Accurate Modeling of Multi Knife-edge Slit Collimator System Response for MeV Prompt Gamma Photons in Proton Therapy Monitoring

Prompt gamma imaging (PGI) is a promising approach for real-time proton therapy monitoring. A PGI system is being developed in our lab with a multi-knife-edge slit collimator and a pixelated scintillation detector. Accurate characterization of system response in image reconstruction is of critical importance for optimized system performance. However, the high energy of prompt gamma photons (2~8 MeV) leads to much more significant edge penetration in collimator and parallax effect in detector. In this work, we propose a hybrid method to accurately model the system response which combines analytical calculation of collimator penetration effect and Monte Carlo simulation of parallax effect in detector. The system point spread function was modelled as the convolution of collimator response and detector response. Collimator response was defined as the probability of a photon emitted from a voxel reaching the front surface of a crystal. Analytically calculation was studied to calculate the intersection length of photon path and the collimator materials in 21 different geometrical cases. Monte Carlo simulation was performed to generate the detector response by calculating the possibility of gamma ray interaction in neighboring crystal pixels when gamma hits a crystal pixel with a given incidence angle. To validate the accuracy of the proposed system response model, point source projections of single knife-edge and multi knife-edge slit collimator were obtained with our modeling method and compared with that obtained from GATE simulation. We also reconstructed 2D prompt gamma sources in different position with our system modeling method, and with data generated in GATE simulations. A series of simulations demonstrates excellent alignment of calculated PSFs with simulated ones. Reconstructed prompt gamma images demonstrated the feasibility and accuracy of the proposed model.