Probabilistic proton treatment planning
a novel approach for optimizing underdosage and overdosage probabilities of target and organ structures
J. R. de Jong (TU Delft - Applied Sciences)
S. Breedveld (Erasmus MC)
S. J. M Habraken (Holland Proton Therapy Centre, Leiden University Medical Center)
M. S. Hoogeman (Holland Proton Therapy Centre, Erasmus MC)
D. Lathouwers (TU Delft - Applied Sciences)
Z. Perkó (TU Delft - Applied Sciences)
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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[d] ± δ ⋅ SD[d], 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[d] ± 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 60Gy) abutted by an OAR in different directions and a horseshoe-shaped CTV surrounding a cylindrical spine, under Gaussian-distributed setup (3mm) 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 (7.5–11.5h vs 9–20min). Significance. Compared to discrete scenario-based optimization, the probabilistic approach offered better OAR sparing or target coverage, depending on individualized priorities.
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