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Time-resolved reflectance

measurements on layered tissues

with strongly varying optical

properties

Andreas H. Hielscher, Hanli Liu, Lihong V. Wang, Frank K.

Tittel, Britton Chance, et al.

Andreas H. Hielscher, Hanli Liu, Lihong V. Wang, Frank K. Tittel, Britton

Chance, Steven L. Jacques, "Time-resolved reflectance measurements on

layered tissues with strongly varying optical properties," Proc. SPIE 2323,

Laser Interaction with Hard and Soft Tissue II, (18 January 1995); doi:

10.1117/12.199216

Event: International Symposium on Biomedical Optics Europe '94, 1994, Lille,

France

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Time resolved reflectance measurements on layered tissues

with strongly varying optical properties

Andreas H. Hielscher1'2, Hanli Liu3, L. Wang1,

Frank K. Tittel2, Britton Chance3 and Steven L. Jacques1

1University of Texas M.D. Anderson Cancer Center,

Laser Biology Research Laboratory, Houston, Texas 77030

2Rice University, Dept. of Electrical and Computer Engineering,

Houston, Texas 77251-1892

3University of Pennsylvania, Dept. of Biochemistry and Biophysics,

Philadelphia, Pennsylvania 19104-6089

1. INTRODUCTION

Most biological tissues consist of layers with different optical properties. A few

examples are the skin, the esophagus, the stomach and the wall of arteries. An

understanding of how the light propagates in such layered systems, is a prerequisite for any

light based therapy or diagnostic scheme. For example different methods like continuous

light, time or frequency resolved reflectance measurements have been employed to

determine the blood oxygenation status of the brain. 1,2,3 However, little attention has been

paid to the fact that the brain is actually encapsulated by several layers of optically very

different tissues (skin, skull, meninges). The arachnoid, a substructure of the meninges, is

almost absorption and scattering free. On the other hand the capillary bed in the gray

matter has a high content of strongly absorbing blood.

In this study we investigated the influence of these kind of layers on time resolved

reflectance measurements. Experiments were performed on layered gel phantoms and the

results compared to Monte Carlo simulations and diffusion theory. It is shown that when a

low absorbing medium is situated on top of a high absorbing medium, the absorption

coefficient of the lower layer is accessible if the differences in the absorption coefficient

are only small. In the case of large difference the optical properties of the upper layer

dominate the signal and shield information on the lowest layer. The degree of this shielding

effect depends on layer thickness as well as optical properties.

In the case of an almost absorption and scattering free layer inbetween two normal

tissues, an overall increase of the signal is visible. However, the overall shape of the curve

is about preserved. The apparent scattering coefficient is slightly decrease, while the

apparent absorption coefficient is unaltered.

2. TIME RESOLVED REFLECTANCE MEASUREMENTS

Time resolved reflectance measurements on tissues can be used to determine the

absorption and reduced scattering coefficient (ga,

of tissues.4 In this technique a pico

second pulsed light source is used as an input signal and the reflectance is measured as a

function of time at a distance of a few centimeter. A detailed description of the

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experimental set up, which uses the method of single photon counting, can be found

elsewhere.5

Once the time resolved signal has been obtained, the absorption and scattering

coefficient can be found by fitting a diffusion theory curve to the data. Assuming a semi-

infinite medium the zero boundary condition one finds for the reflectance R measured at a

distance r at time t (for a more detailed derivation see [4]):

r2+(1/ ')2 i

R(r,t) =

ic c D)312 t5'2 exp(

)

exp(

)

(1)

where

the reduced scattering coefficient, D =

[3(ia

J.1s')]

the diffusion coefficient

and c the speed of light in the medium. Eq. (1) can be linearized in ia and is' by taking

the natural logarithm of R and assuming p'>>l:

ln(R(r,t)) =

const

5/2 ln(t)

us'

( c

t + )

(2)

with a =

(2a)

This provides a simple and fast linear fitting algorithm. Notice that for t<< 1 ,

which is

usually much larger than .ta dominates the behavior of the reflectance signal. For t>>O on

the other hand ia has the strongest influence.

It has to be emphasized that the expression given in Eq.(2) is derived for a semi-

infinite medium with the so called zero boundary condition. This boundary conditions is an

oversimplification and leads to a deviation of diffusion theory from the actual data at early

times.6 In general oncan say that the closer the source detector separation the higher the

overestimation of the scattering and underestimation of the ia. Using a more appropriate

boundary condition leads to better results at early times, however for the price of

complexity.7 A linearization of Eq.(1) in .ta and is' is not possible anymore and more

advanced and more time consuming fitting algorithms are required. As a rule of thumb we

found that for the optical properties of interest, the diffusion theory with zero boundary

condition can be considered accurate after ''5OOps.6 Thus fitting data only beyond this

point leads to an accurate determination of especially of the absorption coefficient .ta. In

the case of blood oxygenation measurements of the brain, ia is actually the parameter of

interest. Inaccuracies in the determination are in this case acceptable.

3. LAYERED TISSUE STRUCTURES

In medical situation one usually does not encounter a semi-infinite homogenous

medium. The first approximation (semi-infinite) is actually acceptable, since for all practical

purposes significant contribution to measurements come only from a few centimeters

around the source. However, the second assumption (homogenous) is almost always not

true. Tissues are more or less in homogenous. The strongest absorbers, like blood, are

actually localized in blood vessels which are surrounded by low absorbing background

tissues. Furthermore one frequently encounters layered tissue structures. Layers can be as

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thin as a few im (e.g. the epidermis) up to about a centimeter (e.g. skull). Details of the

actual tissue structure are often unknown. The question arises: Can time resolved

reflectance spectroscopy nevertheless yield some useful information? Can the simple

linear fitting routine based on Eq.(2) still be applied and how have the results to be

interpreted?

3.1. Low absorbing layer on high absorbing medium

An example is considered in the Fig. 1 .

Here

a time resolved Monte Carlo simulation8

of two homogenous media and one layered medium is shown. The layered medium is

composite of the material which constitutes the two homogenous media. The 4 mm thick

upper layer has a low absorption coefficient of .ta 0.01 cm1. The underlying bulk material

has a twenty-time higher absorption coefficient. The scattering coefficient '

= 10

cm1 is

the same in both media. It can be seen that the time response of the layered tissue follows in

the early time the curve (I) for the homogenous medium with lower absorption. The

photons travel only in the upper layer and are not influenced by the lower, stronger

absorbing bulk material. After roughly 150 ps curve (III) and (I) start to deviate. This

indicates that photons which have reached the lower layer contribute to the signal. After

—5OO P5 the curve of the layered medium becomes parallel to the curve (II) of the homo-

genous medium with the optical properties of the underlying medium. As discussed earlier,

the absorption coefficient of a tissue mostly influences the late part of the time resolved

reflectance. Thus a fit of diffusion theory (Eq.(2)) to curve (II) (homogenous medium) and

curve (III) (layered medium) yields the same 1a. This suggests, that one can measure through

the upper layer the absorption coefficient ia of the hidden tissue. The layered structure of

the tissue seems only to affect the apparent scattering coefficient.

This might be surprising, on the first view. However, if one considers that after 1 ns the

photons actually have traveled -22 cm in the tissue (n=1 .37). This means that by far most of

the time a photon propagates, it spends in the lower layer. The 4 mm thick upper layer

becomes optically thinner and thinner the more time elapses.

In Figure 2 another Monte Carlo simulation is shown. The absorption coefficient of

the lower layer has been increased ten times to

2 cm and is thus 200 time higher than

the ia of the upper layer. Now the slope of the time resolved impulse response measured on

layered system is not any longer parallel to the homogenous medium with the high

absorption. Thus, a diffusion theory fit gives different scattering and absorption coefficient

for both system.

The results of the simulations were also tested experimentally on layered tissue

phantoms, made out of collagen gels. Ti02 powder was added to the gel to introduce

scatterers into the medium. India ink in different concentrations served as absorber. Gels with

different optical properties were stacked on top of each other to yield a layered tissue

structure. As a light source a pulsed laser diode with a wavelength of 780 nm and a pulse

with of —5O

was used. The findings from Monte Carlo simulations could be confirmed as

shown in figure 3. Through the upper layer one can measure the absorption coefficient of

the underlying medium, by fitting the late part of the time resolved reflectance if the

difference in absorption coefficient is not to high. Different thicknesses of the upper layer

seem only to affect the amplitude of the signal, but not the determination of the absorption

coefficient of the lower layer. In Fig.4 the absorption coefficient of the lower layer has been

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