Group for Research in Decision Analysis

# Depth-of-interaction bias in the achievable ultra-fast timing of detectors for TOF-PET

## Maxime Toussaint, Francis Loignon-Houle, Jean-Pierre Dussault, and Roger Lecomte

In Positron Emission Tomography (PET), deep crystals (>20 mm) must be used to enhance detection efficiency and increase overall scanner sensitivity. However, for fast time-of-flight (TOF) scanners, this may come at a cost for the achievable coincidence time resolution (CTR), since the propagation time of annihilation photons differs depending on the depth-of-interaction (DOI) location. In the literature, DOI effect in CTR computation is modeled by incorporating the attenuation probability density function (PDF) with the PDFs for the scintillation pulse emission, propagation and detection. However, the resulting PDF would not describe accurately the variation, in timestamps distribution, due to annihilation photon DOI. In this study, we propose to investigate the DOI bias effect on CTR for a typical and a near-ideal scintillation detector. We also calculated the CTR of some estimators (k-th trigger, average of first-k triggers, and Gauss-Markov estimator) based on the ordered primary detected scintillation photons. The root-mean-square error (RMSE) of the coincidence detection process is a straightforward metric to compare the quality of different estimators. The RMSE of the different estimators was calculated using DOI probability in coincidence. A small difference in the calculated CTR was found for a typical LYSO/SiPM scintillation detector when assessing RMSE; this was expected since the DOI error influence remains negligible against other parameters. However, the difference becomes crucial for near-ideal scintillation detectors: the standard method predicts 10-20 ps CTR, but RMSE remains above $$\sim$$55 ps CTR, which seems more likely since the difference in TOF introduced by the crystal length can almost be of the same magnitude. Thus, in the absence of DOI measurement, investigation of the achievable ultra-fast CTR in TOF-PET detectors should include the bias introduced by DOI.

, 8 pages