Modeling RBE with other quantities than LET significantly improves prediction of in vitro cell survival for proton...

For proton therapy, a relative biological effectiveness (RBE) of 1.1 has broadly been applied clinically. However, as unexpected toxicities have been observed by the end of the proton tracks, variable RBE models have been proposed. Typically, the dose-averaged linear energy transfer (LET_d ) has been used as an input variable for these models but the way the LET_d was defined, calculated, or determined was not always consistent, potentially impacting the corresponding RBE value.

This study compares consistently calculated LET_d with other quantities as input variables for a phenomenological RBE model and attempts to determine which quantity that can best predicts proton RBE. The comparison was performed within the frame of introducing a new model for the proton RBE.

High-throughput experimental setups of in vitro cell survival studies for proton RBE determination are simulated using the SHIELD-HIT12A Monte Carlo particle transport code. Together with LET, $$ , here called effective Q (Q_eff ), and Q are scored. Each quantity is calculated using the dose and track averaging methods, because the scoring includes all hadronic particles, all protons or only primaries. A phenomenological linear-quadratic-based RBE model is subsequently applied to the in vitro data with the various beam quality descriptors used as input variables and the goodness of fit is determined and compared using a bootstrapping approach. Both linear and nonlinear fit functions were tested.

Versions of Q_eff and Q outperform LET with a statistically significant margin, with the best nonlinear and linear fit having a relative root mean square error (RMSE) for RBE_2Gy ± one standard error of 1.55 ± 0.04 (Q_{eff, t, primary} ) and 2.84 ± 0.07 (Q_{eff, d, primary} ), respectively. For comparison, the corresponding best nonlinear and linear fits for LET_{d, all protons} had a relative RMSE of 2.07 ± 0.06 and 3.39 ± 0.08, respectively. Applying Welch's t-test for comparing the calculated RMSE of RBE_2Gy resulted in two-tailed p-values of <0.002 for all Q and Q_eff quantities compared to LET_{d, all protons} .

The study shows that Q or Q_eff could be better RBE descriptors that dose averaged LET.