Sub-100 ps Coincidence Time Resolution in Depth-Encoding Prism-PET Modules: A Monte Carlo Simulation Study

1506 Introduction: Coincidence time resolution (CTR) in PET is limited by scintillator size, scintillation response to photon absorption, and the timing of the readout system, all of which contribute to the so-called “time-walk” of the leading edge of the energy deposition curve. Previous studies have shown how CTR can be enhanced by estimating the depth-of-interaction (DOI) of gamma rays in scintillators to deconvolve the effects of optical photon transport on timing. In addition, having multiple timestamps per interaction enables time-walk correction by estimating the slope of the leading edge of the energy response. Using a shallow convolutional neural network (CNN), we’ve developed a method that accurately estimates the time-of-flight (TOF) difference between coincident gamma rays in depth-encoding PET modules when 2 timestamps are available per gamma ray. Methods: TracePro, a Monte Carlo optical ray tracing software, was used to simulate PET data in two 3 x 3 x 20 mm3 LYSO scintillator crystals. The simulated 511 keV gamma ray absorptions were uniformly distributed with respect to depth in the scintillators. Optical photon transport and variability of the LYSO response (rise/decay constants, light output, etc.) were accounted for. Energy deposition curves as a function of time were generated for each absorption and convolved with the photoresponse of silicon photomultipliers (SiPMs) with various single-photon time resolutions (SPTR = 100, 50 and 10 ps). Timestamps were generated based on two trigger thresholds corresponding to a number of photons collected on the readout side (n = 5 and 10 photons). A uniformly distributed timing offset (toff = 0-1667 ps) was added to the timestamps from one of the two crystals for each coincidence pair. Ground truth DOI was convolved with a 2 mm FWHM Gaussian to replicate the DOI resolution of Prism-PET. 30,000 coincidence pairs were simulated. A shallow CNN was formulated that incorporates timing and DOI to estimate toff, which is the ground truth for the difference in TOF for each coincidence pair. The CNN was initialized 4 different ways: (1) 1 timestamp (n = 10, no time-walk correction) and no DOI, (2) 2 timestamps (n = 5 and 10, CNN time-walk correction via rising edge slope estimation) and no DOI, (3) 1 timestamp with DOI and (4) 2 timestamps with DOI. CTR was calculated based on the CNN error in estimating toff. Classical CTR calculation was performed with and without DOI correction for comparison with CNN performance. Results: Our CNN and classical estimation performed nearly identically when using a single timestamp without DOI correction. When using a single timestamp with DOI correction, classical methods performed 15.5% better than our CNN. In all cases, having DOI without time-walk correction performed the same as having time-walk correction without DOI, while having both in the CNN resulted in the best overall performance (CTR = 124 ps, 84 ps and 61 ps for SPTR = 100 ps, 50 ps and 10 ps, respectively). Our CNN achieved a 73.3% improvement over classical estimation with no DOI and a 12.8% improvement over DOI-corrected classical estimation. Conclusions: Our results show that the excellent DOI resolution of Prism-PET enables sub-100 ps CTR when using readout pixels with low SPTR. Having a larger training dataset may further improve the CNN performance to enable CTR < 100 ps with 100 ps SPTR. Our next step is to acquire data with multiple timestamps using Prism-PET modules to determine how our results translate from simulation to experiment. Figure 1. (a) Simulated experimental setup in TracePro. (b) Workflow diagram showing how PET-like energy deposition curves were simulated by convolving the Monte Carlo optical photon transport output from TracePro, the LYSO scintillation response and the SiPM photoresponse. (c) Shallow CNN architecture used for CTR estimation with 4 different inputs (ts = timestamp). (d) Table of calculated CTR as a function of number of timestamps and DOI using classical estimation and our CNN.