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

Objective.Geometric uncertainty can degrade treatment quality in radiation therapy. While margins and robust optimization mitigate these effects, they provide only implicit control over the probability of meeting the clinical goals. The goal of this work is to develop and evaluate a probabilistic optimization framework that explicitly targets a specified probability of clinical goal fulfillment over full treatment courses, while remaining computationally tractable.Approach.A probabilistic planning framework using a percentile-based optimization function was formulated. Systematic and random uncertainties were explicitly modeled over full treatment courses. To enable efficient optimization, treatment course doses were approximated using interpolation between a precomputed set of dose distributions. 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 with randomly sampled simulated treatment courses.Main results.For the prostate VMAT 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 PBS case, probabilistic optimization improved target minimum dose passing probabilities (e.g. 84% vs 19% forD95) and brainstem core maximum dose passing probability (56% vs 2%), while maintaining comparable or improved OAR sparing compared to worst-case optimization.Significance.Percentile-based probabilistic optimization enables explicit and interpretable control over clinical goal fulfillment probabilities. By combining full treatment course modeling with efficient approximate dose calculation, the proposed framework provides a practical approach for incorporating probabilities into treatment planning.