An empirical model of proton RBE based on the linear correlation between x-ray and proton radiosensitivity

Background: Proton relative biological effectiveness (RBE) is known to depend on physical factors of the proton beam, such as its linear energy transfer (LET), as well as on cell-line specific biological factors, such as their ability to repair DNA damage. However, in a clinical setting, proton RBE is still considered to have a fixed value of 1.1 despite the existence of several empirical models that can predict proton RBE based on how a cell's survival curve (linear-quadratic model [LQM]) parameters α and β vary with the LET of the proton beam. Part of the hesitation to incorporate variable RBE models in the clinic is due to the great noise in the biological datasets on which these models are trained, often making it unclear which model, if any, provides sufficiently accurate RBE predictions to warrant a departure from RBE = 1.1. Purpose: Here, we introduce a novel model of proton RBE based on how a cell's intrinsic radiosensitivity varies with LET, rather than its LQM parameters. Methods and materials: We performed clonogenic cell survival assays for eight cell lines exposed to 6 MV x-rays and 1.2, 2.6, or 9.9 keV/µm protons, and combined our measurements with published survival data (n = 397 total cell line/LET combinations). We characterized how radiosensitivity metrics of the form D_SF%, (the dose required to achieve survival fraction [SF], e.g., D_10%) varied with proton LET, and calculated the Bayesian information criteria associated with different LET-dependent functions to determine which functions best described the underlying trends. This allowed us to construct a six-parameter model that predicts cells’ proton survival curves based on the LET dependence of their radiosensitivity, rather than the LET dependence of the LQM parameters themselves. We compared the accuracy of our model to previously established empirical proton RBE models, and implemented our model within a clinical treatment plan evaluation workflow to demonstrate its feasibility in a clinical setting. Results: Our analyses of the trends in the data show that D_SF% is linearly correlated between x-rays and protons, regardless of the choice of the survival level (e.g., D_10%, D_37%, or D_50% are similarly correlated), and that the slope and intercept of these correlations vary with proton LET. The model we constructed based on these trends predicts proton RBE within 15%–30% at the 68.3% confidence level and offers a more accurate general description of the experimental data than previously published empirical models. In the context of a clinical treatment plan, our model generally predicted higher RBE-weighted doses than the other empirical models, with RBE-weighted doses in the distal portion of the field being up to 50.7% higher than the planned RBE-weighted doses (RBE = 1.1) to the tumor. Conclusions: We established a new empirical proton RBE model that is more accurate than previous empirical models, and that predicts much higher RBE values in the distal edge of clinical proton beams.