Probabilistic proton treatment planning: a novel approach for optimizing underdosage and overdosage probabilities of target and organ structures

Abstract Objective . Uncertainties in treatment planning are typically managed using either margin-based or robust optimization. Margin-based methods expand the clinical target volume (CTV) towards a planning target volume, which is generally unsuited for proton therapy. Robust optimization considers worst-case scenarios, but its quality depends on the chosen uncertainty (scenario) set : excluding extremes reduces robustness, while including too many make plans overly conservative. Probabilistic optimization overcomes these limitations by modeling a continuous scenario distribution, enabling the use of statistical measures. Approach . We propose a novel approach to probabilistic optimization that steers plans towards individualized probability levels, to control CTV and organs-at-risks (OARs) under- and overdosage. Voxel-wise dose percentiles ( d ) are estimated by expected value ( E ) and standard deviation (SD) as E ± δ ⋅ SD , where δ is iteratively tuned to match the target percentile of the underlying probability distribution (given setup and range uncertainties). The approach involves an inner optimization of E ± δ ⋅ SD for fixed δ , and an outer optimization loop that updates δ . Polynomial chaos expansion provides accurate and efficient dose estimates during optimization. We validated the method on a spherical CTV (prescribed 60 Gy) abutted by an OAR in different directions and a horseshoe-shaped CTV surrounding a cylindrical spine, under Gaussian-distributed setup (3 mm) and range (3%) uncertainties. Main results . For spherical cases with similar CTV coverage, P ( D 2 % > 30 Gy ) dropped by 10%–15%; for matched OAR dose, P ( D 98 % > 57 Gy ) increased by 67.5%–71%. In spinal plans, P ( D 98 % > 57 Gy ) increased by 10%–15% while P ( D 2 % > 30 Gy ) dropped by 24%–28% in the same plan. Probabilistic and robust optimization times were comparable for spherical (hours) but longer for spinal cases (7.5–11.5 h vs 9–20 min). Significance . Compared to discrete scenario-based optimization, the probabilistic approach offered better OAR sparing or target coverage, depending on individualized priorities.