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Theoretical studies of optimal light

delivery for tumor treatment

Lihong V. Wang, Wei R. Chen, Robert E. Nordquist

Lihong V. Wang, Wei R. Chen, Robert E. Nordquist, "Theoretical studies of

optimal light delivery for tumor treatment," Proc. SPIE 2975, Laser-Tissue

Interaction VIII, (16 June 1997); doi: 10.1117/12.275462

Event: BiOS '97, Part of Photonics West, 1997, San Jose, CA, United States

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Theoretical Studies of Optimal Light Delivery for Tumor Treatment

Lihong Wang, Ph. D.

Bioengineering Program, Texas A&M University

College Station, Texas 77843-3 120

Tel: (409) 847-9040; Fax: (409) 847-9005

E-mail: LWang@taxnu.edu; URL: http://biomed.tamu.edui—lw

Wei R. Chen, Ph. D.

Oklahoma School of Science and Mathematics

1 141 North Lincoln Boulevard, Oklahoma City, OK 73104

and

Department of Physics and Astronomy, University of Oklahoma

Norman, OK 73109

Robert E. Nordquist, Ph. D.

Wound Healing of Oklahoma, Inc.

3939 N. Walnut Street

Oklahoma City, OK 73105

ABSTRACT

Optimal laser light delivery into turbid biological tissues was studied using Monte Carlo

simulations. The goal was to efficiently deliver maximum amount of optical power into buried

tumors being treated while avoiding damage to normal tissue caused by strong optical power

deposition underneath the tissue surface illuminated by the laser beam. The buried tumors were

considered to have much higher absorption than the surrounding normal tissue via selective uptake

of absorption-enhancement dye by the tumor. The power delivering efficiency to buried tumors

was investigated for various diameters of the laser beam. An optimal beam diameter was estimated

to achieve the maximum product of the power coupling efficiency and the power delivered to the

buried tumor. The distribution of power deposition was simulated for single beam delivery and

multiple beam delivery as well. The simulated results showed that with an appropriate dye

enhancement and an optimal laser delivery configuration, a high selectivity for laser treatment of

tumor could be achieved.

KEY WORDS

Monte Carlo, light delivery, optical therapy, turbid media, biological tissues.

SPIE Vol. 2975 S 0277-786X/971$1 0.00

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INTRODUCTION

Laser-tissue interactions and their therapeutic applications is a fast growing research area.

Biological tissues are turbid media, in which light attenuates rapidly because of light absorption

augmented by strong light scattering. As a consequence, deeply buried tumors usually receive

much less optical power than the subsurface normal tissues, which hampers efficacious optical

treatment of tumors. By maximizing the power delivered to the target tumors while avoiding

damaging subsurface nonnal tissues, laser treatments may be improved in several aspects. First,

the absorption coefficient of tumors may be significantly increased by infusing dyes into the

tumors. Secondly, the wavelength of the laser light may be selected to maximize the ratio between

the absorption of the tumor and that of the surrounding normal tissue. Thirdly, the light delivery

scheme may be optimized to maximize the power absorption by the target tumors. We wifi

concentrate on the third approach in this paper.

Previous studies have investigated the effect of the diameter of the laser beam while the

power density of the laser beam was kept

an'2 In this paper, Monte Carlo simulations were

used to identify the optimal diameters of the laser beam and to investigate the effect of multiple

beam delivery compared with single beam delivery under the condition that the location of the

buried tumor is known and the absorption of the tumor is enhanced.

METHOD

Monte Carlo simulations of light transport in tissues have been implemented previously for

simple tissue geometry.37 To compute light distributions according to the tissue geometry and

optical properties, including refractive index n, absorption coefficient

scattering

coefficient

and

anisotropy factor g, we have written a Monte Carlo program in C for tissues with buried

objects. We used the delta-scattering technique8 for photon tracing to greatly simplify the

algorithm because this technique allows a photon packet to be traced without directly dealing with

photon crossings of interfaces between different types of tissues. This technique can be used only

for refractive-index-matched tissues, although it allows the ambient clear media (e.g., air) and the

tissue to have mismatched refractive indices.

We assume that the tissue system has multiple tissue types with identical refractive indices.

The interaction coefficient of the ith tissue type, defined as the sum of ta

and

denoted by

The

technique is briefly summarized as follows.

Define a majorant interaction coefficient 1km' where

for

all i.

Select a step size R between two consecutive interactions based on the majorant interaction

coefficient,

R=—1n()/pm,

(1)

where is a uniformly distributed random number between 0 and 1 (0 < 1). Then,

determine the tentative next collision site rk' by:

r = rkl +

Uk!,

(2)

where rkl is the current site and Uk.! is the direction of the flight.

Play a rejection game:

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a. Get a random number i,

which

is a uniformly distributed random number between 0

and 1 (0<i 1).

a. If ii

ij(r')/j.t, i.e., with a probability of pj(r')/i, accept this point as a real

interaction site (rk

rk).

b .

Otherwise,

do not accept rk as a real interaction site but select a new path starting from

r with the unchanged direction Uk1 (i.e., set rkl = r and return to Step 2).

The treatment of photon tracing after step 3 is similar to that in Ref. 7 and will not be repeated here.

The validity can be easily understood by introducing an imaginaiy interaction event that

changes neither the weight nor the direction of the photon. This definition implies that such

imaginaiy interactions are not physically observable, i.e., they can be introduced with any

interaction coefficient at any point. We may assume that the majorant interaction coefficient ji

sum of the real

and

imaginary 1im interaction coefficients, where the real interaction coefficient

is re is .tI(rk'). In the procedure outlined above, a fraction of the interactions,

1 -

Jre4m = 1ima41m

(3)

are imaginary interactions. From another point of view, it is easy to see that on the average, for

every JtO interactions, there will be j.t

interactions

accepted as real interactions. The mean free

path for the majorant interactions in the delta-scattering method is 1/p, and the mean free path for

the real interactions in the direct method is 1/x. Therefore, the photon will move to the correct

interaction site using the delta-scattering technique as it would using the direct method because

J1m( 14Lm) = re (

1/j.t),

(4)

where the left-hand side means the average distance traveled by the photon packet with

total

steps or with Itre real interactions in the delta-scattering method, and the right-hand side means the

average distance traveled with

real

interactions in the direct method.

During the tracing of each weighted photon,7 the light absorption, reflection, or

transmission were correspondingly scored into different arrays according to the spatial positions of

the photon. Multiple photons are traced to achieve an acceptable statistical variation. For this

study, 100,000 photons were traced.

This Monte Carlo program was used to simulate power deposition for tissue configurations

as shown in Fig. 1. Fig. 1(a) shows a single beam delivery scheme to a tissue slab with a tumor

buried in the center. The lateral dimensions in the xy-plane was considered optically infinite, i.e.,

much greater than the penetration depth of light. Fig. 1(b) illustrates a multiple beam delivery

scheme to a tissue cube with a tumor buried in the center. One or more of the four beams may be

selected to illuminate the tissue while the other beams were blocked.

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