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

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 () and standard deviation (SD) as , 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 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, dropped by 10%–15%; for matched OAR dose, increased by 67.5%–71%. In spinal plans, increased by 10%–15% while 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.