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

<i>Objective</i>. 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<i>uncertainty (scenario) set</i>: 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.<i>Approach</i>. 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 (<i>d</i>) are estimated by expected value (E) and standard deviation (SD) asE±δ⋅SD, where<i>δ</i>is iteratively tuned to match the target percentile of the underlying probability distribution (given setup and range uncertainties). The approach involves an inner optimization ofE±δ⋅SDfor fixed<i>δ</i>, and an outer optimization loop that updates<i>δ</i>. 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.<i>Main results</i>. For spherical cases with similar CTV coverage,P(D2%>30Gy)dropped by 10%-15%; for matched OAR dose,P(D98%>57Gy)increased by 67.5%-71%. In spinal plans,P(D98%>57Gy)increased by 10%-15% whileP(D2%>30Gy)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).<i>Significance</i>. Compared to discrete scenario-based optimization, the probabilistic approach offered better OAR sparing or target coverage, depending on individualized priorities.