Incorporating count-rate dependence into model-based PET scatter estimation

Pile-up in a PET detector changes the sensitivity of the detector to unscattered and scattered annihilation photons differently. If the detection of a 511 keV photon is confounded by the arrival of a second photon during signal integration, it may be lost by failing the upper energy threshold, so its detection probability decreases as activity increases. If, however, the first photon is a scattered photon of energy less than the lower energy threshold, pile-up may lead to an energy signal that lies within the energy window; detection probability for this photon increases as activity increases. As a result, the measured scatter fraction will increase as activity increases in a PET scanner. This effect is readily observed in the NEMA NU 2-2007 Scatter Fraction and Count Losses test as an increase in measured scatter fraction, and a broadening of the scatter tails, as activity in the phantom increases. We incorporate this phenomenon into the model-based scatter estimate through a function, parameterized by a measurement of the detectors busy time, which modifies the detection probability matrix for the scattered and unscattered photons in the model. The function was determined by Monte Carlo simulation of the pileup performance of the block, and is therefore a function of the block configuration, the scintillator decay time and the signal integration time in the detector electronics, and the energy window used in the acquisition. The function is fit by a polynomial from 170 to 511 keV, the possible energy range for a single scattered annihilation photon. The resulting scatter model demonstrates a count rate dependence that better matches the scatter tails from the NEMA count rate experiment, and improves the quality of the scatter correction in certain high count rate patient studies.