A study of inter-crystal scatter in dual-layer offset scintillator arrays for brain-dedicated PET scanners

Inter-crystal scattering recovery of light-sharing PET detectors using convolutional neural networks

Inter-crystal scattering (ICS) is a type of Compton scattering of photons from one crystal to adjacent crystals and causes inaccurate assignment of the annihilation photon interaction position in positron emission tomography (PET). Because ICS frequently occurs in highly light-shared PET detectors, its recovery is crucial for the spatial resolution improvement. In this study, we propose two different convolutional neural networks (CNNs) for ICS recovery, exploiting the good pattern recognition ability of CNN techniques. Using the signal distribution of a photosensor array as input, one network estimates the energy deposition in each crystal (ICS-eNet) and another network chooses the first-interacted crystal (ICS-cNet). We performed GATE Monte Carlo simulations with optical photon tracking to test PET detectors comprising different crystal arrays (8 × 8 to 21 × 21) with lengths of 20 mm and the same photosensor array (3 mm 8 × 8 array) covering an area of 25.8 × 25.8 mm². For each detector design, we trained ICS-eNet and ICS-cNet and evaluated their respective performance. ICS-eNet accurately identified whether the events were ICS (accuracy > 90%) and selected interacted crystals (accuracy > 60%) with appropriate energy estimation performance (R² > 0.7) in the 8 × 8, 12 × 12, and 16 × 16 arrays. ICS-cNet also exhibited satisfactory performance, which was less dependent on the crystal-to-sensor ratio, with an accuracy enhancement that exceeds 10% in selecting the first-interacted crystal and a reduction in error distances compared when no recovery was applied. Both ICS-eNet and ICS-cNet exhibited consistent performances under various optical property settings of the crystals. For spatial resolution measurements in PET rings, both networks achieved significant enhancements particularly for highly pixelated arrays. We also discuss approaches for training the networks in an actual experimental setup. This proof-of-concept study demonstrated the feasibility of CNNs for ICS recovery in various light-sharing designs to efficiently improve the spatial resolution of PET in various applications.

The effects of inter-crystal scattering events on the performance of PET detectors

The probability of inter-crystal scattering (ICS) events for 511 keV gamma rays in all current scintillation crystals is high and the ICS events degrade the spatial resolution of PET scanners. In this work, Monte Carlo simulations were performed to study the effects of ICS events on the sensitivity and spatial resolution of PET detectors. LaBr₃, LYSO, and PWO that represent scintillation crystals of low, medium and high density, respectively, were used. For a point source placed in the middle of two scintillation detectors of 50  ×  50  ×  20 mm³ and a lower energy threshold (LET) of 350 keV, the probabilities that at least one gamma ray undergoes ICS are 94%, 84% and 76% for LaBr₃, LYSO, and PWO, respectively. The ICS events still provide useful spatial information. The full width at half maximum (FWHM), the full width at tenth maximum (FWTM) and the mean absolute error (MAE) of the curve of the mispositioning of a point source caused by ICS events are 0.45, 3.0 and 0.9 mm if the most popular PET scintillator LYSO is used. The MAE is smaller than the spatial resolution of most current PET scanners. The effect of ICS increases as the detector LET increases, scintillator density decreases, and crystal size decreases. The intrinsic spatial resolutions of a pair of LYSO detectors were calculated using curves of the coincidence counts between one column of the crystals in the two detectors and the sum of the coincidence counts between two opposite crystals of the columns in the two detectors that are in line with the point source changing with the source positions. The latter method removes almost all of ICS events. The FWHM (FWTM) intrinsic spatial resolutions obtained by the two methods are 0.40 (2.0) mm and 0.33 (0.8) mm if the crystal size is 0.5 mm, and are 0.8 (3.0) and 0.68 (1.5) mm if the crystal size is 1.0 mm. ICS events have much bigger contributions to the FWTM rather than the FWHM of the intrinsic spatial resolution of PET detectors. The spatial resolution of a PET scanner can still be improved by decreasing the crystal size to as small as 0.5 mm.