TISSUE OPTICS

Outline

What is Tissue Optics

Absorption in Tissue

Absorption Process and Parameters

Typical absorbers in Tissue

Scattering in Tissue

Scattering Process and Parameters

Typical scatterers in Tissue

What is Tissue Optics?

Definitions from dictionary

Optics: a science that deals with

genesis and propagation of light

changes that it undergoes and produces

Tissue: an aggregate of cells

usually of a particular kind together with their intercellular substance that form one of the structural materials of a plant or an animal

What is Tissue Optics?

Tissue Optics

Investigating PrincipleSubject of Interest

+ = Tissue Optics

• Constituents of Tissue• Optical Properties of Tissue• Propagation of Light• Interaction between Light and Tissue• Diagnostic and Therapeutic Implications

We are interested in …

Is Tissue Optics Special?

Three Major Components• Optical Source – Sun• Medium - Atmosphere• Detector – Human Eyes

• Interaction between light and particles in atmosphere- Absorption - Scattering (Rayleigh & Mie)

• Propagation of Light through Atmosphere

Optical Signal from Tissue

Large number of Biological Molecules

Functional and Structural information

Noninvasive

Near real time

Objectives of Tissue Optics

Key Question: How many photons per second will reach the tissue chromophore and be absorbed?

Absorption is important because it transfers energy to tissue

1. To find the light energy per unit area per unit time that reaches a target chromophore at some position

2. To develop methods by the absorption and scattering properties of tissue can be measured

Ultimate Goal of Tissue Optics

Assess all optical properties

noninvasive in living tissue (in vivo)

Difficulties

Tissue is a complicated heterogeneous system

Requires noninvasive in vivo information for meaningful diagnostic and therapeutic purposes

ABSORPTION

in

TISSUE

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 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. pulse-

oximetry)

Therapeutic applications: Absorption of energy is the primary mechanism that allows light form a source (laser) to produce physical effects on tissue for treatment purpose Lasik (Laser Assisted in situ Keratomileusis) Eye Surgery, Tatoo

Removal, PDT

Absorption (quantum view)

Absorption occurs when the photon frequency matches the „frequency‟ associated with the molecule‟s energy transition

The absorption of a photon results in: quantized change in charge separation quantized excitation of vibrational modes

Metrics for Absorption

Absorption Cross-section, s [m2]

Consider a chromophore idealized as a sphere with a particular geometrical size. Consider that this sphere blocks incident light and casts a shadow, which constitutes absorption.

The size of absorption shadow = absorption cross-section

Qa: absorption

efficiencyAQaa s

Metrics for Absorption

Pin =IoA

Incident Beam

Pabs = IosaPout = Io(A-sa)

Outgoing Beam

area = A - sa

Area = sa

Pout = Io(A-sa)- =Area =A

o

absa

I

Ps

Metrics for Absorption

Assumptions

Cross section is independent of relative orientation of the impinging light and absorber

uniform distribution of identical absorbing particles

Absorption Coefficient, ma [1/m]

Absorption cross-sectional area per unit volume of

medium

Absorption mean free path, la [m]

Represents the average distance a photon travels before being absorbed

aaa N sm

a

a

1l

m

Absorption Fundamentals

Transmission and Absorbance (macroscopic view)

Transmission

Absorbance (attenuation, or optical density)

oI

IT

I

Ilog)Tlog(A o

Connection between T/A and ma

Now, absorbing medium is characterized by

ma, transmission, and absorbance. Are they

related?

Lambert – Beer Law: the linear relationship

between absorbance and concentration of an

absorbing species.

Lambert-Beer Law

s= absorption cross-sectional area = [cm2]

IO = The intensity entering the sample at z = 0 [w/cm2]

I = The intensity of light leaving the sample

IZ = The intensity entering the infinitesimal slab at Z

dI = the intensity absorbed in the slab

O

absa

I

Ps

Lambert-Beer Law

Total opaque area on the slab

due to absorbers

dzANaa s

Number of absorbers

in the slab volume

dzN

I

dIaa s

Fraction of photons

absorbed

Loss of intensity

sb

0aa

I

oIdzN

)z(I

dI

bNI

Iaa

o

sln

Lambert-Beer Law

bNI

Iaa

o

sln

liter

molc

liter

cm1000

molec10x023.6

mol1

cm

molecN

3

233

)xlog(303.2)elog(

)xlog()xln(

Since

and

bcbcx

I

I

I

IA a

oo

s

303.2

10023.6ln

303.2

1log

20

, Molar Extinction Coefficient [cm-1M-1]

Measure of „Absorbing Power‟ of species

Abc

oI

IT 1010

Lambert-Beer Law

ma = 2.303c

(1) By measuring Transmission or Absorbance for given M, we can obtain

usually ex vivo

(2) With knowledge of , if we can measure ma in vivo, we can quantify

concentration of chromophores

bN

I

I

I

Ibc

aa

oO

s

303.2

1

ln303.2

1log

cNaa s 303.2

Absorbers in Tissue

NIR• Hemoglobin

• Lipids

• Water

UV-VIS• DNA

• Hemoglobin

• Lipids

• Structural protein*

• Electron carriers*

• Amino acids*

* Absorbers that fluoresce when excited in the UV-VIS

NIR UVVISIBLE

UV Absorption

Protein, amino acid, fatty acid and DNA absorption dominate UV absorption Protein is dominant „non-water‟

constituent of all soft tissue, ~ 30%

Absorption properties determined by peptide bonds and amino acid residues

Peptide excitation about l = 190 nm

amino acids absorption at l = 210 - 220 nm and 260 – 280 nm

DNA absorbs radiation for l ≤ 320 nm

Peptide

Amino Acid

Large water absorption l < 180 nm

Infrared Absorption

Protein IR absorption

peaks at 6.1, 6.45, and 8.3

mm due to amide excitation

Absorption depth ≤ 10 mm in l 6 7 mm region

Water absorption peak at

0.96, 1.44, 1.95, 2.94 and

6.1mm

Absorption depth

~ 500 mm at l = 800 nm, <1 mm at l=2.94 mm

≤ 20 mm throughout l ≥ 6 mm

Respiratory Enzymes: NADH, FAD,

Cytochrome a3

These enzymes play a key role in providing the proton-motive force

necessary for oxidative phosphorylation

If tissue is oxygen starved, [NADH] and [FADH2] will be enhanced

Reduced NADH conc. is indicative of high oxygen consumption and is

characteristic of tumor tissue

NADH FAD

NADH (FAD) strongly fluoresce while NAD+ (FADH2) does not Cytochrome a3 has a prominent absorption peak at l = 840 nm

Visible and NIR Absorption

400 500 600 700 800 900 100010

2

103

104

105

106

Extin

ctio

n C

oe

ff (

1/c

m M

)

WAVELENGTH (NM)

Hb

HbO2

Main Absorbers at visible and NIR Hemoglobin Lipid

Hemoglobin

• 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 well as metabolic activity

Hemoglobin

Deoxyhemoglobin has lower absorption than oxyhemoglobin in the blue and green

Bright red arterial blood (blushing)

Bluish venous blood (cold pale face)

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

Lipid (Fat)

Important energy store in the

body

Site-specific measurements

of body composition

Monitoring of physiological

changes in female breast

tissue

Tissue layer model

600 700 800 900 10000.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00

0.01

0.02

0.03

0.04

0.05

0.06

HE

MO

GLO

BIN

(1/m

m m

M)

WAVELENGTH (nm)

HB

HbO2

Water

Lipid

WA

TE

R &

FA

T (

1/ m

m m

M)

Summary - Absorber

UV Visible & NIR IR

• Protein• Amino acid• Fatty Acid• Peptide • DNA• NADH• FAD• Water

• Hemoglobin• Lipid• Cytochrome a3

• Water• Protein• Glucose

“Therapeutic Window”600 nm ~ 1000 nm

SCATTERING

in

TISSUE

Scattering in Tissue

Much more complicated than absorption

Light is hardly observed from the source, but

reaches our eyes indirectly through scattering

Inhomogeneity causes scattering; cloud,

raindrop, etc

Elastic (Rayleigh, Mie) or inelastic (raman)

Scattering in Tissue

Diagnostic applications: Scattering depends on the size,

morphology, and structure of the components in tissues (e.g.

lipid membrane, collagen fibers, nuclei). Variations in these

components due to disease would affect scattering

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 therapy

Scattering - Example

Purely absorbing With Scattering

Lambert- Beer Law does not apply here!!!Need to calculate true pathlength of light

Photon pathlength >> LPhoton pathlength = L

L

Scattering – Blue sky revisited

• Blue skies are produced due to scattering at shorter wavelengths• Visible light (violet & blue) are selectively scattered by O2 and N2 – much smaller than wavelengths of the light• violet and blue light has been scattered over and over again

• When light encounters larger particles (cloud, fog), Mie scattering occurs• Mie scattering is not wavelength dependent – appears white

Mechanism for Light Scattering

Light scattering arises from the presence of heterogeneities within a bulk medium Physical inclusions

Fluctuations in dielectric constant from random thermal motion

Heterogeneity/fluctuations result in 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

Elastic vs. Inelastic Scattering

Elastic scattering: no energy change

Frequency of the scattered wave = frequency of incident wave

Probes static structure of material

Rayleigh and Mie scattering

Inelastic scattering: energy change

Frequency of the scattered wave ≠ frequency of incident wave

Internal energy levels of atoms and molecules are excited

Probes vibrational bonds of the molecule

Raman scattering (stokes↓ and anti-stokes ↑)

Elastic Scattering

The light scattered by a system has interacted with the inhomogeneities of the system

Photons are mostly scattered by the structure whose size matches the wavelength

Principal parameters that affect scattering

Wavelength, l

Relative refractive index

Particle radius

Shape and orientation

Two types of scattering: Rayleigh and Mie

Rayleigh Scattering

LightSource Detector

Scattering from very small particles ≤ l/10

Rayleigh scattering is inversely related to fourth power of the wavelength of the incident light

4

1I

l l is the wavelength of the incident light

I is the intensity of the scattered light

Mie Scattering

For scattering of particles comparable or

larger than the wavelength, Mie scattering

predominates

Because of the relative particle size, Mie

scattering is not strongly wavelength

dependent

Forward directional scattering

Scattering in Tissue (I)

Tissue is composed of a „mixture‟ of Rayleigh

and Mie scattering

Hierarchy of ultrastructure

cells

nuclei

mitochondria

lysosomes, vesicles

striations in collagen fibrilsmacromolecular aggregates

membranes

10 mm

1 mm

0.1 mm

0.01 mm

Mie Scattering

Rayleigh Scattering

* TiO2 : 0.2 ~ 2 mm

Source of Scattering in Tissue

Refractive index mismatch between lipid and surrounding aqueous medium Soft tissues are dominated by lipid contents

Celluar membranes, membrane folds, and membraneous structure

Mitochondria, ~ 1mm Intracelluar organelle composed of many folded membrane, cristae

Collegan fibers, 2 ~ 3mm Collegan fibrils, 0.3 mm

Periodic fluctuation in collegan ultrastructure source of Rayleigh scattering in UV and Visible range

Cells

Metrics for Optical Scattering

Pin =IoA

Incident Beam

Pscatt = IossPout = Io(A-ss)

Outgoing Beam

Scattering Cross Section, sscatt [m2]

‘area’ of an index-matched, perfectly absorbing disc necessary to produce

The measured reduction of light

sscatt = 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]

Metrics of Optical Scattering

Scattering Coefficient, ms [1/m]

ms =Nsss ,

Ns = the number density of scatterers

ss = scattering efficiency

Cross-sectional area for scattering per unit volume of

medium

Scattering Mean Free Path, ls Average distance a photon travels between scattering

events

s

s

1l

m

Anisotropy, g

Imagine that a photon is scattered by a particle so that its trajectory is deflected by an angle, q

Then, component of a new trajectory aligned forward direction is cos(q)

Anisotropy is a measure of forward direction retained after a single scattering event, < cos(q)>

Scatterer

hvIncidenet

Photon

Scattering

Angle (q)

Scattering

event

cos (q)

dW

Photon

trajectory

S

scattered

photon

hv

S‟

Anisotropy factor, g

1

0

1

g

totally backward scattering

totally forward scattering

isotropic scattering

Biological Tissues, 0.65 < g <0.95

Reduced Scattering Coefficient, ms‟ [1/m]

ms’ incorporates the scattering coefficient, ms and the anisotropy

factor, g

ms’ can be regarded as an effective isotropic scattering

coefficient that represent the cumulative effect of several forward-

scattering events

Special significant with respect to photon diffusion theory

ss )g1(' mm

Reduced Scattering Coefficient

'/1'mpf

/1mpf

10.0)g1('

26

90.0cosg

s

s

sss

o

m

m

mmm

q

q

'/1'mpf sm

Each step involves isotropic

scattering.

Such a description is equivalent to

description of photon movement

using many small steps 1/µs that

each involve only a partial

deflection angle

Useful for description of

photon propagation in

diffuse Regime

1 iso-scatt step

=1/(1-g)

aniso-scatt.

steps

Light Transport in Tissue

Scattering and absorption occur simultaneously and are wavelength

dependent

Scattering monotonically decreases with wavelength

Absorption is large in UV, near visible, and IR

Absorption is low in red and NIR Therapeutic window (600 ≤λ≤ 1000 nm)

45.0

s

b

s

~'

A'

llm

lm

Light Transport in Tissue

Modeling of light transport in tissues are often governed by

the relative magnitudes of optical absorption and scattering

ma >> ms‟ : Lambert-Beer Law (l ≤300nm;l≥2000nm)

ms‟ >> ma : Diffusion Approximation (600nm ~ 1000nm)

ms‟ ~ ma : Equation of Radiative Transfer, Monte Carlo (300nm ~ 600 nm; 1000nm ~ 2000nm)

Propagation of Photons through Tissue

Scattering and absorbing tissue

• Absorption Coefficient: ma

• Scattering Coefficient: ms

• Physical Pathlength: Lp

• Optical Pathlength: Lo

Biological Tissue

Lo/Lp = 4 or ↑

Use Monte Carlo, Transport Theory, or Diffusion Theory !!!!

Modeling Photon Propagation

ma, ms, g, phase function S

“Stochastic” Description

Radiative Transport Theory

The direct application of EM theory is complicated

RTT deals with the transport of light energy

RTT ignores wave phenomena (polarization, interference)

of EMT

s,rS'sds,rL's,sp

s,rLs

,rL

4s

sa

m

mm

W

Steady State Radiative Transport Equation ds

dA

gain due to scattering

from s’ to s at r

Source

term

Loss due to

scatt and abs

Overall Energy

balance at position

r and direction s

L = radiance [W/m2 sr], propagation of photon power

P(s, s’) = phase (scattering) function

s, s’ = directional vectors of photon propagation

S‟

S

Diffusion Approximation

Simplified form of RTT at “diffusion limit” ms‟ >> ma

the number of photon undergoing the random walk is large

(~ 200 GHz)

Isotropic source beyond 1/mt‟ ~10/mt‟ (~ 1mm in biological tissue) far from sources & boundaries

assume tissue is “macroscopically homogeneous”

'c'ct/)t,r(j tsa mmm

s)t,r(j4

3)t,r(

4

1)t,s,r(L

)r()r(3/1)r(Dwhere

t,rSt,rr)r(Dt

t,r

c

1

sa

a

mm

m

Measurement Strategies

TISSUEH(ma, ms)

Optical

Source

„input‟

H: System Function

Detector

„output‟

“Black Box”

• Goal: To find out H(ma, ms)

• Requires Non-Static system

Perturbations in either optical source or

tissue

Measurement Schemes

CW (Continuous Wave) Measurement Simplest form of measurement

Static, continuous wave input

requires dynamic tissue property changes

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

TDPM (II)

Temporal Point Spread Function

(TPSF)

• Directly measure ma and ms from TPSF using

Diffusion Equation

• Complicated and expensive detection system

• rather low SNR

FDPM

AC src

DC src

DC det

AC det

TIME

AM

PL

ITU

DE

TISSUE

AC src

DC src

stuff happens

SOURCE DETECTED

ACSRC

ACDET

DCSRC

DCDET

~ TIME

M = AC/DC