Stopping power and range estimations in proton therapy based on prompt gamma timing: motion models and automated parameter optimization

Objective. Particle therapy treatments are currently limited by uncertainties of the delivered dose. Verification techniques like Prompt-Gamma-Timing-based Stopping Power Estimation (PGT-SPE) may allow for reduction of safety margins in treatment planning. Approach. From Prompt-Gamma-Timing measurements, we reconstruct the spatiotemporal distribution of prompt gamma emissions, which is linked to the average motion of the primary particles. The stopping power is determined by fitting a model of the average particle motion. Here, we compare a previously published implementation of the particle motion model with an alternative formulation and present two formulations to automatically select the hyperparameters of our procedure. The performance was assessed using Monte-Carlo simulations of proton beams (60 MeV-219 MeV) impinging on a homogeneous PMMA phantom. Main results. The range was successfully determined within a standard deviation of 3 mm for proton beam energies from 70 MeV to 219 MeV. Stopping power estimates showed errors below 5% for beam energies above 160 MeV. At lower energies, the estimation performance degraded to unsatisfactory levels due to the short range of the protons. The new motion model improved the estimation performance by up to 5% for beam energies from 100 MeV to 150 MeV with mean errors ranging from 6% to 18%. The automated hyperparameter optimization matched the average error of previously reported manual selections, while significantly reducing the outliers. Significance. The data-driven hyperparameter optimization allowed for a reproducible and fast evaluation of our method. The updated motion model and evaluation at new beam energies bring us closer to applying PGT-SPE in more complex scenarios. Direct comparison of stopping power estimates between treatment planning and measurements during irradiation would offer a more direct verification than other secondary-particle-based techniques.