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.
Computed tomography (CT) is currently the standard modality to provide anatomical reference for positron emission tomography (PET) in molecular imaging applications. Since both PET and CT rely on detecting radiation to generate images, using the same detection system for data acquisition is a compelling idea even though merging PET and CT hardware imposes stringent requirements on detectors. These requirements include large signal dynamic range with high signal-to-noise ratio for good energy resolution in PET and energy-resolved photon-counting CT, high pixelization for suitable spatial resolution in CT, and high count rate capability for reasonable CT acquisition time. To meet these criteria, the avalanche photodiode (APD)-based LabPET II module is proposed as the building block for a truly combined PET/CT scanner. The module is made of two monolithic APD pixel arrays mounted side-by-side on a custom ceramic holder. Individual APD pixels have an active area of mm at a 1.2 mm pitch. The APD arrays are coupled to a 12-mm high, LYSO scintillator array made of mm pixels also at a pitch of 1.2 mm to ensure direct one-to-one coupling to individual APD pixels. The scintillator array was designed with unbound specular reflective material between pixels to maximize the difference between refractive indices and enhance total internal reflection at the crystal side surfaces for better light collection, and the APD quantum efficiency was improved to at 420 nm to optimize intrinsic detector performance. Mean energy resolution was at 511 keV and at 60 keV. The measured intrinsic spatial and time resolution for PET were respectively mm mm FWTM and ns FWHM with an energy threshold of 400 keV. Initial phantom images obtained using a CT test bench demonstrated excellent contrast linearity as a function of material density.
The challenge to reach 10 ps coincidence time resolution (CTR) in time-of-flight positron emission tomography (TOF-PET) is triggering major efforts worldwide, but timing improvements of scintillation detectors will remain elusive without depth-of-interaction (DOI) correction in long crystals. Nonetheless, this momentum opportunely brings up the prospect of a fully time-based DOI estimation since fast timing signals intrinsically carry DOI information, even with a traditional singleended readout. Consequently, extracting features of the detected signal time distribution could uncover the spatial origin of the interaction and in return, provide enhancement on the timing precision of detectors. We demonstrate the validity of a time-based DOI estimation concept in two steps. First, experimental measurements were carried out with current LSO:Ce:Ca crystals coupled to FBK NUV-HD SiPMs read out by fast high-frequency electronics to provide new evidence of a distinct DOI effect on CTR not observable before with slower electronics. Using this detector, a DOI discrimination using a double-threshold scheme on the analog timing signal together with the signal intensity information was also developed without any complex readout or detector modification. As a second step, we explored by simulation the anticipated performance requirements of future detectors to efficiently estimate the DOI and we proposed four estimators that exploit either more generic or more precise features of the DOI-dependent timestamp distribution. A simple estimator using the time difference between two timestamps provided enhanced CTR. Additional improvements were achieved with estimators using multiple timestamps (e.g. kernel density estimation and neural network) converging to the Cramér-Rao lower bound developed in this work for a time-based DOI estimation. This two-step study provides insights on current and future possibilities in exploiting the timing signal features for DOI estimation aiming at ultra-fast CTR while maintaining detection efficiency for TOF PET.
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