Sparse probabilistic evaluation for treatment planning: a feasibility study in IMPT head and neck patients

Abstract Objective. Probabilistic evaluation improves the trade-off between target coverage and OAR sparing in IMPT but remains computationally demanding. This study proposes sparse probabilistic evaluation (SPE), a computationally efficient approach integrated into a clinical treatment planning system. Approach. Clinical plans of 20 IMPT head and neck cancer patients treated in 2024 were included. SPE used a predefined setup and range error grid with Monte Carlo (MC) computed dose distributions. Two grid settings were evaluated: the maximum error E max (3 σ or 4 σ ), with σ = ( σ randomerror ) 2 + ( σ systematicerror ) 2 , and the number of setup error points n setup (7, 33, 123). Accuracy and duration of SPE with each grid were evaluated in the calibration group (5 patients). A total of 1000 treatments with normally distributed random ( σ = 1 mm) and systematic ( σ = 0.92 mm) setup and range ( σ = 1.5%) errors were simulated. The dose distribution of the nearest error point in the grid was assigned to each fraction. Probability distributions derived from SPE were compared with those from a reference based on 35 000 MC calculations. Agreement was quantified using the mean percentile error (MPE), the mean absolute difference across percentiles 0.01, 0.02, …, 1. The found optimal grid ( E max = 3 σ, n setup = 33) was applied to the validation group (15 patients). Main results. The median MPE in the calibration group decreased significantly as the number of error points increased from 7 ( t avg = 2 min) to 33 ( t avg = 9 min), with no further improvement between 33 and 123 ( t avg = 27 min) error points. Increasing E max from 3 σ to 4 σ only improved accuracy for values above the 98th percentile. Applying SPE to the validation group resulted in median errors of 0.02 Gy RBE (range: −0.11–0.07) for the 10th percentile of the D 99.8%, CTV distribution and 0.0 Gy RBE (range: −0.14–0.23) for the 95th percentile of the D 0.03cc,SpinalCord Core distribution. Significance. SPE achieves sufficient accuracy while requiring clinically acceptable computation times, paving the way for probabilistic evaluation in clinical practice.