Incorporation of relative biological effectiveness uncertainties into proton plan robustness evaluation

Abstract

Background: The constant relative biological effectiveness (RBE) of 1.1 is typically assumed in proton therapy. This study presents a method of incorporating the variable RBE and its uncertainties into the proton plan robustness evaluation.Material and methods: The robustness evaluation was split into two parts. In part one, the worst-case physical dose was estimated using setup and range errors, including the fractionation dependence. The results were fed into part two, in which the worst-case RBE-weighted doses were estimated using a Monte Carlo method for sampling the input parameters of the chosen RBE model. The method was applied to three prostate, breast and head and neck (H&N) plans for several fractionation schedules using two RBE models. The uncertainties in the model parameters, linear energy transfer and α/β were included. The resulting DVH error bands were compared with the use of a constant RBE without uncertainties.Results: All plans were evaluated as robust using the constant RBE. Applying the proposed methodology using the variable RBE models broadens the DVH error bands for all structures studied. The uncertainty in α/β was the dominant factor. The variable RBE also shifted the nominal DVHs towards higher doses for most OARs, whereas the direction of this shift for the clinical target volumes (CTVs) depended on the treatment site, RBE model and fractionation schedule. The average RBE within the CTV, using one of the RBE models and 2 Gy(RBE) per fraction, varied between 1.11–1.26, 1.06–1.16 and 1.14–1.25 for the breast, H&N and prostate patients, respectively.Conclusions: A method of incorporating RBE uncertainties into the robustness evaluation has been proposed. By disregarding the variable RBE and its uncertainties, the variation in the RBE-weighted CTV and OAR doses may be underestimated. This could be an essential factor to take into account, especially in normal tissue complication probabilities based comparisons between proton and photon plans.