WE-AB-209-01: A Monte Carlo-Based Method to Include Random Errors in Robust Optimization

Purpose: To develop an efficient method to implement random set-up errors and organ motion in robust optimization for proton therapy treatment planning. Methods: The plans were created with an in-house robust optimizer, coupled with a super-fast Monte Carlo (MC) engine (less than 1 minute for final dose). MC simulates random errors by shifting randomly the starting point of each particle, according to their probability distribution. Such strategy assumes a sufficient number of treatment fractions. Two strategies are presented: 1) Full robust optimization with beamlets that already include the effect of random errors and 2) Mixed robust optimization, where the nominal beamlets are involved but a correction term C modifies the prescription. Starting from C=0, the method alternates optimization of the spot weights with the nominal beamlets and updates of C, with C=Drandom-Dnominal and where Drandom results from a regular MC computation (without pre-computed beamlets) that simulates random errors. Updates of C can be triggered as often as necessary by running the MC engine with the last corrected values for the spot weights as input. The method was applied to lung and prostate cases. For both patients the range error was set to 3%, systematic setup error to 5mm and standard deviation for random errors to 5 mm. Comparison between full robust optimization and the mixed strategy (with 3 updates of C) is presented. Results: Target coverage was far below the clinical constraints (D₉₅ > 95% of the prescribed dose) for plans where random errors were not simulated, especially for lung case. However, by using the proposed strategies the plans achieved a target coverage above clinical constraints. Conclusion: Full robust optimization gives better results than the mixed strategy, but the latter can be useful in cases where a MC engine is not available or too computationally intensive for beamlets calculation.