Reducing the set of considered scenarios in robust optimization of intensity-modulated proton therapy

Robust optimization is a commonly employed method to mitigate uncertainties in the planning of intensity-modulated proton therapy (IMPT). In certain contexts, the large number of uncertainty scenarios makes the robust problem impractically expensive to solve. Recent developments in research on IMPT treatment planning indicate that the number of ideally considered error scenarios may continue to increase. In this paper, we therefore investigate methods that reduce the size of the scenario set considered during the robust optimization. Six cases of patients with non-small cell lung cancer are considered. First, we investigate the existence of an optimal subset of scenarios that needs to be considered during robust optimization, and perform experiments to see if the set can be found in a reasonable time and substitute for the full set of scenarios during robust IMPT optimization. We then consider heuristic methods to estimate this subset or find subsets with similar properties. Specifically, we select a subset of maximal diversity in terms of scenario-specific features such as the dose distributions and function gradients at the initial point. Finally, we consider adversarial methods as an alternative to solving the full robust problem and investigate the impact on computation times. The results indicate that the optimal subset can be well approximated by solving the robust IMPT problem with conventional methods. Of the methods designed to approximate it within a practically useful time frame, the results of the diversity-maximization methods indicate that they may perform better than a manual selection of scenarios based on the patient geometry. In addition, the adversarial approaches decreased the computation time by at least half compared to the conventional approach.