Timing Estimation and Limits in TOF-PET Detectors Producing Prompt Photons.

The production of prompt photons providing high photon time densities is a promising avenue to reach ultrahigh coincidence time resolution (CTR) in time-of-flight PET. Detectors producing prompt photons are receiving high interest experimentally, ignited by past exploratory theoretical studies that have anchored some guiding principles. Here, we aim to consolidate and extend the foundations for the analytical modeling of prompt generating detectors. We extend the current models to a larger range of prompt emission kinetics where more stringent requirements on the prompt photon yield rapidly emerge as a limiting factor. Lower bound and estimator evaluations are investigated with different underlying models, notably by merging or keeping separate the prompt and scintillation photon populations. We further show the potential benefits of knowing the proportion of prompt photons within a detection set to improve the CTR by mitigating the detrimental effect of population (prompt vs scintillation) mixing. Taking into account the fluctuations on the average number of detected prompt photons in the model reveals a limited influence when prompt photons are accompanied by fast scintillation (e.g., LSO:Ce:Ca) but a more significant effect when accompanied by slower scintillation (e.g., BGO). Establishing performance characteristics and limitations of prompt generating detectors is paramount to gauging and targeting the best possible timing capabilities they can offer.

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

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 single-ended 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.

Experimental validation of a coincidence time resolution metric including depth-of-interaction bias for TOF-PET.

Depth-of-interaction (DOI) variability of annihilation photons is known to be a source of coincidence time resolution (CTR) degradation for fast time-of-flight-positron emission tomography detectors. An analytical model was recently proposed to explicitly include the DOI time bias separately from variance-related statistical factors, such as scintillation photon emission and photosensor jitter, in the CTR evaluation. In the present work, an experimental validation of this new model is provided. An unconventional signal readout configuration was used to magnify the DOI bias with 20 mm long LYSO:Ce crystals. In a head-to-head orientation of the crystals, simulations performed using the metric with DOI bias exhibited a much better agreement (within 21 ps) with the experimentally measured CTR of 413 ± 8 ps full-width at half maximum, whereas simulations without DOI bias underestimated the CTR by 138 ps. The metric including DOI bias was shown to also be effective at predicting the CTR of the head-to-head setup (without DOI information) using data from a DOI-collimated experimental setup (with partial DOI information). With the development of new low-variance ultra-fast detectors, the DOI timing blur will become increasingly important and will need to be taken into account in analytical predictions and in some experimental measurements through the proposed metric.

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

In positron emission tomography (PET), long crystals ([Formula: see text]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.

Simulation of scintillation light output in LYSO scintillators through a full factorial design.

Individually coupled scintillation detectors used in positron emission tomography (PET) imaging suffer from important signal losses due to the suboptimal light collection from crystals. As only a fraction of the light is generally extracted from long and thin scintillators, it is important to identify and understand the predominant causes of signal loss in order to eventually recover it. This simulation study investigates the multiple factors affecting the light transport in high-aspect ratio LYSO scintillators wrapped in specular reflectors through a full factorial design. By exploring various combinations of crystal geometry, readout conditions and wrapping conditions, it was found that an optimum light output can only be achieved through a careful selection of highly reflective material along with high-transmittance optical adhesive used to bond the reflector. Decreasing the adhesive thickness was also found to have a positive outcome in most explored configurations, however to a much lesser extent. Suboptimal reflectivity and adhesive transmittance also lead to an asymmetric light output distribution dependent on the depth of interaction of the radiation, potentially degrading energy resolution. By identifying the factors causing the most significant scintillation light losses through a factorial design, the most promising detector configurations have been identified in the quest for optimal light collection from scintillators.