Probabilistic Proton Treatment Planning: a novel approach for optimizing underdosage and overdosage probabilities of target and organ structures

TL;DR

This paper introduces a probabilistic optimization method for proton treatment planning that models continuous uncertainties to better control target and organ-at-risk dose probabilities, improving plan robustness.

Contribution

It presents a novel probabilistic approach using dose percentiles and Polynomial Chaos Expansion for efficient, individualized treatment plan optimization under uncertainties.

Findings

Reduced probability of underdosage and overdosage in target and OARs.

Achieved better OAR sparing or target coverage compared to scenario-based methods.

Comparable or longer computation times depending on case complexity.

Abstract

Treatment planning uncertainties are typically managed using margin-based or robust optimization. Margin-based methods expand the clinical target volume (CTV) to a planning target volume, generally unsuited for proton therapy. Robust optimization considers worst-case scenarios, but its quality depends on the uncertainty scenario set: excluding extremes reduces robustness, while too many make plans overly conservative. Probabilistic optimization overcomes these limits by modeling a continuous scenario distribution. We propose a novel probabilistic optimization approach that steers plans toward individualized probability levels to control CTV and organs-at-risk (OARs) under- and overdosage. Voxel-wise dose percentiles ($d$) are estimated by expected value ($E$) and standard deviation (SD) as $E[d] \pm \delta \cdot SD[d]$, where $\delta$ is iteratively tuned to match the target percentile given Gaussian-distributed setup (3 mm) and range (3%) uncertainties. The method involves an inner optimization of $E[d] \pm \delta \cdot SD[d]$ for fixed $\delta$, and an outer loop updating $\delta$. Polynomial Chaos Expansion (PCE) provides accurate and efficient dose estimates during optimization. We validated the method on a spherical CTV abutted by an OAR in different directions and a horseshoe-shaped CTV surrounding a cylindrical spine. 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 24-28%. Probabilistic and robust optimization times were comparable for spherical (hours) but longer for spinal cases (7.5 - 11.5 h vs. 9 - 20 min). Compared to discrete scenario-based optimization, the probabilistic method offered better OAR sparing or target coverage depending on the set priorities.