A Preclinical Positron Emission Tomography (PET) and Electron-Paramagnetic-Resonance-Imaging (EPRI) Hybrid System: PET Detector Module

We report the design and experimental validation of a compact positron emission tomography (PET) detector module (DM) intended for building a preclinical PET and electron-paramagnetic-resonance-imaging hybrid system that supports submillimeter image resolution and high-sensitivity, whole-body animal imaging. The DM is eight detector units (DUs) in a row. Each DU contains <inline-formula> <tex-math notation="LaTeX">$12\times 12$ </tex-math></inline-formula> lutetium–yttrium oxyorthosilicate (LYSO) crystals having a 1.05-mm pitch read by <inline-formula> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> silicon photomultipliers (SiPMs) having a 3.2-mm pitch. A small-footprint, highly multiplexing readout employing only passive electronics is devised to produce six outputs for the DM, including two outputs derived from SiPM cathodes for determining event time and active DU and four outputs derived from SiPM anodes for determining energy and active crystal. Presently, we have developed two DMs that are <inline-formula> <tex-math notation="LaTeX">$1.28\times 10.4$ </tex-math></inline-formula> cm2 in extent and approximately 1.8 cm in thickness, with their outputs sampled at 0.7GS/s and analyzed offline. For both DMs, our results show successfully discriminated DUs and crystals. With no correction for SiPM nonlinearity, the average energy resolution for crystals in a DU ranges from 14% to 16%. While not needed for preclinical imaging, the DM may support 300–400-ps time-of-flight resolution.

A Preclinical Positron Emission Tomography (PET) and Electron-Paramagnetic-Resonance-Imaging (EPRI) Hybrid System: PET Detector Module Heejong Kim , Member, IEEE, Yuexuan Hua, Boris Epel, Subramanian Sundramoorthy, Howard Halpern, Chin-Tu Chen , Member, IEEE, and Chien-Min Kao , Senior Member, IEEE Abstract-We report the design and experimental validation of a compact positron emission tomography (PET) detector module (DM) intended for building a preclinical PET and electronparamagnetic-resonance-imaging hybrid system that supports submillimeter image resolution and high-sensitivity, whole-body animal imaging.The DM is eight detector units (DUs) in a row.Each DU contains 12×12 lutetium-yttrium oxyorthosilicate (LYSO) crystals having a 1.05-mm pitch read by 4×4 silicon photomultipliers (SiPMs) having a 3.2-mm pitch.A small-footprint, highly multiplexing readout employing only passive electronics is devised to produce six outputs for the DM, including two outputs derived from SiPM cathodes for determining event time and active DU and four outputs derived from SiPM anodes for determining energy and active crystal.Presently, we have developed two DMs that are 1.28×10.4cm 2 in extent and approximately 1.8 cm in thickness, with their outputs sampled at 0.7 GS/s and analyzed offline.For both DMs, our results show successfully discriminated DUs and crystals.With no correction for SiPM nonlinearity, the average energy resolution for crystals in a DU ranges from 14% to 16%.While not needed for preclinical imaging, the DM may support 300-400-ps time-of-flight resolution.

I. INTRODUCTION
H YPOXIA (low oxygenation) is a tissue microenvironment factor of significance to cancer diagnosis and treatment [1].As the tumor is heterogeneous and hypoxic tissues are resistant to radiation, it has been long hypothesized that hypoxia targeting-a strategy that concentrates more radiation dose on the resistant, hypoxic subvolumes of the tumor while delivering less dose on the more sensitive, well oxygenated portions-can improve cancer treatment [2], [3].Presently, clinical hypoxia imaging is often performed by using positron emission tomography (PET) with a hypoxia probe such as 18 F-Misonidazole (FMISO) [4], [5].In a recent study, hypoxia targeting based on FMISO-PET oxygen maps was shown to fail to improve clinical tumor control [6].On the contrary, using mice models we have reported the successful use of electron paramagnetic resonance imaging (EPRI) to obtain absolute oxygen partial pressure images and shown positive hypoxia-targeting outcome when using hypoxic tumor regions defined on the EPRI oxygen maps [7].We surmise that the failure of the clinical FMISO-PET study was due to the semi-quantitative nature of the technology given the multifactorial dependence of FMISO uptake.However, clinical EPRI is currently not available.Toward developing successful hypoxia targeting in the clinic, a preclinical PET-EPRI hybrid system is, therefore, a significant tool for studying and developing PET-based quantitative oxygen imaging, validated against spatiallyand temporally-aligned absolute oxygen pressure images generated by EPRI [8], [9].Temporal alignment is important because tissue oxygenation can vary considerably during a typical imaging duration [10], [11].
The challenges in developing the proposed system are similar to those in developing a PET-MRI system [12].They are derived from the need to make the PET system physically and electromagnetically compatible with the preclinical EPRI system while achieving superior imaging performance properties.As will be discussed below, consideration for these challenges calls for the development of compact detector modules (DMs) that are based on lutetium-yttrium oxyorthosilicate (LYSO) and silicon photomultipliers (SiPMs) and that use as few electronics as possible, avoid active electronics in particular, and produce as few outputs as possible.LYSO is favorable due to its superior detection efficiency, energy resolution, and light output.SiPM is the photosensor of choice due to its compactness and tolerance of magnetic fields.The DM shall use as few electronics as possible because this helps maintain detector compactness and minimize the presence of materials that potentially can disturb the EPRI magnetic fields and are susceptible to the generation of eddy currents.Active electronics shall be avoided for they are a source of RF signals and heat; the former interfere with EPRI and the latter can cause performance degradation or instability as SiPM response characteristics vary strongly with temperature.The standard approach for handling them is to implement detector shielding and apply cooling to maintain an adequate and stable temperature for all SiPMs.However, nontrivial shielding and cooling can destroy detector compactness.The consideration for RF signals and heat also favors placement of the dataacquisition (DAQ) electronics away from the EPRI magnets.For this, the DM shall produce only a few outputs so that it is practical to transmit them via long coaxial cables that can maintain signal integrity.
We previously reported DMs of the above kind [13] and a proof-of-concept PET-EPRI system employing them [9].However, this prototype is not adequate for many applications due to its short axial field-of-view (FOV) (and so a low sensitivity) and limited image resolution.We are developing a new system that employs 1.0-mm width crystals for supporting a submillimeter image resolution and has a 10.4-cm axial FOV for achieving high sensitivity and allowing wholebody (WB) rodent imaging by using a single bed position.So far, PET-EPRI systems having such superior imaging properties do not exist.Compared to the prototype, the new system uses significantly more crystals and yet it must satisfy the same physical and electronic conditions.The main contribution of this work is to devise and experimentally validate a DM that can meet these conditions.This DM employs light sharing and a small-footprint, highly multiplexing readout based on resistive networks (RNs) and stripline (SL) to allow 1152 crystals to share only six output channels.For SiPM-based PET detectors, multiplexing readout is often needed for reducing electronics complexity and an excellent review on this topic was recently given by Park et al. [14].RN and SL readouts are not new.They are chosen for this work in consideration of, as discussed above, their simplicity and use of only a few passive electronics.In addition, they are combined in a novel way to provide a two-tiered readout to achieve a level of multiplexing not reported before.This article describes the design of the new PET system and reports the development and evaluation of the new DM.

A. Overview of the Design of the PET-EPRI System
Fig. 1(a) shows the prototype we previously developed [9], [13].To fit between the approximately 12 cm spacing between the EPRI magnets and provide a useful animal port, the PET detector ring (DR) employs 14 compact DMs to yield an outer diameter (OD) of 11.5 cm and an inner diameter (ID) of 6.0 cm.The DM, shown in Fig. 1(b), contains a 4×8 array of detector pixels (DPs), each of which is an LYSO crystal coupled one-to-one (1:1) to an SiPM.These DPs, whose pitch is 3.2 mm, are read by using two SLs to produce four outputs.The SL readout uses only a small amount of passive electronics to achieve substantial channel reduction [see Fig. 1(b)].The DR has 56 outputs; they are connected via 5-m miniature coaxial cables to a single 72-ch sampling DAQ board based on the multivoltage threshold (MVT) technology [15].As a proof-of-concept system, the DR has an axial FOV of 2.54 cm and hence a low imaging sensitivity.Based on the pitch of the DP and verified by measurement, its image resolution is about 1.6 mm [13].We have used this prototype, which employs no shielding or explicit cooling, for many PET-EPRI imaging that lasted 60 min or longer [16] without observing signs of interference to EPRI or degradation/instability in PET imaging.Without shielding, the EPRI RF pulses could affect PET signals but the affected signals could be discarded at a cost of 2.3% reduction in PET imaging sensitivity [9,Table I].To the best of our knowledge, to date animal PET-EPRI imaging has been reported only with this prototype.
Fig. 1(c) shows the new PET DR in development.It has the same OD and ID as the prototype and also employs 14 DMs.The axial length is now increased four times to 10.4 cm to greatly increase the imaging sensitivity and enable WB rodent imaging by using a single bed position.To satisfy these geometric parameters, the thickness of the DM cannot exceed 2.75 cm.For achieving submillimeter image resolution, the LYSO crystal width is decreased to 1.0 mm.However, due to considerations for cost and electronics complexity, the same 3.2-mm pitch SiPM array is used.Therefore, the new DM does not have 1:1-coupled DPs and the SL readout of the prototype is not applicable.

B. Design of the Detector Module
The new DM consists of eight detector units (DUs) in a row.Each DU is a 12×12 array of 1.0×1.0×10mm 3 LYSO crystals coupled to a 4×4 array of SiPMs.Estimated by Monte Carlo (MC) calculations using Geant4 [17], the sensitivity of the resulting DR is 8.3% when assuming a 15% ER and accepting ≥400 keV events.
Each DM, therefore, has 128 SiPMs and 1152 LYSO crystals.Fig. 2 depicts the readout electronics for the DM by  combining the use of RNs and SL.The RN, whose principle and design can be found in [14], [18], and [19], is a popular method for merging an array of SiPM outputs into four signals.Fig. 2(a) and (b) shows the specific RN used for reading the 4×4 SiPM anode outputs of the proposed DU.Let A, B, C, and D be the pulse heights (PHs) of the signals at outputs A, B, C, and D of the RN, respectively.If Z is the event PH and (X, Y) its 2-D position, then they can be calculated by Next, we assume at any instant there is at most one DU that interacts with a γ -ray within a DM.(The crystal or DU that interacts with a γ -ray is called the active crystal or active DU below.)Under this assumption, we can simply wire all the A outputs of the eight DUs together, without using summing buffers or amplifiers to avoid active electronics, to yield a single A output for the DM.The B, C, and D outputs of the DM are similarly obtained.Equation (1) then can be applied to the A, B, C, and D outputs of the DM to obtain the event PH and 2-D position within the yet-to-be-identified active DU.
Information about the event time and active DU is derived from signals generated by using the SL readout whose principle and design were previously described by us [13], [20], [21].As depicted in Fig. 2(a) and (c), for each DU its 16 SiPM cathode outputs are wired together, again without using summing buffers or amplifiers to avoid active electronics, to yield a single output .The outputs of the eight DUs of the DM are injected into an SL at various positions.The SL readout is designed to maintain the timing characteristics of the injected signal while yielding adequate propagation delays for the signal to arrive at the two SL outputs.If t1 and t2 are the pulse arrival times determined from the SL out1 and SL out2 signals, then their average t e = (t1 + t2)/2 gives the event time and their difference δt = t1 − t2, called SL differential time below, gives the injection position of the signal, and hence identifies the active DU.
In summary, for the proposed DM, an RN+SL readout is developed to produce only six outputs from its 128 SiPMs to carry the information about a γ -ray that interacts with its 1152 LYSO crystals.These outputs include two SL outputs for determining event time and active DU and four RN outputs for determining event PH and active crystal within the active DU.Both RN and SL use only a small amount of passive electronics.Some degree of signal isolation between the RN and SL signal paths is achieved without using active electronics by deriving their signals from the anodes and cathodes of the SiPMs, respectively.Table I compares the design parameters of the new DM with that of the prototype.
The readout assumes that there is at most one active DU at any instant.To assess this assumption, we consider a 200-μCi point source emitting 511-keV photon pairs at the center of the system (3 cm from a DM) and take the duration of an event pulse to be 1.5 μs (estimated based on the waveforms shown below in Fig. 4).Based on the solid angle subtended by the DM and the 10-mm LYSO thickness, the mean number of γ -rays interacting with a DM during an event duration is estimated to be 0.75.It follows that the probability for a DM to produce overlapping event pulses (i.e., when there are two or more interacting γ -rays during an event duration) is 17%.The same calculation also yields a small probability of 1.4% for a DU to see two or more events during an event duration.It is noted that typically the radioactivity is distributed over the body of the rodent and that attenuation of the γ -rays by the animal is not considered in the above estimation.If these factors lead to a 50% reduction in the singles rate, then the probability for a DM (DU) to produce overlapping event pulses becomes 5.5% (0.4%).In addition, partially overlapped event pulses still may be correctly processed.Therefore, we consider the assumption acceptable.

C. Performance Measurements
For event positioning and energy measurement, a 68 Ge rod source (about 80 μCi, 19-cm long) was placed at 7 cm above and parallel to the length of the DM to create an approximately uniform irradiation to all DUs.The output signals of the DM were sampled by using CAEN DT5742 digitizers.The recorded waveform samples were then analyzed offline as follows.
1) For computing δt, the digital constant-fraction discrimination (dCFD) method using a fractional threshold of 0.35 was applied to the SL signals.The ability to identify the active DU was assessed by examining the resulting δt histogram.A mapping from δt to active DU was obtained (see Section III-B).2) For calculation of ((1)), the PH of an RN output signal was given by its integration (the integrated charge, IC).The ability to identify the active crystal was assessed by examining the resulting (X, Y) histogram (the flood map).A mapping from (X, Y) to active crystal was obtained (see Section III-C).3) After the active DUs and crystals were assigned for all events by using the mappings obtained above, pulseheight spectra (PHS) were obtained for individual crystals.They were examined for the ability to identify the photopeak and the variability of the photopeak position.ERs of individual crystals were derived from their PHS.For measuring the coincidence resolving time (CRT), a 22 Na button source (about 20 μCi) was placed midway between two DMs using the setup in Fig. 3(d).For determining t e , the digital leading-edge discrimination (dLED) method using a 4 mV threshold was applied to the SL signals.This is because, consistent with findings previously reported by us and others [22], [23], [24], dLED could yield better CRT than dCFD.The coincidence differential time t was the difference between t e 's of the two γ -rays detected in coincidence.After the active DUs and crystals all events as described above, t-histograms and CRTs were obtained for all DU pairs.A sampling rate of 0.7 GS/s was used.This yielded a sampling interval of 1.46 μs and in step 2 above all samples acquired in this interval were used for computing IC.Previously we reported that a sampling rate of 1.5 GS/s or above is needed for CRT measurement of LYSO-type scintillators [25].The CAEN DT5742 provides 2.5 and 5 GS/s sampling rates also; however, using them led to shorter sampling intervals (hence, shorter integration times for PH) and degraded energy resolution and flood map.Therefore, for examining the CRT potentially achievable between crystals of two DMs, we also similarly performed coincidence measurement between a reference detector (D-ref), which was a single 3×3×10 mm 3 LYSO read by a Ketek SiPM biased at 31.0 V, and a DM by using a 2.5-GS/s sampling rate 1 to obtain the CRTs of selected crystals of the DM in coincidence with D-ref. 2 The CRT of D-ref was previously measured to be 260 ps.

A. Implementation of the DM and Output Signals
Fig. 3(a) shows the developed DM.The readout circuits were implemented on a printed circuit board (PCB) that was 30×185 mm 2 in extent.The left-hand side of the PCB had a single connector for receiving the bias voltage for the SiPMs and the diodes in the SL circuits [see Fig. 1(b)].The right-hand side had six micro-miniature coaxial (MMCX) connectors; two of them can be seen in front for the SL outputs and four at back for the RN outputs.MMCX cables connected the DM outputs to RF preamplifiers (ZFL-1000LNB+, mini-Circuits, 20-dB gain) and then to CAEN DT5742 digitizers, using a 0.7-GS/s sampling rate unless stated otherwise.
The readout PCB received eight DUs.In Fig. 3(a), the RN circuits can be seen above and below the DUs and the SL circuit to the right of the DUs.As shown in Fig. 3(b), two DUs were implemented as a unit on a small PCB for routing the SiPM cathode and anode outputs to the readout PCB.Each DU contained an LYSO array and an SiPM array that matched in size.The LYSO array was obtained from Suzhou JTC (China).For each crystal, all six sides were polished.Except for the side coupling to SiPM, the other five sides were also covered with BaSO 4 , approximately 0.1-mm thick, to minimize the escape of scintillation light.The resulting crystal pitch was 1.05 mm.The SiPM array was the Hamamatsu 14161-3050HS-04 multipixel photon counter (MPPC) that contained 3.2-mm pitch pixels, each having an effective detection area of 3.0×3.0mm 2 .As SiPMs in the MPPC array showed rather uniform response properties, all SiPMs of the DM received the same 42.5-Vbias.This bias voltage was chosen to give a large signal gain without drastically increasing the noise, 3but no experiments were conducted to determine if it was optimal.The LYSO and SiPM arrays were coupled by use of RTV silicon adhesive whose refractive index was 1.4.No lightguide was used between them.Empirically, we found that the adhesive and the thickness of the MPPC window (nominal value = 0.15 mm) led to adequate spreading of the scintillation lights to achieve successful crystal discrimination (see Fig. 6 below).The gap between two DUs in a DM was 0.3 mm.Fig. 3(c) shows the SL readout where the numbers indicate the injection positions of the DUs, which were not contiguous with the physical locations of the DUs for simplification of the PCB layout.The propagation delay between neighboring injection positions was increased by use of a 25-mm serpentine SL path [21].The front face and thickness of the resulting DM were 1.28×10.24cm 2 and about 1.8 cm, respectively.As discussed in Section II-A, we intend not to implement shielding and cooling for the DM and place the preamplifiers and CAEN digitizers, or other practical DAQ solutions yet to be developed, away from the EPRI system.With a 6-cm ID, the gap between two DMs is estimated to be 1.5 mm.Fig. 3(d) shows a 3D-printed frame for holding DMs in positions for measurement.Mimicking the DR, its OD and ID are 11.5 and 6.0 cm, respectively.exhibit some undershootings at the beginning and appear to be longer than the larger RN signals (blue and green curves).These undershootings were not noticeable (reduced in amplitude) if the SL outputs derived from SiPM cathodes were left disconnected (read via a 50-resistor).Hence, we speculated that they were due to impedance mismatch created when loading the SL circuit onto the cathode outputs of the SiPMs.To examine their impacts to event detection, we compared the flood maps derived from the RN outputs obtained when the SL outputs were connected to the DAQ or not.When using IC for PH, the resulting maps showed no noticeable differences (data not shown).However, this issue needs to be investigated further.

B. Discrimination of DUs in DM
Fig. 5 shows the histograms of the SL differential time δt obtained for a DM.The all-event histogram, shown in black, was obtained by using events whose SL pulses have a peak amplitude between 60 and 350 mV.On the other hand, the photopeak-event histogram, shown in red, was obtained by using events whose energies, determined as described below in Section III-C, were inside the photopeak energy window of [420 keV, 600 keV].Both histograms show eight clearly resolved peaks.Let δt (i) p , i = 1, . . ., 8, be the location of the ith peak occurs.We calculated d i = (δt )/2 for i = 1, . . ., 7 and defined d 0 = −∞ and d 8 = +∞.Subsequently, an event was assigned to DU i if its δt value satisfied For both histograms, the peaks grow wider as the magnitude of δt increases.In [21], we attributed this to the fact that, although only slightly, the amplitude and shape of the signal pulse progressively reduces and widens as it travels a longer SL pathlength.Consequently, δt shows a larger variation when the pathlengths from the signal injection point to the two SL outputs have a larger difference.The photopeak-event histogram has low valleys between peaks, yielding an average peak-to-valley ratio (P/V ratio) of 35.2 and suggesting a small percentage of DU misidentification.In comparison, the all-event histogram has higher valleys but the average P/V ratio remains large, equal 13.4.As the difference between these histograms is caused by the rejection of lower-energy events outside the photopeak energy window, we observe that most events in the valley interact with the DM via Compton interaction.This suggests that they are scattered inside a DM across multiple DUs.

C. Crystal Identification and Energy Resolution
Fig. 6 shows the flood map (256×256) obtained for one of the DUs, and selected horizontal and vertical profiles of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.map.As shown in Fig. 6(a), the 8×8 inner peaks are well discriminated and those at the edges are resolvable.This is also true on the profiles in Fig. 6(b) and (c).The average P/V ratio of the horizontal (vertical) profile was 6.0 (7.6) but the average P/V ratio of two peaks at edge decreased to 1.8 (3.1).We speculate that the reduced spacing for edge crystals was due to the fact that the light spread was effectively truncated to the extent of the DU.Hence, for a crystal on the right (left) edge, for example, in (1), the B and C (A and D) values were reduced, leading to a smaller (larger) X than that otherwise would be obtained if there was no truncation.
A heuristic algorithm was developed to identify 12×12 peaks in a flood map.Based on the horizontal profile in Fig. 6(b), the algorithm first determined two values that separated the eight inner peaks from the four edge peaks.The same was done for the vertical profile in Fig. 6(c).As a result, as shown in Fig. 7(a), we obtained two horizontal lines and two vertical lines that partitioned the flood map into nine submaps in which submap 5 contained the 8×8 inner peaks.For each submap, the algorithm then found the largest peak inside it and removed a small neighborhood (5×5 for submap 5, 2×4 for submaps 4 and 6, 4×2 for submaps 2 and 8, and 2×2 for the rest) around the peak from the submap.The process was applied to the modified submap again to identify the second largest peak and remove a small neighborhood around it.This was repeated until the expected number of peaks in the submap was obtained (4 in submaps 1, 3, 7, and 9; 16 in submaps 2, 4, 6, and 8; and 64 in submap 5).Fig. 7(b) shows the 12×12 peaks identified for the flood map in Fig. 7(a).Based on the identified peaks, an event was assigned to the crystal corresponding to the peak that was closest to the event's (X, Y) position.The PHS of a crystal was then obtained by histogramming the Z values of the events that were assigned to that crystal.Fig. 8(a) show the PHS of three selected crystals in a DU.Overall, all PHS obtained for a DU shows a unique and identifiable peak.Fig. 8(b) shows that the PHS peak position remains rather stable across crystals in a DU.By relating the PH value of the peak to 511 keV, a scaling factor for translating event PH to energy in keV was derived for each crystal.This conversion does not correct for possible nonlinear response of SiPM with γ -ray energy [26].The apparent energy resolution (AER) at each crystal was then obtained by fitting a Gaussian function to the photopeak, reported as the percentage ratio of the FWHM of the Gaussian to its mean.All DUs of the two developed DMs showed rather similar performance characteristics in terms of crystal discriminability, PHS, and AER.For example, Fig. 10 shows all the flood maps obtained for one DM.The peak-finding algorithm described above was successfully applied to all of these flood maps.The average AER obtained for a DU in these DMs ranges from 14% to 16% and the standard deviation ranges from 1.2% to 2.0%.The DU-level CRT includes the contribution due to time shifts across crystals.Also, a suboptimal sampling rate of 0.7 GS/s was used.Fig. 11(c) is the histogram obtained between D-ref and a central crystal of a DM by using a 2.5-GS/s sampling rate, showing a CRT of 330 ps.Similarly, we obtained CRTs of 270 and 317 ps for two other selected crystals in coincidence with D-ref (histograms not shown).Therefore, after proper time alignment, the DM may support a CRT of 300-400 ps for ToF imaging.

IV. CONCLUSION AND DISCUSSION
A major contribution of this work is the development and experimental validation of a compact DM that contains as few electronics as possible, uses no active electronics in particular, and produces as few outputs as possible for building a preclinical PET-EPRI system whose PET subsystem has a 10.4-cm axial FOV so that it can support WB rodent imaging by using a single bed position and yield a high sensitivity, a detector resolution on the order of 1 mm so that it can support submillimeter image resolution, an OD of 11.5 cm so that it can be embedded inside a preclinical EPRI scanner, and an ID (animal port) of 6 cm so that it can conveniently receive the animal and EPRI RF coil.To meet these conditions, a new highly compact and highly multiplexing RN+SL readout for the DM is devised.Presently, preclinical PET-EPRI systems having the stated compactness and imaging performance properties do not exist.
The resulting DM contains 12×96 (1,152) LYSO crystals read by using 4×32 (128) SiPMs, organized into a linear array of eight DUs.Each crystal is 1.0×1.0×10.0mm 3 in size with a 1.05-mm pitch, and each SiPM has a detection active area of 3.0×3.0mm 2 with a 3.2-mm pitch.We build two DMs and employ them to verify that active DUs and crystals can be correctly identified.The AER within a DU is good and rather uniform.For example, we obtained 14.4±1.3%for a specific DU.In terms of crystal identifiability and AER, the DM also shows good uniformity across DUs, with the average and standard deviation of the AER obtained for a DU ranging from 14% to 16% and from 1.2% to 2.0%, respectively.Without performing time alignment, the average CRT between two DUs is 1.5 ns.We also obtain CRTs in the range of 270-330 ps between selected crystals of a DM and a single-pixel reference detector.Therefore, the DM may support ToF after proper time alignment.The PET DR consists of 14 such DMs.By MC calculation, the sensitivity of the system is 8.3% when accepting ≥400 keV events.
As described shown in Fig. 3(a), this readout has a small footprint, yielding a 30-mm height readout board.This height in fact is still too large for the stated 11.5-cm OD and 6.0-cm ID of the DR.During development, we chose to work with a larger PCB board because it was easier to make changes.After the design is validated, Fig. 12 shows that we have now implemented the readout on a 20×175 mm 2 board while maintaining the same thickness.This smaller board is compatible with the stated OD and ID.As already mentioned above, the readout does not use active electronics.It also provides a significant channel reduction to enable detachment of the DAQ electronics from the DR.These features allowed us to avoid implementing explicit shielding and cooling for the prototype.For the new system, as more SiPM and electronics are used, airflow is less efficient with a longer system, and SiPM response is very sensitive to temperature, some RF shielding and cooling for temperature stabilization may be necessary.In this case, we, however, expect simple shielding and cooling to be sufficient.
As expected, the highly multiplexing readout has a compromised count-rate capability.With the high sensitivity of the proposed system, we expect that lower radioactivities will be used and we estimate that the count-rate capability of the readout is acceptable for radioactivity up to 200 μCi.However, this issue needs to be experimentally validated in future studies.If necessary, we may introduce modifications to shorten the duration of the signal pulse and improve its count-rate capability.Or, we can reduce the number of DUs sharing one readout.For example, the 16 DUs of two neighboring DMs may be handled by using three readout circuits.
In this work, the outputs of the DM were sampled at 0.7 or 2.5 GS/s by using CAEN digitizers and then digitally processed offline.As the DR has only 84 (6×14) outputs, it is not unacceptable to use this waveform-sampling DAQ but a more practical solution is preferred.Moreover, the count-rate capability of this sampling DAQ can be inadequate.Based on our results, this practical DAQ shall provide IC measurement for the RN signals with an integration time of about 1.5 μs.As ToF is not needed for preclinical imaging, the resolution required for timing measurement is determined by the discriminability of the δt histogram.The narrowest peak of the black curve in Fig. 5 has a 320-ps FWHM.To achieve this resolution for δt, the DAQ shall have a single-channel timing resolution of 226 ps or better.The above two conditions can be met by using, for example, the PETsys readout system [27] that designed to be scalable and capable of a high countrate capability and that has been successfully used by the PET research community.The development of practical DAQ will be addressed in future work.

Fig. 1 .
Fig. 1.(a) PET-EPRI prototype whose PET DR employs 14 DMs to yield an OD of 11.5 cm and an ID of 6 cm.The insert (inside the 3D-printed blue enclosure) and its OD and ID are pointed by arrows.(b) Photograph of the DM of the prototype and the circuit for injecting a signal into an SL.Two SLs are used, each receiving 16 SiPM signals (8 seen at the front for each SL).(c) Drawing of the new PET DR in development.It also employs 14 DMs and has the same OD and ID as the prototype.However, its axial length and crystal pitch are four times (10.4 cm versus 2.54 cm) and one third (1.05 mm versus 3.2 mm) as large as those of the prototype, respectively.

Fig. 2 .
Fig. 2. (a) 16 SiPM anode outputs of a DU are fed into an RN while the 16 SiPM cathode outputs are summed and fed into an SL.(b) RN merges the 4×4 SiPM anode outputs of a DU to yield four outputs A, B, C, and D. (c) DM has six outputs: S1-S8 represent the eight DUs of the DM, and An, Bn, Cn, and Dn are the RN outputs, and n the summed cathode output, of Sn.The A, B, C, and D outputs of the DM are the summed signals of An, Bn, Cn, and Dn, respectively.The n signals are fed into an SL at various positions to yield two outputs SL out1 and SL out2 .See text for details.

Fig. 3 .
Fig. 3. (a) DM with all eight DUs (white squares with red numbers on top) installed on the readout PCB that is 30 mm by 185 mm in extent.The circuits seen above and below the DUs are the RN circuits while that to the right are the SL circuit.(b) Two DUs are implemented as a unit on a small PCB that routes the SiPM outputs to the readout PCB.Each DU contains a 12×12 LYSO array coupled to a 4×4 SiPM array.(c) Zoomed-in view of the SL circuit and connectors; the numbers show the signal injection positions of the 8 DUs.(d) Front view of a cylindrical frame for housing two DMs and a holder for positioning a 22 Na source at the center.

Fig. 4 .
Fig. 4. Sample output signals produced by a DM.(a) Two SL outputs from which event time and active DU are determined.The inset shows a zoomedin view of their rising edge.(b) Four RN outputs from which event PH and position within the active DU are determined.

Fig. 4
shows sample SL and RN output signals produced in response to a γ -ray hit, all showing good quality.As expected, the two SL signals in Fig. 4(a) are almost identical.The slight difference in amplitude is due to the different amounts of attenuation experienced by the signals as they travel different SL pathlengths to reach the outputs [21].Upon a closer examination of Fig. 4(b), the smaller RN signals (black and red curves)

Fig. 5 .
Fig.5.Histogram of the SL different time δt.The all-event histogram, in black, is obtained by using SL pulses whose peak amplitudes are between 60 and 350 mV.The photopeak-event histogram, in red, is obtained by using events whose energies are between 420 and 600 keV.

Fig. 6 .
Fig. 6.(a) Sample flood map obtained for a DU, showing 12×12 crystals in the LYSO array.(b) and (c) Horizontal and vertical profiles in the red-box areas marked in (a).

Fig. 7 .
Fig. 7. (a) Peak-finding algorithm partitions the flood map into nine submaps and then iteratively looks for a specific number of peaks inside each submap.(b) Identified 12×12 peaks.See text for details.

Fig. 8 .
Fig. 8. (a) PH spectra obtained for three selected crystals.(b) Image showing the photopeak position for each crystal in a DU.The PHS in (a) are obtained from those crystals enclosed in rectangles.

Fig. 9 .
Fig. 9. (a) Crystal-level AERs obtained for one DU.(b) Histogram of the AERs shown in (a), yielding a mean and standard deviation of 14.4% and 1.3%, respectively.

Fig. 9 (
a) is a 12×12 image showing AERs obtained for crystals in a DU; they range from 11% to 20%, with the majority between 13% and 16%.Fig. 9(b) is their histogram, showing an AER of 14.4 ± 1.3%.

Fig. 10 .
Fig. 10.Flood maps obtained for eight DUs of one DM.

Fig. 11 .
Fig. 11.(a) t-histogram (black curve) obtained between two DUs in an opposing pair of DMs and the CRT estimated by Gaussian fitting (red curve).(b) Distribution of the 8×8 DU-level CRTs obtained for the two developed DMs.The average is 1.5 ns.(c) t-histogram (black curve) and CRT obtained between a selected crystal of a DM and D-ref.The SL output signals were acquired at 0.7 GS/s in (a) and (b) and at 2.5 GS/s in (c).

Fig. 11 (
Fig. 11(a) shows the histogram of the coincidence differential time t obtained for two DUs in two opposing DMs.By fitting a Gaussian function to the histogram, we obtain a DU-level CRT of 1.4 ns.Fig. 11(b) shows the distribution of the CRTs thus obtained for the 8×8 DU pairs between the two developed DMs.It is observed that these CRTs have a narrow distribution around 1.4 ns, yielding an average CRT of 1.5 ns.The DU-level CRT includes the contribution due to time shifts across crystals.Also, a suboptimal sampling rate of 0.7 GS/s was used.Fig.11(c) is the histogram obtained between D-ref and a central crystal of a DM by using a 2.5-GS/s sampling rate, showing a CRT of 330 ps.Similarly, we obtained CRTs of 270 and 317 ps for two other selected crystals in coincidence with D-ref (histograms not shown).Therefore, after proper time alignment, the DM may support a CRT of 300-400 ps for ToF imaging.

Fig. 12 .
Fig. 12.New 20 mm by 175 mm readout board.Its dimension supports the geometry of the PET DR shown in Fig. 1(c).

TABLE I PARAMETERS
OF THE DMS OF THE PROTOTYPE AND NEW SYSTEM