An Analytical System Response Model for Spatiotemporal Emission Reconstruction from Multi-Detector Prompt Gamma Timing

Particle therapy verification using induced prompt gamma radiation is a field of active research. We employ an iterative reconstruction algorithm to reconstruct the spatiotemporal emission distribution. Due to the fast emission of the prompt gamma radiation after the interaction, their spatiotemporal distribution can be used as a surrogate for the primary particle motion. Using a motion model, we extract the particle range and the stopping power, which should allow direct validation of expected values from treatment planning without additional imaging time. The reconstruction is based on Prompt Gamma Timing spectra from multiple detectors, i.e. the combination of primary particle time of flight before nuclear interaction and secondary photon time of flight until detection outside the patient. Reconstruction requires an accurate model of photon transport and detection, which we previously calculated using extensive Monte-Carlo simulations. Here, we present an analytical model that accelerates calculations by almost 200 times, while matching the Monte-Carlo implementation within 6% of the global maximum value for 99% of all non-zero entries. Furthermore, detection delay caused by secondary particles created by the photons in the detector is studied and its integration into the analytical model demonstrated. First reconstructions of spatiotemporal emission distributions from simulated data using both models show almost perfect agreement. The impact on range and stopping power estimates is currently under investigation.