Calculation of water equivalent ratios for various materials at proton energies ranging 10-500 MeV using MCNP, FLUKA, and GEANT4 Monte Carlo codes

Dosimetry of proton beams is generally evaluated in liquid water, or alternatively in solid phantoms via water equivalent ratios (WER). WER is defined as the ratio of proton range in liquid water to that in a phantom of certain material. Presently, WER is not available in the literature neither for a wide range of energies nor for variety of relevant materials. Thus, the goal of this study is to provide such data through Monte Carlo simulations. WER is calculated for 10-500 MeV energies for compact bone, adipose tissue, polymethyl methacrylate (PMMA), PTFE (teflon), graphite (C), aluminum (Al), copper (Cu), titanium (Ti), and gold (Au) using MCNPX.2.70, GEANT4, and FLUKA Monte Carlo (MC) codes. The MCNPX code was considered as the reference to which other codes were compared. The mean values of WER obtained through the MCNPX simulations for Au, Cu, Ti, Al, PTFE, graphite, PMMA, bone, and adipose tissue were 8.83, 5.40, 3.18, 2.03, 1.87, 1.52, 1.13, 1.71, and 0.96, respectively, for 10-500 MeV energy range. The maximum deviations of WER values between MCNPX and GEANT4 results were about 6.85% for adipose tissue at energies  <20 MeV, whereas they were about 7.74%, 7.74% between MCNPX and FLUKA, for adipose and Al, respectively. This inter-code uncertainties are mainly due to different physic models and stopping powers in each code. Comparing the results to that in the literature, the range of discrepancy was found to be 0-8% with greatest discrepancy for Au. Based on the materials evaluated, the PMMA remained the closest to water, for a non-tissue solid material, with an average WER of 1.13, for proton energy ranging 10-500 MeV.