Variable RBE in proton therapy: comparison of different model predictions and their influence on clinical-like scenarios

Background: In proton radiation therapy a constant relative biological effectiveness (RBE) of 1.1 is usually assumed. However, biological experiments have evidenced RBE dependencies on dose level, proton linear energy transfer (LET) and tissue type. This work compares the predictions of three of the main radio-biological models proposed in the literature by Carabe-Fernandez, Wedenberg, Scholz and coworkers. Methods: Using the chosen models, a spread-out Bragg peak (SOBP) as well as two exemplary clinical cases (single field and two fields) for cranial proton irradiation, all delivered with state-of-the-art pencil-beam scanning, have been analyzed in terms of absorbed dose, dose-averaged LET $(LET_D)$, RBE-weighted dose $(D_{RBE})$ and biological range shift distributions. Results: In the systematic comparison of RBE predictions by the three models we could show different levels of agreement depending on $(α/β) x$ and LET values. The SOBP study emphasizes the variation of LET D and RBE not only as a function of depth but also of lateral distance from the central beam axis. Application to clinical-like scenario shows consistent discrepancies from the values obtained for a constant RBE of 1.1, when using a variable RBE scheme for proton irradiation in tissues with low $(α/β) x$ , regardless of the model. Biological range shifts of 0.6– 2.4 mm (for high $(α/β) x )$ and 3.0 – 5.4 mm (for low $(α/β) x )$ were found from the fall-off analysis of individual profiles of RBE-weighted fraction dose along the beam penetration depth. Conclusions: Although more experimental evidence is needed to validate the accuracy of the investigated models and their input parameters, their consistent trend suggests that their main RBE dependencies (dose, LET and $(α/β) x )$ should be included in treatment planning systems. In particular, our results suggest that simpler models based on the linear-quadratic formalism and $LET_D$ might already be sufficient to reproduce important RBE dependencies for re-evaluation of plans optimized with the current RBE = 1.1 approximation. This approach would be a first step forward to consider RBE variations in proton therapy, thus enabling a more robust choice of biological dose delivery. The latter could in turn impact clinical outcome, especially in terms of reduced toxicities for tumors adjacent to organs at risk.