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.

DOI estimation through signal arrival time distribution: a theoretical description including proof of concept measurements

“…Two timestamps are used from the n timestamps dataset. The first timestamp t early is chosen among the first detected photons since they typically have the lowest statistical time variability (Gundacker et al 2015, Toussaint et al 2019. The second timestamp t late is chosen so that there is ideally the strongest DOI dependence on the time difference between the two timestamps.…”

“…Simulations were performed using the analytical timing model described in Toussaint et al (2019) which deals separately with the light propagation time profiles as a function of DOI to keep separated the variance-related effects (emission, transport and photodetection) and the bias induced by DOI, then combined in a root mean squared error to describe the global timing error. The influence of DOI bias with detectors affected by a strong DOI impact was shown experimentally in Loignon-Houle et al (2020), validating the model presented in Toussaint et al (2019).…”

Physics and technology of time-of-flight PET detectors

“…In essence, three causes of time resolution loss are associated with optical transfer: (1) the dependence of the mean optical path length between the point of interaction  x and the photosensor on  x, which in conventional, high-aspect-ratio crystals introduces a DOI-dependent signal delay; (2) the spread in the optical path lengths of the first detected photons for given  x, which depends on the detector geometry and the properties of the optical interfaces; and (3) the dependence of this spread on  x. Equation (18) offers a measure of the best achievable CRT in the presence of these three effects (Toussaint et al 2019). A simple way to reduce all of them in a conventional TOF-PET detector would be to reduce the crystal length, but this is at odds with the FOM defined in equation (2).…”

Time of Flight in Perspective: Instrumental and Computational Aspects of Time Resolution in Positron Emission Tomography

“…Another factor not to be overlooked is the reduction in optical transfer time spread that has become possible due to the introduction of SiPMs. Section II.A discussed the three causes of time resolution loss that occur in non-infinitesimal scintillation crystals [28,36]. Each of these effects are minimized when as many of the scintillation photons as possible are transferred to the photosensor as quickly as possible.…”