Purpose: The robustness of proton therapy plans is typically verified by simulating multiple scenarios of treatment errors. The reliability of such robustness test highly depends on the scenario selection process. Most commercial tools rely on worst-case scenario selection methods, which does not guarantee the robustness for intermediate errors and makes the comparison with previous clinical experience (based on PTV) difficult. Alternatively, random scenario selection methods do not require any assumption on how different error types are combined and selected. However, it generally requires simulating many scenarios to cover the entire error space. We propose a variance reduction (VR) method to reduce the number of scenarios to simulate.
Methods: In the context of random scenario selection, range and setup errors are typically sampled according to their respective Gaussian probability distribution. After dose calculation, the 10% worst DVHs are discarded to generate a DVH-band representing the possible dose variation with a 90% confidence interval (equivalent to PTV). Due to Gaussian distributions large errors are rarely sampled, which makes the convergence of the results very slow. Replacing Gaussian distributions with uniform distributions enables a more homogeneous sampling. A weighting factor is then applied to each scenario during the statistical analysis in order to compensate for the distribution differences.
Results: Robustness of a lung proton therapy plan was tested with and without VR. The process was repeated 10 times to estimate the statistical fluctuation of results for both methods. The simulation of 95 scenarios was required to reach a statistical noise of 1% at the D95 level. Using VR decreased the number of scenarios to 30, dividing the computation time by 3.
Conclusion: The random scenario selection method enables a statistically sound analysis of the robustness. A faster convergence of the test was achieved using a variance reduction technique.
Funding Support, Disclosures, and Conflict of Interest: Kevin Souris is supported by a research grant from Ion Beam Application (IBA s.a., Louvain-la-Neuve, Belgium).