Novel radiation quality metrics accounting for proton energy spectra for RBE proton models

Background: For proton therapy, a relative biological effectiveness (RBE) of 1.1 is widely applied clinically. However, due to abundant evidence of variable RBE in vitro, and as suggested in studies of patient outcomes, RBE might increase by the end of the proton tracks, as described by several proposed variable RBE models. Typically, the dose averaged linear energy transfer ((Formula presented.)) has been used as a radiation quality metric (RQM) for these models. However, the optimal choice of RQM has not been fully explored. Purpose: This study aims to propose novel RQMs that effectively weight protons of different energies, and assess their predictive power for variable RBE in proton therapy. The overall objective is to identify an RQM that better describes the contribution of individual particles to the RBE of proton beams. Methods: High-throughput experimental set-ups of in vitro cell survival studies for proton RBE determination are simulated utilizing the SHIELD-HIT12A Monte Carlo particle transport code. For every data point, the proton energy spectra are simulated, allowing the calculation of novel RQMs by applying different power levels to the spectra of LET or effective (Formula presented.) ((Formula presented.)) values. A phenomenological linear-quadratic-based RBE model is then applied to the in vitro data, using various RQMs as input variables, and the model performance is evaluated by root-mean-square-error (RMSE) for the logarithm of cell surviving fractions of each data point. Results: Increasing the power level, that is, putting an even higher weight on higher LET particles when constructing the RQM is generally associated with an increased model performance, with dose averaged (Formula presented.) (i.e., dose averaged cubed LET, (Formula presented.)) resulting in a RMSE value 0.31, compared to 0.45 for a model based on (linearly weighted) (Formula presented.), with similar trends also observed for track averaged and (Formula presented.) -based RQMs. Conclusions: The results indicate that improved proton variable RBE models can be constructed assuming a non-linear RBE(LET) relationship for individual protons. If similar trends hold also for an in vitro-environment, variable RBE effects are likely better described by (Formula presented.) or tracked averaged cubed LET ((Formula presented.)), or corresponding (Formula presented.) -based RQM, rather than linearly weighted (Formula presented.) or (Formula presented.) which is conventionally applied today.