Parameterising microdosimetric distributions of mono-energetic proton beams for fast estimates of yD and y∗

Abstract

Wepresent analytical models of the dose-mean lineal energy (yD) and the saturation-corrected dosemean lineal energy (y∗) for fast and accurate radiobiological calculations in proton therapy. These models are based on the modelling of microdosimetric distributions f(ϵs) obtained from Monte Carlo (MC) simulations of the energy deposited per interaction event, ϵs, for mono-energetic proton beams in water with an energy range from 0.6 MeV to 95 MeV.Wealso performed calculations of Relative Biological Effectiveness (RBE) based on both,MCand the analytical models of y∗, using the Microdosimetric Kinetic Model (MKM) for Human Salivary Gland (HSG) cells. Both RBE calculations were then compared to demonstrate the consistency of the agreement between the microdosimetric distributions themselves as well as of any other distributions based on them. Maximum, mininum and average relative differences betweenMCand analytical values were reported as well as paired Student t-tests to display the goodness of our tool to model y, D y∗ and RBE distributions. For yD values the maximum, minimum and average relative discrepancies were 0.99%, ?1.67% and?0.06% respectively. In the case of y∗ values these differences were 0.98%,?1.55% and ?0.07%, while for RBE values they were 0.37%,?0.75% and?0.04% respectively. The Student t-tests showed that no statistically significant differences were observed betweenMCand analytical values. Our analytical tool has provided instantaneous calculations of the magnitudes of interest, in contrast with the computation times required withMCsimulations.Wehave developed an algorithm which provides fast calculations of yD and y∗, maintaining a clinically relevant accuracy level.