Monte Carlo simulations of time-of-flight PET with double-endedreadout: calibration coincidence resolving times and statistical lowerbounds

摘要

This paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound.One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Another Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set.Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3 × 3 ×30 mm³ scintillators: Lu2SiO5:Ce,Ca (LSO),LaBr3:Ce, and a hypothetical ultra-fast scintillator. To isolatethe factors that depend on the scintillator length and the ability to estimatethe DOI, CRT values are tabulated for perfect scintillator-photodetectors. ForLSO with 4000 photoelectrons and single photoelectron time jitter of thephotodetector J = 0.2 ns (FWHM), the CRT value usingthe statistically weighted average of corrected trigger times is 0.098 ns FWHMand the statistical lower bound is 0.091 ns FWHM. For LaBr3:Ce with8000 photoelectrons and J = 0.2 ns FWHM, the CRT valuesare 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with1 ns decay time, 4000 photoelectrons, and J = 0.2 nsFWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. The examplesalso show that calibration and correction for depth-dependent variations inpulse height and in annihilation and optical photon transit times are necessaryto achieve these CRT values.