Effect of inter-crystal scatter on estimation methods for random coincidences and subsequent correction.

Random coincidences can contribute substantially to the background in positron emission tomography (PET). Several estimation methods are being used for correcting them. The goal of this study was to investigate the validity of techniques for random coincidence estimation, with various low-energy thresholds (LETs). Simulated singles list-mode data of the MADPET-II small animal PET scanner were used as input. The simulations have been performed using the GATE simulation toolkit. Several sources with different geometries have been employed. We evaluated the number of random events using three methods: delayed window (DW), singles rate (SR) and time histogram fitting (TH). Since the GATE simulations allow random and true coincidences to be distinguished, a comparison between the number of random coincidences estimated using the standard methods and the number obtained using GATE was performed. An overestimation in the number of random events was observed using the DW and SR methods. This overestimation decreases for LETs higher than 255 keV. It is additionally reduced when the single events which have undergone a Compton interaction in crystals before being detected are removed from the data. These two observations lead us to infer that the overestimation is due to inter-crystal scatter. The effect of this mismatch in the reconstructed images is important for quantification because it leads to an underestimation of activity. This was shown using a hot-cold-background source with 3.7 MBq total activity in the background region and a 1.59 MBq total activity in the hot region. For both 200 keV and 400 keV LET, an overestimation of random coincidences for the DW and SR methods was observed, resulting in approximately 1.5% or more (at 200 keV LET: 1.7% for DW and 7% for SR) and less than 1% (at 400 keV LET: both methods) underestimation of activity within the background region. In almost all cases, images obtained by compensating for random events in the reconstruction algorithm were better in terms of quantification than the images made with precorrected data.