title: Latent uncertainties of the precalculated track Monte Carlo method.
abstract: OBJECTIVE
  While significant progress has been made in speeding up Monte Carlo (MC) dose calculation methods, they remain too time-consuming for the purpose of inverse planning. To achieve clinically usable calculation speeds, a precalculated Monte Carlo (PMC) algorithm for proton and electron transport was developed to run on graphics processing units (GPUs). The algorithm utilizes pregenerated particle track data from conventional MC codes for different materials such as water, bone, and lung to produce dose distributions in voxelized phantoms. While PMC methods have been described in the past, an explicit quantification of the latent uncertainty arising from the limited number of unique tracks in the pregenerated track bank is missing from the paper. With a proper uncertainty analysis, an optimal number of tracks in the pregenerated track bank can be selected for a desired dose calculation uncertainty.
  
  
  METHODS
  Particle tracks were pregenerated for electrons and protons using EGSnrc and geant4 and saved in a database. The PMC algorithm for track selection, rotation, and transport was implemented on the Compute Unified Device Architecture (cuda) 4.0 programming framework. PMC dose distributions were calculated in a variety of media and compared to benchmark dose distributions simulated from the corresponding general-purpose MC codes in the same conditions. A latent uncertainty metric was defined and analysis was performed by varying the pregenerated track bank size and the number of simulated primary particle histories and comparing dose values to a "ground truth" benchmark dose distribution calculated to 0.04% average uncertainty in voxels with dose greater than 20% of Dmax. Efficiency metrics were calculated against benchmark MC codes on a single CPU core with no variance reduction.
  
  
  RESULTS
  Dose distributions generated using PMC and benchmark MC codes were compared and found to be within 2% of each other in voxels with dose values greater than 20% of the maximum dose. In proton calculations, a small (≤ 1 mm) distance-to-agreement error was observed at the Bragg peak. Latent uncertainty was characterized for electrons and found to follow a Poisson distribution with the number of unique tracks per energy. A track bank of 12 energies and 60000 unique tracks per pregenerated energy in water had a size of 2.4 GB and achieved a latent uncertainty of approximately 1% at an optimal efficiency gain over DOSXYZnrc. Larger track banks produced a lower latent uncertainty at the cost of increased memory consumption. Using an NVIDIA GTX 590, efficiency analysis showed a 807 × efficiency increase over DOSXYZnrc for 16 MeV electrons in water and 508 × for 16 MeV electrons in bone.
  
  
  CONCLUSIONS
  The PMC method can calculate dose distributions for electrons and protons to a statistical uncertainty of 1% with a large efficiency gain over conventional MC codes. Before performing clinical dose calculations, models to calculate dose contributions from uncharged particles must be implemented. Following the successful implementation of these models, the PMC method will be evaluated as a candidate for inverse planning of modulated electron radiation therapy and scanned proton beams.
authors.affiliation: Medical Physics Unit, McGill University, Montreal, Quebec H3G 1A4, Canada.
authors.forename: Marc-André
authors.initials: MA
authors.lastname: Renaud
authors.affiliation: Département de radio-oncologie, Centre Hospitalier de l'Université de Montréal, Montreal, Quebec H2L 4M1, Canada.
authors.forename: David
authors.initials: D
authors.lastname: Roberge
authors.affiliation: Medical Physics Unit, McGill University, Montreal, Quebec H3G 1A4, Canada.
authors.forename: Jan
authors.initials: J
authors.lastname: Seuntjens
mesh_terms: D000465:Algorithms; D001842:Bone and Bones / Q000528:radiation effects; D016208:Databases, Factual; D004583:Electrons; D006257:Head / Q000528:radiation effects; D006801:Humans; D008168:Lung / Q000528:radiation effects; D008954:Models, Biological; D009010:Monte Carlo Method; D009333:Neck / Q000528:radiation effects; D019047:Phantoms, Imaging; D016012:Poisson Distribution; D011522:Protons; D011874:Radiometry / Q000379:methods*; D014057:Tomography, X-Ray Computed; D035501:Uncertainty; D014867:Water
chemical_list: D011522:Protons; D014867:Water