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Near-infrared spectroscopy of a

heterogeneous turbid system

containing distributed absorbers

Hanli Liu, Andreas H. Hielscher, Bertrand Beauvoit,

Lihong V. Wang, Steven L. Jacques, et al.

Hanli Liu, Andreas H. Hielscher, Bertrand Beauvoit, Lihong V. Wang, Steven

L. Jacques, Frank K. Tittel, Britton Chance, "Near-infrared spectroscopy of a

heterogeneous turbid system containing distributed absorbers," Proc. SPIE

2326, Photon Transport in Highly Scattering Tissue, (31 January 1995); doi:

10.1117/12.200817

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

France

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Near infrared spectroscopy of a heterogeneous turbid system

containing distributed absorbers

Hanli Liu1 ,

Andreas

H. Hielscher2'3, Bertrand Beauvoit1 ,

Lihong

Wang2,

Steven L. Jacques2, Frank K. Tittel3, and Britton Chance1

1 University of Pennsylvania

Department of Biochemistry and Biophysics

Philadelphia, PA 19104-6089

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

Laser Biology Research Laboratory

Houston, TX 77030

3 Rice University

Department of Electrical and Computer Engineering

Houston, TX 77251-1892

ABSTRACT

In most biological tissues, absorbers such as blood in the blood vessels are localized within a

low-absorbing background medium. To study the effect of distributed absorbers on the near infrared

reflectance, we developed a Monte Carlo code and performed time-domain measurements on

heterogeneous tissue-vessel models. The models were made of low absorbing polyester resin mixed with

Ti02 as scatters. A series of tubes with diameters of 3.2 or 6.4 mm were made in the resin sample. The

volume ratio of the tubes to the total sample is about 20%. During the measurement, these tubes were

filled with turbid fluids with different absorption coefficients to simulate blood in various oxygenation

states. We found that the apparent absorption coefficient of the resin/tube system, determined by using

the diffusion equation fit, can be approximated by a volume-weighted sum of the absorption coefficients

of the different absorbing components. This approximation has to be replaced by a more complex

expression if the difference in absorption between the absorbers and background is very large (.

times). The results of the tissue phantom study are supported by the Monte Carlo simulation. Possible

explanations for the photon migration in this kind of heterogeneous systems are also presented.

1. INTRODUCTION

In recent years, researchers have developed near infrared (NIR) techniques, including steady-

state, time-domain, and frequency-domain measurements, to monitor the brain oxygenation non-

invasively. 1,2,3,4

particular, NIR time- or frequency- resolved spectroscopy has a great potential to

determine an absolute oxygenation state of cerebral blood and tissue since these techniques can measure

accurately absorption coefficients and path lengths.5 However, the brain is a very complex biological

organ, consisting of various blood vessels and brain tissue. The detected signal in NIR measurements

may result from the high-absorbing blood in arteries, veins, and capillaries, embedded in a large brain

tissue background. It is known that in the wavelength range of 700-900 nm, the absorption coefficient of

hemoglobin is much larger than that of tissue or water.6'7 Is it reasonable to ignore tissue background

absorption? Does the absorption coefficient obtained from the NIR spectroscopy result from blood only

or from a combination of blood in the vessels and background tissue?

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In searching for the answers to the above questions, we conducted this study on a tissue-vessel

model, with 1) time-resolved Monte Carlo simulation and 2) time-resolved spectroscopy (TRS) in

reflectance geometry. Our goal is to investigate the effect of the distribution and sizes of the distributed

absorbers on the NIR time resolved reflectance. This study is essential towards understanding the light

absorption by cerebral bloodin various blood vessels and achieving quantitative brain oximetry.

2. METHODS

2. 1 Monte Carlo simulation

We have modified a well-test Monte Carlo simulation8 to provide time-resolved photon migration

in an infinite heterogeneous model, whose cross section is shown in Figure 1 .

Small

tubes are

distributed uniformly in a large homogenous medium. The absorption and reduced scattering coefficients

of the background and the material filled in the tubes are represented by j.ta(back), i5t(back), .ta(tube),

and jt5'(tube), respectively. Since the large background can act as hemoglobin-free tissue, jia(back) is

chosen to be relatively small, around 0.05 cm1 .

the simulation, the input parameters are optical

parameters, the diameter of the tubes, d, and the tube distribution distance, 1. Thus, the volume ratio of

the tubes to the total system is known. The output of the simulation is a time-resolved impulse response,

at a chosen source-detector separation, p. From the simulated data, we can obtain an apparent absorption

coefficient, la-app for the heterogeneous system, using a diffusion theory fit.

Ma-app, JIs-app

S • • •:

4La(back)

. . . . Ji(back)

S...

S S S S •

-J1a(tube)

(tube)

S 5555

Figure

1 .

cross section of a heterogeneous tissue/vessel model for the Monte Carlo

simulation. The optical parameters are labeled by jia(back) and p5t(back) for the

background, .ta(tube) and i5t(tube) for the filling material in the tubes, ia-app and .L's-app

for the apparent optical parameters for the system.

2.2 Time-resolved reflectance measurements

The absorption and reduced scattering coefficients of a biological sample can be determined using

NIR time resolved spectroscopy, and the experimental setup can be found elsewhere.9 The experimental

model for this study is made of a polyester resin, which simulates a low-absorbing tissue background.

The resin is mixed with a certain concentration of Ti02 to obtain a proper value of the reduced scattering

coefficient lls'(back).1° As illustrated in Figure 2, a series of small tubes (vertical holes) are made

through the resin sample, and they can be filled with an absorbing turbid fluid. The samples used for the

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measurements have values of ia(back)=O.O2--O.O6 cm1 and is'(back)=6--9.2 cm1 .

The

tube diameters

in two samples have 3 mm and 6 mm diameters and make up 18% to 20%, respectively, of the entire

volume. The measurement was performed on the side of the sample with a separation of 2.5-3 cm at a

wavelength of either 670 nm or 780 nm.

Pa(back), J(back)

1 a(tube), p(tube)

Figure 2. The experimental model made of a polyester resin with many empty tubes

simulating the blood vessels. The absorption and reduced scattering coefficients for the

filling materials are ta(tube) and ts'(tube).

To study the dependence of 11a.app on ia(hole), a set of TRS measurement was performed on the

resin sample with an absorbing turbid solution filled in the tubes while increasing the absorption

coefficient of the solution. The liquid absorbers in the tubes were either ink or met hemoglobin solutions,

the latter of which were made from the hemoglobin (Sigma, H2625) totally converted to met hemoglobin

by adding potassium ferricyanide. 0.5% or 1% intralipid was used to dilute the absorbing solutions.

The absorption coefficients, J.ta(tube), of the solution at different concentrations were determined

separately by taking the TRS measurement on the solution alone. By fitting the TRS spectra taken from

the tissue/vessel system with the diffusion theory, we obtained 1a-app as a function of ia(hole).

2.3 Calculation of the apparent absorption coefficient

In order to study the dependence of the apparent absorption coefficient, ia-app of the system on

the I-ta(tube) and .ta(back), we first assume that the jtaapp is a volume-weighted sum of the absorption

coefficients of the different absorbing components contained in the medium, as written below:

pta—app =rjia(i)

(1)

where rj =Vj/Vtotai is a weighting factor for thei th kind of absorbers in the system, and V1 is the tube

volume occupied by the I th kind of absorbers. When only one kind of absorber is present in the tubes,

then equation (1) becomes

pta-app =

ia(tube) +

-r) .ta(back)

(2)

With the simulation and experiment in the following, we wish to investigate the validity of

equation (2) and to find a suitable formula to express the photon behavior in this kind of tissue-vessel

systems.

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