Neural network modelling of proton RBE values at predominant survival fractions of in vitro data

While a constant relative biological effectiveness (RBE) of 1.1 is applied in clinical proton therapy, longstanding clinical concern and in vitro evidence demonstrate a variable proton RBE. Several RBE models for protons have been developed based on general assumptions of RBE dependencies together with fitting to in vitro data, for which some modelling authors have included greater diversity of cell types than others. In this study we use neural networks (NNs) to model the proton RBE without any predefined dependencies, investigate the effect of using different biological inputs and combinations of input parameters in the modelling, and compare the results to previous approaches. A comprehensive in vitro RBE database of 431 data points was used, including parameter values for the proton linear energy transfer (LET), the (α/β)_x value of the linear quadratic model parameters of the reference photon radiation, and survival fraction (SF)-specific photon doses (D_x(SF)). NNs were used to model RBEs at specific SFs (RBE_SF) as a function of (1) LET, (2) LET and (α/β)_x and (3) LET, (α/β)_x and D_x(SF). Models with inputs LET, (α/β)_x and D_x(SF) showed overall best performance, particularly inputs with D_x(0.1) and D_x(0.2), indicating that an appropriate standardized input parameter for D_x(SF) could be established by choosing an SF between 0.1 and 0.2. The presented approach to assumption-free NN-based modelling of proton RBE showed similar RBE dependencies as previously published models with similar predictive power. Further, it was demonstrated that adding the photon dose sensitivity as an input parameter to modelling could increase the quality of RBE models.