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.

PET scanners are sophisticated and highly sensitive biomedical imaging devices that can produce highly quantitative images showing the 3-dimensional distribution of radiotracers inside the body. PET scanners are commonly integrated with x-ray CT or MRI scanners in hybrid devices that can provide both molecular imaging (PET) and anatomical imaging (CT or MRI). Despite decades of development, significant opportunities still exist to make major improvements in the performance of PET systems for a variety of clinical and research tasks. These opportunities stem from new ideas and concepts, as well as a range of enabling technologies and methodologies. In this paper, we review current state of the art in PET instrumentation, detectors and systems, describe the major limitations in PET as currently practiced, and offer our own personal insights into some of the recent and emerging technological innovations that we believe will impact the field. Our focus is on the technical aspects of PET imaging, specifically detectors and system design, and the opportunity and necessity to move closer to PET systems for diagnostic patient use and in vivo biomedical research that truly approach the physical performance limits while remaining mindful of imaging time, radiation dose, and cost. However, other key endeavors, which are not covered here, including innovations in reconstruction and modeling methodology, radiotracer development, and expanding the range of clinical and research applications, also will play an equally important, if not more important, role in defining the future of the field.

Achieving excellent timing resolution in gamma ray detectors is crucial in several applications such as medical imaging with time-of-flight positron emission tomography (TOF-PET). Although many factors impact the overall system timing resolution, the statistical nature of scintillation light, including photon production and transport in the crystal to the photodetector, is typically the limiting factor for modern scintillation detectors. In this study, we investigated the impact of surface treatment, in particular, roughening select areas of otherwise polished crystals, on light transport and timing resolution. A custom Monte Carlo photon tracking tool was used to gain insight into changes in light collection and timing resolution that were observed experimentally: select roughening configurations increased the light collection up to 25% and improved timing resolution by 15% compared to crystals with all polished surfaces. Simulations showed that partial surface roughening caused a greater number of photons to be reflected towards the photodetector and increased the initial rate of photoelectron production. This study provides a simple method to improve timing resolution and light collection in scintillator-based gamma ray detectors, a topic of high importance in the field of TOF-PET. Additionally, we demonstrated utility of our Monte Carlo simulation tool to accurately predict the effect of altering crystal surfaces on light collection and timing resolution.

In a scintillation detector, the light generated in the scintillator by a gamma interaction is converted to photoelectrons by a photodetector and produces a time-dependent waveform, the shape of which depends on the scintillator properties and the photodetector response. Several depth-of-interaction (DOI) encoding strategies have been developed that manipulate the scintillator's temporal response along the crystal length and therefore require pulse shape discrimination techniques to differentiate waveform shapes. In this work, we demonstrate how maximum likelihood (ML) estimation methods can be applied to pulse shape discrimination to better estimate deposited energy, DOI and interaction time (for time-of-flight (TOF) PET) of a gamma ray in a scintillation detector. We developed likelihood models based on either the estimated detection times of individual photoelectrons or the number of photoelectrons in discrete time bins, and applied to two phosphor-coated crystals (LFS and LYSO) used in a previously developed TOF-DOI detector concept. Compared with conventional analytical methods, ML pulse shape discrimination improved DOI encoding by 27% for both crystals. Using the ML DOI estimate, we were able to counter depth-dependent changes in light collection inherent to long scintillator crystals and recover the energy resolution measured with fixed depth irradiation (~11.5% for both crystals). Lastly, we demonstrated how the Richardson-Lucy algorithm, an iterative, ML-based deconvolution technique, can be applied to the digitized waveforms to deconvolve the photodetector's single photoelectron response and produce waveforms with a faster rising edge. After deconvolution and applying DOI and time-walk corrections, we demonstrated a 13% improvement in coincidence timing resolution (from 290 to 254 ps) with the LFS crystal and an 8% improvement (323 to 297 ps) with the LYSO crystal.

Machine learning has found unique applications in nuclear medicine from photon detection to quantitative image reconstruction. While 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 and position information from the detector signals. Now with the availability of fast waveform digitizers, machine learning techniques have been applied to estimate the position and arrival time of high-energy photons. In quantitative image reconstruction, machine learning has been used to estimate various corrections factors, including scattered events and attenuation images, as well as to reduce statistical noise in reconstructed images. Here machine learning either provides a faster alternative to an existing time-consuming computation, such as in the case of scatter estimation, or creates a data-driven approach to map an implicitly defined function, such as in the case of estimating the attenuation map for PET/MR scans. In this article, we will review the abovementioned applications of machine learning in nuclear medicine.

Purpose

In support of a project to build a total-body PET scanner with an axial field-of-view of 2 m, the authors are developing simple, cost-effective block detectors with combined time-of-flight (TOF) and depth-of-interaction (DOI) capabilities.

Methods

This work focuses on investigating the potential of phosphor-coated crystals with conventional PMT-based block detector readout to provide DOI information while preserving timing resolution. The authors explored a variety of phosphor-coating configurations with single crystals and crystal arrays. Several pulse shape discrimination techniques were investigated, including decay time, delayed charge integration (DCI), and average signal shapes.

Results

Pulse shape discrimination based on DCI provided the lowest DOI positioning error: 2 mm DOI positioning error was obtained with single phosphor-coated crystals while 3-3.5 mm DOI error was measured with the block detector module. Minimal timing resolution degradation was observed with single phosphor-coated crystals compared to uncoated crystals, and a timing resolution of 442 ps was obtained with phosphor-coated crystals in the block detector compared to 404 ps without phosphor coating. Flood maps showed a slight degradation in crystal resolvability with phosphor-coated crystals; however, all crystals could be resolved. Energy resolution was degraded by 3%-7% with phosphor-coated crystals compared to uncoated crystals.

Conclusions

These results demonstrate the feasibility of obtaining TOF-DOI capabilities with simple block detector readout using phosphor-coated crystals.

Purpose

We are investigating the use of promptly emitted Cerenkov photons to improve scintillation detector timing resolution for time-of-flight (TOF) positron emission tomography (PET). Bismuth germanate (BGO) scintillator was used in most commercial PET scanners until the emergence of lutetium oxyorthosilicate, which allowed for TOF PET by triggering on the fast and bright scintillation signal. Yet BGO is also a candidate to generate fast timing triggers based on Cerenkov light produced in the first few picoseconds following a gamma interaction. Triggering on the Cerenkov light produces excellent timing resolution in BGO but is complicated by the very low number of photons produced. A better understanding of the transport and collection of Cerenkov photons is needed to optimize their use for effective triggering of the detectors.

Methods

We simultaneously generated and tracked Cerenkov and scintillation photons with a new model of light transport that we have released in GATE V8.0. This crystal reflectance model was used to study photon detection and timing properties, building realistic waveforms as measured with silicon photomultipliers.

Results

We compared the behavior and effect of detecting Cerenkov and scintillation photons at several levels, including detection time stamps, travel time, and coincidence resolving time in 3 × 3 × 20 mm³ BGO crystals. Simulations showed excellent agreement with experimental results and indicated that Cerenkov photons constitute the majority of the signal rising edge. They are therefore critical to provide early triggering and improved the coincidence timing resolution by 50%.

Potential applications

To our knowledge, this is the first complete simulation of the generation, transport, and detection of the combination of Cerenkov and scintillation photons for TOF detectors. This simulation framework will allow for quantitative study of the factors influencing timing resolution, including the photodetector characteristics, and ultimately aid the development of BGO and other Cerenkov-based detectors for TOF PET.

Current research in the field of positron emission tomography (PET) focuses on improving the sensitivity of the scanner with thicker detectors, extended axial field-of-view, and time-of-flight (TOF) capability. These create the need for depth-of-interaction (DOI) encoding to correct parallax errors. We have proposed a method to encode DOI using phosphor-coated crystals. Our initial work using photomultiplier tubes (PMTs) demonstrated the possibilities of the proposed method, however, a major limitation of PMTs for this application is poor quantum efficiency in yellow light, corresponding to the wavelengths of the converted light by the phosphor coating. In contrast, the red-green-blue-high-density (RGB-HD) silicon photomultipliers (SiPMs) have a high photon detection efficiency across the visible spectrum. Excellent coincidence resolving time (CRT; [Formula: see text]) was obtained by coupling RGB-HD SiPMs and [Formula: see text] lutetium fine silicate crystals coated on a third of one of their lateral sides. Events were classified in three DOI bins ([Formula: see text] width) with an average sensitivity of 83.1%. A CRT of [Formula: see text] combined with robust DOI encoding is a marked improvement in the phosphor-coated approach that we pioneered. For the first time, we read out these crystals with SiPMs and clearly demonstrated the potential of the RGB-HD SiPMs for this TOF-DOI PET detector.

Current developments in positron emission tomography focus on improving timing performance for scanners with time-of-flight (TOF) capability, and incorporating depth-of-interaction (DOI) information. Recent studies have shown that incorporating DOI correction in TOF detectors can improve timing resolution, and that DOI also becomes more important in long axial field-of-view scanners. We have previously reported the development of DOI-encoding detectors using phosphor-coated scintillation crystals; here we study the timing properties of those crystals to assess the feasibility of providing some level of DOI information without significantly degrading the timing performance. We used Monte Carlo simulations to provide a detailed understanding of light transport in phosphor-coated crystals which cannot be fully characterized experimentally. Our simulations used a custom reflectance model based on 3D crystal surface measurements. Lutetium oxyorthosilicate crystals were simulated with a phosphor coating in contact with the scintillator surfaces and an external diffuse reflector (teflon). Light output, energy resolution, and pulse shape showed excellent agreement with experimental data obtained on 3 × 3 × 10 mm³ crystals coupled to a photomultiplier tube. Scintillator intrinsic timing resolution was simulated with head-on and side-on configurations, confirming the trends observed experimentally. These results indicate that the model may be used to predict timing properties in phosphor-coated crystals and guide the coating for optimal DOI resolution/timing performance trade-off for a given crystal geometry. Simulation data suggested that a time stamp generated from early photoelectrons minimizes degradation of the timing resolution, thus making this method potentially more useful for TOF-DOI detectors than our initial experiments suggested. Finally, this approach could easily be extended to the study of timing properties in other scintillation crystals, with a range of treatments and materials attached to the surface.

The performance of an 8 × 8 array of 6.0 × 6.0 mm² (active area) SiPMs was evaluated for PET applications using crystal arrays with different pitch sizes (3.4 mm, 1.5 mm, 1.35 mm and 1.2 mm) and custom designed five-channel front-end readout electronics (four channels for position information and one channel for timing information). The total area of this SiPM array is 57.4 × 57.4 mm², and the pitch size is 7.2 mm. It was fabricated using enhanced blue sensitivity SiPMs (MicroFB-60035-SMT) with peak spectral sensitivity at 420 nm. The performance of the SiPM array was characterized by measuring flood histogram decoding quality, energy resolution, timing resolution and saturation at several bias voltages (from 25.0 V to 30.0 V in 0.5 V intervals) and two different temperatures (5 °C and 20 °C). Results show that the best flood histogram was obtained at a bias voltage of 28.0 V and 5 °C and an array of polished LSO crystals with a pitch as small as 1.2 mm can be resolved. No saturation was observed up to a bias voltage of 29.5 V during the experiments, due to adequate light sharing between SiPMs. Energy resolution and timing resolution at 5 °C ranged from 12.7 ± 0.8% to 14.6 ± 1.4 % and 1.58 ± 0.13 ns to 2.50 ± 0.44 ns, for crystal array pitch sizes of 3.4 mm and 1.2 mm respectively. Superior flood histogram quality, energy resolution and timing resolution were obtained with larger crystal array pitch sizes and at lower temperature. Based on our findings, we conclude that this large-area SiPM array can serve as a suitable photodetector for high-resolution small-animal PET or dedicated human brain PET scanners.