Statistical evaluation of worst-case robust optimization intensity-modulated proton therapy plans using an exhaustive sampling approach

Purpose: To assess the worst-case robust optimization IMPT plans with setup and range uncertainties and to test the hypothesis that the worst-case robust optimization strategies could cover most possible setup and range uncertainties in the real scenarios. Methods: We analyzed the nominal and worst-case robust optimization IMPT plans of seven patients with head and neck cancer patients. To take uncertainties into account for the dose calculation, we performed a comprehensive simulation in which the dose was recalculated 625 times per given plan using Gaussian systematic setup and proton range uncertainties. Subsequently, based on the simulation results, we calculated the target coverage in all perturbation scenarios, as well as the ratios of target coverage located within the threshold of eight worst-case scenarios. We set the criteria for the optimized plan to be the ratios of 1) the dose delivered to 95% (D95%) of clinical target volumes 1 and 2 (CTV1 and CTV2) above 95% of the prescribed dose, and 2) the D95% of clinical target volume 3 (CTV3) above 90% of the prescribed dose in worst-case situations. Results: The probability that the perturbed-dose indices of the CTVs in each scenario were within the worst-case scenario limits ranged from 89.51 to 91.22% for both the nominal and worst-case robust optimization IMPT plans. A quartile analysis showed that the selective robust optimization IMPT plans all had higher D95% values for CTV1, CTV2, and CTV3 than did the nominal IMPT plans. Conclusions: The worst-case strategy for robust optimization is adequately models and covers most of the setup and range uncertainties for the IMPT treatment of head and neck patients in our center.