Monte Carlo calculation of proton stopping power and ranges in water for therapeutic energies

Monte Carlo is a statistical technique for obtaining numerical solutions to physical or mathematical problems that are analytically impractical, if not impossible, to solve. For charged particle transport problems, it presents many advantages over deterministic methods since such problems require a realistic description of the problem geometry, as well as detailed tracking of every source particle. Thus, MC can be considered as a powerful alternative to the well-known Bethe-Bloche equation where an equation with various corrections is used to obtain stopping power and ranges of electrons, positrons, protons, alphas, etc. This study presents how a stochastic method such as MC can be utilized to obtain certain quantities of practical importance related to charged particle transport. Sample simulation geometries were formed for water medium where disk shaped thin detectors were employed to compute average values of absorbed dose and flux at specific distances. For each detector cell, these quantities were utilized to evaluate the values of the range and the stopping power, as well as the shape of Bragg curve, for mono-energetic point source pencil beams of protons. The results were found to be +/- 2% compared to the data from the NIST compilation. It is safe to conclude that this approach can be extended to determine dosimetric quantities for other media, energies and charged particle types.