title: A study of potential numerical pitfalls in GPU-based Monte Carlo dose calculation.
abstract: The purpose of this study was to evaluate the impact of numerical errors caused by the floating point representation of real numbers in a GPU-based Monte Carlo code used for dose calculation in radiation oncology, and to identify situations where this type of error arises. The program used as a benchmark was bGPUMCD. Three tests were performed on the code, which was divided into three functional components: energy accumulation, particle tracking and physical interactions. First, the impact of single-precision calculations was assessed for each functional component. Second, a GPU-specific compilation option that reduces execution time as well as precision was examined. Third, a specific function used for tracking and potentially more sensitive to precision errors was tested by comparing it to a very high-precision implementation. Numerical errors were found in two components of the program. Because of the energy accumulation process, a few voxels surrounding a radiation source end up with a lower computed dose than they should. The tracking system contained a series of operations that abnormally amplify rounding errors in some situations. This resulted in some rare instances (less than 0.1%) of computed distances that are exceedingly far from what they should have been. Most errors detected had no significant effects on the result of a simulation due to its random nature, either because they cancel each other out or because they only affect a small fraction of particles. The results of this work can be extended to other types of GPU-based programs and be used as guidelines to avoid numerical errors on the GPU computing platform.
authors.affiliation: Département de Génie Informatique et Génie Logiciel, École Polytechnique de Montréal, Montréal QC, Canada.
authors.forename: Vincent
authors.initials: V
authors.lastname: Magnoux
authors.forename: Benoît
authors.initials: B
authors.lastname: Ozell
authors.forename: Éric
authors.initials: É
authors.lastname: Bonenfant
authors.forename: Philippe
authors.initials: P
authors.lastname: Després
mesh_terms: D009010:Monte Carlo Method; D011829:Radiation Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D012984:Software