The systematic errors in the random coincidence estimation using a delayed window

With the advance of new technology, PET systems nowadays have much higher sensitivities than before with the adoption of faster scintillators, faster electronics, larger solid angle detectors and full 3D data collection mode. All of these lead to the increasing of the random coincidences that will affect the image quality. Accurate random correction is important for the quantitative imaging in PET applications. Delayed window method is widely used for random coincidences estimation. However, this method is not mathematically accurate. The difference between the delayed window randoms and the prompt window randoms can be significant under certain conditions. We studied the details of these differences using Monte Carlo simulations since this is the only way to separate the real random events from the true and scattered events. Three phantoms are used in the study, including the NEMA1994 20-cm long phantom, NEMA2001 70-cm long phantom and a 10-cm long, 1-cm diameter small cylinder phantom. The PET system used in this study is a 12-module LYSO camera with 20-cm axial FOV and 54-cm ring diameter to simulate a brain PET system. Two policies for the multiple events handling are used: reject-all-multiples, and take-all-goods. Random rates and NECR as the function of activities from prompt window and delayed window are obtained. The simulation results show that 1) The take-all-goods policy will underestimate the randoms rate and the reject-all-multiples will overestimate the randoms, which results overestimation of NECR for take-all-goods policy and underestimation of NECR for reject-all-multiples policy; 2) The discrepancy is more significant for smaller phantom than bigger phantom. This study demonstrates the intrinsic discrepancy for random coincidence estimation by the delayed window method. When the phantom is relatively small compared to the FOV dimension of the PET system, the discrepancy is big enough to produce non-negligible errors.