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Light dosimetry in photodynamic

therapy using optical fiber delivery

Steven L. Jacques, Martin R. Ostermeyer, Lihong V.

Wang, Andreas H. Hielscher

Steven L. Jacques, Martin R. Ostermeyer, Lihong V. Wang, Andreas H.

Hielscher, "Light dosimetry in photodynamic therapy using optical fiber

delivery," Proc. SPIE 2133, Optical Methods for Tumor Treatment and

Detection: Mechanisms and Techniques in Photodynamic Therapy III, (19

July 1994); doi: 10.1117/12.179977

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

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Light dosimetry in PDT

using optical fiber delivery.

Steven L. Jacques, Martin Ostermeyer, Lthong Wang, Andreas Hielscher

Laser Biology Research Lab.

Univ. of Texas M. D. Anderson Cancer Center, Houston, TX 77030

ABSTRACT

The paper considers rapid calculations of light distributions in a tissue for photodynamic

therapy. The delivery system considered is a single optical fiber, although other configurations are

easily modeled. The influence of optical heterogeneities in the tissue is considered.

The optical distributions surrounding an optical fiber within a tissue can be well approximated

by a point source of light placed one "reduced mean free path" (mfp') in front of the fiber tip. One

mfp' equals 1I(tL,a

ji(1-g)). Then the simple diffusion theory expression for 3D diffusion from a

point source predicts the light distribution in the tissue.

The influence of optical heterogeneities in the tissue can also be well approximated. A method

is described for representing regions of increased absorption (such as a region with increased

vascularity) as virtual sources of "negative radiant power" such that linear superposition of the true

primary source and the virtual sources yields the net light distribution in the heterogeneous tissue.

The method is rapid, flexible, and generally accurate to within about 15 % error. The method yields

light distributions in optically complex tissues.

1. INTRODUCTION

During photodynamic therapy, the ability of light to penetrate a tissue is limited by absorbing

and scattering properties of the tissue. A tumor often will have optical properties not too dissimilar

from the surrounding normal tissue, but the presence of increased tumor vascularity may increase the

local average absorption coefficient. Also, as PDT proceeds, the effect of PDT on the tumor

vasculature in some cases has been reported to be an increase in the density of blood in the tumor

which further decreases the light penetration.

This paper addresses two issues: (1) What is the light distribution around an optical fiber

imbedded within a homogeneous tissue?

(2) How can one calculate the effect of optical

heterogeneities caused by regions of increased light absorption (such as increased blood content)?

THEORY

2.1 An optical fiber within a homogeneous tissue

When an imbedded optical fiber delivers light to a homogeneous tissue, the light distribution

(fluence rate, F, [W/cm2]) can be well predicted in regions distant from the source by the simple

diffusion theory expression. If the source has a power of 1 W, the fluence rate is:

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F(r) =

exp(-rTh)

[W/cm2]

41tJ.taö

mfp' =

ta+ps(1g)

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2133 / 141

(1)

(2)

where is the optical penetration depth:

[cm]

"/3 La

(J.ta

+ j.(1-g))

The light appears to diffuse from a central source point (r =

which is located just in front of

the optical fiber (see Fig. 1). The distance between the tip of the fiber and the apparent center of the

spherical diffusion field is one "reduced mean free path" (mfp'):

___________

(3)

This

data for this conclusion is not shown here, but is the result of our computer simulations and

experiments.

Fig. 1: When an optical fiber delivers light, a wave of spherical light diffusion is generated whose

center is located 1 mfp' in front of the tip of an optical fiber.

2.2 A single small absorbing object within a homogeneous tissue

To treat the case of regions of increased absorbance within an otherwise homogeneous tissue, a

simple method of calculation was devised. Assume there is a single point source of light (So [W])

located at the origin of our coordinate system.

Consider a very small volume (Vi) of tissue which has an absorption coefficient (P-al)

which

elevated relative to the surrounding tissue with homogeneous optical properties (Ja,

jig, g).

The

center of the small volume is at a distance ri from the point source at the origin. The amount of light

incident on that volume is specified:

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F(r1) =

S0C(r1)

exp(-ri/)

41CP'a

where C(ri) refers to the coupling factor [cm2] between the source So [W] and the fluence

[W/cm2]at position ri and is identica' to Eq. 1 .

The

amount of light additionally absorbed by the

small volume, relative to the background absorption, is well approximated by the calculation:

Qi =

(i.ti

ha) F(ri)

V1 [W]

(5)

The

influence of this locally absorbed power Qi on the overall light field can be approximated by

assigning a source value, S1 =

-Qi, to

a virtual point source of light centered on the small volume,

negative in sign, which superimposes a negative field of fluence rate onto the original field due to the

primary source at the origin.

Therefore, the net field of light at any position r, or (x, y, z), is described:

exp(-r/)

exp(-rTh)

(6)

F(r) =

41t1..Laö2

41t1a&

where r is the distance from the point source at the origin to some observation point (x, y, z):

r =

x2+y2+z2

(7)

and r* refers to the distance between the observation point (x, y, z) and the position of the small

volume (xi,

yi,

r* (x -

xi)2 + (y

yi)2

+ (z -

zi)2

(8)

and the term S1 has a negative value:

Si =

(J.taiJia)F(11)Vi

(9)

The above example illustrates the case of a single small object with only a slightly elevated

absorption coefficient relative to that of the surrounding tissue. Therefore, the small object only

slightly perturbs the light field. The fluence rate at the center of the volume is approximately equal to

the mean of the fluence at the front and rear of the volume along the axis defined by the origin and

the position of the volume.

2.3

Multiple

absorbing objects

If there are several small absorbing objects within the tissue, their influence can still be

calculated using superposition. However, one must allow for the mutual influence of the objects on

each other. With many objects, some objects will shade other objects from the primary source.

Despite the interaction of the many objects, the problem remains a linear system which can be solved

by standard matrix operations. In this section, we first present the solution as an iterative matrix

calculation to illustrate the nature of the solution. In the next section, we restate the solution as

solvable by standard matrix operations.

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