Evaluation of Uncertainty-Based Stopping Criteria for Monte Carlo Calculations of Intensity-Modulated Radiotherapy and Arc Therapy Patient Dose Distributions

Abstract

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. For each structure of interest, stopping criteria were formulated as follows: sigma(rel) <or=sigma(rel,tol) or Dsigma(rel) <or=D(lim)sigma(rel,tol) within >or=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. 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). 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.