A novel inter-crystal scattering event classification method for PET detectors with light sharing readout scheme

Objectives: Inter-crystal scattering (ICS) event occurs when a gamma-ray undergoes Compton scattering within PET detector elements, and it deposits its energy in more than one detector elements. ICS events cause mis-positioning of gamma interaction position which degrades image resolution, and by classifying and recovering ICS events into first interaction position, we can minimize resolution degradation. However, classifying ICS event is challenging since most of the current PET detectors use light sharing of crystal to photosensor and multiplexing readout schemes. Up to now, 1-to-1 coupling and individual readout is only possible solution. In this study, we propose a new method to extract ICS events that is even applicable to light sharing designs.

Methods: Suppose that we observe m detector responses when a 511-keV gamma fully deposits its energy at i^th crystal: y_i = [y₁, ⋯, y_m]^T. Consider that an ICS event occurred at i^th and j^th crystals with energies of E_i and E_j (E_total = E_i + E_j). The observation y of an ICS event can be expressed as the sum of independent observations of y_i and y_j multiplied with corresponding energy ratios: y = y_i × E_i/E_total + y_j × E_j/E_total. We can simply model the observation y into matrix formation: y = Ax; where [m×1] vector y is observation, [m×n] matrix A is characteristic m detector responses for n crystals, and [n×1] vector x is energy ratio for n crystals. Consequently, by solving linear matrix formation, finding vector x, we can extract ICS event positions and deposited energies. For the concept verification, a simulation study was conducted using GATE v.7.0 Monte Carlo simulation toolkit with optical photon tracking. In the simulated detector, 8×8 photosensor with the pixel size of 3.2×3.8775 mm² was coupled with LSO crystals (3×3×20 mm³) with the array size of 8×8 and 10×10 for 1-to-1 coupling and light sharing geometry. Simulation data was modified to test three readout schemes: 1) individual, 2) row-column (RC) sum, and 3) four corner. Also, we compared three different methods to classify ICS events: 1) Method 1: maximum peak detection, 2) Method 2: matrix pseudoinverse, and 3) Method 3: convex constrained optimization. In Method 2 and 3, ICS interaction positions were determined by choosing indices of two or more maximum values in energy ratio vector (x). For each method, classification ratio, a ratio of correctly classified events into first interaction position, was calculated for non-ICS and ICS events. Based on vector x values, deposited energies of ICS events were estimated and compared with true values. Energy linearity and correlation were evaluated by linear fitting.

Results: For 1-to-1 coupling with individual readout, high classification ratios were shown for three methods, while the proposed one showed the best result of 0.94. Estimated energy showed high linear correlation with true energy. In RC sum readout, classification ratio and energy correlation degraded, but Method 3 showed good ICS classification ratio of 0.716 and high energy correlation. In case of four corner readout, ICS recovery was not possible for all methods. In light sharing design, where Method 1 is not applicable, proposed Method 2 and 3 resulted in ICS classification ratios of 0.672 and 0.852. In addition, Method 3 was proven to be effective even after multiplexing with ratio of 0.658. Energy estimation accuracy degraded in Method 2 significantly, while Method 3 was robust even after multiplexing.

Conclusion: We proposed a new method to classify ICS events in PET detector. Proposed method showed good ICS classification even in light sharing design with multiplexing. Research Support: This work is supported by grants from the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Science, ICT and Future Planning (grant no. NRF-2014M3C7034000, NRF-2016R1A2B3014645).