Download Tissue Optical Properties

University of Cyprus
Biomedical Imaging and Applied Optics
Tissue Optical Properties
Introduction
• Interaction between
Light and Tissue
•
•
•
•
•
Reflection
Refraction
Absorption
Fluorescence
Scattering
Light
Source
Optical
Signal
Tissue
• Depends on
• Constituents of tissue
• Optical properties of
tissue
• Propagation of light
2
Absorption
• Extraction of energy from light by a molecular species
• Diagnostic applications: Transitions between two energy
levels of a molecule that are well defined at specific
p
wavelengths could serve as spectral fingerprint of the
molecule
• Various types of Chromophores (light absorbers) in Tissue
• Wavelength-dependent absorption
• Tumor detection and other physiological assessments (e.g. pulseo
oximetry)
et y)
• Therapeutic applications: Absorption of energy is the primary
mechanism that allows light
g form a source (laser)
(
) to produce
p
physical effects on tissue for treatment purpose
• Lasik (Laser Assisted in situ Keratomileusis) Eye Surgery, Tatoo
Removal, PDT
3
Absorption
• Absorption occurs when the photon frequency matches the
frequency associated with the molecule
molecule’s
s energy transition
‘frequency’
• Electrons absorb the energy of the light and transform it into vibrational
motion
• The
Th absorption
b
ti off a photon
h t results
lt in:
i
•
quantized change in charge separation
•
quantized excitation of vibrational modes
• Electrons interact with neighboring atoms Æ convert vibrational energy
into thermal energy
4
• Each electronic energy
gy
levels is associated with
many vibrational energy
levels
• Absorption of UV and
visible
i ibl light
li ht promotes
t
transition between
electronic energy levels
Potentia
al Energy
Absorption
Vibrational Energy Level
S1
Electronic
E
Energy
Level
• Absorption of infrared
light promotes
transitions between
vibrational energy
gy levels
5
S0
Absorption
• Absorption
p
Cross-section,,
σ [m2]
• Consider a chromophore
id li d as a sphere
idealized
h
with
ith a
particular geometrical size.
• Consider that this sphere
p
blocks incident light and casts
a shadow, which constitutes
absorption.
absorption
• The size of absorption shadow
= absorption cross-section
• Qa: absorption efficiency
σ a = Qa ⋅ A
6
Absorption
Pabs = Ioσa
Pin =IoA
Pout = Io(A-σa)
Outgoing Beam
Incident Beam
Area =A
-
Area = σa
=
Pout = Io(A-σa)
area = A - σa
Pabs
σa =
Io
7
Absorption
• Assumptions
• Cross section is independent of relative orientation of the impinging
light and absorber uniform distribution of Na (molecules/cm3) identical
absorbing particles
• Absorption Coefficient, ma [1/m]
μa = N a ⋅ σ a
• Absorption
p
cross-sectional area p
per unit volume of medium
• Absorption mean free path, la [m]
la =
1
μa
• Represents the average distance a photon travels before being
absorbed
8
Absorption
• Transmission and Absorbance ((macroscopic view))
• Transmission
I
T=
Io
• Absorbance (attenuation, or optical density)
⎛ Io ⎞
A = − log(T ) = log ⎜ ⎟
⎝ I ⎠
9
Absorption
• Lambert – Beer Law:
• The linear relationship between absorbance and
concentration of an absorbing
g species.
p
• Relates μα, transmission, and absorbance
I = Ioe
− μa ⋅b
μa = N a ⋅ σ a
Pabs
σa =
IO
σ= absorption cross-sectional area [cm2]
IO = The intensity entering the sample at z = 0 [w/cm2]
I = The intensity of light leaving the sample [w/cm2]
b = pathlength traveled in the sample [cm]
10
Absorption
Absorbers in Tissue
NIR
• NIR
• Hemoglobin
• Lipids
• Water
VISIBLE
UV
• UV-VIS
•
•
•
•
•
•
DNA
Hemoglobin
Lipids
Structural protein*
protein
Electron carriers*
Amino acids*
* Absorbers that fluoresce when excited in the UV-VIS
11
Absorption
UV Absorption
• Protein
Protein, amino acid,
acid fatty acid
and DNA absorption dominate
UV absorption
• Protein
• Dominant ‘non-water’
constituent of all soft tissue, ~
30%
• Absorption properties
determined by peptide bonds
and amino acid residues
• Peptide excitation about λ =
190 nm
• Amino acids absorption at λ =
210 - 220 nm and 260 – 280 nm
• DNA
Amino Acid
Peptide
• Absorbs radiation for λ ≤ 320 nm
• Large water absorption λ< 180
nm
12
Absorption
Infrared Absorption
• Protein IR absorption peaks at
6.1, 6.45, and 8.3 μm due to
amide excitation
• Absorption depth ≤ 10 μm in λ
= 6-7 μm region
• Water absorption peak at
0.96, 1.44, 1.95, 2.94 and
6.1 μm
• Absorption depth
• ~ 500 mm at λ = 800 nm
• <1 μm at λ=2.94 μm
• ≤ 20 μm throughout λ ≥ 6 μm
13
Extinction Coe
eff (1/cm M)
Absorption
10
6
10
5
10
4
Main Absorbers at visible and NIR
¾ Hemoglobin
¾ Lipid
p
Hb
10
3
10
2
Hemoglobin
HbO2
400
500
600
700
800
900
WAVELENGTH (NM)
1000
Each hemoglobin has 4 heme
(Fe2+) sites to bind O2
• Responsible for oxygen transport
•HbO2 and Hb
• oxygen saturation is an indicator
of oxygen delivery and utilization
as wellll as metabolic
b li activity
i i
•
14
Hemoglobin
• Responsible for oxygen transport
• HbO2 and Hb
• oxygen saturation is an indicator of
o gen delivery
oxygen
deli er and utilization
tili ation as well
ell
as metabolic activity
• Deoxyhemoglobin has lower
absorption than oxyhemoglobin in
the blue and green
• Bright red arterial blood
• Bluish venous blood
Ex
xtinction Coe
eff (1/cm M)
Absorption
10
6
10
5
10
4
Hb
10
3
HbO2
10
2
400
500
600
700
800
900
WAVELENGTH (NM)
• Absorption peaks for HbO2
• 418, 542, 577, and 925 nm
• Absorption peaks for Hb
• 550, 758, 910 nm
• Isosbestic points
• 547, 569, 586, and 798 nm
15
1000
Absorption
Lipid (Fat)
• Monitoring of physiological
changes in female breast tissue
• Tissue layer model
HEMOGLO
OBIN (1/mm mM
M)
• Site-specific measurements of
body composition
3.0
0.06
Water
25
2.5
0.04
2.0
HB
0.03
1.5
0.02
1.0
0.5
0.05
Lipid
HbO2
0.01
0.00
0.0
0
0
600
700
800
900
1000
WAVELENGTH (nm)
16
WATER & FA
AT (1/ mm mM)
• Important energy store in the
body
Scattering
• Change
g of direction of propagation
p p g
and/or energy
gy of
light by a molecular species
• Diagnostic applications: Scattering depends on the
size, morphology, and structure of the components
in tissues (e.g. lipid membrane, collagen fibers,
nuclei).
l i)
• Variations in these components due to disease would
affect scattering properties
properties, thus providing a means for
diagnostic purpose
• Therapeutic applications: Scattering signals can be
used to determine optimal light dosimetry and
provide useful feedback during
p
g therapy
py
17
Scattering
Purely absorbing
With Scattering
Photon pathlength = L
Photon pathlength >> L
L
Lambert- Beer Law does not apply here!!!
Need to calculate true pathlength of light
18
Scattering
• Why is the sky blue, clouds
white and sunsets red?
white,
• Blue skies are produced due to
scattering at shorter wavelengths
• Visible light (violet & blue) are
selectively
l ti l scattered
tt d b
by O2 and
d N2 –
much smaller than wavelengths of the
light
• violet and blue light has been
g
scattered over and over again
• When light encounters larger
particles (cloud, fog), Mie scattering
occurs
• Mie scattering is not wavelength
dependent – appears white
• Cigarette smoke, too
• At sunset
• The light must travel over a longer
path in the atmosphere
• Blue/green is scattered away and only
red/orange (scattered less) reaches
your eyes
19
Scattering
• Mechanism for Light
g Scattering
g
• Light scattering arises from the presence of
heterogeneities within a bulk medium
• Physical inclusions
• Fluctuations in dielectric constant from random
thermal motion
• Heterogeneity/fluctuations Æ non-uniform
temporal/spatial distribution of refractive index
in the medium
• Passage of an incident EM wave sets electric
charges into oscillatory motion and can excite
vibrational modes
• Scattered light is re-radiated by acceleration of
these charges and/or relaxation of vibrational
transition
20
Scattering
• Elastic scattering:
g no energy
gy change
g
• Frequency of the scattered wave = frequency of incident
wave
• Probes static structure of material
• Rayleigh and Mie scattering
• Inelastic scattering: energy change
• Frequency
q
y of the scattered wave ≠ frequency
q
y of incident
wave
• Internal energy levels of atoms and molecules are excited
• Probes vibrational bonds of the molecule
• Raman scattering (stokes↓ and anti-stokes ↑)
21
Scattering
Elastic Scattering
• The light scattered by a system
has interacted with the
inhomogeneities
g
of the system
y
• Photons are mostly scattered
by the structure whose size
matches the wavelength
• Principal parameters that
affect scattering
•
•
•
•
Wavelength,
W
l
th λ
Relative refractive index
Particle radius
Sh
Shape
and
d orientation
i t ti
• Two types of scattering:
y g and Mie
Rayleigh
22
Scattering
Rayleigh
y g Scattering
g
Light
Source
Detector
• Scattering from very small particles Æ ≤ λ/10
• Rayleigh scattering is inversely related to fourth power of the
wavelength of the incident light
1
I∝ 4
λ
λ is the wavelength of the incident light
I is the intensity of the scattered light
23
Scattering
Mie Scattering
g
• For scattering of particles comparable or larger than the
wavelength, Mie scattering predominates
• Because of the relative particle size
size, Mie scattering is not
strongly wavelength dependent
• Forward directional scattering
24
Scattering
Pin =IoA
Pscatt = Ioσs Pout = Io(A-σs)
Incident Beam
Outgoing Beam
• Scattering Cross Section, σscatt [m2]
• ‘area’ of an index-matched, perfectly absorbing disc necessary to produce
• The measured reduction of light
σscatt = Qs*As
• Qs: Scattering efficiency (calculated by Mie theory); defined as the ratio of the
scattering section to the projected area of the particle on the detector
• As: Area of Scatterer [m2]
25
Scattering
• Scattering
g Coefficient, μs [[1/m]]
• μs =Nsσs ,
• Ns = the number density of scatterers
• σs = scattering
tt i efficiency
ffi i
• Cross-sectional area for scattering per unit volume of medium
• Scattering Mean Free Path
Path, ls
• Average distance a photon travels between scattering events
1
ls =
μs
26
Scattering
• Anisotropy, g
dΩ
scattered
• Imagine that a photon is
photon S’
scattered by a particle so
hv
that its trajectory is
Scatterer
d fl t d b
deflected
by an angle,
l θ
Scattering
• Then, component of a new
hv
Angle (θ)
S
trajectory aligned forward Incidenet
Photon
direction is cos(θ)
cos (θ)
Photon
• Anisotropy is a measure of
trajectory
forward direction retained
Scattering
after a single scattering
event
event, < cos(θ)>
totally
y backward
bac a d scattering
scatte g
⎧−11 tota
⎪
g = ⎨ 0 isotropic scattering
⎪ 1 totally forward scattering
⎩
Biological Tissues:
0.65 < g <0.95
27
Scattering
• Reduced Scattering
C ffi i t μs’’ [1/m]
Coefficient,
[1/ ]
• μs’ incorporates the
scattering
g coefficient,, μ
μs
and the anisotropy factor, g
μ s ' = (1 − g)μ s
• μs’ can be regarded as an
effective isotropic
scattering coefficient that
represent the
h cumulative
l i
effect of several forwardscattering events
• Special significant with
respect to photon diffusion
theory
θ ≈ 26o
g = cos θ = 0.90
μ s ' = (1 − g ) μ s = 0.10
0 10μ s
mpf = 1/ μ s
mpf ' = 1/ μ s ' = 10mpf = 10 / μ s
28
Scattering
• Scattering
g in Tissue
• Tissue is composed of a ‘mixture’
of Rayleigh and Mie scattering
10 μm
cells
nuclei
1 μm
Mie Scattering
0 1 μm
0.1
mitochondria
lysosomes, vesicles
striations in collagen fibrils
macromolecular aggreagates
Rayleigh Scattering
0.01 μm
membranes
29
Scattering
• Scattering in Tissue
• Refractive
R f ti index
i d mismatch
i
t h
between lipid and
surrounding aqueous
medium
ed u
• Soft tissues are dominated by
lipid contents
• Celluar membranes, membrane
folds,, and membraneous
structure
• Mitochondria, ~ 1μm
• Intracelluar organelle
composed of many folded
membrane, cristae
• Collegan fibers, 2 ~ 3μm
• Collegan fibrils, 0.3 μm
• Periodic
P i di fl
fluctuation
t ti iin collegan
ll
ultrastructure Æsource of
Rayleigh scattering in UV and
Visible range
• Cells
30
Light Transport in Tissue
• Scattering and absorption
occur simultaneously and
are wavelength dependent
μt = μ s' + μa
• Scattering monotonically
decreases with
wavelength
• Absorption is large in UV,
near visible,
visible and IR
• Absorption is low in red
and NIR Æ Therapeutic
window (600 ≤λ≤ 1000 nm)
μs ' = A ⋅ λ
−b
μ s ' ~ λ −0.5 − λ −4
31
Light Transport in Tissue
• Modeling of light transport in
tissues are often governed by
the relative magnitudes of
optical
p
absorption
p
and
scattering
• μa >> μs’ : Lambert-Beer Law
(λ ≤300nm;λ≥2000nm)
• μs’ >> μa : Diffusion
Approximation (600nm ~
1000nm)
• μs’ ~ μa : Equation of Radiative
Transfer, Monte Carlo (300nm
~ 600 nm; 1000nm ~ 2000nm)
• Use Monte Carlo, Transport
Theory,
y, or Diffusion Theory
y
Physical Pathlength:
Optical Pathlength:
Lp
Lo
Biological Tissue
Lo/Lp = 4 or ↑
32
Light Transport in Tissue
• Modeling Photon Propagation
μa, μs, g, phase function S
“Stochastic” Description
p
33
Light Transport in Tissue
• Radiative Transport
p
Theory
y
• The direct application of EM theory is complicated
• RTT deals with the transport of light energy
• RTT ignores wave phenomena (polarization, interference) of EMT
ds
y State Radiative Transport
p
Equation
q
Steady
Loss due to
G G ∂L r , Ω
scatt and abs
= −(μ a + μ s )L( r , s )
∂s
G G + μ s p(s , s ') L( r , s ) d s ' + S( r , s )
( )
Overall Energy
balance at position
r and direction s
dA
S
∫
4π
Source
gain due to scattering
term
from s’ to s at r
L = radiance [W/m2 sr], propagation of photon power
P(s, s’) = phase (scattering) function
s, s’ = directional vectors of photon propagation
S’
34
Light Transport in Tissue
• Diffusion Approximation
• Simplified
S
f
form
f
off RTT at “diffusion
“ ff
limit”
• μs’ >> μa
• the number of photon undergoing the random walk is large
G
∂j( r , t ) / ∂t << c(μ a + μ s ') = cμ t '
G 1 G
3 G G
L( r , s , t ) ≈
φ( r , t ) +
j( r , t ) ⋅ s
4π
4π
• Isotropic source beyond 1/μt’
• ~10/μt’ (~ 1mm in biological tissue)
• far
f from
f
sources & boundaries
• assume tissue is “macroscopically homogeneous”
G
1 ∂φ ( r , t )
G
G
G
G
− ∇ ⋅ D(r )∇φ ( r ) − μaφ ( r , t ) = S ( r , t )
c ∂t
G
G
G
where D(r ) = 1/ 3[ μa (r ) + μ s (r )]
35
Tissue Optical Properties
• Measurement Strategies
g
“Black Box”
Optical
Source
‘input’
TISSUE
H(μa,
(μ μ
μs))
Detector
‘output’
p
H: System Function
• Goal: To find out H(μa, μs)
• Requires Non-Static
Non Static system Æ Perturbations in either optical source
or tissue
36
Tissue Optical Properties
Measurement Schemes
• CW (Continuous Wave) Measurement
•
•
•
•
Simplest
p
form of measurement
Static, continuous wave input
requires dynamic tissue property changes
E.g. pulse oximetery
• Time-Resolved Measurements
• Temporal changes in optical sources
• Time Domain Photon Migration (TDPM)
• Frequency Domain Photon Migration (FDPM)
• Spatially-Resolved Measurement
• Spatial changes in optical path
37
attenuation μt-total
Tissue Optical Properties
arterial
μt-oxy
pulsatile
venous (Hb-O2)
μt-background
ti
tissue
time
μt =
non-pulsatile
?
• CW
(continuous
wave)
• pulse
l oximetry
i t
locks into
pulse
• healthy adult
calibration
accounts for
tissue scatter
(ms’)
• typically
t i ll att 2
wavelengths
(660, 940 nm)
μa + μs’
38
Tissue Optical Properties
• Time Domain Photon Migration
(TDPM)
•
Impulse
Function,
δ
Directly measure ma and ms from
TPSF using Diffusion Equation
• Complicated and expensive
detection system
• rather low SNR
Temporal Point
Spread Function
(TPSF)
39
Tissue Optical Properties
• Frequency Domain Photon Migration (FDPM)
SOURCE
TISSUE
DETECTED
stuff
happens
AMPLIT
TUDE
φ
ACsrc AC
SRC
ACdet
ACDET
DCsrc
DC
SRC
DC
DCdet
DET
TIME
φ ~ TIME
M = AC/DC
40