Exact modeling of analog pulses for PET detector modules

The quality of PET images depends on the position, energy and time resolution of the gamma detector, which usually consists of scintillation crystals coupled to an array of photomultiplier tubes (PMTs). We have developed a simulation tool which models the conversion of scintillation photons into PMT waveforms, thereby bridging the gap between Monte Carlo simulations of the gamma interaction and pure electronics simulations of the data acquisition system. In our model, we track the scintillation photons individually from the crystal through the light guide to the photocathode of the PMT. The PMT characteristics are treated on a single photoelectron basis, incorporating pulse height distribution and single-photon response as well as spatially dependent quantum efficiency, transit time and transit time spread. From the PMT waveforms, we derive the position, energy and time resolution. The time resolution depends on the scintillator material, the PMT properties and the time-stamping method. By separating the different contributions, the limiting factors in the performance of a detector can be identified, facilitating its optimization. A comparison with measured data is included.