Pulse shape discrimination and classification methods for continuous depth of interaction encoding PET detectors

Precise positioning of gamma ray interactions in multiplexed pixelated scintillators using artificial neural networks

Introduction. The positioning ofγray interactions in positron emission tomography (PET) detectors is commonly made through the evaluation of the Anger logic flood histograms. machine learning techniques, leveraging features extracted from signal waveform, have demonstrated successful applications in addressing various challenges in PET instrumentation.Aim. This paper evaluates the use of artificial neural networks (NN) forγray interaction positioning in pixelated scintillators coupled to a multiplexed array of silicon photomultipliers (SiPM).Methods. An array of 16 Cerium doped Lutetium-based (LYSO) crystal pixels (cross-section 2 × 2 mm2) coupled to 16 SiPM (S13360-1350) were used for the experimental setup. Data from each of the 16 LYSO pixels was recorded, a total of 160000 events. The detectors were irradiated by 511 keV annihilationγrays from a Sodium-22 (22Na) source. Another LYSO crystal was used for electronic collimation. Features extracted from the signal waveform were used to train the model. Two models were tested: i) single multiple-class neural network (mcNN), with 16 possible outputs followed by a softmax and ii) 16 binary classification neural networks (bNN), each one specialized in identifying events occurred in each position.Results. Both NN models showed a mean positioning accuracy above 85% on the evaluation dataset, although the mcNN is faster to train.DiscussionThe method's accuracy is affected by the introduction of misclassified events that interacted in the neighbour's crystals and were misclassified during the dataset acquisition. Electronic collimation reduces this effect, however results could be improved using a more complex acquisition setup, such as a light-sharing configuration.ConclusionsThe methods comparison showed that mcNN and bNN can surpass the Anger logic, showing the feasibility of using these models in positioning procedures of future multiplexed detector systems in a linear configuration.

A depth-of-interaction rebinning method based on both geometric and activity weights

BACKGROUND AND OBJECTIVE

For positron emission tomography (PET) scanners with depth-of-interaction (DOI) measurement, the DOI rebinning method that utilizes DOI information to process the projection data is critical to image quality. Current DOI rebinning methods map coincidence events onto the rebinned sinogram based on the correlation of lines of response (LOR). This study aims to incorporate prior radioactivity distribution of the imaging object into DOI rebinning to obtain better image quality.

METHODS

A DOI rebinning method based on both geometric and activity weights was proposed to assign coincidence events to the rebinned sinogram defined by a virtual ring. The geometric weights, representing the correlation between LORs, were calculated based on the areas of intersection. The activity weights, reflecting the activity distribution of the imaging object, were derived from the previous reconstructed image.

RESULTS

Monte Carlo simulation data from four phantoms, including the image quality phantom, Derenzo phantom, and two rat-like ROBY phantoms, was used to evaluate the proposed method. The recovery coefficient (RC), contrast recovery coefficient (CRC), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR) were used as image quality metrics. Compared to other DOI rebinning methods, the proposed method achieved the highest RC (maximum improvement of 32%) and CRC at the same noise level and was also optimal in terms of the SSIM and PSNR. Meanwhile, incorporating the prior activity distribution into DOI rebinning also improved the image reconstruction speed.

CONCLUSIONS

This work developed a new DOI rebinning method combining the correlation of LORs with the prior activity distribution, achieving relatively optimal image quality and reconstruction speed. Furthermore, it still needs to be evaluated on the actual equipment.

Edge effect reduction of high-resolution PET detectors using LYSO and GAGG phoswich crystals

Objective. Small-animal positron emission tomography (PET) is a powerful preclinical imaging tool in animal model studies. The spatial resolution and sensitivity of current PET scanners developed for small-animal imaging need to be improved to increase the quantitative accuracy of preclinical animal studies. This study aimed to improve the identification capability of edge scintillator crystals of a PET detector which will enable to apply a crystal array with the same cross-section area as the active area of a photodetector for improving the detection area and thus reducing or eliminating the inter-detector gaps.Approach. PET detectors using crystal arrays with mixed lutetium yttrium orthosilicate (LYSO) and gadolinium aluminum gallium garnet (GAGG) crystals were developed and evaluated. The crystal arrays consisted of 31 × 31 array of 0.49 × 0.49 × 20 mm³crystals; they were read out by two silicon photomultiplier arrays with pixel sizes of 2 × 2 mm²that were placed at both ends of the crystal arrays. The second or first outermost layer of the LYSO crystals was replaced by GAGG crystals in the two crystal arrays. The two crystal types were identified using a pulse-shape discrimination technique to provide better edge crystal identification.Main results. Using the pulse shape discrimination technique, almost all (except for a few edge) crystals were resolved in the two detectors; high sensitivity was achieved by using the scintillator array and the photodetector with the same areas and achieved high resolution by using crystals with sizes equal to 0.49 × 0.49 × 20 mm³. Energy resolutions of 19.3 ± 1.8% and 18.9 ± 1.5%, depth-of-interaction resolutions of 2.02 ± 0.17 mm and 2.04 ± 0.18 mm, and timing resolutions of 1.6 ± 0.2 ns and 1.5 ± 0.2 ns were achieved by the two detectors, respectively.Significance. In summary, novel three-dimensional high-resolution PET detectors consisting of a mixture of LYSO and GAGG crystals were developed. The detectors significantly improve the detection area with the same photodetectors and thus improve the detection efficiency.

Investigation of a Model-based Time-over-threshold Technique for Phoswich Crystal Discrimination

The best crystal identification (CI) algorithms proposed so far for phoswich detectors are based on adaptive filtering and pulse shape discrimination (PSD). However, these techniques require free running analog to digital converters, which is no longer possible with the ever increasing pixelization of new detectors. We propose to explore the dual-threshold time-over-threshold (ToT) technique, used to measure events energy and time of occurence, as a more robust solution for crystal identification with broad energy windows in phoswich detectors. In this study, phoswich assemblies made of various combinations of LGSO and LYSO scintillators with decay times in the range 30 to 65 ns were investigated for the LabPET II detection front-end. The electronic readout is based on a 4 × 8 APD array where pixels are individually coupled to charge sensitive preamplifiers followed by first order CR-RC shapers with 75 ns peaking time. Crystal identification data were sorted out based on the measurements of likeliness between acquired signals and a time domain model of the analog front-end. Results demonstrate that crystal identification can be successfully performed using a dual-threshold ToT scheme with a discrimination accuracy of 99.1% for LGSO (30 ns)/LGSO (45 ns), 98.1% for LGSO (65 ns)/LYSO (40 ns) and 92.1% for LYSO (32 ns)/LYSO (47 ns), for an energy window of [350-650] keV. Moreover, the method shows a discrimination accuracy >97% for the two first pairs and ~90% for the last one when using a wide energy window of [250-650] keV.

Improving depth-of-interaction resolution in pixellated PET detectors using neural networks

Parallax error is a common issue in high-resolution preclinical positron emission tomography (PET) scanners as well as in clinical scanners that have a long axial field of view (FOV), which increases estimation uncertainty of the annihilation position and therefore degrades the spatial resolution. A way to address this issue is depth-of-interaction (DOI) estimation. In this work we propose two machine learning-based algorithms, a dense and a convolutional neural network (NN), as well as a multiple linear regression (MLR)-based method to estimate DOI in depolished PET detector arrays with single-sided readout. The algorithms were tested on an 8× 8 array of 1.53× 1.53× 15 mm³ crystals and a 4× 4 array of 3.1× 3.1× 15 mm³ crystals, both made of Ce:LYSO scintillators and coupled to a 4× 4 array of 3× 3 mm³ silicon photomultipliers (SiPMs). Using the conventional linear DOI estimation method resulted in an average DOI resolution of 3.76 mm and 3.51 mm FWHM for the 8× 8 and the 4× 4 arrays, respectively. Application of MLR outperformed the conventional method with average DOI resolutions of 3.25 mm and 3.33 mm FWHM, respectively. Using the machine learning approaches further improved the DOI resolution, to an average DOI resolution of 2.99 mm and 3.14 mm FWHM, respectively, and additionally improved the uniformity of the DOI resolution in both arrays. Lastly, preliminary results obtained by using only a section of the crystal array for training showed that the NN-based methods could be used to reduce the number of calibration steps required for each detector array.

Time-over-threshold for pulse shape discrimination in a time-of-flight phoswich PET detector

It is well known that a PET detector capable of measuring both photon time-of-flight (TOF) and depth-of-interaction (DOI) improves the image quality and accuracy. Phoswich designs have been realized in PET detectors to measure DOI for more than a decade. However, PET detectors based on phoswich designs put great demand on the readout circuits, which have to differentiate the pulse shape produced by different crystal layers. A simple pulse shape discrimination approach is required to realize the phoswich designs in a clinical PET scanner, which consists of thousands of scintillation crystal elements. In this work, we studied time-over-threshold (ToT) as a pulse shape parameter for DOI. The energy, timing and DOI performance were evaluated for a phoswich detector design comprising [Formula: see text] mm LYSO:Ce crystal optically coupled to [Formula: see text] mm calcium co-doped LSO:Ce,Ca(0.4%) crystal read out by a silicon photomultiplier (SiPM). A DOI accuracy of 97.2% has been achieved for photopeak events using the proposed time-over-threshold (ToT) processing. The energy resolution without correction for SiPM non-linearity was [Formula: see text]% and [Formula: see text]% FWHM at 511 keV for LYSO and LSO crystal layers, respectively. The coincidence time resolution for photopeak events ranges from 164.6 ps to 183.1 ps FWHM, depending on the layer combinations. The coincidence time resolution for inter-crystal scatter events ranges from 214.6 ps to 418.3 ps FWHM, depending on the energy windows applied. These results show great promises of using ToT for pulse shape discrimination in a TOF phoswich detector since a ToT measurement can be easily implemented in readout electronics.

Reaching 200-ps timing resolution in a time-of-flight and depth-of-interaction positron emission tomography detector using phosphor-coated crystals and high-density silicon photomultipliers

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.

Improving Depth, Energy and Timing Estimation in PET Detectors with Deconvolution and Maximum Likelihood Pulse Shape Discrimination

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.

A combined time-of-flight and depth-of-interaction detector for total-body positron emission tomography

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.

Positron Emission Tomography: Current Challenges and Opportunities for Technological Advances in Clinical and Preclinical Imaging Systems

Positron emission tomography (PET) imaging is based on detecting two time-coincident high-energy photons from the emission of a positron-emitting radioisotope. The physics of the emission, and the detection of the coincident photons, give PET imaging unique capabilities for both very high sensitivity and accurate estimation of the in vivo concentration of the radiotracer. PET imaging has been widely adopted as an important clinical modality for oncological, cardiovascular, and neurological applications. PET imaging has also become an important tool in preclinical studies, particularly for investigating murine models of disease and other small-animal models. However, there are several challenges to using PET imaging systems. These include the fundamental trade-offs between resolution and noise, the quantitative accuracy of the measurements, and integration with X-ray computed tomography and magnetic resonance imaging. In this article, we review how researchers and industry are addressing these challenges.

Characterization of stacked-crystal PET detector designs for measurement of both TOF and DOI

A PET detector with good timing resolution and two-level depth-of-interaction (DOI) discrimination can be constructed using a single-ended readout of scintillator stacks of Lanthanum Bromide (LaBr3), with various Cerium dopant concentrations, including pure Cerium Bromide (CeBr3). The stacked crystal geometry creates a unique signal shape for interactions occurring in each layer, which can be used to identify the DOI, while retaining the inherently good timing properties of LaBr3 and CeBr3. In this work, single pixel elements are used to optimize the choice of scintillator, coupling of layers, and type of photodetector, evaluating the performance using a fast, single-channel photomultiplier tube (PMT) and a single 4 × 4 mm(2) silicon photomultiplier (SiPM). We also introduce a method to quantify and evaluate the DOI discrimination accuracy. From signal shape measurements using fast waveform sampling, we found that in addition to differences in signal rise times, between crystal layers, there were also differences in the signal fall times. A DOI accuracy of 98% was achieved using our classification method for a stacked crystal pair, consisting of a 15 mm long LaBr3(Ce:20%) crystal on top of a 15 mm long CeBr3 crystal, readout using a PMT. A DOI accuracy of 95% was measured with a stack of two, identical, 12 mm long, CeBr3 crystals. The DOI accuracy of this crystal pair was reduced to 91% when using a SiPM for readout. For the stack of two, 12 mm long, CeBr3 crystals, a coincidence timing resolution (average of timing results from the top and bottom layer) of 199 ps was measured using a PMT, and this was improved to 153 ps when using a SiPM. These results show that with stacked LaBr3/CeBr3 scintillators and fast waveform sampling nearly perfect DOI accuracy can be achieved with excellent timing resolution-timing resolution that is only minimally degraded compared to results from a single CeBr3 crystal of comparable length to the stacked crystals. The interface in the stacked crystal geometry itself plays a major role in creating the differences in signal shape and this can be used to construct stacked DOI detectors using the same scintillator type, thereby simplifying and broadening the application of this technique.

Timing properties of phosphor-coated polished LSO crystals

This study investigates a time-of-flight (TOF)-depth-of-interaction (DOI) detector design for positron emission tomography (PET), based on phosphor-coated lutetium oxyorthosilicate (LSO) scintillator crystals coupled to fast single channel photomultiplier tubes. Interaction of the scintillation light with the phosphor coating changes the pulse shape in a depth-dependent manner. 3 × 3 × 10 mm(3) LSO scintillation crystals with polished surfaces were characterized, with and without phosphor coating, to assess DOI capability and timing properties. Two different phosphor coating geometries were studied: coating of the top surface of the crystal, and the top plus half of the crystal sides. There was negligible depth dependency in the decay time when coating only the top surface, however there was a ∼10 ns difference in end-to-end decay time when coating the top plus half of the crystal sides, sufficient to support the use of three DOI bins (3.3 mm DOI bin width). The rise time of the half-coated phosphor crystal was slightly faster at all depths, compared to uncoated crystals, however the signal amplitude was lower. Phosphor coating resulted in depth-dependent photopeak positions with an energy resolution of 13.7%, at a depth of 1 mm, and 15.3%, at a depth of 9 mm, for the half-coated crystal. Uncoated LSO crystals showed no change in photopeak position as a function of depth, with an energy resolution of 10.4%. The head-on coincidence timing resolution (CTR) of two uncoated LSO crystals was 287 ps using constant fraction discrimination for time pick-off. With phosphor coating, the CTR of the top-coated crystal was 314 ps, compared to 384 ps for the half-coated crystal. We demonstrate that the trade-off between timing resolution and DOI resolution can be controlled by the phosphor coating geometry. Here we present preliminary results demonstrating that good DOI resolution can be achieved with only a modest 26% degradation in CTR.

Predicting the timing properties of phosphor-coated scintillators using Monte Carlo light transport simulation

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.