Proton RBE models: commonalities and differences

Uncertainties in the relative biological effectiveness (RBE) of protons remains a major barrier to the biological optimisation of proton therapy. While a constant value of 1.1 is widely used in treatment planning, extensive preclinical in vitro and in vivo data suggests that proton RBE is variable, depending on proton energy, target tissue, and endpoint. A number of phenomenological models have been developed to try and explain this variation, but agreement between these models is often poor. This has been attributed to both the models' underlying assumptions and the data to which they are fit. In this brief note, we investigate the underlying trends in these models by comparing their predictions as a function of relevant biological and physical parameters, to determine where models are in conceptual agreement or disagreement. By doing this, it can be seen that the primary differences between models arise from how they handle biological parameters (i.e. α and β from the linear-quadratic model for photon exposures). By contrast, when specifically explored for LET-dependence, all models show extremely good correlation. These observations suggest that there is a pressing need for more systematic exploration of biological variation in RBE across different cells in well-controlled conditions to help distinguish between these different models and identify the true behaviour.