Timing, Energy, and 3-D Spatial Resolution of the BING PET Detector Module

Abstract

We evaluated the 3D spatial, energy, and timing resolution of the Brain (or Breast)-Initiative Next-Generation (BING) PET detector.

The BING detector is an array of 1-mm-thick slats of LYSO scintillator with lapped specular-reflective faces (15-mm by 52-mm) that are stacked together and oriented with their long-narrow edges normal to the imaging field of view. Interaction positions are determined from the signals of silicon-photomultiplier (SiPM) arrays placed on the entrance (top) and exit (bottom) faces. The SiPM arrays are offset to determine the slat of interaction (SOI) without requiring any optical light sharing between slats. Maximum likelihood 2D location within the SOI is determined using the sensor signals. Interaction time is determined with a modified first-optical-photon pickoff method. Performance of the BING detector was measured as a function of position using a sideways coincidence-collimated beam.

Slats were accurately identified, with an effective tangential detector resolution of 1 mm. Average resolutions (and ranges) are: 0.96 mm (0.85 mm to 1.11 mm) for lateral (axial) detector resolution, 1.6 mm (1.0 mm to 2.1 mm) for depth resolution, 13.6% (12.7% to 16.0%) for energy resolution, and 317 ps (241 ps to 404 ps) for coincidence timing resolution.

Initial spatial and timing resolution results demonstrated that the BING detector can be effective in a small field-of view (e.g., brain or breast) PET system.

I. Introduction

The overall goal of this research is to develop positron emission tomography (PET) detector technology to support imaging at spatial and temporal resolutions currently not achievable with clinical systems. Initial uses are application-specific or dedicated brain and breast imaging systems. The desired PET detector performance requirements are:

• ≤ 1 mm intrinsic detector spatial resolution,

• ≤ 2 mm continuous depth (DOI) positioning

• ≤ 100 ps PET coincidence timing resolution

• ≥ 15 mm thick scintillator detectors

While PET detector modules using discrete crystal arrays have been designed that achieve one or two of these performance metrics, no practical detector module has been designed that attains all of them [1, 2]. However, all the above requirements, plus MRI compatibility, are needed to impactfully advance neuro-PET imaging with dual-mode PET/MRI scanners.

Over the last 20 years there has been a significant amount of effort in the development of monolithic crystal PET detector modules because of their potential for outstanding intrinsic spatial resolution, depth of interaction positioning and possibly lower cost than detector modules using discrete crystal arrays with similar three dimensional (3D) positioning resolution characteristics [3, 4, 5, 6, 7, 8, 9, 10, 11]. About 10 years ago a few groups began to investigate slat-based or semi-monolithic PET detector designs as an alternative to fully monolithic crystal designs [12, 13, 14].

One significant advantage of slat-based detectors is that they reduce the area with deleterious effects to intrinsic spatial resolution that occur near the edge of monolithic crystal detectors (i.e., resolution blurring and positioning bias). Using thin slats, weighted centroid positioning can be used along one axis of the detector to mitigate edge effects. We have also previously reported on a novel slat-shaped scintillation detector with single-sided readout that used light spread along the slat to resolve depth of interaction [15, 16]. One mm intrinsic detector spatial resolution was achieved and better than 3 mm DOI positioning using single-sided readout for slat detectors with 10 mm thick detectors and for slats as thin as 0.44 mm. Depth resolution in that design benefited from diffuse and slightly (~1%) absorptive side- and rear-surface treatments.

Another advantage of slat-based detector geometry is the expected improvement in timing performance due to the concentration of light over fewer photosensors compared to a monolithic detector. However, our prior work [15, 16] was not optimized for timing performance. Reconsidering this single-sided readout slat design with the goal of improving timing resolution, we added photosensors to the entrance surface and changed the side surface treatment to be specular. Using two-sided readout minimizes the pathlength each light photon needs to travel before being detected by a photosensor versus single-sided readout. Further, using a specularly polished surface combined with dual-sided readout should also increase the amount of light collected for each event, which we hope in turn improves event timing resolution. Normally when using dual-sided readout, the side surfaces of the crystal are roughened to promote some light loss along the length of the crystal. The ratio of light collected from the front versus back sensors is then used to estimate DOI. In contrast, for our design, DOI is estimated from the light spread along the long axis of the slat detector, so we used specularly polished side surfaces to improve light collection efficiency and hopefully timing resolution.

Further, our previous work also showed that by optically coupling the axial ends of the detector modules (preferably with a high-index optical adhesive such as Cargille Meltmount^™ 1.704), enough light is shared to enable accurate positioning across the physical interface [17, 18]. Therefore, the axial field of view of a neuroPET or breast-PET imaging system using our new slat detector design could be made arbitrarily long without breaks/gaps in the detector system. Just like monolithic crystal PET detector designs, the number of groups investigating slat-based or “semi-monolithic” PET detector designs has increased in recent years [12, 13, 14, 15, 16, 19, 20, 21, 22, 23] [24, 25, 26] . It is worth noting similarities and differences of the detector design and processing in [14] compared to the one we are reporting here; we expand upon this comparison in our Discussion section. Each of these designs are able to achieve very good three-dimensional positioning resolution within the crystal array. In our current work and the work by Barrio [23], noteworthy time-of-flight level coincidence timing resolution is also achieved. We report on the performance of our current design, which we term the Brain (or Breast)-Initiative Next-Generation (BING) detector.

II. Materials and Methods

Detector

An illustration of the BING detector and its potential arrangement in a cylindrical PET system is illustrated in Figure 1. Figure 2 is a photograph and diagram of the BING detector coupled to PETsys^® TOFPET2 front-end data readout modules [27]. The prototype detector design consists of twelve LYSO scintillator slats (52-mm by 15-mm by 1.0 mm) with 65-μm-thick ESR mirror film by 3M^® between and on the sides of the slats. The slats were specularly polished on all sides and the slat crystal assembly was held together with ESR reflectors between them using about 5-μm thickness of optical adhesive per side. The slat pitch measured 1.07 mm, or 3 slats per row of the SiPM array. The narrow end of the 12-slat assembly was covered with four layers of 0.1mm-thick Teflon tape.

Figure 1.

Illustration of a cylindrical PET scanner comprised of BING semi-monolithic slat detector units. The BING detector is comprised of slats of LYSO with offset SiPM arrays on the top (entrance) and bottom (exit) surfaces. Optical isolation between slats is obtained with 65 μm thick sheets of mirror film.

Figure 2.

Left: End-view photograph of BING scintillator sandwiched between two SiPM arrays. Right: End-view and side-view diagrams of the same BING scintillator detector. The SiPM arrays were readout using PETsys TOFPET2 front-end data acquisition modules.

As depicted in Figures 1 and 2, two 5-by-16 silicon-photomultiplier (SiPM) arrays (each a subset of two adjacent Hamamatsu^® S14161–3050HS-08 devices) were attached to the long-narrow edges of the slats on both sides. Optical coupling was achieved with BC-630 optical grease from Saint Gobain^®. Each SiPM pixel has a 3-mm by 3-mm active area and a 3.2-mm center-to-center spacing between adjacent pixels. As shown in Figure 2, the top and bottom SiPM arrays were laterally offset by one slat (i.e., one third of the 3.2 mm pixel pitch). This arrangement gives each crystal slat a unique combination of top and bottom sensor rows that distinguish its response from others. Thus, some slats are viewed by 32 sensors (i.e., 16 sensors on the entrance surface and 16 sensors on the exiting surface). Other slats are viewed by 48 sensors (i.e., 16 sensors on the entrance or exit surface and 32 sensors (i.e., two rows) on the opposite surface). The assembly was held together using a 3D printed plastic frame specified with 0.1 mm precision.

Detector Electronics and Data Acquisition:

Signals and trigger times were read out for every channel independently using TOFPET2 data-acquisition electronics by PETsys. A subset of two 128-channel front end modules (FEMs) were used to readout the signals from the BING detector prototype (80 sensor channels for each side); unused sensors were masked with Tedlar^® Polyvinyl Fluoride film and their readout channels were suppressed in software. A third FEM was used to acquire amplitude and timing signals from a single-pixel coincidence detector. This single pixel is a 3 mm × 3 mm polished LYSO crystal, 5 mm height, wrapped in 4 layers of white Teflon tape with signal readout on the opposing side using a KETEK^® PM3315-WB-B0 SiPM array. We chose this single-pixel reference sensor because it was conveniently available from PETsys as part of their evaluation kit for TOFPET2. We selected bias and discriminator thresholds [27] for this single-pixel coincidence detector to optimize coincidence timing resolution (CTR) of two identical single-pixel detectors (measured to be 201.5 ps).

CTR optimization of bias and discriminator threshold settings were performed as follows. Bias was initially set to 29.4V (+4.5V over breakdown as recommended by PETsys) and the E discriminator threshold was fixed at 15 Analog-to-Digital Units (ADU) while the T1 and T2 discriminator thresholds were scanned from 3 to 25 ADU in steps of 1 ADU. Note that the ADU scales differ for E, T1 and T2 and are set during the front-end module (FEM) calibration. Initial T1 and T2 threshold were selected to minimizing CTR. Next, bias was scanned in steps of 0.5V between +2.0V and +5.5V over breakdown. We then repeated the T1 and T2 scan at the optimal bias setting. Finally, we lowered the E threshold to maximize count rate without degrading CTR.

Our final settings for the KETEK reference detector that minimized CTR were 29.4V bias (+4.5V over breakdown), 11 ADU for the T1 threshold, 15 ADU for the T2 threshold, and 9 ADU for E threshold. A similar procedure was used to optimize bias and threshold settings for the Hamamatsu-based BING detector while holding the settings for the KETEK reference detector fixed to their optimized values above. Settings for the Hamamatsu-based BING detector were +4.0V over breakdown (breakdown varied from 38.5V to 38.8V for the four arrays used), 5 ADU for the T1 threshold, 13 ADU for the T2 threshold, and 9 ADU for E threshold.

Experimental Setup and Detector Calibration

Electronic collimation was used to selectively measure DOI. The coincidence detector was placed on a two-dimensional (2D) translation stage 120 mm from the side of the BING detector, i.e., perpendicular to the slat faces, as shown in Figure 3. A 40 μCi, 0.25 mm diameter Na-22 point source was placed in line between the two detectors, 10 mm from the entrance side of the BING detector’s crystal array. The point source was coupled to the coincidence detector unit assembly, allowing the coincidence-collimated gamma-ray beam to be scanned in 2D over the 52 mm by 15 mm side of the slat detector assembly. Although the beam shape is determined by this electronic-collimation setup, a 4-mm thick tungsten plate with 2-mm bore hole was placed between the source and BING detector (centered on the electronically collimated beam) to reduce event pileup.

Figure 3.

Top: Arrangement of calibration setup for BING detector. Bottom: photograph of experimental setup. The source-to-coincidence detector distance was increased to 12 cm for calibration.

Based upon the geometry of the setup, the beam width was determined to be 0.4 mm in diameter for the nearest slat and 0.7 mm for the farthest slat. However, we expect small-angle inter-slat scatter to affect event distribution in the slats further from the side that the beam enters. We therefore characterized performance in the first 4 of 12 slats. Spatial resolution is computed as the full width at half maximum and then corrected for beam size, assuming beam size adds to the estimate distribution in quadrature:

$$FWH{M}_k^{\prime }=\sqrt{FWH{M}_k^2-W_{\mathit{\text{beam}}}{}^2}\text{, }$$ (1)

where k = x or z, and W_beam = 0.4 + 0.03N_slat

The detector assemblies were operated in a temperature controlled dark box with a nominal operating temperature of 15° C. The FEM temperature sensor consistently reported at 18.5 °C ±0.2 °C during acquisition.

After edge alignment, the coincidence-collimated beam was scanned every 1.07 mm along the detector length and every 1.00 mm in depth to collect an average of 250k coincidence events for each of 720 beam positions at an average rate of 80 coincidence counts per second. To allow for intermediate analysis and to evaluate sensor-response drift, data was acquired as a series of 52 raster scans of 1-minute dwell time at each beam position (26 days total). Half of the data was used for calibration and the other half for performance evaluation. The energy threshold per channel was set to trigger at 9 ADU (about 1 detected photoelectron [27]) to allow most channels directly coupled to a slat to report for each detected event (i.e., 32 or 48 depending on slat-to-sensor configuration).

Event Positioning

Determination of the slat of interaction was performed by partitioning the Centroid-position distribution in the inter-slat direction (Y-axis). 2D positioning within a slat along length (X-axis) and depth (Z-axis) was performed by maximum-likelihood estimation (MLE) assuming an independently distributed Normal signal model [28].

Detector response statistics used for intra-slat maximum-likelihood positioning were computed for photopeak events using a ±17% energy window about the peak for each beam and slat position. We chose this lower energy threshold, which is half way between the photopeak and back-scatter peak, because our measured energy resolution (see Figure 12 in Results) is 16% or better over the full detector. To mitigate the effect of inter-slat scatter, we also apply a 2D-contour filter on the first and second moments of the signal’s spatial distribution along the inter-slat direction (Y-axis). An example of this filter is shown later in the Bottom of Figure 5 of the Results. A similar scatter filter was used for timing calibration, discussed below. Spatial performance is reported in terms of the Full Width at Half Maximum (FWHM).

Figure 12.

(Top) Energy spectra for a few representative beam positions, and (Bottom) Energy resolution vs beam position

Figure 5.

Slat identification for beam position (X, Z) = (−4.8 mm, 7.5 mm). Top: Signal centroid distribution along inter-slat direction (Y-axis). Bottom: Energy-windowed 2D histogram of first and second moments of signal distribution with red contours indicating filters for identifying single-interaction events in each slat.

Timing Resolution

Event times were estimated with respect to a coincidence detector using an energy-weighted average of the first several sensors reporting. We uniformly varied the number of sensor times averaged to determine the optimal average timing performance over all 3D interaction positions (2D beam position and slat number). Sensor times were first corrected for skew and energy-dependence (time walk) before computing their energy-weighted average [29].

The relative skew of timing for each BING sensor was computed as the peak time delay with respect to the reference sensor using side-illuminated coincidence collimated interactions. The coincidence-collimated beam was stepped in 3.2 mm increments along the long axis of the BING detector, with the beam positioned over the center and 1.5 mm above each BING sensor. Events were partitioned by slat and only interactions in the slat centered over the BING sensor were used for computing the skew correction. A tight energy window (5%) about the photopeak was used during skew calibration for both the BING and coincidence detectors. We also rejected inter-crystal scatter events as described in the event-positioning methods above.

Energy dependence of trigger-time delay (time walk) of the i^th sensor, Δt_walk,i, was calibrated by non-linear Least Squares fitting of the coincidence time delay as a function of the energy, E, measured by the sensor:

$$\text{Δ}{t}_{\mathit{\text{walk}},i}=a_{w,i}{E}^{b_{w,i}}+c_{w,i},$$ (2)

where the coefficients a_w,i, and c_w,i, and the exponent b_w,i are fit parameters for the i^th sensor.

As with the skew correction, only interactions over the given BING sensor were used for the time walk calibration. Time walk of the BING and coincidence detectors were performed separately, using a tight energy window (±5%) about the photopeak for whichever BING sensor was considered the reference sensor. For time walk calibration of the coincidence detector, this process was repeated using each of the BING detectors as a reference sensor and resulting fit parameters were averaged.

Due to low count statistics and a timing distribution that is more-sharply peaked than a Gaussian distribution, we did not find that reporting FWHM of the actual distribution or a Gaussian fit of the actual distribution was representative of the actual timing performance. Therefore, we computed timing performance using the width of the central 76% interval (from the 12^th to the 88^th percentiles); an example of this measured interval is given on the top of Figure 10. This percentile distribution is what we would expect the Full Width at Half Maximum (FWHM) to give for a Gaussian distribution. Detector-timing resolution (DTR) of the BING detector was then computed from the measured coincidence timing resolution (CTR) by subtracting off in quadrature the DTR of the 3-by-3-by-5 mm³ single-pixel coincidence detector (DTR₁), which we measure to be 142ps.

Figure 10.

(Top) Example of measured coincidence-timing distribution versus number of sensors averaged for the central beam position (X=0 mm and Z=7.5. mm) in slat 0. (Bottom) CTR averaged across all beam positions versus number of photosensors used for energy-weighted coincidence-time average.

$$DT{R}_{\mathit{\text{BING}}}=\sqrt{CT{R}^2-DT{R_1}^2}$$ (3)

Energy Resolution

The photopeak for each slat at each beam position was identified and scaled to 511keV. The percent energy resolution for the composite spectrum of all slats at each beam position was then computed as the FWHM divided by the peak position. From simulation of the light spread in this geometry, we expect the photon density to be low enough to make energy-saturation correction unnecessary.

III. Results

Detector Calibration

An illustrative set of the 2D mean detector response functions (MDRF) for each SiPM sensor directly coupled to the first LYSO slat crystal is shown in Figure 4. Each horizontal rectangular box corresponds to the mean of the signal response for a SiPM sensor viewing the crystal slat. There is a single row of 16 SiPM sensors directly coupled to either the entrance or exit surfaces. The left column of rectangular boxes corresponds to the MDRF of the 16 SiPM sensors coupled to the entrance surface of the slat crystal. The right column of rectangular boxes corresponds to the MDRF of the 16 SiPM sensors coupled to the exit face of the slat crystal.

Figure 4.

Mean detector response of the first LYSO slat versus position for the 32 sensors over this slat. Left column: Entrance-side sensors. Right column: Exit-side sensors.

Looking at each of the rectangular boxes in Figure 4, the width of the box corresponds to the length of the crystal slat (i.e., 52 mm long). The height of the box corresponds to the height of each crystal slat (i.e., 15 mm). The top side of each box corresponds to the entrance surface of the detector. The two-dimensional MDRF was mapped out by scanning a coincidence-collimated gamma-ray beam in 2D over the 52 mm by 15 mm side of the slat detector assembly.

Considering the first box in the top left of Figure 4, when the interactions are occurring near the upper corner of the crystal slat (i.e., 0–3 along the long axis of the slat and at the entrance surface of the slat) the mean response function is around 80. As the interactions occur in the same position along the length of the slat but further from the entrance surface the MDRF decreases to about 30. For interactions further along the length of the slat (i.e., from 5–52 mm) the mean response for the first SiPM sensor is less than 20.

Slat Decoding

The slat decoding characteristics of the BING detector module are illustrated in Figure 5. The top plot shows the histogram of counts versus the value of the weighted centroid for the detected signals. The black curve is for all events without any energy windowing applied. The blue curve has a ±17% energy window applied to the summed energy of all SiPM channels. In looking at the blue curve one notes that there are events that are positioned between the peaks associated with the slats. We think that those events represent events that first Compton scatter in the crystal array before being photoelectrically absorbed in a different slat crystal. These inter-crystal scatter or multi-interaction events will reduce the effective spatial resolution of the detector module. The red line in the upper plot is the profile that we get if we impose both an energy filter and a contour filter on the collected data. The contour filter that we used is illustrated in the bottom plot. The bottom plot is the energy-windowed 2D histogram of the first and second moments of the signal distribution of the collected data. We observe clusters in this 2D histogram that represent events which localized in each slat. Events involving interactions in multiple slats would be positioned between these peaks and/or have a larger 2^nd moment. Because we are considering only photopeak-windowed events, we consider clusters to be single photoelectric interactions in each slat.

We therefore apply a contour filter level that rejects a fixed percentage (e.g., 50%) that represent multiple-interaction events involving more than one slat. This is similar to an “island-based” crystal boundary map used for discrete crystal detector decoding [30, 31, 10]. By only keeping events that map to a single-interaction “cluster” or “island”, inter-crystal scatter events can be effectively discriminated against during event positioning. One can either discard inter-crystal scatter events; position them to a pseudo-slat between the two neighboring slats; or assign them a partial weight of the event to each of the neighboring slats. Because these results were collected using side illumination of the crystal array, there is slightly more inter-crystal scatter events that we would expect to see than from a flood map from a photon flux entering the entrance surface of the crystal array. This is because most scatter is small angle forward scatter and would be more likely to interact in the same slat twice than events entering from the side of the crystal array. Still, the basic concept of using contour filters on the 2D histogram of the first and second moments of the collected data will work and as stated above once each event has been classified as a single photoelectric interaction or an inter-crystal scatter event, a decision can be made on what to do with the event.

Spatial Resolution Along Slat

Figure 6 is a 2-dimensional histogram of the positioning of point beam sources stepped every 3.2 mm along the long axis of the BING detector. As computed by equation (1) in the Methods section, the point beam flux has a FWHM of 0.4 mm for the front slat and about 0.7 mm FWHM for the 12^th slat. Events are filtered by energy (±17% about photopeak) and by slat (two-moment contour filter). The estimate distributions shown are in the first slat at a depth of 3.5 mm from the entrance surface of the crystal array (top of figure). The two-dimensional plot illustrates both the lateral spatial resolution and the depth of interaction or Z-axis spatial resolution.

Figure. 6.

Maximum-likelihood estimate distribution of events for a series of beam position separated by 3.2 mm in the first slat.

Figure 7 shows 1-dimensional profiles of the lateral-positioning estimate distribution in the first slat for a set of beams positioned every 2.14 mm. Counts for this profile are for a 0.75-mm-wide swath in estimated depth through the beams centered at a depth of 3.5 mm. The average lateral spatial resolution for this BING detector module corrected for beam width is 0.96-mm FWHM with a range of 0.85 mm to 1.11 mm FHWM.

Figure 7.

Lateral positioning distribution and performance versus lateral beam position. Results shown are for a DOI of 3.5 mm from the entrance face of the detector in the first slat. FWHM values have not yet been corrected for beam width.

Depth of Interaction (DOI) Spatial Resolution

An exemplary plot of DOI positioning profile for the coincidence-collimated beam at different depth positions along the height of the BING crystal array is illustrated in Figure 8. The plot shown is for interactions in the fourth slat with the beam stepped in the depth direction at a lateral position a quarter of the length (13 mm) from one lateral edge. The beam-center position is stepped in 1 mm increments along the height of the crystal array. The average DOI positioning resolution corrected for beam width is 1.6 mm FWHM with a range of 1.0 mm FWHM to 2.1 mm FWHM.

Figure 8.

Depth of interaction positioning distribution and performance versus beam depth. FWHM values have not yet been corrected for beam width.

Combined Lateral and DOI Spatial Resolution

A map of beam-width-corrected spatial resolution for lateral position (X) and depth (Z) is given in Figures 9a and 9b, respectively. Slats 0 and 3 are fully over one row of photosensors on both top and bottom readout faces. Slats 1 and 2 are fully over a row of photosensors on one output face (bottom for slat 1 and top for slat 2), but halfway between sensors on the other output face (top for slat 1 and bottom for slat 2). Results for the remaining slats (4–11) are not being reported due to insufficient calibration data and due to unaccounted broadening of the beam resulting from small-angle Compton scatter that cannot be distinguished from non-scattered photons.

Figure 9a.

Lateral (axial) spatial resolution versus position for slats 0 through 3 (from top to bottom).

Figure 9b.

Depth (DOI) spatial resolution versus position for slats 0 through 3 (from top to bottom).

Timing Resolution

An example of the coincidence timing distribution for the BING detector versus a reference detector is shown for one beam position and slat Figure 10 (Top). Coincidence times are computed as the energy-weighted average time difference from the reference detector for up to the first 16 BING photosensors reporting. To illustrate the timing resolution methodology (central 76% interval) the computed time resolution for the 16-photosensor weighted-average timing distribution is given. The number of photosensors included in the energy-weighted timing average that minimizes the timing resolution depends on the sensor configuration of a slat. Thus, Figure 10 (Bottom), CTR versus number of sensors is plotted separately for slats centered on sensor rows for both faces (slats 0 and 3) and for slats between sensor rows on one face (slats 1 and 2). For slats split over two rows of photosensors on one face, minimum timing resolution occurs when using 9 sensors with comparable performance when using 8 or 10 sensors. For slats fully over a row of photosensors on both sides (centered slats), minimum timing resolution occurs when using 11 photosensors and has a broader valley, extending from 10 to 14 sensors. As a compromise, we chose to use 10 photosensors in reporting summary timing performance for the BING detector. The spatially averaged detector-timing resolution using 10 photosensors is 306 ps for centered slats and 328 ps for slats split between rows on one face. The average detector-timing resolution over all slats and beam positions is 317 ps and the range for all positions and slats is 241 to 404 ps.

A map of the DTR computed by equation (3) versus beam position for the first four slats of the BING detector is given in Figure 11. We think that the DTR variability with depth of interaction is a result of offsetting the crystal slats between the sensors on the entrance face and the sensors on the rear face of the detector. As shown in Figure 1, slats 0 and 3 are each centered over a single row of photosensors on both entrance and exit faces. In contrast, slat 1 shares light with two rows of SiPM arrays on the rear surface of the detector but is centered over a single row of SiPM sensors on the entrance face. The sensor configuration for slat 2 is reversed from slat 1; it shares light with two rows of SiPM arrays on the entrance surface of the detector but is centered over a single row of SiPM sensors on the rear face. Given this configuration, we reason that the timing resolution is slightly better for events occurring near the faces of the slats that are centered on a row of photosensors. Overall, timing resolution is expected to be best of slats that are situated over a single row of sensors for both the entrance and rear surfaces of the detector, such as slat 0 and 3 in Figure 1.

Figure 11.

Map of the measured DTR using 10 sensors as a function of 2D position in slats 0 through 3 (from top to bottom). The DTR values range from 241 ps (white) to 405 ps (black).

Energy Resolution

A map of FWHM energy resolution versus beam position (averaged across slats) and representative spectra versus beam position are shown in Figure 12. Some degradation is observed near crystal edges between SiPM gaps. Unexpectedly, energy resolution is slightly better near the two axial ends of the slats. Upon reflection, this result may be due to the concentration of light to fewer sensors near the slat ends, which in turn can increase signal to noise. Looking at a flood spectrum for a Na-22 source (not shown), the sum-signal response of the detector is nearly proportional for the 511 keV and 1274 keV photopeaks. Thus, our assumption about not needing to perform saturation correction due to modest photon densities for individual SiPM sensors is valid.

IV. Discussion

In this paper, we present the 3-dimensional intrinsic spatial resolution performance and timing resolution performance for a slat-based PET detector module using dual-sided sensor readout. We have been investigating the slat-based detector design as an alternative to both detector modules using either discrete crystal arrays or fully monolithic crystals [13, 15, 16]. We have previously shown that one can achieve less than 3 mm FWHM DOI positioning resolution in trapezoidal shaped slats as thin as 0.44–0.64 mm with a height of 8 mm or 0.71–1.11-mm thick with a height of 10 mm using single-sided readout [16]. In our new design, we increased the height of the detectors to 15 mm to improve detection efficiency and added a staggered dual-sided readout to maintain a comparable intrinsic 3D spatial resolution (i.e., X, Y, and DOI). This sensor configuration was also chosen to decrease interaction-to-sensor distance and to permit slat identification without the use of light-spreading lightguides; in this way we can reduce the optical path length variance of scintillation photons to the nearest sensors, which has a direct impact on timing resolution.

Our prototype BING detector consists of twelve 1.0×15.0×52 mm³ LYSO crystals with all sides specularly polished and glued together as a slat crystal array with 3M mirror film material placed between each slat to optically isolate them from each other. The crystal array is coupled to Hamamatsu S14161–3050HS-08 MPPC arrays and readout using PETsys TOFPET2 electronics. Our goals for slat decoding, lateral intrinsic spatial resolution along the long axis of the crystal slat and depth of interaction positioning resolution are all achieved with this design. Further, based upon our previous results using slat crystal arrays, the axial extent of the detector can be extended by optically coupling the axial edges of arrays together.

We have improved CTR over our prior work with slat-based detectors [15, 16]. However, we did not achieve our desired goal of better than 100 ps. Furthermore, other groups such as [19] have been able to achieve a CTR closer to 200 ps. While 100 ps CTR for a semi-monolithic crystal detector design may be too ambitious, we are currently examining five methods that may further improved our CTR. The first is to investigate methods to improve time-walk corrections for lower energy signals. In this work, we employ a low-energy cutoff for this modelled timing correction, limiting how sensors with smaller amplitude would contribute to timing performance. The second method is exploring the use of very fast discrete component electronics. The PETsys TOFPET2 electronics is a great option for rapid assembly and testing of a prototype detector design; however, it has some limitations associated with the intrinsic timing resolution of the hardware [32, 33]. Going to faster discrete amplifier electronics [34] and fast digitization of the detector signals [35, 36] should lead to improved coincidence timing performance. Third, we are investigating other timing estimation approaches. In particular, we are in the process of examining a bag of tree regression (BTR) estimator [37, 38] which we will be reporting in a separate paper. Fourth, due to cost differences, we chose to use the Hamamatsu S14 series MPPC arrays rather than their S13 series. However, the S13 series has a lower capacitance that may significantly improve timing. Finally, there have been studies that indicate that the use of a high index-of-refraction material to couple the 3M mirror film material can decrease reflectivity, causing more light to be shared with neighboring crystals [39]. Since our decoding methodology does not require any light sharing between crystal slats to decode the slat of interaction, we will investigate fabrication and testing of crystal slat arrays with an air gap between the highly polished crystal faces and the 3M mirror film reflector used to optically isolate the slats from one another. Using the five described methods, we expect to achieve improved timing performance for the next generation of the BING PET detector.

In addition, after completion of this experiment, photosensors on the Z=0 mm surface were removed and the optical coupling on the Z=15 mm surface was inspected through a microscope. We observed many small bubbles (~0.1 mm in diameter) in the optical coupling grease over the length of the interface, but more concentrated on the side corresponding to X<0 mm. For this reason, we think the asymmetries (both vertically and horizontally) evident in the resolution maps of DOI (Figure 9b), DTR (Figure 11), and Energy (Figure 12) are caused by the quality of this optical coupling. Although care was taken during the coupling process to avoid trapped air, we think degassing of the optical coupling medium under vacuum would have removed these microbubbles. We believe that better optical coupling would lead to slightly better performance for all measured metrics that we reported in this paper.

It is instructive to note the similarities and differences in design, processing, and performance of the work reported here to that reported Zhang et al. in [14]. In our design, we used smaller crystals (1.07mm vs 1.37mm width and 15-mm vs 20-mm height); we made slat ends reflective rather than blackened; and we did not add a lightguide between slats and the 0.15mm resin window on the MPPC arrays (1 mm was used in [14]). For processing, we used a maximum-likelihood position estimator for 2D positioning within a given slat rather than the analytic estimators used in [14]; we calibrated time skews using the same slat data and not a 1-to-1 pixelated crystal setup; we performed time-walk corrections (not done in [14]); our arrival-time estimator used an energy-weighted sum of timestamps for the ten SiPMs with the largest signal rather than just the earliest skew-corrected SiPM timestamp. These design and processing differences reduced the uncertainty in the BING detector of lateral (X) positioning, depth (Z) positioning, and timing (DTR) to 55%, 60% and 63% of those reported in [14], respectively.

Another notable difference of our current results compared to other reported works is in the relation of DTR performance on the number of channels used in the energy-weighted timing. The exact number of channels will depend on detector geometry and the density of photosensors (i.e., single-sided vs double-sided readout). However, other works such as [19] or [29] exhibit a sharper rise of DTR when increasing the number of channels above its optimal value. We think the relatively broader valley shown in Figure 10 may be due to differences in the optical-surface properties that caused the broad light distribution seen in the MDRF in Figure 4. Specifically, the sides of the current BING detector were lapped for a specular finish, which is not the standard grade of polish (e.g., note the diffuse appearance of the polished slats shown in [19]).

Finally, we should note that the data acquisition for calibration and evaluation of the BING detector in this manuscript took just over 26 days. A calibration time of 13 days would clearly be too long for practical implementation. Using a higher activity point source (100 μCi) would shorten the calibration to 5 days. Using an array of multiple 100-μCi point sources (one every centimeter) would cut calibration time to one day [40]. Furthermore, software-collimation methods using a pair of matched BING detectors could further reduce calibration time by another order of magnitude without significantly affecting positioning performance [41].

V. Conclusion

The unique arrangement and position decoding scheme of the BING detector unit provides close to sub-mm intrinsic detector spatial resolution with a detector-timing resolution (DTR) of 320±80 ps using the commercially available PETsys data acquisition electronics. The BING detector consists of an array of 1.0-mm thick slat-shaped LYSO crystals, dual-sided SiPM-array readout, and electronics that report both amplitude and time signals for each SiPM sensor. The 15-mm thickness ensures reasonable sensitivity. We measured a lateral resolution of 1.06 mm FWHM on average with a range of 0.94 mm to 1.22 mm over the full detector. Depth resolution was measured to be 1.6 mm FWHM on average with range of 1.0 mm to 2.1 mm over the full detector. The average energy resolution was measured to be 13.6% with a range of 12.7% to 16.0% over the full detector.

The overall spatial positioning performance of our BING detector met our initial design goals. And while our coincidence timing resolution (CTR) was a significant improvement over our previous semi-monolithic crystal design, in future work we aim to further improve timing performance by continuing to optimize the detector design (e.g., higher speed electronics; time-walk corrections; interface between crystal slats and optical barriers in the crystal arrays; side and end surface treatments, scintillator material, and newer generation SiPMs). Finally, we are also exploring the use of machine learning methods to increase performance. While machine learn methods can potentially improve both timing and spatial resolution performance, our focus is on improvements in timing resolution as our intrinsic spatial resolution using our current methods already meets our design goals.