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Animated simulation of light transport
in tissues
Lihong V. Wang, Steven L. Jacques
Lihong V. Wang, Steven L. Jacques, "Animated simulation of light transport in
tissues," Proc. SPIE 2134, Laser-Tissue Interaction V; and Ultraviolet
Radiation Hazards, (17 August 1994); doi: 10.1117/12.182939
Event: OE/LASE '94, 1994, Los Angeles, CA, United States
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Animated Simulation of Light Transport in Tissues
Lihong Wang 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
Time-resolved light transport in composite tissues is simulated using the Monte Carlo
technique. Snapshots of spatial distributions of physical quantities, including light absorption rate,
light fluence rate, and diffuse reflectance rate, are presented. Such multiple snapshots with a given
time interval can be shown sequentially to achieve an animation effect. This animated simulation is a
tool that aids in the general understanding of light transport in tissues. For example, the simulation of
time-resolved spatial distribution of light fluence rate inside a tissue illustrates how fast light is
dispersed inside tissues. The simulation of diffuse reflectance rate as a function of time of a short-
pulsed laser incident upon a piece of tissue containing a buried object shows that early reflected light
does not carry imaging information of the object. The imaging quality of the object can thus be
improved by rejecting the early-arriving reflected light.
INTRODUCTION
In laser-tissue interactions, it is important to model light transport in tissues, which are turbid
media. Modeling helps understand the mechanism of laser-tissue interactions, provides algorithms for
laser diagnosis of diseases, and guides dosimetry for laser therapy of diseases. Among the available
models are Monte Carlo simulations,17 diffusion theories,8'44 finite difference methods,15 fmite
element methods,16 and hybrid models of Monte Carlo-diffusion theory.17'18
The general use of Monte Carlo simulations is well established in the literature.h7 Our Monte
Carlo simulation program for multi-layered tissues has been distributed in the public domain for over
a year.19 The program can be downloaded by anonymous ftp (File Transfer Protocol) to
laser.mda.uth.tmc.edu (129.106.60.92). Monte Carlo simulations are the most accurate models but
suffer from long computational requirements. Analytically solvable diffusion theories for simple
geometries are the fastest but are not flexible enough to solve complex geometries and lack accuracy
near the light source and sometimes near the boundaries. Finite difference methods and finite
element methods are sometimes used to solve radiative transfer equations with the diffusion
approximation. They are flexible and considerably faster than Monte Carlo simulations but are
subject to the limitations of the diffusion approximation. The hybrid of Monte Carlo-diffusion theory
combines the accuracy advantage of the Monte Carlo simulations with the speed advantage of the
diffusion theories.
We have recently implemented a more general machine-portable time-resolved Monte Carlo
simulation program in C for tissues with buried objects. The program thus far accepts spheres,
rectangular boxes with faces parallel to the Cartesian coordinate axes of the tissue system, and
cylinders oriented along one of the three Cartesian coordinate axes.
Both our programs compute light distributions according to tissue geometries and optical
properties. The tissue optical properties include refractive index, absorption coefficient, scattering
coefficient, and anisotropy factor.
We applied the time-resolved Monte Carlo program to several examples of tissue
configurations. The simulation results are presented in selected multiple frames as a function of time
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SPIE Vol. 21 34A Laser-Tissue Interaction V (1994)1247
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to show the time course of 2-D images of the light transport. Running the frames sequentially on a
computer generates an animation effect that shows the dynamic light transport in tissues.
METHODS
To compute light distributions according to tissue geometries and optical properties, including
refractive index (n), absorption coefficient (p), scattering coefficient (ps), and anisotropy factor (g),
we have written a Monte Carlo program in C for tissues with buried objects. We use the delta-
scattering technique20 for photon tracing to greatly simplify the algorithm because this technique
allows a photon packet to be traced without worrying about the interfaces between 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 the tissue system has multiple tissue types with matched refractive indices. The
interaction coefficient of the ith tissue type, defined as the sum of ia and
is denoted by
The
technique is briefly summarized as follows.
1 .
Define
a majorant interaction coefficient jim, J1m Jtj for all i.
2 .
Select
a distance R,
R1n()/.Lm,
(1)
where
is a uniformly distributed random number between 0 and 1 (0 < 1). Then,
determine the tentative next coffision site rk' by:
r
+ R Uk4
(2)
where rki is the current site and Uk4 is the direction of the ffight.
3
. Play
a rejection game:
a. With a probability of p(rk')/im ,
accept
this point as a real interaction site (rk =
rk');
b. Otherwise, do not accept r' as a real interaction site but select a new path starting from
r' with the unchanged direction ukl (i.e., set
r1c and return to Step 2).
The validity can be easily understood. Let us introduce an imaginary interaction event that
changes neither the weight nor the direction of the photon. This definition implies that such
imaginary interactions are not physically observable, i.e., they can be introduced with any interaction
coefficient at any point. Now if we assume that the majorant interaction coefficient (pm) is a sum of
the real (.tre) and imaginary (J.tim) interaction coefficients, then in the procedure outlined above, a
fraction of the interactions,
1 —
Jlre/Jim
=
Jtim1Jtm
(3)
are
imaginary interactions. Looking at it from another angle, we see that on the average, for every im
total interactions, there will be tre interactions accepted as real interactions. The mean free path for
the majorant interactions in the delta-scattering method is l/p and the mean free path for the real
interactions in the directe method is l/Jlre. Therefore, the photon will move to the correct interaction
site using the delta-scattering technique as it would using the direct method, i.e.,
1m(14tm) =
1-ke
(1/Jlre),
(4)
where the left-hand side is the average distance traveled by the photon packet with Jlm total steps or
with 1re real interactions in the delta-scattering method and the right-hand side is the average distance
traveled with 1re real interactions in the direct method.
During the tracing of each weighted photon, the light absorption, reflectance, or transmittance
are correspondingly scored into different arrays according to the spatial and temporal positions of the
248
ISPIE
Vol. 2134A
Laser-Tissue Interaction V(1994)
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photon. Multiple photons ( 1 x 1O- 1 x iO) are traced to achieve an acceptable statistical variation.
The averaged results at different times are generated.
To use the imaging program with the animation ability from the National Center for
Supercomputing Applications (NCSA) ,
we
extract multiple frames from the simulation results and
save them in the Hierarchical Data Format (HDF). The NCSA imaging program can read the frames
and play them back as animation. Interested readers can obtain the animation sequences and the
imaging program by contacting the authors.
RESULTS
The difference in fluence rate between an isotropic point source and a pencil beam inside an
infinite tissue is demonstrated in Fig. 1 .
The
optical properties of dermis in the 440 nm wavelength
are used for the simulations.21 The light from the isotropic source remains isotropic and moves
outward from the source point, whereas the light from the pencil source travels downward while
being dispersed by the scattering medium. The sizes of the outer edges in the light distributions
originated from the two sources at a given time are about the same, although the light-distribution
patterns are quite different in the beginning. After light travels 5 picoseconds (ps), the fluence rate
caused by the pencil beam approaches isotropic. Since one transport mean free path (mfp'), defined
as 1/[pa +
(1—g)]
,
of
the tissue is 1/El .4 +
350
x (1—0.8)] =
0.014
cm, the distance that the light
travels in 5 p5, computed as 0.03 (cm/ps) x 5 (ps) / 1 .37 =
0.109
cm, is 7.8 mfp'. In other words, the
fluence rate is approximately isotropic after light travels 7.8 mfp'.
The integrated fluence rate at x =
0
as a function of z in Fig. lp is plotted in Fig. 2. The
smoothed curve shows that the integrated fluence rate is approximately symmetrical about the z-
position that is 1 mfp' from the source position.
The energy-absorption rates integrated along the y-axis are computed for a pencil beam
incident upon a semi-infinite dermis tissue (Figs. 3a-h) and a semi-infinite dermis tissue with buried
high-absorbing melanin (Figs. 3i-p). The optical properties of dermis and melanin in the 440 nm
wavelength are used for the simulations.21 In Figs. 3a-h, an energy center traveling downward can be
observed in the early stage of the propagation and is dispersed with propagation as a result of the
scattering. In Figs. 3i-p, the energy center is not as strong and does not travel as deep as that in Figs.
3a-h as a result of the high absorption of the melanin.
The diffuse reflectance patterns of a circular laser beam incident upon a semi-infinite tissue
(Figs. 4a-h) and a semi-infinite tissue with a buried absorber (Figs. 4i-p) are simulated. In Figs. 4a-h,
the center of the reflectance pattern stays the brightest and the pattern grows symmetrically with time
as a result of scattering. In Figs. 4i-p, the pattern grows as fast as that in Figs. 4a-h, but a dark spot in
the center starts to appear as time elapses because of the buried absorber. The round-trip time
between the light entry point and the top of the sphere is 2 x 0. 1 (cm) / 0.03 (cm/ps) x 1 .37 =
9.
1 ps,
but the effect of the absorber only appears after Fig. 41 that has a 52.5-ps delay.
DISCUSSION
Figs. 1 ,
3
,
and
4 present only a few selected frames of larger animation sequences in false
colors. The goal is to give the reader a feeling of dynamic light propagation in tissues. Figs. 1 and 2
show that when light is delivered into tissues interstitially through a fiber with an isotropic tip or a
regular straight tip that is considered small in diameter compared with 1 mfp' ,
the
light distribution
after light travels a few mfp' caused by the two tips are equivalent except for a spatial shift of 1 mfp'.
Of course the difference is greater when the fiber tip is large compared with 1 mfp' of the tissue. Fig.
3 demonstrates how melanin blocks light as a result of its high absorption coefficient. Fig. 4 suggests
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