title: A Fano cavity test for Monte Carlo proton transport algorithms.
abstract: OBJECTIVE
  In the scope of reference dosimetry of radiotherapy beams, Monte Carlo (MC) simulations are widely used to compute ionization chamber dose response accurately. Uncertainties related to the transport algorithm can be verified performing self-consistency tests, i.e., the so-called "Fano cavity test." The Fano cavity test is based on the Fano theorem, which states that under charged particle equilibrium conditions, the charged particle fluence is independent of the mass density of the media as long as the cross-sections are uniform. Such tests have not been performed yet for MC codes simulating proton transport. The objectives of this study are to design a new Fano cavity test for proton MC and to implement the methodology in two MC codes: Geant4 and PENELOPE extended to protons (PENH).
  
  
  METHODS
  The new Fano test is designed to evaluate the accuracy of proton transport. Virtual particles with an energy of E0 and a mass macroscopic cross section of Σρ are transported, having the ability to generate protons with kinetic energy E0 and to be restored after each interaction, thus providing proton equilibrium. To perform the test, the authors use a simplified simulation model and rigorously demonstrate that the computed cavity dose per incident fluence must equal ΣE0ρ, as expected in classic Fano tests. The implementation of the test is performed in Geant4 and PENH. The geometry used for testing is a 10 × 10 cm(2) parallel virtual field and a cavity (2 × 2 × 0.2 cm(3) size) in a water phantom with dimensions large enough to ensure proton equilibrium.
  
  
  RESULTS
  For conservative user-defined simulation parameters (leading to small step sizes), both Geant4 and PENH pass the Fano cavity test within 0.1%. However, differences of 0.6% and 0.7% were observed for PENH and Geant4, respectively, using larger step sizes. For PENH, the difference is attributed to the random-hinge method that introduces an artificial energy straggling if step size is not small enough.
  
  
  CONCLUSIONS
  Using conservative user-defined simulation parameters, both PENH and Geant4 pass the Fano cavity test for proton transport. Our methodology is applicable to any kind of charged particle, provided that the considered MC code is able to track the charged particle considered.
authors.affiliation: Université catholique de Louvain, Center of Molecular Imaging, Radiotherapy and Oncology, Institut de Recherche Experimentale et Clinique, Avenue Hippocrate 54, 1200 Brussels, Belgium.
authors.forename: Edmond
authors.initials: E
authors.lastname: Sterpin
authors.affiliation: Université catholique de Louvain, Center of Molecular Imaging, Radiotherapy and Oncology, Institut de Recherche Experimentale et Clinique, Avenue Hippocrate 54, 1200 Brussels, Belgium and Université catholique de Louvain, ICTEAM institute, Chemin du cyclotron 6, 1348 Louvain-la-Neuve, Belgium.
authors.forename: Jefferson
authors.initials: J
authors.lastname: Sorriaux
authors.affiliation: Université catholique de Louvain, Center of Molecular Imaging, Radiotherapy and Oncology, Institut de Recherche Experimentale et Clinique, Avenue Hippocrate 54, 1200 Brussels, Belgium and Université catholique de Louvain, ICTEAM institute, Chemin du cyclotron 6, 1348 Louvain-la-Neuve, Belgium.
authors.forename: Kevin
authors.initials: K
authors.lastname: Souris
authors.affiliation: Université catholique de Louvain, Center of Molecular Imaging, Radiotherapy and Oncology, Institut de Recherche Experimentale et Clinique, Avenue Hippocrate 54, 1200 Brussels, Belgium and Département de Radiothérapie, Cliniques Universitaires Saint-Luc, Avenue Hippocrate 54, 1200 Brussels, Belgium.
authors.forename: Stefaan
authors.initials: S
authors.lastname: Vynckier
authors.affiliation: Département de radio-oncologie, Centre hospitalier de l'Université de Montréal (CHUM), 1560 Sherbrooke est, Montréal, Québec H2L 4M1, Canada.
authors.forename: Hugo
authors.initials: H
authors.lastname: Bouchard
mesh_terms: D000465:Algorithms; D004583:Electrons; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D061766:Proton Therapy