Evaluation of uncertainty-based stopping criteria for Monte Carlo calculations of intensity-modulated radiotherapy and arc therapy patient dose distributions

Purpose: To formulate uncertainty-based stopping criteria for Monte Carlo (MC) calculations of intensity-modulated radiotherapy and intensity-modulated arc therapy patient dose distributions and evaluate their influence on MC simulation times and dose characteristics. Methods and Materials: For each structure of interest, stopping criteria were formulated as follows: sigma(re1) = 95% of the voxels, where sigma(rel) represents the relative statistical uncertainty on the estimated dose, D. The tolerated uncertainty (sigma(rel,tol)) was 2%. The dose limit (D-lim) equaled the planning target volume (PTV) prescription dose or a dose value related to the organ at risk (OAR) planning constraints. An intensity-modulated radiotherapy-lung, intensity-modulated radiotherapy-ethmoid sinus, and intensity-modulated arc therapy-rectum patient case were studied. The PTV-stopping criteria-based calculations were compared with the PTV+OAR-stopping criteria-based calculations. Results: The MC dose distributions complied with the PTV-stopping criteria after 14% (lung), 21% (ethmoid), and 12% (rectum) of the simulation times of a 100 million histories reference calculation, and increased to 29%, 44%, and 51%, respectively, by the addition of the OAR-stopping criteria. Dose-volume histograms corresponding to the PTV-stopping criteria, PTV+OAR-stopping criteria, and reference dose calculations were indiscernible. The median local dose differences between the PTV-stopping criteria and the reference calculations amounted to 1.4 % (lung), 2.1 % (ethmoid), and 2.5 % (rectum). Conclusions: For the patient cases studied, the MC calculations using PTV-stopping criteria only allowed accurate treatment plan evaluation. The proposed stopping criteria provided a flexible tool to assist MC patient dose calculations. The structures of interest and appropriate values of sigma(rel,tol) and D-lim should be selected for each patient individually according to the clinical treatment planning goals