Percentile-based probabilistic optimization for systematic and random uncertainties in radiation therapy

Abstract

Geometric uncertainty can degrade treatment quality in radiation therapy. While margins and robust optimization mitigate these effects, they provide only implicit control over clinical goal fulfillment probability. We therefore develop a probabilistic planning framework using a percentile-based optimization function that targets a specified probability of clinical goal fulfillment. Systematic and random uncertainties were explicitly modeled over full treatment courses. A scenario dose approximation method based on interpolation between a fixed set of doses was used, enabling efficient simulation of treatment courses during optimization. The framework was evaluated on a prostate case treated with volumetric-modulated arc therapy (VMAT) and a brain case treated with pencil beam scanning (PBS) proton therapy. Plans were compared to conventional margin-based and worst-case robust optimization using probabilistic evaluation. For the prostate case, probabilistic optimization improved organ at risk (OAR) sparing while maintaining target coverage compared to margin-based planning, increasing average OAR goal fulfillment probability by 13.3 percentage points and reducing 90th percentile OAR doses by an average of 3.5~Gy. For the brain case, probabilistic optimization improved target minimum dose passing probabilities (e.g., 88\% vs.~22\% for $D_{95}$) and brainstem maximum dose passing probability (70\% vs.~30\%), while maintaining comparable or improved OAR sparing compared to worst-case optimization. Probabilistic optimization enables explicit and interpretable control over goal fulfillment probabilities. Combining full treatment course modeling with efficient approximate dose calculation, the proposed framework improved the trade-off between target coverage and OAR sparing compared to conventional planning approaches in both photon and proton therapy.