Robustness Recipes for Minimax Robust Optimization in Intensity Modulated Proton Therapy for Oropharyngeal Cancer Patients

Purpose: We aimed to derive a "robustness recipe" giving the range robustness (RR) and setup robustness (SR) settings (ie, the error values) that ensure adequate clinical target volume (CTV) coverage in oropharyngeal cancer patients for given gaussian distributions of systematic setup, random setup, and range errors (characterized by standard deviations of Σ, σ, and ρ, respectively) when used in minimax worst-case robust intensity modulated proton therapy (IMPT) optimization. Methods and Materials: For the analysis, contoured computed tomography (CT) scans of 9 unilateral and 9 bilateral patients were used. An IMPT plan was considered robust if, for at least 98% of the simulated fractionated treatments, 98% of the CTV received 95% or more of the prescribed dose. For fast assessment of the CTV coverage for given error distributions (ie, different values of Σ, σ, and ρ), polynomial chaos methods were used. Separate recipes were derived for the unilateral and bilateral cases using one patient from each group, and all 18 patients were included in the validation of the recipes. Results: Treatment plans for bilateral cases are intrinsically more robust than those for unilateral cases. The required RR only depends on the ρ, and SR can be fitted by second-order polynomials in Σ and σ. The formulas for the derived robustness recipes are as follows: Unilateral patients need SR = −0.15Σ² + 0.27σ² + 1.85Σ − 0.06σ + 1.22 and RR=3% for ρ = 1% and ρ = 2%; bilateral patients need SR = −0.07Σ² + 0.19σ² + 1.34Σ − 0.07σ + 1.17 and RR=3% and 4% for ρ = 1% and 2%, respectively. For the recipe validation, 2 plans were generated for each of the 18 patients corresponding to Σ = σ = 1.5 mm and ρ = 0% and 2%. Thirty-four plans had adequate CTV coverage in 98% or more of the simulated fractionated treatments; the remaining 2 had adequate coverage in 97.8% and 97.9%. Conclusions: Robustness recipes were derived that can be used in minimax robust optimization of IMPT treatment plans to ensure adequate CTV coverage for oropharyngeal cancer patients.