefficient
1
s
Mean Free Path
Absorption Cross Section
Pabs
sa 
I0
a  s a
 1
la 
a
Absorption Coefficient
Absorption Mean Free Path=
Absorption length
Beer Lambert Law
dI  a Idz
I  I0 exp[a z]
I  I0 exp[laz]
Molar concentration mol/cm3
T  I /I0
Extinction Coefficient (cm2 /mol)
TRANSMISSION
ATTENUATION
ABSORBANCE
A  OD  log10 (I0 /I)  log10 (T)
Absorption and Emission
• Absorption Spectrum - l 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 ratio
Mie 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
Some concepts - Interference Contribution
Total Electric Field - Two light scatterers
Etotal(r,t)  E1(r,t)  E2 (r,t)
Total Energy = Square of Amplitude
U(r)  E total (r) E total(r)  [E (r)  E (r)  2E1(r) E 2 (r)]
 U1(r)  U 2 (r)  2E1 (r) E 2 (r)
2
1
= medium permittivity
E1 . E2 > 0 constructive interference
E1 . E2 < 0 destructivee interference
Average Interference E1 . E2 = 0
2
2
L
Pscatt  P(z)s sL
P(z)

L
Multiple Scattering
P(z  L) 
P(z)(1 s sL)
Mutliple Scattering - “Decoherence”
Radiation Transport Model
Power Scattered Out of Incident Wave
I0s sz  I0s Az  I0s sN layer
Remaining power after passing through layer
Pc (0  z)  I0 A  I0s sAz  I0 A(1 s sz)
Meaning of
(1 s sz)
What is it if it is zero???

L  z
Layers in length L of thickness deltaz
L 
Pc (L)  I0 A(1 s sz)  I0 A(1 s s )

As increases --- exponential convergence

L 
I0 A(1 s s )  I0 Aexp(s sL)

No absorption -

total
Pscatt
 Ic (0)A  Ic (L)A  I0 A(1 exp[s sL])
 I0 A(1 exp[s sN / A])
Power Expansion

(s sN / A) m s s
1 s s2 2 1 s s3 3
 N
N 
N  ..
1 exp[s sN / A]  
2
3
A
2A
6A
m!
m1
Limiting Cases
• When can we say
scatt
total
P
 NI0s s
Waves Scattered only Once

Multiple
versus Single Scattering
sL 1
Radiation Transport
(Boltzmann Equation)
1 I(r, sˆ,t)
 sˆ  I (r, sˆ,t)  (a  s )I(r, sˆ,t)
cm
t
a  s
 Q(r, sˆ,t)

p(sˆ  sˆ )I(r, sˆ ,t)d

4 4 
DYNAMICS
sˆ
dA
r
q
d
dP  I(r, sˆ,t)cosqdad
Light power - Specific intensity I

Incident and Diffuse Light
I(r, sˆ,t)  Ic (r, sˆ,t)  Id (r, sˆ,t)
Coherent Light
1 Ic (r, sˆ,t)
 sˆ  Ic (r, sˆ,t)  (a  s )Ic (r, sˆ,t)
cm
t
Coherent and Incoherent Light
1 Id (r, sˆ,t)
 sˆ  Id (r, sˆ,t)  (a  s )Id (r, sˆ,t)
cm
t
a  s
 Q(r, sˆ,t)

p( sˆ  sˆ )Id (r, sˆ ,t)d

4 4 
a  s

p( sˆ  sˆ )Ic (r, sˆ ,t)d

4 4 
Incident and Diffuse Light
a  s
p(sˆ  sˆ)Ic (r, sˆ ,t)d

4 4 
- Single scattering
0 at steady state
1 Id (r, sˆ,t)
 sˆ  Id (r, sˆ,t)  (a  s )Id (r, sˆ,t)
cm
t
0 = ignore multiple scattering
a  s
 Q(r, sˆ,t)

p( sˆ  sˆ )Id (r, sˆ ,t)d

4 4 
a  s

p( sˆ  sˆ )Ic (r, sˆ ,t)d

4 4 
Absorption Dominant Limit
sˆ  Id (r, sˆ )  (a  s )Id (r, sˆ )
a  s

p( sˆ  sˆ )Ic (r, sˆ )d

4 4 
Straight line path of length s parallel to s^ is
dId
a  s
(r, sˆ)  (a  s )Id (r, sˆ) 
ds
4
dy
 P(s)y  Q(s)
ds
 p(sˆ  sˆ)I (r, sˆ)d
c
4
---- Remember????

Scattering Phase Function
SPF = Fraction of light scattered in s from incidence at s’
p( sˆ  sˆ ) 
4  ds s
( sˆ  sˆ )
s s  s a d
1
W0 
4

4
p( sˆ  sˆ )d
ss
s

s s  s a s  a
G= average cosine of scatter = measure of scatter retained in
the forward direction
1
g
p(cos q )cosq sin qdq

2W 0 4 
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
s  (1 g)s
cm
D
3(a  (1 g)s )
t'  a  (1 g)s
Reduced Scattering Coefficient
Diffusion Coefficient
Attenuation of medium

Diffusion Equation
Angular Dependence of specific intensity
1
3
Id (r, sˆ,t) 
d (r,t) 
Fd (r,t) sˆ f  sˆ
4
4
d (r,t)   Id (r, sˆ,t)d
Total Intensity
4
Fd (r,t)  Fd (r,t)sˆ f 
I
d
(r, sˆ,t) sˆ d Net Intensity Vector
4
1
d (r,t)   Fd (r,t)  a d (r,t)  Qc  Qs
c t
Fick’s Law
c m Fd (r,t)  Dd (r,t)

d (r,t)  D 2d (r,t)  a c m d (r,t)  Qc  Qs
t
Discussion Points
Human 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)  [C]L
AB = Absorbance
L=Photon Path length (cm)
[C]= Absorber Concentration
Eis
 the molar extinction coefficient moles/liter cm-1 or cm 2/mole
I  I0 exp(a L)
a  2.303[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