Fast and realistic Monte Carlo evaluation of the robustness of proton therapy plans

Purpose Proton range uncertainties jeopardize the theoretical advantage of intensity modulated proton therapy over photon-based modalities. Depending on the heterogeneity level, this range uncertainty can grow up to 4.6% of the nominal range + 1.2mm with typical analytical dose calculation methods (Paganetti 2012, PMB). The robustness of treatment plans can be further evaluated by simulating possible realizations of uncertainties with systematic and random components. Such a strategy may be a daunting task for analytical algorithms because computation time scales linearly with the number of scenarios simulated, which increases strongly if random errors are considered. Monte Carlo (MC) simulations offer here a double advantage: 1) they reduce the range uncertainty down to 2.4% + 1.2 mm; 2) they potentially allow simulating random errors with no significant increase in computation time. This study employs a fast MC tool, which can compute the impact of random errors in a single simulation. Methods MCsquare, the new software created for this study, implements optimized algorithms on the Xeon Phi coprocessor to accelerate MC computations. MCsquare can compute a dose distribution in less than one minute. Multiple uncertainty scenarios are created. A 2.5 mm systematic setup error is modeled by shifting the CT image in all 6 directions of space. Random setup errors are modeled by a 1 mm random [Répétition de random dans la même phrase, mais sans doute avec des sens différents : dans ce cas-ci tu sous-entends qu’il y un générateur aléatoire et donc une distribution (Gaussienne) sous-jacente ?][Effectivement, c’est bien le sens d’échantillonnage aléatoire suivant une distribution]shift for each particle simulated by the MC engine. The uncertainty in the conversion from Hounsfield units to stopping powers is taken into account by applying a +/- 3% uniform bias to the patient densities. The experiment involves a water phantom, considering both a traditional plan with a PTV (2.5mm isotropic margin) and a robust plan (3% density uncertainty, 2.5 mm systematic setup errors). The CTV surrounds a circular organ-at-risk. The random error model employed in this study considers a large number of sampling, meaning an infinite number of fractions. The second experiment aims at determining the minimal number of fractions required to ensure the validity of this approximation. For this purpose, various sequences of fractions are generated, with different random errors. Results The robustness of the treatment plan is easily verified by looking at the deviations of the DVH curve with respect to the nominal plan (red curve). The robust plan shows small deviations compared to the traditional PTV plan. Considering only random errors, the DVH distributions no longer vary for treatment with more than 30 fractions. This result validates the assumption of the infinite random sampling for our robustness test for typical fractionation strategies. Conclusion Fast and accurate MC tools allow range uncertainties to be reduced and random errors to be integrated efficiently into robustness evaluation. In proton therapy, robust optimization is preferred to traditional PTV margins, which do not suffice to ensure homogeneous coverage of the CTV in case of uncertainties