Technical Note: Monte Carlo methods to comprehensively evaluate the robustness of 4D treatments in proton therapy.

Introduction: Proton therapy is very sensitive to treatment uncertainties. These uncertainties can induce proton range variations and may lead to severe dose distortions. However, most commercial tools only offer a limited integration of these uncertainties during treatment planning. In order to verify the robustness of a treatment plan, this study aims at developing a comprehensive Monte Carlo simulation of the treatment delivery, including the simulation of setup and range errors, variation of the breathing motion, and interplay effect.

Method: Most clinically relevant uncertainties have been modeled and implemented in the fast Monte Carlo dose engine MCsquare. Especially, variation of the breathing motion is taken into account by deforming the initial Four-dimensional computed tomography (4DCT) series and generating multiple new 4DCT series with scaled motion. Systematic and random errors are randomly sampled, following a Monte Carlo approach, to generate individual erroneous treatment scenarios. The robustness of treatment plans is analyzed and reported with dose-volume histogram (DVH) bands. The statistical uncertainty coming from the Monte Carlo scenario sampling is studied.

Results: A validation demonstrated the ability of the motion model to generate new 4DCT series with scaled motion amplitude and improved image quality in comparison to the initial 4DCT. The robustness analysis is applied to a lung tumor treatment. Considering the proposed uncertainty model, the simulation of 300 treatment scenarios was necessary to reach an acceptable level of statistical uncertainty on the DVH band.

Conclusion: A comprehensive and statistically sound method of treatment plan robustness verification is proposed. The uncertainty model presented in this paper is not specific to protons and can also be applied to photon treatments. Moreover, the generated 4DCT series, with scaled motion, can be imported in commercial TPSs.