Analytical model of prompt gamma timing for spatiotemporal emission reconstruction in particle therapy

Objective.Particle therapy relies on up-to-date knowledge of the stopping power of the patient tissues to deliver the prescribed dose distribution. The stopping power describes the average particle motion, which is encoded in the distribution of prompt-gamma photon emissions in time and space. We reconstruct the spatiotemporal emission distribution from multi-detector prompt gamma timing (PGT) data. Solving this inverse problem relies on an accurate model of the prompt-gamma transport and detection including explicitly the dependencies on the times of emission and detection.Approach.Our previous work relied on Monte-Carlo (MC) based system models. The tradeoff between computational resources and statistical noise in the system model prohibits studies of new detector arrangements and beam scanning scenarios. Therefore, we propose here an analytical system model to speed up recalculations for new beam positions and to avoid statistical noise in the model.Main results.We evaluated the model for the MERLINO multi-detector-PGT prototype. Comparisons between the analytical model and a MC-based reference showed excellent agreement for single-detector setups. When several detectors were placed close together and partially obstructed each other, intercrystal scatter led to differences of up to 10% between the analytical and MC-based model. Nevertheless, when evaluating the performance in reconstructing the spatiotemporal distribution and estimating the stopping power, no significant difference between the models was observed. Hence, the procedure proved robust against the small inaccuracies of the model for the tested scenarios.Significance.The model calculation time was reduced by a factor of 1500, now enabling many new studies for PGT-based systems.