Achieving picosecond timing and micrometer-scale spatial resolution is a central challenge for next-generation nuclear-medicine imaging. This thesis investigates a detector concept that couples an ultrafast perovskite scintillator, PEA2PbBr4, with Amorphous-Silicon Microchannel Plates (AMCPs). First, detailed GEANT4 simulations of PEA2PbBr4 quantify photon-arrival statistics and demonstrate timing characteristics compatible with time-of flight PET. Second, to model charge multiplication in AMCPs, a stochastic framework that uses calibrated secondary-electron-yield (SEY) tables together with energy and angular distributions of secondaries was developed. This approach predicts ultra-fast AMCP response with low jitter, strengthening the case for AMCP-based photodetectors matched to fast scintillators.