Statistical uncertainty estimation in the calculation of the proton range in water phantom.

Introduction: GATE (Geant4 Application for Tomographic Emission) is a Monte Carlo simulation platform developed by the OpenGATE collaboration since 2001 and first publicly released in 2004. In Geant4, each physics process is described by a model (several models are sometimes available for a given physics process) and a corresponding cross-section table. All Geant4 physics models and cross-sections below 10 GeV are now available in GATE. In particular, models describing the transport of optical photons and hadronic interactions have recently been introduced. The purpose of this study is to investigate the physics lists of the Geant4 code, as well as to examine the accuracy of energy deposition and statistical uncertainty in the calculation of the dose. Materials and Methods: In this study, GATE code was used to compute absorbed dose and fluence of protons in the energy range of 50-200 MeV and with energy step of 50 MeV. A water phantom (40*40*40 cm3) was modeled in a vacuum world volume (5*5*5 m3). Several physics lists have been defined in the GATE code that we used FTFP_BERT. The mono-energetic protons were emitted mono-directionally from a point source at one end of the water phantom. The DoseActor has been added to store distributions of dose with the associated statistical uncertainty in any volume The simulations were carried out for 10^6 proton histories that yielded better than 0.3% statistical errors.   Results: In the current study, we obtained normalized energy deposited for 5-200 MeV proton beams as a function of depth in water and its associated relative statistical uncertainty. The statistical uncertainty for all voxels before the Bragg peak is below 0.01%. Fluctuations after the Bragg peak are due to near zero values of deposited energy at these depths. Conclusion: The results of this study showed that the statistical uncertainty of the dose in the energy of 200 MeV is about 0.25%. And by calculation the difference of proton ranges in this energy with NIST data, it is seen that this difference is greater than the statistical uncertainty. In order to obtain more accurate results, it is suggested that the accuracy of other physics lists is also examined..