Analytical model of DOI-induced time bias in ultra-fast scintillation detectors for TOF-PET

Abstract

In positron emission tomography (PET), long crystals (20 mm) are used to enhance detection efficiency and increase scanner sensitivity. However, for fast time-of-flight (TOF) scanners, this may affect the achievable coincidence time resolution (CTR) due to depth-of-interaction (DOI) induced blur on timing. Currently, the effect of DOI on CTR evaluation with analytical modeling is incorporated using the probability density function (PDF) for attenuation of the annihilation photons with the PDFs of the other scintillation processes. However, we show that the resulting PDF would not describe accurately the variation in timestamps distribution at different DOIs. We propose a new analytical model for the CTR evaluation, which consists of computing a DOI dependent CTR weighted by the DOI probability in coincidence. The CTR was thus defined as the weighted root-mean-square error (RMSE) of the DOI-wise variance and bias in order to explicitly describe the positioning bias induced by coincident annihilation photons at different DOIs. The effect of DOI bias on CTR was investigated by using four classic estimators found in the literature, each applied on contemporary scintillation detectors and nearly ideal detectors. A limited difference in the calculated CTR was found for typical scintillation detectors when assessing RMSE with and without DOI time offset correction. This was expected since the DOI bias remains negligible against other phenomena in such case. However, the difference becomes significant for nearly ideal scintillation detectors, where optimal CTR would only be attainable with DOI correction. For these nearly ideal cases, the revised model has better predictive power since the DOI time offset correction is included. Investigation with analytical approaches for realistically achievable ultra-fast CTR in TOF-PET detectors should be performed with a model that genuinely takes into account the DOI effect. We show that the proposed model is a valid candidate for such a task.