A GPU/CUDA Based Monte Carlo Code for Proton Transport ...

A GPU/CUDA Based Monte Carlo Code for Proton Transport: Preliminary Results of
Proton Depth Dose in Water
Introduction and Innovation
Monte Carlo (MC) methods provide the most accurate calculation of radiation dose
absorbed in human organs or tissues. However, the simulations traditionally performed on the
central processing unit (CPU) are usually very time-consuming, creating difficulties for routine
clinical applications. On the other hand, the graphics processing unit (GPU) has recently
emerged as a powerful and affordable tool for high performance parallel computing. GPUs
provide extensive thread-level parallelism and high efficiency for energy consumption. Compute
Unified Device Architecture (CUDA) [11] is a parallel computing architecture developed by Nvidia,
which greatly facilitates the GPU programming. Recently, a number of GPU/CUDA-based
Monte Carlo codes for medical physics application have been reported, including of Badal et al
for x-ray radiography [1] [2] , and Hissoiny et al [3] and Jia et al [4] [5] on photon treatment planning.
As reviewed by Pratx and Xing [6] , there is limited or no reported effort in developing such a
code for proton radiotherapy which is gaining popularity rapidly. The goal of this project was to
develop a 3D proton transport code for dose calculations. This paper describes the methods
and preliminary results that compare the timing in the CPU and GPU platforms. The
innovation: one of the first attempts to take advantage of GPUs to accelerate the Monte Carlo
simulation for proton dose calculations.
Methods
In this study, protons were transported in a 3D homogeneous material (water) and the
energy deposition was tallied at different depths. The energy-loss fluctuation due to the
Coulomb collisions with atomic electrons and the multiple-scattering deflections due to elastic
scattering by atoms were included. Nuclear reaction was not yet incorporated, which contributes
less than 10% to the total dose. The secondary electrons were assumed to deposit the energies
locally. The condensed history method [7] was used in the proton transport simulation. In this
method, the effect of the extremely large number of interactions was grouped into a few single
condensed steps. The angular deflection in one step was sampled from the Moliere distribution
[8] , with the energy loss being sampled from the Valilov distribution [9] . The position change of a
proton after one step follows those given by Berger [7] .
The pathlength of each collision step was pre-calculated via continuous slowing down
approximation (CSDA). Expected energy loss in each step was chosen as a constant value, or a
fraction (several percent) of the initial energy, whichever is smaller. For each step, the Moliere
distribution and Valilov distribution were evaluated. The distributions and parameters were precalculated
for each step. Cubic spline interpolation was used for parameters from pre-calculated
table. The sampling of the distribution was based on the Alias Sampling Method [10] .
The GPU used in this study is NVIDIA Tesla M2090 and the CPU is Intel Xeon X5660
with 2.80 GHz and 9.00 GB RAM. The CPU code was written in C++ and GPU code was
developed in CUDA C 4.0 [11] , both under the IDE Microsoft Visual Studio 2010. CUDA scalable
programming model has a thread hierarchy for parallel computation. The lowest level is called a
thread, which was designed to simulate a fixed number of protons. A total of 512 threads in our
case were grouped together to form a block. Threads in a block cooperate with each other in
such a way that a warp of threads (32 threads) are able to execute one common instruction at a
time in parallel, making the calculation faster than a typical serialized CPU program. Thread
blocks are executed independently to accommodate for very large number of CUDA cores.
Results
The proton dose distributions in water were calculated for energies of 40 MeV, 80 MeV,
100 MeV, 160 MeV, and 200 MeV. Our CPU and GPU codes yield almost identical results (less
than 0.1% difference). The relative error is within 1% for 98% of the tally depths. The results
were compared with extensively benchmarked general purpose Monte Carlo code MCNPX
2.5.0 [12] and GEANT4.8.2 [13]. Figure 1 compares the 200-MeV proton pencil-beam depth
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dose distribution in water between our code and GEANT4.8.2 (nuclear interaction turned off).
The speedup factor, herein defined as the ratio of the number of particles simulated per second
by GPU to that by CPU is about 57. For the simulation of 1 million proton transport histories in
water, our GPU code is ~620 times faster
than MCNPX 2.5.0(nuclear interaction on).
Conclusion
The goal of this project was to demonstrate
that the GPUs can be used to accelerate
Monte Carlo calculations for protons. A
proton transport code was developed to
calculate the dose distribution in a water
phantom. The code was first developed for
CPU and then ported to GPU/CUDA
platform for timing comparison. The dose
results were benchmarked against those
from the Geant4 code. A speedup of 57 in
the GPU/CUDA version was observed in
comparison with the identical CPU code.
To the best of our knowledge, it is one of
the first efforts to successfully demonstrate
a GPU/CUDA-based proton transport MC
code. It does not yet include the nuclear
interactions and the protons were only
Figure 1: 200 MeV pencil beam proton depth dose in
water, our GPU result compared with Geant4 (nuclear
interaction turned off)
transported in homogenous water phantom. Despite these limitations, we were able to
demonstrate a significant reduction in the computing time, thus suggesting a promising future to
use such extremely fast Monte Carlo tools for routine treatment planning and verification.
References
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voxelized geometry using a massively parallel GPU”, Med. Phys. 36, p. 4878-4880 (2009)
[2] Badal, A. and Badano, A. “Fast and accurate estimation of organ doses in medical imaging
using a GPU GPU-accelerated Monte Carlo simulation code”, AAPM 2011 annual meeting
[3] Hissoiny, S. and Ozell, B. “GPUMCD: A new GPU-oriented Monte Carlo dose calculation
platform” Med. Phys. 38, 754 (2011)
[4] Jia, X. et al, “Development of a GPU-based Monte Carlo dose calculation code for coupled
electron–photon transport” Phys. Med. Biol. 55(2010) 3077
[5] Jia, X. et al, “GPU-based fast Monte Carlo simulation for radiotherapy dose calculation”
Phys. Med. Biol. 56 (2011) 7017–7031
[6] Pratx, G. and Xing, L. “GPU computing in medical physics: a review” Med Phys. 38(5):2685-
97 (2011).
[7] Berger, M. J., “Monte Carlo Calculation of the penetration and Diffusion of Fast Charged
Particles,in: Methods in Computational Physics”, Vol I, Accad. Press, New York, 1963, p. 135
[8] Bethe, H. A., “Moliere's Theory of Multiple Scattering”, Phys. Rev., 89 (1953), pp. 1256-1266
[9] Vavilov, P. V., “Ionizational Losses of High Energy Heavy Particle” J. of Phys USSR, 32
(1957),4, pp. 920-923
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variables, The Amer. Statistian, 33 (1979), 214
[11] NVIDIA, “NVIDIA CUDA C Programming Guide” V4.0, 2011
[12] Pelowitz, D. B. MCNPX User’s manual version 2.5.0 Los Alamos National Laboratory
Report LA-CP-05–0369 (2005)
[13] Agostinelli, S. et al. Geant4 - a simulation toolkit, Nuclear Instruments and Methods in
Physics Research A 506 (2003) 250-303
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