Optimizing light transport in scintillation crystals for time-of-flight PET: an experimental and optical Monte Carlo simulation study

PET System Technology: Theoretical Aspects and Experimental Methodology

Positron emission tomography (PET) imaging provides unique information of the cellular and molecular pathways of disease occurring within the human body, using measurements made from outside the body, which has shown utility in a variety of studies from basic research to clinical applications. This chapter describes some of the most relevant PET system parameters that impact its imaging performance such as 3D spatial, energy, and coincidence timing resolutions and the methodology typically used to evaluate those parameters. In addition, the physical principles underlying PET imaging, PET photon detector technology, and coincidence detection are also described. As a closing remark, the future perspectives of PET imaging and its simultaneous use with anatomical imaging techniques (e.g., computed tomography [CT] and magnetic resonance imaging [MRI]) are outlined.

Calibration method of crosshair light sharing PET detector with TOF and DOI capabilities

Objective. A crosshair light sharing (CLS) PET detector as a TOF-DOI PET detector with high spatial resolution has been developed. To extend that work, a detector calibration method was developed to achieve both higher coincidence resolving time (CRT) and DOI resolution.Approach. The CLS PET detector uses a three-layer reflective material in a two-dimensional crystal array to form a loop structure within a pair of crystals, enabling a CRT of about 300 ps and acquisition of DOI from multi-pixel photon counter (MPPC) output ratios. The crystals were 1.45 × 1.45 × 15 mm3fast LGSO, and the crystal array was optically coupled to an MPPC array. It is important to reduce as many inter-crystal scattering (ICS) events as possible in advance for the accurate detector calibration. DOI information is also expected to improve the CRT because it can estimate the time delay due to the detection depth of crystals.Main results. Using crystal identification and light collection rate of the highest MPPC output reduces the number of ICS events, and CRT is improved by 26%. In addition, CRT is further improved by 13% with a linear correction of time delay as a function of energy. The DOI is ideally estimated from the output ratio of only the MPPC pairs optically coupled to the interacted crystals, which is highly accurate, but the error is large due to light leakage in actual use. The previous method, which also utilizes light leakage to calculate the output ratio, is less accurate, but the error can be reduced. Using the average of the two methods, it is possible to improve the DOI resolution by 12% while maintaining the smaller error.Significance. By applying the developed calibration method, the CLS PET detector achieves the CRT of 251 ps and the DOI resolution of 3.3 mm.

Tracking the same fast-LGSO crystals by changing surface treatments for better coincidence timing resolution in PET

Achieving fast coincidence timing resolution (CTR) is an important issue in clinical time-of-flight positron emission tomography (TOF-PET) to improve the reconstructed image quality. One of the major factors affecting the CTR is the crystal surface treatment, which is often parameterized as surface roughness. However, previous studies on the crystal surface treatment optimization had two limitations of crystal-by-crystal variation and worse CTR over 200 ps. Here, we report the effects of the crystal surface treatment on the performance of a 20 mm long fast-LGSO crystal based TOF detector by tracking the same crystals in the sub-180 ps CTR regime. The light collection efficiency (LCE), energy resolution (ER) and CTR of the TOF detector were evaluated with six different crystal surface treatments of chemically polished (C.P), C.P half side roughened (1/2S) treatment, and then the C.P one side roughened (1S) treatment, mechanically polished (M.P) treatment, M.P 1/2S treatment, and M.P 1S treatment. The four lateral surfaces of each crystal were wrapped by using enhanced specular reflector film while the top surface was covered by using Teflon tape. The bottom surface of the crystal was optically coupled to a silicon photomultiplier. The timing and energy signals were extracted by using a custom-made high-frequency readout circuit, and then digitized by using a waveform digitizer. All the experimental conditions were same except the crystal surface treatment. Among the six different crystal surface treatments, the M.P 1S would be the optimal crystal surface treatment which balanced enhancements in the CTR (165 ± 3 ps) and ER (10.5 ± 0.5%). Unlike the M.P 1S, the C.P 1S did not enhance the CTR and ER. Hence, the C.P without roughening would be the second-best optimal crystal surface treatment which balanced the CTR (169 ± 3 ps) and ER (10.5 ± 0.5%).

Effect of detector geometry and surface finish on Cerenkov based time estimation in monolithic BGO detectors

Objective.Time-of-flight positron emission tomography based on bismuth germanate (BGO) detectors is made possible due to fast emission of Cerenkov light. Only around 17 Cerenkov photons are produced per 511 keV photoelectric event, making high photon collection efficiency crucial for obtaining good time-of-flight capabilities. In this study, we investigate how different lateral and back surface finishes affect the photon collection efficiency and Cerenkov based timing performance in monolithic BGO.Approach.The study is performed using GATE for gamma and optical photon modeling, with surface reflections of photons simulated by the LUT Davis model. We compare for different detector configurations (regarding size and surface finishes) the photon collection efficiency, detection delays of the first few optical photons and coincidence time resolution estimations obtained by modeling the SiPM signals and performing leading edge discrimination. An additional comparison is made to LYSO scintillators and pixelated detectors.Main results.Although Cerenkov photon emission is directional, many high incidence angle Cerenkov photons are emitted due to electron scattering in the crystal. Substituting a polished back (photodetector side) surface for a rough surface increases the collection efficiency of these high angle of incidence photons. Results show that for a monolithic 50 × 50 × 12 mm³BGO detector with reflective side surfaces, this leads to an overall increase in photon collection efficiency of 34%. Cerenkov photon collection efficiency is also improved, resulting in a reduction of the photon detection delays (and the variation therein) of the first few optical photons. This leads to a better coincidence time resolution, primarily achieved by a shortening of the tails in the time-of-flight kernel, with an 18% reduction in full width at tenth maximum.Significance.This study shows the importance of the photon collection efficiency for timing performance in Cerenkov based monolithic detectors, and how it can be improved with different surface finishes.

Optimization of GFAG crystal surface treatment for SiPM based TOF PET detector

Coincidence timing resolution (CTR) is an important parameter in clinical positron emission tomography (PET) scanners to increase the signal-to-noise ratio of PET images by using time-of-flight (TOF) information. Lutetium (Lu) based scintillators are often used for TOF-PET systems. However, the self-radiation of Lu-based scintillators may influence the image quality for ultra-low activity PET imaging. Recently, a gadolinium fine aluminum gallate (Ce:GFAG) scintillation crystal that features a fast decay time (~55 ns) and no self-radiation was developed. The present study aimed at optimizing the GFAG crystal surface treatment to enhance both CTR and energy resolution (ER). The TOF-PET detector consisted of a GFAG crystal (3.0 × 3.0 × 20 mm3) and a SiPM with an effective area of 3.0 × 3.0 mm2. The timing and energy signals were extracted using a high-frequency SiPM readout circuit and then were digitized using a CAMAC DAQ system. The CTR and ER were evaluated with nine different crystal surface treatments such as partial saw-cut and chemical polishing and the 1-side saw-cut was the best choice among the treatments. The respective CTR and ER of 202±2 ps and 9.5±0.1% were obtained with the 1-side saw-cut; the other 5-side mechanically polished GFAG crystals had respective values which were 18 ps (9.0%) and 1.3% better than those of the all-side mechanically polished GFAG crystal. The chemically polished GFAG crystals also offered enhanced CTR and ER of about 17 ps (8.2%) and 2.1%, respectively, over the mechanically polished GFAG crystals.

Study of optical reflectors for a 100ps coincidence time resolution TOF-PET detector design

Positron Emission Tomography (PET) reconstructed image signal-to-noise ratio (SNR) can be improved by including the 511 keV photon pair coincidence time-of-flight (TOF) information. The degree of SNR improvement from this TOF capability depends on the coincidence time resolution (CTR) of the PET system, which is essentially the variation in photon arrival time differences over all coincident photon pairs detected for a point positron source placed at the system center. The CTR is determined by several factors including the intrinsic properties of the scintillation crystals and photodetectors, crystal-to-photodetector coupling configurations, reflective materials, and the electronic readout configuration scheme. The goal of the present work is to build a novel TOF-PET system with 100 picoseconds (ps) CTR, which provides an additional factor of 1.5-2.0 improvement in reconstructed image SNR compared to state-of-the-art TOF-PET systems which achieve 225-400 ps CTR. A critical parameter to understand is the optical reflector's influence on scintillation light collection and transit time variations to the photodetector. To study the effects of the reflector covering the scintillation crystal element on CTR, we have tested the performance of four different reflector materials: Enhanced Specular Reflector (ESR) -coupled with air or optical grease to the scintillator; Teflon tape; BaSO4paint alone or mixed with epoxy; and TiO2paint. For the experimental set-up, we made use of 3 × 3 × 10 mm3fast-LGSO:Ce scintillation crystal elements coupled to an array of silicon photomultipliers (SiPMs) using a novel 'side-readout' configuration that has proven to have lower variations in scintillation light collection efficiency and transit time to the photodetector.Results: show CTR values of 102.0 ± 0.8, 100.2 ± 1.2, 97.3 ± 1.8 and 95.0 ± 1.0 ps full-width-half-maximum (FWHM) with non-calibrated energy resolutions of 10.2 ± 1.8, 9.9 ± 1.2, 7.9 ± 1.2, and 8.6 ± 1.7% FWHM for the Teflon, ESR (without grease), BaSO4(without epoxy) and TiO2paint treatments, respectively.

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.

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.

Technical Note: Standalone application to generate custom reflectance Look-Up Table for advanced optical Monte Carlo simulation in GATE/Geant4

PURPOSE

The need for high-fidelity modeling of radiation detectors to perform reliable detector performance optimization using Monte Carlo simulations requires to accurately simulate the light transport in the scintillator and the light collection by the photodetector. In this work, we implement our well-validated crystal reflectance model computed from three-dimensional (3D) crystal surface measurement in a standalone open-source application to allow researchers to generate fully customized crystal reflectance look-up-tables (LUTs) to be used in optical Monte Carlo simulation.

METHODS

The LUTDavisModel application can be installed in a few minutes on Windows, macOS, and Linux, using 26 MB of space. MATLAB Runtime is required and is automatically installed with the application. The core algorithm has been previously validated experimentally and implemented in GATE v8.0. The standalone is divided into five panels, each of which performing a specific task: generate LUTs from a combination of surface type, scintillator, and coupling medium available in the database (such as LSO or BGO) or custom; compute LUTs with the reflectors available and custom coupling thickness; create a mixture of coupling media to account for possible defects in the optical coupling; plot precomputed LUTs for visual comparison. Tooltips and errors/warnings facilitate the navigation. The reported computational times were obtained with an Intel Core i7 MacBook Pro.

RESULTS

LUTs can be generated with computational time ranging from a few minutes to several hours depending on the selected surface, sampling, and computational power. A longer time is needed when using rough surfaces and thick coupling media (hundreds of μ m ) due to increased photon tracking.

CONCLUSIONS

We developed a user-friendly standalone application to generate LUTs that can be used inside GATE Monte Carlo simulations. It can be easily downloaded, installed, and used. Future optimizations will expand the database, decrease the computational time through greater parallelization, and include the generation of LUTs to study Cerenkov photons transport.

A layered single-side readout depth of interaction time-of-flight-PET detector

We are exploring a scintillator-based PET detector with potential of high sensitivity, depth of interaction (DOI) capability, and timing resolution, with single-side readout. Our design combines two previous concepts: (1) multiple scintillator arrays stacked with relative offset, yielding inherent DOI information, but good timing performance has not been demonstrated with conventional light sharing readout. (2) Single crystal array with one-to-one coupling to the photodetector, showing superior timing performance compared to its light sharing counterparts, but lacks DOI. The combination, where the first layer of a staggered design is coupled one-to-one to a photodetector array, may provide both DOI and timing resolution and this concept is here evaluated through light transport simulations. Results show that: (1) unpolished crystal pixels in the staggered configuration yield better performance across all metrics compared to polished pixels, regardless of readout scheme. (2) One-to-one readout of the first layer allows for accurate DOI extraction using a single threshold. The number of multi pixel photon counter (MPPC) pixels with signal amplitudes exceeding the threshold corresponds to the interaction layer. This approach was not possible with conventional light sharing readout. (3) With a threshold of 2 optical photons, the layered approach with one-to-one coupled first layer improves timing close to the MPPC compared to the conventional one-to-one coupling non-DOI detector, due to effectively reduced crystal thickness. Single detector timing resolution values of 91, 127, 151 and 164 ps were observed per layer in the 4-layer design, to be compared to 148 ps for the single array with one-to-one coupling. (4) For the layered design with light sharing readout, timing improves with increased MPPC pixel size due to higher signal per channel. In conclusion, the combination of straightforward DOI determination, good timing performance, and relatively simple design makes the proposed concept promising for DOI-Time-of-Flight PET detectors.

Experimental validation of the ANTS2 code for modelling optical photon transport in monolithic LYSO crystals

In this work the scintillation energy spectra originating from the background radioactivity from polished monolithic lutetium yttrium oxyorthosilicate coupled to position-sensitive silicon photomultipliers (SiPM) was studied using the open source Monte Carlo simulation package ANTS2. Two crystal sizes, fully and partially covering the photosensor area, three surface crystal wrappings (black, specular or diffuse) and the full signal formation process in the photosensor were considered. The simulation results were validated with experimental data acquired under the same geometric and detector operating conditions. In all cases ANTS2 simulated spectra have very good agreement with experimental results, reproducing the expected shape, with correct onset and end at 88 and 1190 keV, respectively, as well as sharp edges at the reference energies of 88, 88 + 202, 88 + 307 and 88 + 202 + 307 keV. The normalized root-mean square error between simulated and measured spectra varied between 4.3% and 10.4%.

Use of non-Gaussian time-of-flight kernels for image reconstruction of Monte Carlo simulated data of ultra-fast PET scanners

Introduction

Time-of-flight (TOF) positron emission tomography (PET) scanners can provide significant benefits by improving the noise properties of reconstructed images. In order to achieve this, the timing response of the scanner needs to be modelled as part of the reconstruction process. This is currently achieved using Gaussian TOF kernels. However, the timing measurements do not necessarily follow a Gaussian distribution. In ultra-fast timing resolutions, the depth of interaction of the γ-photon and the photon travel spread (PTS) in the crystal volume become increasingly significant factors for the timing performance. The PTS of a single photon can be approximated better by a truncated exponential distribution. Therefore, we computed the corresponding TOF kernel as a modified Laplace distribution for long crystals. The obtained (CTR) kernels could be more appropriate to model the joint probability of the two in-coincidenceγ-photons. In this paper, we investigate the impact of using a CTR kernel vs. Gaussian kernels in TOF reconstruction using Monte Carlo generated data.

Materials and methods

The geometry and physics of a PET scanner with two timing configurations, (a) idealised timing resolution, in which only the PTS contributed in the CTR, and (b) with a range of ultra-fast timings, were simulated. In order to assess the role of the crystal thickness, different crystal lengths were considered. The evaluation took place in terms of Kullback–Leibler (K-L) distance between the proposed model and the simulated timing response, contrast recovery (CRC) and spatial resolution. The reconstructions were performed using STIR image reconstruction toolbox.

Results

Results for the idealised scanner showed that the CTR kernel was in excellent agreement with the simulated time differences. In terms of K-L distance outperformed the a fitted normal distribution for all tested crystal sizes. In the case of the ultra-fast configurations, a convolution kernel between the CTR and a Gaussian showed the best agreement with the simulated data below 40 ps timing resolution. In terms of CRC, the CTR kernel demonstrated improvements, with values that ranged up to 3.8% better CRC for the thickest crystal. In terms of spatial resolution, evaluated at the 60th iteration, the use of CTR kernel showed a modest improvement of the peek-to-valley ratios up to 1% for the 10-mm crystal, while for larger crystals, a clear trend was not observed. In addition, we showed that edge artefacts can appear in the reconstructed images when the timing kernel used for the reconstruction is not carefully optimised. Further iterations, can help improve the edge artefacts.

Monte Carlo Optical Simulations of a Small FoV Gamma Camera. Effect of Scintillator Thicknesses and Septa Materials

Optical Monte Carlo simulations have been extensively used for the accurate modeling of light transport in scintillators for the improvement of detector designs. In the present work, a GATE Monte Carlo toolkit was used to study the effect of scintillator thicknesses and septa materials in the performance parameters evaluation of a commercially available small animal gamma-optical camera, named “γ-eye”. Firstly, the simulated γ-eye system was validated against experimental data. Then, part of the validated camera was modeled defining all of the optical properties by means of the UNIFIED model of GATE. Different CsI:Na scintillator crystals with varying thicknesses (from 4 mm up to 6 mm) and different reflector (septa) materials were simulated and compared in terms of sensitivity, light output and spatial resolution. Results have demonstrated the reliability of the model and indicate that the thicker crystal array presents higher sensitivity values, but degraded spatial resolution properties. Moreover, the use of black tape around crystals leads to an improvement in spatial resolution values compared to a standard white reflector material.

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.

Simulation study of light transport in laser-processed LYSO:Ce detectors with single-side readout

A tightly focused pulsed laser beam can locally modify the crystal structure inside the bulk of a scintillator. The result is incorporation of so-called optical barriers with a refractive index different from that of the crystal bulk, that can be used to redirect the scintillation light and control the light spread in the detector. We here systematically study the scintillation light transport in detectors fabricated using the laser induced optical barrier technique, and objectively compare their potential performance characteristics with those of the two mainstream detector types: monolithic and mechanically pixelated arrays. Among countless optical barrier patterns, we explore barriers arranged in a pixel-like pattern extending all-the-way or half-way through a 20 mm thick LYSO:Ce crystal. We analyze the performance of the detectors coupled to MPPC arrays, in terms of light response functions, flood maps, line profiles, and light collection efficiency. Our results show that laser-processed detectors with both barrier patterns constitute a new detector category with a behavior between that of the two standard detector types. Results show that when the barrier-crystal interface is smooth, no DOI information can be obtained regardless of barrier refractive index (RI). However, with a rough barrier-crystal interface we can extract multiple levels of DOI. Lower barrier RI results in larger light confinement, leading to better transverse resolution. Furthermore we see that the laser-processed crystals have the potential to increase the light collection efficiency, which could lead to improved energy resolution and potentially better timing resolution due to higher signals. For a laser-processed detector with smooth barrier-crystal interfaces the light collection efficiency is simulated to  >42%, and for rough interfaces  >73%. The corresponding numbers for a monolithic crystal is 39% with polished surfaces, and 71% with rough surfaces, and for a mechanically pixelated array 35% with polished pixel surfaces and 59% with rough surfaces.

Modelling the transport of optical photons in scintillation detectors for diagnostic and radiotherapy imaging

Computational modelling of radiation transport can enhance the understanding of the relative importance of individual processes involved in imaging systems. Modelling is a powerful tool for improving detector designs in ways that are impractical or impossible to achieve through experimental measurements. Modelling of light transport in scintillation detectors used in radiology and radiotherapy imaging that rely on the detection of visible light plays an increasingly important role in detector design. Historically, researchers have invested heavily in modelling the transport of ionizing radiation while light transport is often ignored or coarsely modelled. Due to the complexity of existing light transport simulation tools and the breadth of custom codes developed by users, light transport studies are seldom fully exploited and have not reached their full potential. This topical review aims at providing an overview of the methods employed in freely available and other described optical Monte Carlo packages and analytical models and discussing their respective advantages and limitations. In particular, applications of optical transport modelling in nuclear medicine, diagnostic and radiotherapy imaging are described. A discussion on the evolution of these modelling tools into future developments and applications is presented.

An integrated model of scintillator-reflector properties for advanced simulations of optical transport

Accurately modeling the light transport in scintillation detectors is essential to design new detectors for nuclear medicine or high energy physics. Optical models implemented in software such as Geant4 and GATE suffer from important limitations that we addressed by implementing a new approach in which the crystal reflectance was computed from 3D surface measurements. The reflectance was saved in a look-up-table (LUT) then used in Monte Carlo simulation to determine the fate of optical photons. Our previous work using this approach demonstrated excellent agreement with experimental characterization of crystal light output in a limited configuration, i.e. when using no reflector. As scintillators are generally encapsulated in a reflector, it is essential to include the crystal-reflector interface in the LUT. Here we develop a new LUT computation and apply it to several reflector types. A second LUT that contains transmittance data is also saved to enable modeling of optical crosstalk. LUTs have been computed for rough and polished crystals coupled to a Lambertian (e.g. Teflon tape) or a specular reflector (e.g. ESR) using air or optical grease, and the light output was computed using a custom Monte Carlo code. 3  ×  3  ×  20 mm³ lutetium oxyorthosilicate crystals were prepared using these combinations, and the light output was measured experimentally at different irradiation depths. For all reflector and surface finish combinations, the measured and simulated light output showed very good agreement. The behavior of optical photons at the interface crystal-reflector was studied using these simulations, and results highlighted the large difference in optical properties between rough and polished crystals, and Lambertian and specular reflectors. These simulations also showed how the travel path of individual scintillation photons was affected by the reflector and surface finish. The ultimate goal of this work is to implement this model in Geant4 and GATE, and provide a database of scintillators combined with a variety of reflectors.

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.