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

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 errorE_max(3σor 4σ), withσ=(σrandomerror)2+(σsystematicerror)2, and the number of setup error pointsn_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= 3σ, 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. IncreasingE_maxfrom 3σto 4σonly 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 theD_{99.8%, CTV}distribution and 0.0 Gy RBE (range: -0.14-0.23) for the 95th percentile of theD_{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.