Systematics of relative biological effectiveness measurements for proton radiation along the spread out Bragg peak: experimental validation of the local effect model

The purpose of this study is to compare the predictions of the local effect model (LEM) in an extensive analysis to proton relative biological effectiveness (RBE) experiments found in the literature, and demonstrate the capabilities of the model as well as to discuss potential limitations. 19 publications with in vitro experiments and 10 publications with in vivo experiments focusing on proton RBE along the spread out Bragg peak (SOBP) were considered. In total the RBE values of over 100 depth positions were compared to LEM predictions. The treatment planning software TRiP98 was used to reconstruct the proton depth dose profile, and, together with the physical dose distribution, the RBE prediction was conducted based on the LEM. Only parameters from photon dose response curves are used as input for the LEM, and no free parameters are introduced, thus allowing us to demonstrate the predictive power of the LEM for protons. The LEM describes the RBE adequately well within the SOBP region with a relative deviation of typically less than 10% up to 10 keV mu m(-1). In accordance with previous publications a clear dependence of RBE on the dose-averaged linear energy transfer (LETD) was observed. The RBE in the experiments tends to increase above 1.1 for LETD values above 2 keV mu m(-1) and above 1.5 for LETD values higher than 10 keV mu m(-1) (distal part of the SOBP). The dose dependence is most pronounced for doses lower than 3 Gy (RBE). However, both the LEM predictions and experimental data show only a weak dependence of RBE on the tissue type, as characterized by the alpha/beta ratio, which is considered insignificant with regard to the general uncertainties of RBE. The RBE predicted by the LEM shows overall very good agreement with the experimental data within the SOBP region and is in better agreement with the experimental data than the constant RBE of 1.1 that is currently applied in the clinics. All RBE trends deduced from the experiments were also reflected by the LEM predictions, which are purely based on input parameters derived from low-LET photon radiation.