A phenomenological model for the relative biological effectiveness in therapeutic proton beams.

To study the effects of a variable relative biological effectiveness (RBE) in inverse treatment planning for proton therapy, fast methods for three-dimensional RBE calculations are required. We therefore propose a simple phenomenological model for the RBE in therapeutic proton beams. It describes the RBE as a function of the dose, the linear energy transfer (LET) and tissue specific parameters. Published experimental results for the dependence of the parameters alpha and beta from the linear-quadratic model on the dose averaged LET were evaluated. Using a linear function for alpha(LET) in the relevant LET region below 30 keV per micrometre and a constant beta, a simple formula for the RBE could be derived. The new model was able to reproduce the basic dependences of RBE on dose and LET, and the RBE values agreed well with experimental results. The model was also applied to spread-out Bragg peaks (SOBP), where the main effects of a variable RBE are an increase of the RBE along the SOBP plateau, and a shift in depth of the distal falloff. The new method allows fast RBE estimations and has therefore potential applications in iterative treatment planning for proton therapy.