The relative biological effectiveness (RBE) of protons varies with multiple physical and biological factors. Phenomenological RBE models have been developed to include such factors in the estimation of a variable RBE, in contrast to the clinically applied constant RBE of 1.1. In this study, eleven published phenomenological RBE models and two plan-based models were explored and applied to simulated patient cases. All models were analysed with respect to the distribution and range of linear energy transfer (LET) and reference radiation fractionation sensitivity ((α/β) ) of their respective experimental databases. Proton therapy plans for a spread-out Bragg peak in water and three patient cases (prostate adenocarcinoma, pituitary adenoma and thoracic sarcoma) were optimised using an RBE of 1.1 in the Eclipse treatment planning system prior to recalculation and modelling in the FLUKA Monte Carlo code. Model estimated dose-volume parameters for the planning target volumes (PTVs) and organs at risk (OAR) were compared. The experimental in vitro databases for the various models differed greatly in the range of (α/β) values and dose-averaged LET (LET). There were significant variations between the model estimations, which arose from fundamental differences in the database definitions and model assumptions. The greatest variations appeared in organs with low (α/β) and high LET, e.g. biological doses given to late responding OARs located distal to the target in the treatment field. In general, the variation in maximum dose (D) was larger than the variation in mean dose and other dose metrics, with D of the left optic nerve ((α/β) =  2.1 Gy) in the pituitary adenoma case showing the greatest discrepancies between models: 28-52 Gy(RBE), while D for RBE was 30 Gy(RBE). For all patient cases, the estimated mean RBE to the PTV was in the range 1.09-1.29 ((α/β) =  1.5/3.1/10.6 Gy). There were considerable variations between the estimations of RBE and RBE-weighted doses from the different models. These variations were a consequence of fundamental differences in experimental databases, model assumptions and regression techniques. The results from the implementation of RBE models in dose planning studies should be evaluated in light of these deviations.

The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LET based models should be further evaluated in clinically realistic scenarios.

MC simulations accurately modeled the dose distribution from the proton beam and could be used to estimate the LET at any position in the setup. The setup can be used to study the RBE for protons at high LET, which is not achievable in clinical proton therapy facilities.

The increased radioresistance of hypoxic cells compared to well-oxygenated cells is quantified by the oxygen enhancement ratio (OER). In this study we created a FLUKA Monte Carlo based tool for inclusion of both OER and relative biological effectiveness (RBE) in biologically weighted dose (ROWD) calculations in proton therapy and applied this to explore the impact of hypoxia. Methods: The RBE-weighted dose was adapted for hypoxia by making RBE model parameters dependent on the OER, in addition to the linear energy transfer (LET). The OER depends on the partial oxygen pressure (pO 2 ) and LET. To demonstrate model performance, calculations were done with spread-out Bragg peaks (SOBP) in water phantoms with pO 2 ranging from strongly hypoxic to normoxic (0.01-30 mmHg) and with a head and neck cancer proton plan optimized with an RBE of 1.1 and pO 2 estimated voxel-by-voxel using [ 18 F]-EF5 PET. An RBE of 1.1 and the Rørvik RBE model were used for the ROWD calculations. Results: The SOBP in water had decreasing ROWD with decreasing pO 2 . In the plans accounting for oxygenation, the median target doses were approximately a factor 1.1 lower than the corresponding plans which did not consider the OER. Hypoxia adapted target ROWDs were considerably more heterogeneous than the RBE 1.1weighted doses. Conclusion:We realized a Monte Carlo based tool for calculating the ROWD. Read-in of patient pO 2 and estimation of ROWD with flexibility in choice of RBE model was achieved, giving a tool that may be useful in future clinical applications of hypoxia-guided particle therapy.