Maximum-Likelihood Estimation of Scintillation Pulse Timing

Improving timing resolution of BGO for TOF-PET: a comparative analysis with and without deep learning

BACKGROUND

The renewed interest in BGO scintillators for TOF-PET is driven by the improved Cherenkov photon detection with new blue-sensitive SiPMs. However, the slower scintillation light from BGO causes significant time walk with leading edge discrimination (LED), which degrades the coincidence time resolution (CTR). To address this, a time walk correction (TWC) can be done by using the rise time measured with a second threshold. Deep learning, particularly convolutional neural networks (CNNs), can also enhance CTR by training with digitized waveforms. It remains to be explored how timing estimation methods utilizing one (LED), two (TWC), or multiple (CNN) waveform data points compare in CTR performance of BGO scintillators.

RESULTS

In this work, we compare classical experimental timing estimation methods (LED, TWC) with a CNN-based method using the signals from BGO crystals read out by NUV-HD-MT SiPMs and high-frequency electronics. For2 × 2 × 3 mm 3 crystals, implementing TWC results in a CTR of 129 ± 2 ps FWHM, while employing the CNN yields 115 ± 2 ps FWHM, marking improvements of 18 % and 26 %, respectively, relative to the standard LED estimator. For2 × 2 × 20 mm 3 crystals, both methods yield similar CTR (around 240 ps FWHM), offering a ∼ 15 % gain over LED. The CNN, however, exhibits better tail suppression in the coincidence time distribution.

CONCLUSIONS

The higher complexity of waveform digitization needed for CNNs could potentially be mitigated by adopting a simpler two-threshold approach, which appears to currently capture most of the essential information for improving CTR in longer BGO crystals. Other innovative deep learning models and training strategies may nonetheless contribute further in a near future to harnessing increasingly discernible timing features in TOF-PET detector signals.

Unbiased TOF estimation using leading-edge discriminator and convolutional neural network trained by single-source-position waveforms

Objective. Convolutional neural networks (CNNs) are a strong tool for improving the coincidence time resolution (CTR) of time-of-flight (TOF) positron emission tomography detectors. However, several signal waveforms from multiple source positions are required for CNN training. Furthermore, there is concern that TOF estimation is biased near the edge of the training space, despite the reduced estimation variance (i.e. timing uncertainty). Approach. We propose a simple method for unbiased TOF estimation by combining a conventional leading-edge discriminator (LED) and a CNN that can be trained with waveforms collected from one source position. The proposed method estimates and corrects the time difference error calculated by the LED rather than the absolute time difference. This model can eliminate the TOF estimation bias, as the combination with the LED converts the distribution of the label data from discrete values at each position into a continuous symmetric distribution. Main results. Evaluation results using signal waveforms collected from scintillation detectors show that the proposed method can correctly estimate all source positions without bias from a single source position. Moreover, the proposed method improves the CTR of the conventional LED. Significance. We believe that the improved CTR will not only increase the signal-to-noise ratio but will also contribute significantly to a part of the direct positron emission imaging.

Physics and technology of time-of-flight PET detectors

The imaging performance of clinical positron emission tomography (PET) systems has evolved impressively during the last ∼15 years. A main driver of these improvements has been the introduction of time-of-flight (TOF) detectors with high spatial resolution and detection efficiency, initially based on photomultiplier tubes, later silicon photomultipliers. This review aims to offer insight into the challenges encountered, solutions developed, and lessons learned during this period. Detectors based on fast, bright, inorganic scintillators form the scope of this work, as these are used in essentially all clinical TOF-PET systems today. The improvement of the coincidence resolving time (CRT) requires the optimization of the entire detection chain and a sound understanding of the physics involved facilitates this effort greatly. Therefore, the theory of scintillation detector timing is reviewed first. Once the fundamentals have been set forth, the principal detector components are discussed: the scintillator and the photosensor. The parameters that influence the CRT are examined and the history, state-of-the-art, and ongoing developments are reviewed. Finally, the interplay between these components and the optimization of the overall detector design are considered. Based on the knowledge gained to date, it appears feasible to improve the CRT from the values of 200-400 ps achieved by current state-of-the-art TOF-PET systems to about 100 ps or less, even though this may require the implementation of advanced methods such as time resolution recovery. At the same time, it appears unlikely that a system-level CRT in the order of ∼10 ps can be reached with conventional scintillation detectors. Such a CRT could eliminate the need for conventional tomographic image reconstruction and a search for new approaches to timestamp annihilation photons with ultra-high precision is therefore warranted. While the focus of this review is on timing performance, it attempts to approach the topic from a clinically driven perspective, i.e. bearing in mind that the ultimate goal is to optimize the value of PET in research and (personalized) medicine.

An edge-readout, multilayer detector for positron emission tomography

PURPOSE

We present a novel gamma-ray-detector design based on total internal reflection (TIR) of scintillation photons within a crystal that addresses many limitations of traditional PET detectors. Our approach has appealing features, including submillimeter lateral resolution, DOI positioning from layer thickness, and excellent energy resolution. The design places light sensors on the edges of a stack of scintillator slabs separated by small air gaps and exploits the phenomenon that more than 80% of scintillation light emitted during a gamma-ray event reaches the edges of a thin crystal with polished faces due to TIR. Gamma-ray stopping power is achieved by stacking multiple layers, and DOI is determined by which layer the gamma ray interacts in.

METHOD

The concept of edge readouts of a thin slab was verified by Monte Carlo simulation of scintillation light transport. An LYSO crystal of dimensions 50.8 mm × 50.8 mm × 3.0 mm was modeled with five rectangular SiPMs placed along each edge face. The mean-detector-response functions (MDRFs) were calculated by simulating signals from 511 keV gamma-ray interactions in a grid of locations. Simulations were carried out to study the influence of choice of scintillator material and dimensions, gamma-ray photon energies, introduction of laser or mechanically induced optical barriers (LIOBs, MIOBs), and refractive indices of optical-coupling media and SiPM windows. We also analyzed timing performance including influence of gamma-ray interaction position and presence of optical barriers. We also modeled and built a prototype detector, a 27.4 mm × 27.4 mm × 3.0 mm CsI(Tl) crystal with 4 SiPMs per edge to experimentally validate the results predicted by the simulations. The prototype detector used CsI(Tl) crystals from Proteus outfitted with 16 Hamamatsu model S13360-6050PE MPPCs read out by an AiT-16-channel readout. The MDRFs were measured by scanning the detector with a collimated beam of 662-keV photons from a ¹³⁷ Cs source. The spatial resolution was experimentally determined by imaging a tungsten slit that created a beam of 0.44 mm (FWHM) width normal to the detector surface. The energy resolution was evaluated by analyzing list-mode data from flood illumination by the ¹³⁷ Cs source.

RESULT

We find that in a block-detector-sized LYSO layer read out by five SiPMs per edge, illuminated by 511-keV photons, the average resolution is 1.49 mm (FWHM). With the introduction of optical barriers, average spatial resolution improves to 0.56 mm (FWHM). The DOI resolution is the layer thickness of 3.0 mm. We also find that optical-coupling media and SiPM-window materials have an impact on spatial resolution. The timing simulation with LYSO crystal yields a coincidence resolving time (CRT) of 200-400 ps, which is slightly position dependent. And the introduction of optical barriers has minimum influence. The prototype CsI(Tl) detector, with a smaller area and fewer SiPMs, was measured to have central-area spatial resolutions of 0.70 and 0.39 mm without and with optical barriers, respectively. These results match well with our simulations. An energy resolution of 6.4% was achieved at 662 keV.

CONCLUSION

A detector design based on a stack of monolithic scintillator layers that uses edge readouts offers several advantages over current block detectors for PET. For example, there is no tradeoff between spatial resolution and detection sensitivity since no reflector material displaces scintillator crystal, and submillimeter resolution can be achieved. DOI information is readily available, and excellent timing and energy resolutions are possible.

Using convolutional neural networks to estimate time-of-flight from PET detector waveforms

Although there have been impressive strides in detector development for time-of-flight positron emission tomography, most detectors still make use of simple signal processing methods to extract the time-of-flight information from the detector signals. In most cases, the timing pick-off for each waveform is computed using leading edge discrimination or constant fraction discrimination, as these were historically easily implemented with analog pulse processing electronics. However, now with the availability of fast waveform digitizers, there is opportunity to make use of more of the timing information contained in the coincident detector waveforms with advanced signal processing techniques. Here we describe the application of deep convolutional neural networks (CNNs), a type of machine learning, to estimate time-of-flight directly from the pair of digitized detector waveforms for a coincident event. One of the key features of this approach is the simplicity in obtaining ground-truth-labeled data needed to train the CNN: the true time-of-flight is determined from the difference in path length between the positron emission and each of the coincident detectors, which can be easily controlled experimentally. The experimental setup used here made use of two photomultiplier tube-based scintillation detectors, and a point source, stepped in 5 mm increments over a 15 cm range between the two detectors. The detector waveforms were digitized at 10 GS s-1 using a bench-top oscilloscope. The results shown here demonstrate that CNN-based time-of-flight estimation improves timing resolution by 20% compared to leading edge discrimination (231 ps versus 185 ps), and 23% compared to constant fraction discrimination (242 ps versus 185 ps). By comparing several different CNN architectures, we also showed that CNN depth (number of convolutional and fully connected layers) had the largest impact on timing resolution, while the exact network parameters, such as convolutional filter size and number of feature maps, had only a minor influence.