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.

Background and purpose Until now, carbon ion RT (CIRT) dose constraints for the optic nerve (ON) have only been validated and reported in the NIRS RBE-weighted dose (DNIRS). The aim of this work is to improve CNAO's RBE-weighted dose (DLEM) constraints by analyzing institutional toxicity data and by relating it to DNIRS. Material and methods A total of 65 ONs from 38 patients treated with CIRT to the head and neck region in the period 2013-14 were analyzed. The absorbed dose (DAbs) of the treatment plans was reproduced and subsequently both DLEM and DNIRS were applied, thus relating CNAO clinical toxicity to DNIRS. Results Median FU was 47 (26-67) months. Visual acuity was preserved for the 56 ONs in which the old constraints were respected. Three ONs developed visual decline at DLEM│1%≥71 Gy(RBE)/DLEM│20%≥68 Gy(RBE), corresponding to DNIRS│1%≥68 Gy(RBE)/DNIRS│20%≥62 Gy(RBE). Dose recalculation revealed that NIRS constraints of DNIRS│1%≤40 Gy(RBE)/DNIRS│20%≤28 Gy(RBE) corresponded to DLEM│1%≤50 Gy(RBE)/DLEM│20%≤40 Gy(RBE). Reoptimization of treatment plans with these new DLEM constraints showed that the dose distribution still complied with NIRS constraints when evaluated in DNIRS. However, due to uncertainties in the method, and to comply with the EQD2-based constraints used at GSI/HIT, a more moderate constraint relaxation to DLEM│1%≤45 Gy(RBE)/DLEM│20%≤37 Gy(RBE) has been implemented in CNAO clinical routine since October 2018. Conclusion New DLEM constraints for the ON were derived by analyzing CNAO toxicity data and by linking our results to the experience of NIRS and GSI/HIT. This work demonstrates the value of recalculating and reporting results in both DLEM and DNIRS.

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Background and PurposeThe Italian National Center of Oncological Hadrontherapy (CNAO) has applied dose constraints for carbon ion RT (CIRT) as defined by Japan’s National Institute of Radiological Sciences (NIRS). However, these institutions use different models to predict the relative biological effectiveness (RBE). CNAO applies the Local Effect Model I (LEM I), which in most clinical situations predicts higher RBE than NIRS’s Microdosimetric Kinetic Model (MKM). Equal constraints therefore become more restrictive at CNAO. Tolerance doses for the brainstem have not been validated for LEM I-weighted dose (DLEM I). However, brainstem constraints and a Normal Tissue Complication Probability (NTCP) model were recently reported for MKM-weighted dose (DMKM), showing that a constraint relaxation to DMKM|0.7 cm3 <30 Gy (RBE) and DMKM|0.1 cm3 <40 Gy (RBE) was feasible. The aim of this work was to evaluate the brainstem NTCP associated with CNAO’s current clinical practice and to propose new brainstem constraints for LEM I-optimized CIRT at CNAO.Material and MethodsWe reproduced the absorbed dose of 30 representative patient treatment plans from CNAO. Subsequently, we calculated both DLEM I and DMKM, and the relationship between DMKM and DLEM I for various brainstem dose metrics was analyzed. Furthermore, the NTCP model developed for DMKM was applied to estimate the NTCPs of the delivered plans.ResultsThe translation of CNAO treatment plans to DMKM confirmed that the former CNAO constraints were conservative compared with DMKM constraints. Estimated NTCPs were 0% for all but one case, in which the NTCP was 2%. The relationship DMKM/DLEM I could be described by a quadratic regression model which revealed that the validated DMKM constraints corresponded to DLEM I|0.7 cm3 <41 Gy (RBE) (95% CI, 38–44 Gy (RBE)) and DLEM I|0.1 cm3 <49 Gy (RBE) (95% CI, 46–52 Gy (RBE)).ConclusionOur study demonstrates that RBE-weighted dose translation is of crucial importance in order to exchange experience and thus harmonize CIRT treatments globally. To mitigate uncertainties involved, we propose to use the lower bound of the 95% CI of the translation estimates, i.e., DLEM I|0.7 cm3 <38 Gy (RBE) and DLEM I|0.1 cm3 <46 Gy (RBE) as brainstem dose constraints for 16 fraction CIRT treatments optimized with LEM I.