Iterative crystal efficiency calculation in fully 3-D PET

The calculation of the intrinsic efficiency of individual crystals is one of the steps needed to obtain accurate images of the radioisotope distribution in positron emission tomography (PET). These efficiencies can be computed by comparing the number of coincidence counts obtained when the crystals are equally illuminated by the same source. However, because the number of coincidence counts acquired for one crystal also depends on the efficiency of the other crystals in coincidence, most methods of crystal efficiency calculation need to assume that the influence of the other crystals is negligible. If there are large crystal efficiency variations, this approximation may lead to systematic errors. We have recently implemented an iterative method for a single ring of detectors that does not rely on this assumption. In this paper, we describe a fully three-dimensional (3-D) iterative method that better exploits the sensitivity of the tomograph and allows reduced acquisition times or the use of narrow energy windows. We compare the performance of the iterative method (single-ring and extended to fully 3-D) with noniterative techniques for different acquisition times of a uniform cylinder. Two different energy windows were used to assess the performance of each method with different levels of variations of crystal efficiency. The results showed that the iterative methods are more accurate when large efficiency variations exist and that only the fully 3-D methods provided good efficiency estimates with very low duration scans. We, thus, conclude that iterative fully 3-D methods provide the best estimations and can be used in a larger range of situations than can the other methods tested.