The timing resolution of scintillation-detector systems: Monte Carlo analysis

Recent advancements in fast scintillating materials and fast photomultiplier tubes (PMTs) have stimulated renewed interest in time-of-flight (TOF) positron emission tomography (PET). It is well known that the improvement in the timing resolution in PET can significantly reduce the noise variance in the reconstructed image resulting in improved image quality. In order to evaluate the timing performance of scintillation detectors used in TOF PET, we use Monte Carlo analysis to model the physical processes (crystal geometry, crystal surface finish, scintillator rise time, scintillator decay time, photoelectron yield, PMT transit time spread, PMT single-electron response, amplifier response and time pick-off method) that can contribute to the timing resolution of scintillation-detector systems. In the Monte Carlo analysis, the photoelectron emissions are modeled by a rate function, which is used to generate the photoelectron time points. The rate function, which is simulated using Geant4, represents the combined intrinsic light emissions of the scintillator and the subsequent light transport through the crystal. The PMT output signal is determined by the superposition of the PMT single-electron response resulting from the photoelectron emissions. The transit time spread and the single-electron gain variation of the PMT are modeled in the analysis. Three practical time pick-off methods are considered in the analysis. Statistically, the best timing resolution is achieved with the first photoelectron timing. The calculated timing resolution suggests that a leading edge discriminator gives better timing performance than a constant fraction discriminator and produces comparable results when a two-threshold or three-threshold discriminator is used. For a typical PMT, the effect of detector noise on the timing resolution is negligible. The calculated timing resolution is found to improve with increasing mean photoelectron yield, decreasing scintillator decay time and decreasing transit time spread. However, only substantial improvement in the timing resolution is obtained with improved transit time spread if the first photoelectron timing is less than the transit time spread. While the calculated timing performance does not seem to be affected by the pixel size of the crystal, it improves for an etched crystal compared to a polished crystal. In addition, the calculated timing resolution degrades with increasing crystal length. These observations can be explained by studying the initial photoelectron rate. Experimental measurements provide reasonably good agreement with the calculated timing resolution. The Monte Carlo analysis developed in this work will allow us to optimize the scintillation detectors for timing and to understand the physical factors limiting their performance.