Randoms from singles estimation for long PET scans

We have previously described the algorithm for estimating the contribution of random coincidences to the PET dataset using a set of singles counters, one per detector element, which accumulate the single events transmitted to the coincidence processor over the course of an acquisition frame. In this algorithm, the effect of isotope decay during the acquisition was neglected, as it was shown to be small (<;60;1% change for an acquisition time of one-half the isotope half-life). While this is sufficient for most PET acquisitions, it may not be for scans that are long compared to the isotope half-life, such as static or gated ⁸²Rb (75 sec half-life) acquisitions of several minutes duration. In several sample ⁸²Rb scans from a whole-body PET/CT scanner, the singles-based algorithm underestimated the total randoms by 33-45% compared with the randoms estimate from a delayed coincidence window. We have developed a correction term for the previous algorithm to account for activity changes during long-duration PET frames. This correction term produces a more accurate estimate of randoms from singles which also takes into account the effect of the decaying activity on the deadtime of the scanner and the effect of the intrinsic singles rate and resulting deadtime from the background activity present in a lutetium-based scintillator material. The resulting correction term is a function of the measured total singles, the average deadtime and the duration of the frame, the average intrinsic counts per crystal and intrinsic deadtime per block (set to zero for a non-lutetium containing detector) and the isotope half-life. Applying this correction term to the studies described above reduced the difference between the single-based estimate and the delayed window randoms counts to 1-3%.