A phenomenological relative biological effectiveness approach for proton therapy based on an improved description of the mixed radiation field

Proton therapy treatment planning systems (TPSs) are based on the assumption of a constant relative biological effectiveness (RBE) of 1.1 without taking into account the found in vitro experimental variations of the RBE as a function of tissue type, linear energy transfer (LET) and dose. The phenomenological RBE models available in literature are based on the dose-averaged LET (LET D ) as an indicator of the physical properties of the proton radiation field. The LET D values are typically calculated taking into account primary and secondary protons, neglecting the biological effect of heavier secondaries. In this work, we have introduced a phenomenological RBE approach which considers the biological effect of primary protons, and of secondary protons, deuterons, tritons (Z = 1) and He fragments (3He and 4He, Z = 2). The calculation framework, coupled with a Monte Carlo (MC) code, has been successfully benchmarked against clonogenic in vitro data measured in this work for two cell lines and then applied to determine biological quantities for spread-out Bragg peaks and a prostate and a head case. The introduced RBE formalism, which depends on the mixed radiation field, the dose and the ratio of the linear–quadratic model parameters for the reference radiation ${{\left(\alpha /\beta \right)}_{\text{ph}}}$ , predicts, when integrated in an MC code, higher RBE values in comparison to LET D -based parameterizations. This effect is particular enhanced in the entrance channel of the proton field and for low ${{\left(\alpha /\beta \right)}_{\text{ph}}}$ tissues. For the prostate and the head case, we found higher RBE-weighted dose values up to about 5% in the entrance channel when including or neglecting the Z = 2 secondaries in the RBE calculation. TPSs able to proper account for the mixed radiation field in proton therapy are thus recommended for an accurate determination of the RBE in the whole treatment field.