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Computation of the optical properties

of tissues from light reflectance using

a neural network

Lihong V. Wang, Xuemei Zhao, Steven L. Jacques

Lihong V. Wang, Xuemei Zhao, Steven L. Jacques, "Computation of the

optical properties of tissues from light reflectance using a neural network,"

Proc. SPIE 2134, Laser-Tissue Interaction V; and Ultraviolet Radiation

Hazards, (17 August 1994); doi: 10.1117/12.182973

Event: OE/LASE '94, 1994, Los Angeles, CA, United States

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Computation of the optical properties of tissues from light reflectance using a neural network

Lihong Wang, Xuemei Zhao, and Steven L. Jacques

Laser Biology Research Laboratory, Box 17

The University of Texas M. D. Anderson Cancer Center

1515 Holcombe Boulevard, Houston, Texas 77030

ABSTRACT

We have established a neural network to quickly deduce optical properties of tissue slabs from

the diffuse reflectance distribution. Diffusion theory based on multiple image sources mirrored about

the two extrapolated boundaries is used to prepare the training and testing sets for the neural

network. The neural network is trained using backpropagation with the conjugate gradient method.

Once the neural network is trained, it is able to deduce optical properties of tissues within on the

order of a millisecond. The range of the tissue optical properties that is covered by our neural

network is 0.01-2 cm1 for absorption coefficient, 5-25

cm1

for reduced scattering coefficient, and

0.001-1 cm for tissue thickness. A separate network is also trained for thick tissue slabs. A simple

experimental setup applying the trained neural network is designed to measure tissue optical

properties quickly.

INTRODUCTION

When lasers are used for diagnosis or for therapy of disease, it is important to know the tissue

optical properties. The many traditional methods of measuring these optical properties use

integrating spheres,1'2 optical-fiber bundles,3 charge-coupled device (CCD) cameras,4 time-resolved

reflectance,57 photon-density waves,8'9 and photo-acoustic waves.'0 Each method has both

advantages and disadvantages.

The method of using integrating spheres,1'2 considered the gold standard for in vitro

measurement, gives reasonably reliable results when it is carefully performed. The most common

source or error results from the lateral loss of light through the tissue slab sandwiched with two glass

slides and from the light bouncing from the sphere wall back into the tissue. The lateral loss is

determined by the port size of the integrating sphere and the optical properties of the tissue. The

inverse problem of finding the optical properties of the tissue from the measurement is very slow

and/or complicated. When the fast adding-doubling method is used to solve the inverse problem,

correction factors have to be used to account for the light loss. When the slow Monte Carlo method is

used to solve the inverse problem, hours of work are required.

The traditional methods of using optical-fiber bundles3 and CCD cameras4 measure the spatial

distribution of diffuse reflectance. Then, nonlinear least-squares fit is used to extract the optical

properties of tissues based on the diffusion theory for infinitely thick tissue slabs. The diffusion

theory is much faster than Monte Carlo simulations but is limited to simple geometries.

Time-resolved diffuse reflectance57 can be used to accurately measure the absorption

coefficient of a semi-infinite medium because the tail of the signal after a sufficiently long time relies

primarily on the absorption coefficient. This method can even be used to measure the optical

properties of a thick tissue layer underlying a thin tissue layer. The diffuse reflectance will depend

more on the bottom layer than on the upper layer as time

and

the slope of the tail of the

diffuse reflectance is primarily determined by the optical properties of the bottom layer. However,

this approach requires expensive ultrashort lasers (<1 picosecond pulse width) and fast detectors.

The equivalent of the time-resolved approach in the frequency domain, photon-density wave

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measurements,8'9 is a cheaper alternative. This technique is currently limited to semi-infinite media.

Photo-acoustic waves'0 can be used to measure the effective attenuation coefficient of a semi-

infinite tissue very easily and to measure the thickness of each layer in multilayered tissues. Instead of

measuring the light escaping from the tissue, this technique measures the light-induced acoustic waves

emitted from inside the tissue and may have the potential for use in tissue imaging. However, the

inverse algorithm to deduce the tissue optical properties can be complicated.

The neural network approach of measuring optical properties of tissue has been recently

introduced by Farrell et al.12 They have established a neural network to deduce the optical

properties of semi-infinite tissues. Kienle et al13 and our group have independently and

simultaneously presented a neural network approach for tissue slabs. They measure the light

transmittance through a tissue slab that has a fixed thickness and then deduce the absorption

coefficient and the reduced scattering coefficient of the tissue slab. We measure the diffuse

reflectance from a tissue slab with a variable thickness between 10 im and 1 cm and deduce the

optical properties of the tissue from the diffuse reflectance. A simple experimental setup is

subsequently presented in this paper. The most salient feature of the neural network approach is that

once the network is trained, it can deduce the optical properties of tissues in real time (on the order of

a miffisecond).

METHODS

A neural network is used to deduce the optical properties of a tissue slab from the spatially

resolved diffuse reflectance. The neural network requires training with examples, which are pairs of

diffuse reflectance and the corresponding optical properties. Monte Carlo simulations would be the

ideal tool to prepare the example set if it were faster. We use the diffusion theory to prepare the

example set, being careful to avoid the region where the diffusion theory fails.

The optical properties that we want to measure are the absorption coefficient (jta)

and

the

reduced scattering coefficient

'). Two

related coefficients are the transport interaction coefficient

(J.tt')

and

the effective attenuation coefficient (p), which are respectively expressed by the following

relationship:

I.tt'=JJa+t.ts'

(1)

and

1eff[31a1t'.

(2)

The inverse of the transport interaction coefficient is defined as one transport mean free path (mfp' =

1/1t).

DIFFUSION

THEORY

Diffusion theories for semi-infinite tissues have been presented

this paper, we

extend the diffusion theory for tissue slabs. An infinitely narrow laser beam (pencil beam) is incident

upon a tissue slab whose optical properties are refractive index n,

j.t', and

thickness d. The pencil

beam is approximated by an isotropic point source that is 1 mfp' below the tissue surface.

A cylindrical coordinate system is set up, where the z axis originates on the top tissue surface

and points downward perpendicularly to the tissue surface. In this cylindrical coordinate system, the

fluence caused by an isotropic point source at z =

in an otherwise infinite medium has been

analytically solved, i.e.,

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1

exp(—iffp)

(3)

(z,r,zs)=4D

where z and r are the cylindrical coordinates of the observation point and p is the distance between

the observation point and the source, i.e.,

=

'.J(z

—

z)2

+

r2,

(4)

and

D is the diffusion constant,

=

11(3 pr').

(5)

Since

we are interested in the reflectance on the top tissue surface, the contribution of this

isotropic point source is

zs (1

+

exp(— -kff

(6)

J(z=O,r,z)=D

z=0

4icp3

The transmittance on the bottom tissue surface can be computed similarly.

To compute the fluence caused by an isotropic point source in a tissue slab based on Eq. (3),

need to convert the slab into an infinite medium by satisfying the boundary condition with an array

of image sources. Since the fluence on the two real boundaries is not zero, two extrapolated virtual

boundaries where the fluence is approximately zero are used. The two virtual boundaries are the

distance z away from the tissue surfaces, where z is

zb=2AD,

(7)

where A is related to the internal reflection r1. When the boundary has matched refractive indices,

A =

;

otherwise,

A can be estimated by

A=(1 +r)/(1—r),

(8)

where

r1 =

—1.440

nrel2 +

0.710

nrel1 +

0.668

0.0636

re1,

(9)

where nrel is the relative refractive index of the tissue.15

Fig. 1 shows the positions of the original isotropic point source and its image sources about the

two virtual boundaries. Each mirroring changes the sign of the point source. The z coordinate of ith

positive or negative image source is

zj(±)

=

—z

(d +

2zb)

(z +

zb)

(10)

Once theses image sources are used, the boundary condition is approximately satisfied, and hence the

true boundaries can be removed. The problem is converted into an array of isotropic sources of both

signs in an infinite medium. A linear combination of Eq. (3)

for

different source positions will,

therefore, yield the fluence of the isotropic point source in the original tissue slab, and a linear

combination of Eq. (6) for different source positions will yield the reflectance.

Results of our method computing the diffuse reflectance and transmittance are compared with

those computed by the Monte Carlo method16 in Fig. 2, in which the Monte Carlo simulation results

are considered accurate. Although the number of image sources is infinite, the series is truncated after

four pairs of sources. For the diffuse reflectance, the diffusion theory is accurate only after r is beyond

a couple of mfp'. For the diffuse transmittance, the diffusion theory seems to be accurate even for

small r values, but the Monte Carlo simulation result is too noisy to permit a definitive conclusion.

SPIE

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