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Method for Fast CT/SPECT-Based 3D Monte Carlo Absorbed Dose

Computations in Internal Emitter Therapy

S. J. Wilderman and

Department of Nuclear Engineering and Radiologic Sciences, University of Michigan, Ann Arbor,

MI 48109 USA (sjwnc@umich.edu)

Y. K. Dewaraja

Department of Radiology, University of Michigan, Ann Arbor, MI 48109 USA

Abstract

The DPM (Dose Planning Method) Monte Carlo electron and photon transport program, designed

for fast computation of radiation absorbed dose in external beam radiotherapy, has been adapted to

the calculation of absorbed dose in patient-specific internal emitter therapy. Because both its photon

and electron transport mechanics algorithms have been optimized for fast computation in 3D

voxelized geometries (in particular, those derived from CT scans), DPM is perfectly suited for

performing patient-specific absorbed dose calculations in internal emitter therapy. In the updated

version of DPM developed for the current work, the necessary inputs are a patient CT image, a

registered SPECT image, and any number of registered masks defining regions of interest. DPM has

been benchmarked for internal emitter therapy applications by comparing computed absorption

fractions for a variety of organs using a Zubal phantom with reference results from the Medical

Internal Radionuclide Dose (MIRD) Committee standards. In addition, the β decay source algorithm

and the photon tracking algorithm of DPM have been further benchmarked by comparison to

experimental data. This paper presents a description of the program, the results of the benchmark

studies, and some sample computations using patient data from radioimmunotherapy studies

using 131I.

Index Terms

Biomedical applications of nuclear radiation; biomedical nuclear imaging; dosimetry; Monte Carlo

methods

I. Introduction

Optimization of treatment plans for internal emitter therapy requires accurate determination of

absorbed dose in both targeted tumors (for estimation of the efficacy of the treatment) and

critical organs (to preclude toxicity). Conventional methods for determining absorbed dose,

such as those based on Medical Internal Radionuclide Dose (MIRD) S values [1], ignore details

of patient-specific anatomy and so are inherently approximate. Such methods typically employ

a single, standard human form and so assume uniform activity distributions in standardized

source organs, yielding uniform absorbed dose distributions in standardized target organs. Such

results can be in error when patient anatomy significantly deviates from the standard. In

contrast, the accuracy of Monte Carlo-based dosimetry methods is limited only by errors in

the specification of patient anatomy (typically obtained from CT) and in the determination of

source activity distributions (typically derived from PET or SPECT studies). A number of

investigators have reported efforts to develop dosimetry platforms for internal emitter therapy

applications based on Monte Carlo computation of absorbed dose [2]–[5].

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Published in final edited form as:

IEEE Trans Nucl Sci. 2007 February 17; 54(1): 146–151. doi:10.1109/TNS.2006.889164.

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While Monte Carlo simulations offer the prospect of greatly improved accuracy, they are

computationally expensive and can involve approximations of their own. For example, Monte

Carlo dosimetry platforms which rely on CT data to describe patient anatomy usually treat the

body as an essentially homogeneous medium (composed of water) but with spatially varying

density. This approximation can lead to errors in absorbed dose computations in regions where

high Z materials (such as bone) are present. In the current work, we report of the adaptation of

the Monte Carlo program DPM (Dose Planning Method) [6] (originally developed specifically

for fast absorbed dose computations in external beam radiotherapy applications), to internal

emitter therapy applications.

DPM is well-suited as a Monte Carlo engine for internal emitter dosimetry problems. Because

it was never meant to be a general-purpose code, during development DPM was optimized

specifically for efficient computation of absorbed dose distributions in CT-derived, voxelized

geometries, and so is faster than conventional Monte Carlo programs for this application. DPM

achieves some of its speed from numerous small optimization practices that were followed

during its construction. For example, since the form of the geometry, source, and required

output is known and fixed (i.e., voxel-based maps), only the most rudimentary user options

are available for specifying physics models, and no “hooks” exist for interrogating the program

for problem tallies. Thus, DPM avoids evaluating scores of conditional tests inside the transport

loops, and it instead calls tallying routines only at those instances when energy is deposited.

Similarly, DPM mandates that the energy thresholds for secondary particle production and

transport cut-off energies be equivalent, also avoiding conditional tests inside its transport

loops.

These and other minor, localized conventions, provide a small part of the speedup realized by

DPM. Two global features of the program account for the bulk of its efficiency. First, DPM

employs the well-known δ-scattering method of Woodcock [7] in its treatment of photon

transport. Woodcock tracking allows for the transport of photons across geometric boundaries

and is most efficient with regular geometries and where interaction cross sections are fairly

uniform over the entire volume. Both of these conditions are fulfilled in internal emitter therapy

simulations. In addition, DPM achieves significant speed-up in electron transport problems

through its use of a novel “transport mechanics” model which permits DPM to take much

longer (and so far fewer) electron transport steps relative to conventional Monte Carlo

programs. Because of the way it has been formulated and implemented, the transport mechanics

model in DPM also permits electron transport across several region boundaries in a single step,

even when those regions are composed of differing materials. In conventional Monte Carlo

algorithms, step-sizes (and hence computational efficiency) for energetic electrons can be

limited by region size. The details of the DPM transport mechanics model, labeled the

“modified random-hinge,” and related implementation issues in the program have been

described in detail by Sempau et al. [6].

Taken together, δ-scattering for photons, the random hinge mechanics with cross-boundary

transport for electrons, and its many other small optimizations provide DPM with significant

speed advantages over other Monte Carlo programs in voxelized geometries, particularly when

the voxel dimensions are small in relation to the mean free paths of source and secondary

photons and the total range of source and secondary electrons. For the simulation of electron

beams in the 10–20 MeV range in typical external beam radiotherapy problems, DPM is

roughly 5–10 times faster than the widely used EGS4 program [8] with 1 mm voxels, primarily

because the random-hinge transport mechanics permits the accurate modeling of very long

electron transport steps [6]. When voxel sizes increase (or electron and photon energies

decrease), however, the speed benefits of both δ-scattering and the random hinge mechanics

diminish. In particular, because of the relatively low energies of the β's emitted by isotopes

typically used in internal emitter therapy applications, the speedup advantages of DPM over

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EGS4 are expected to be less then factor of 5–10 seen in external beam simulations. The average

and maximum β particle energies following a 131I disintegration are .192 and .807 MeV,

respectively, and the corresponding maximum electron ranges in water are roughly .4 mm at

the average energy and 3 mm at the highest energy. Thus, electron transport plays little role in

absorbed dose simulations when this isotope is used. Even for 90Y, in which there has been

significant recent interest as a radioimmunotherapy isotope [9]–[11], the maximum electron

ranges corresponding to the β endpoint energy (2.28 MeV) and average energy (.94 MeV) are

still only 1 cm and 4 mm, respectively, meaning that some of the speedup DPM achieves

through its electron transport model will not be realized except for small voxel sizes. Further,

in many cases, the resolution of SPECT images used for activity quantification may be of the

same order as electron range, thus mandating large voxels and so virtually negating all of DPM's

potential electron transport speedup. Results of a study of the relative efficiency of DPM vs.

EGS4 for internal emitter therapy absorbed dose computations are presented in the Results

section of this work.

In order to reduce memory requirements and at the same time preclude post-processing, DPM

does not employ batch tallies, but instead computes absorbed dose and variance on a particle-

by-particle basis. Performing Monte Carlo calculations with batches of histories is convenient

in that it permits computation of variance in arbitrary regions of interest after the final batches

are complete, but because a minimum of 30 batches must be run to provide accurate estimates

of variance, batch-based programs require either memory allocation of at least 35 times the

total of number voxels or post-processing of the entire absorbed dose distribution computed

for each individual batch. The memory requirements of DPM, in contrast, are roughly six times

the number of voxels, (density, deposited energy, variance, material index and two temporary

variables that score history-by-history data), and so problems of dimension of 256 × 256 × 256

can be run on machines with 2 GB of RAM. The disadvantage of not using batch tallies is that

special scoring must be done to provide estimates of variance (though, not, of course, estimates

of absorbed dose) for regions of interest.

DPM is written in FORTRAN and has been installed and run under Linux, Digital Unix, HP

Unix, and VMS, among other operating systems. The standard source code and all associated

data files and auxiliary files, including the pre-processing programs based on the physics and

data models in PENELOPE, can be downloaded from

http://www-personal.engin.umich.edu/bielajew/DPM.

II. Methods

The primary modifications necessary to adapt DPM for internal emitter therapy applications

involve the source and scoring algorithms. In the current work, DPM has been modified to

treat β decay radiation from generic isotopes, as defined by user through the input of branching

ratio and energy level data. The implementation is generic, though thus far appropriate input

data has been compiled only for 131I sources. The basic unit of radiation corresponding to a

DPM Monte Carlo “history” is a single β decay—all radiation emitted subsequent to the initial

decay is treated as part of a single history. Decay schemes and branching ratios have been taken

from the Lawrence Berkeley/Lund University Isotopes Project [12], and are input in terms of

the isotope energy levels and branching ratios for each level. Beta-particle energies are sampled

from the normalized Fermi distribution using a rejection scheme. The normalized Fermi

distribution is given as

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(1)

where E0 is the maximum total energy of the line, E and p are the energy and momentum,

respectively, of the emitted electron, and η is given by Ze2/hv, with v the ejected electron

velocity and h Planck's constant.

The spatial distribution of the radiation source is input by the user as a PET or SPECT image

registered to a CT image, which is used to define the patient anatomy. DPM reads and stores

relative source intensities in each voxel. During execution, voxel ID numbers are rapidly

chosen using the alias sampling technique of Walker [13], and the actual positions of the

disintegrations are assumed to be uniformly distributed inside each voxel.

DPM permits the user to specify up to 100 regions of interest in the CT image (usually tumors

and organs) via maps which overlay the CT geometry. All voxels not specifically assigned to

be part of a user-defined ROI are taken as an aggregate “rest of body” organ. Absorbed dose

due to all daughter particles originating from the initial β emission and from the subsequent

gamma emission following each decay is tallied distinctly for all combinations of source and

target organs defined in the user input ROIs.

The geometry data required is a map of the actual voxel densities, and in the default case, DPM

assigns each voxel to be either air or water. However, if segmentation has been done a priori

on the reference geometry, exact materials can be specified for chosen voxels when the tallying

regions of interest are input.

SPECT images supplied to DPM are typically single time-frame snapshots of source

distributions which actually have non-uniform time-dependencies, and so DPM provides a

facility for organ-by-organ corrections to the source intensity distribution based on measured

or assumed residence times for the defined regions of interest. This method does, of course,

assume that the time-dependence of the activity curve is uniform for each voxel within each

specific organ.

A facility also is provided for studying the effects of misregistration. Offsets in (x, y, z) can be

input by the user and the SPECT image will be shifted relative to the CT image by the specified

amounts. A study of the magnitude of misregistration effects using DPM and phantoms has

been reported recently [15].

DPM computes and prints absorbed dose rate maps, absorbed dose rate uncertainty maps, and

summary tables for the various ROIs. A sample input activity map is shown in Fig. 1, a sample

input CT in Fig. 2, and the resultant computed absorbed dose rate map in Fig. 3. A sample

output summary table is shown in Fig. 4. Note that in this example, the SPECT activity was

not corrected for the variable residence times in the ROIs. Computations were performed using

a 256 × 256 × 38 CT image with voxel dimensions of 0.2 × 0.2 × 1 cm. This particular data

set included one extremely large and elongated tumor, which evinces higher than usual self-

dose due to gammas.

III. Results and Benchmarking

The initial, external source, version of DPM was originally validated by comparison against

the EGS4 [8] and PENELOPE [14] Monte Carlo programs [6]. DPM has since been bench-

marked against measurements for external beam therapy applications (with both electron and

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photon beams), in homogeneous and heterogeneous media [16]–[18]. DPM is currently being

used extensively in research investigations addressing clinical problems (see for example,

[19]–[21]). Thus, the accuracy of the basic physics and transport and models of DPM is well

established for external sources. We present here results of exercises designed to validate the

features added to DPM for modeling internal emitter therapies.

As reported previously [22], DPM has been validated for internal emitter studies by comparing

conventional MIRD S factors with those calculated by DPM using a Zubal phantom [23] as

the reference geometry. Some of those earlier results are reproduced in Table I. As noted in

the prior work, because some of the organs in the voxelized Zubal phantom differ considerably

in mass and geometry from the organs in the Standard Man mathematical phantom employed

in the MIRD methodology, organ self-dose S factors from DPM must be corrected to account

for this. When this is done using a linear mass-weighting factor, DPM and MIRD agree to

within a few percent. Since organ cross-doses are dependent on photon transport, however, no

simple corrections for the geometric differences in the two phantoms can be applied, and DPM

and MIRD S factors results disagree by up to 30%, as seen in the table.

The photon portion of the β decay routines in DPM were further benchmarked against

experiment. A sphere of volume 16.4 cm3 was filled with 15 cm3 of a solution containing

936.55μCi of 131I and placed in an ellipsoidal phantom made of tissue-equivalent plastic and

filled with water. The phantom had a height of 18.5 cm, a major axis of 31.0 cm (taken in the

y direction) and minor axis of 23.0 cm, and the center of the source sphere was at (0, 2.86,

13.15). Lithium fluoride TLD detectors (dimensions of .32 × .32 × .09 cm) were arrayed in the

shape of a cross centered directly above the source sphere and attached to the outside of the

phantom at positions given in Table II. Total exposure time for the experiment was 67 hours

and 45 minutes.

Because of the difficulty in making precise measurements of the positions of the dosimeters

and the source, the TLDs were placed in symmetric locations about the source to provide

redundancy in the experimental data and to help illuminate positional measurement errors.

Given the small size of the TLDs, even with the modest absorbed dose gradients expected for

the photon-driven experiment, errors in the assumed positions could result in large

discrepancies between measurements and computations. This problem was encountered by

Gardin, et al [24] in comparing TLD measurements with absorbed dose computations (not

Monte Carlo) for internal emitters.

For consistency with the way DPM is used in modeling patients, the phantom was “voxelized”

into a simulated CT-map of an 256 × 256 × 64 array of cells, and the source sphere was similarly

converted into a simulated registered SPECT activity map of the same size.

To simulate the experiment, several modifications were made to DPM, primarily because of

the implications of using Woodcock tracking. Because of the way Woodcock methods are

typically implemented, when a particle escapes a surface, unlike in conventional Monte Carlo

tracking methodologies, its final position is not exactly on that surface, but rather at some

random distance along its direction vector outside the phantom. Thus DPM was first modified

to retrace the paths of escaping photons and put them back on the surface of phantom. Further,

since the TLD dimensions did not conform to the sizes of the voxelized version of the phantom,

they had to be treated as “add-ons,” and not integral parts of the simulation. Thus DPM was

modified to search though the list of TLDs arrayed on the surface of the phantom whenever a

photon escaped and to determine whether the photon would pass through any TLD. This

includes intersections with the side faces of the TLDs, as, even though the devices were less

than a millimeter thick, for those TLDs at large distances from the source sphere, a substantial

fraction of the absorptions come from photons impacting the side faces. While complete

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