Systems and methods for power-efficient multiplexing for high-resolution time-of-flight positron emission tomography modules with inter-crystal light sharing

Abstract

A multiplexing scheme for both energy and timing information is provided for a particle detection system having a photosensor array with multiple photosensors. Each photosensor is associated with multiple scintillator modules. The system has a segmented pseudo-prismatic light guide with multiple pseudo-prismatic segments. Each segment is associated with multiple photosensors, and the photosensors are adjacent. Each scintillator module contacts its associated photosensor at one end and its associated segment at the other end. Each of the multiple photosensors may be connected to an energy readout channel, such that photosensors associated with the same segment are not connected to the same energy readout channel. Each energy readout channel has at least two timestamps associated therewith.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of and priority to U.S. Provisional Application No. 63 / 088,718, filed October 7, 2020, which is incorporated by reference in its entirety.

[0002] FIELD OF THE DISCLOSURE The present disclosure relates generally to the field of radiological imaging, and more particularly to positron emission tomography (PET). [Background technology]

[0003] PET imaging is a powerful technique primarily used for the diagnosis, treatment selection, therapy monitoring, and research of cancer and neuropsychiatric disorders. Despite its high molecular specificity, quantitative nature, and clinical availability, PET has not fully realized its potential as a go-to molecular imaging modality, primarily due to its relatively low spatial resolution. Several attempts have been made to achieve high-resolution PET, such as using n-to-1 scintillator module and readout pixel coupling (n>1) (photosensor), which achieves spatial resolution equal to the size of the scintillator module without increasing the cost of the readout side (e.g., photosensor, connector, readout ASIC). While other attempts have been made, such as using monolithic scintillator modules with nearest neighbor positioning algorithms, n-to-1 optical sharing is the most commercially viable option due to its simultaneous readout capabilities of depth of interaction (DOI) and time-of-flight (TOF) positioning, without any trade-off in sensitivity and / or energy resolution.

[0004] However, improving spatial resolution significantly increases the amount of data per PET scan due to the increased number of voxels. Depth encoding, required to mitigate parallax error and fully realize the benefits of high-resolution PET, further exacerbates the data size problem, as the number of lines of response (LOR) grows exponentially as a function of the number of DOI bins. Combining high resolution with TOF readout increases PET data size because each channel reads a timestamp per pixel, even though multiple timestamps per event are typically not used, making this process computationally inefficient.

[0005] As data increases, the number of connections between the photosensor and the readout ASIC increases, effectively increasing the heat generated by the device.

[0006] Readout systems typically utilize a one-to-one coupling between readout pixels and channels, but this readout method is inefficient because it is not necessary to read out all pixels for every event.

[0007] Signal multiplexing, in which signals read by multiple photosensors (pixels) per event are summed, has been proposed to reduce data size and complexity to reduce the computational cost of PET. However, even when signals are multiplexed, the solution must be able to determine the primary photosensor (pixel) interactions, primary scintillator module interactions, DOI, and TOF. Summary of the Invention [Problem to be solved by the invention]

[0008] In one or more known systems involving multiplexing, the detector modules used do not have depth encoding capabilities (hence the multiplexed readout scheme has not been shown to work with DOI readout), which is paramount to achieving uniformity of spatial resolution at the system level or high temporal resolution capabilities for TOF. The multiplexing scheme may also affect timing resolution. [Means for solving the problem]

[0009] Thus, a particle detection system is disclosed that may include a photosensor array, a scintillator array, and a segmented light guide. The photosensor array may include a first plurality of photosensors. Each photosensor corresponds to a pixel. The scintillator array may include a second plurality of scintillator modules. The number of scintillator modules may be greater than the number of photosensors. The plurality of scintillator modules may be in contact with a respective photosensor at a first end of the respective scintillator module. The segmented light guide may include a plurality of pseudoprismatic segments. The segmented light guide may be in contact with a second end of the second plurality of scintillator modules. Each pseudoprismatic segment may be in contact with a scintillator module that is in contact with at least two different photosensors. The at least two different photosensors may be adjacent photosensors. Each pseudoprismatic segment may be configured to redirect particles between the scintillator modules in contact with the respective pseudoprismatic segment.

[0010] The system may further include a third plurality of energy readout channels. The plurality of optical sensors may be connected to respective energy readout channels, such that optical sensors associated with the same pseudoprismatic segment are not connected to the same energy readout channel. Each energy readout channel may have at least two timestamps associated therewith.

[0011] In one aspect of the disclosure, the photosensors may be arranged in rows and columns, with adjacent photosensors in a row being connected to different energy readout channels and adjacent photosensors in a column being connected to different energy readout channels.

[0012] In one aspect of the present invention, the system may further include at least two comparators for each energy readout channel, each comparator being connected to the multiple optical sensors for the same energy readout channel. Each comparator (for the same readout channel) may have a different threshold value. The comparators may be connected to the anode or the cathode.

[0013] In one aspect of the present disclosure, the energy readout channel may be connected to the same or different terminal as the information for timing.

[0014] In one embodiment of the present disclosure, four light sensors may be connected to the same energy readout channel.

[0015] In one embodiment of the present disclosure, there may be different scintillator module to photosensor couplings, such as 4:1 or 9:1.

[0016] In one aspect of the disclosure, the system may further include a first processor configured to bias the first plurality of optical sensors during a readout period and receive outputs via the third plurality of energy readout channels and at least two timestamps associated with each energy readout channel.

[0017] In one aspect of the disclosure, the system may further include a second processor in communication with the first processor, the second processor configured to determine timing parameters for the event based on the received at least two timestamps.

[0018] In one aspect of the present disclosure, the timing parameter may be based on a combination of at least two timestamps. In some aspects, the timing parameter may be based on at least the earliest timestamp. In some aspects, the timing parameter may be based on a linear regression analysis of the at least two received timestamps.

[0019] In one aspect of the present disclosure, the second processor may be further configured to determine a time of flight (TOF) difference between the coincidence detection modules based on the timing parameter.

[0020] In one aspect of the present disclosure, the second processor may be further configured to determine at least one of a primary interaction pixel, a primary interaction scintillator module, or an interaction depth for the event. In one aspect of the present disclosure, the second processor may select at least two timestamps associated with the determined primary interaction pixel to determine the timing parameter.

[0021] In one aspect of the present disclosure, the second processor may be configured to determine the TOF using a machine learning model inputted with at least two timestamps received from the match detection module. [Brief explanation of the drawings]

[0022] [Figure 1A] FIG. 10 illustrates a multiplexing scheme according to aspects of the present disclosure having the cathode of the photosensor multiplexed to provide energy information and the anode of the photosensor multiplexed to provide multiple timestamps according to aspects of the present disclosure. [Figure 1B] FIG. 10 illustrates a multiplexing scheme for one energy channel and associated timestamp, where the anode of the light sensor is multiplexed to provide energy information and the cathode of the light sensor is multiplexed to provide a timestamp. [Figure 1C]FIG. 10 illustrates a multiplexing scheme for one energy channel and associated timestamp, where the anode of the optical sensor is multiplexed to provide energy information and a timestamp. [Figure 2A] FIG. 1 illustrates a particle detection device having a 4:1 scintillator module to light sensor coupling according to an embodiment of the present disclosure. [Figure 2B] FIG. 1 illustrates a particle detection system according to an embodiment of the present disclosure, in which there is a 4:1 scintillator module to light sensor coupling. [Figure 3A] 10A-B are top views of a segmented light guide and light sensor for a 4:1 scintillator module to light sensor coupling, where there are three different designs of segments of the segmented light guide. [Figure 3B] 1A-1C illustrate examples of 3D views of segments of a segmented optical waveguide, according to an embodiment of the present disclosure. [Figure 4] FIG. 1 illustrates a particle detection system according to an embodiment of the present disclosure, in which there is a 9:1 scintillator module to light sensor coupling. [Figure 5] FIG. 10 is a top view of a segmented light guide and light sensor for a 9:1 scintillator module to light sensor coupling, with three different designs of segments of the segmented light guide. [Figure 6] FIG. 1 illustrates a flowchart of a method according to an aspect of the present disclosure. [Figure 7] 10 is a flowchart of an example of training and testing a machine learning model for demultiplexing multiplexed ASIC energy channels, according to an embodiment of the present disclosure. [Figure 8] FIG. 10 illustrates an example of a machine learning model for demultiplexing multiplexed ASIC energy channels, according to aspects of the present disclosure. [Figure 9A] FIG. 10 illustrates a comparison between ground truth and demultiplexing multiplexed signals using a machine learning model according to an embodiment of the present disclosure for a 4:1 scintillator module to photosensor coupling. [Figure 9B]FIG. 10 illustrates a comparison between ground truth and demultiplexing multiplexed signals using a machine learning model according to an embodiment of the present disclosure for a 4:1 scintillator module to photosensor coupling. [Figure 9C] FIG. 10 illustrates a comparison between a synthetic multiplexed dataset and an actual multiplexed dataset multiplexed in accordance with aspects of the present disclosure. [Figure 9D] FIG. 10 illustrates a comparison between a synthetic multiplexed dataset and an actual multiplexed dataset multiplexed in accordance with aspects of the present disclosure. [Figure 10A] 10A-10C show a comparison of the DOI resolution in a related particle detection system and the DOI resolution of a particle detection system according to an embodiment of the present disclosure for a 4:1 scintillator module to photosensor combination. [Figure 10B] 10A-10C show a comparison of the DOI resolution in a related particle detection system and the DOI resolution of a particle detection system according to an embodiment of the present disclosure for a 4:1 scintillator module to photosensor combination. [Figure 11A] FIG. 10 illustrates a comparison between ground truth and demultiplexing multiplexed signals using a machine learning model according to an embodiment of the present disclosure for a 9:1 scintillator module to photosensor coupling. [Figure 11B] FIG. 10 illustrates a comparison between ground truth and demultiplexing multiplexed signals using a machine learning model according to an embodiment of the present disclosure for a 9:1 scintillator module to photosensor coupling. [Figure 12A] 10A-10C show a comparison of the DOI resolution in a related particle detection system and the DOI resolution of a particle detection system according to an embodiment of the present disclosure for a 9:1 scintillator module to photosensor combination. [Figure 12B] 10A-10C show a comparison of the DOI resolution in a related particle detection system and the DOI resolution of a particle detection system according to an embodiment of the present disclosure for a 9:1 scintillator module to photosensor combination. [Figure 13]1A-1C illustrate exemplary arrangements of optical sensor arrays and segmented optical waveguides according to aspects of the present disclosure. [Figure 14] 1B is a table illustrating multiplexed energy channels according to an embodiment of the present disclosure, as also shown in FIG. 1A. [Figure 15] FIG. 10 illustrates an example of a match detection module according to aspects of the present disclosure. [Figure 16] 1 is a flowchart of an example of training and testing a machine learning model for use in TOF prediction, according to an embodiment of the present disclosure. [Figure 17] FIG. 1 illustrates an example of a machine learning model for use in TOF prediction, according to an aspect of the present disclosure. [Figure 18] 10 is a table showing simulation results based on one, two, or three timestamps with DOI correction, illustrating improved coincidence timing resolution using multiple timestamps according to aspects of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0023] Disclosed is a multiplexing scheme that utilizes deterministic light sharing enabled by using segmented optical waveguides, such as those disclosed in U.S. Patent Publication No. 2020 / 0326434, which is incorporated by reference. The particle detection systems (and devices) described herein have single-ended readout (with depth encoding) with a special pattern of segments of a segmented pseudo-prismatic optical waveguide. The optical waveguide has at least the pseudo-prismatic segments described in detail with respect to FIG. 3A . According to embodiments of the present disclosure, the segmented pseudo-prismatic optical waveguide 200 has at least three distinct pseudo-prismatic designs, e.g., a central pseudo-prismatic prism 162, a corner pseudo-prismatic prism 166, and an edge pseudo-prismatic prism 168. The pseudo-prismatic prisms are designed to mitigate edge and corner artifacts, thereby achieving uniform crystal identification performance even when using the multiplexing scheme described herein.

[0024] Light sharing between scintillator modules 205 is limited to only scintillator modules 205 belonging to adjacent or nearby optical sensors 10 (e.g., nearest neighbors), creating a deterministic and anisotropic light sharing pattern between scintillator modules to maximize the signal-to-background ratio of the optical sensors 10 and improve both energy and DOI resolution while preserving high timing resolution for time-of-flight (TOF).

[0025] Due to the deterministic light sharing pattern, only a subset of photosensors 10 (pixels) from their nearest neighbors are required to accurately perform primary photosensor interactions and DOI (and estimate primary scintillator modules), since the relevant signals are contained within optically isolated pseudoprismatic segments.

[0026] FIG. 1A illustrates an example of a multiplexing scheme according to an embodiment of the present disclosure. As shown in FIG. 1A, optical sensors 101-10 64 (collectively 10) (e.g., photosensor array 210) are multiplexed. In one aspect of the present disclosure, multiplexing provides multiple energy readout channels 1001-100 16 Multiplexed outputs Y01 to Y16 (501 to 50 16 , collectively 50). The multiplexed outputs Y01-Y16 are inputs to the readout ASIC 405. As shown in FIG. 1A, there are four photosensors 10 per energy readout channel. The number of photosensors, the number of multiplexed photosensors, and the energy readout channels are not limited to 64, 4, and 16, respectively. Other combinations may be used. As shown in FIGS. 1A and 1B, a capacitor C may be connected to the cathode between the multiplexed output and the readout ASIC 405, with the cathode also connected to a bias 15.

[0027] Each photosensor 10 has an anode and a cathode. In FIG. 1A, the cathode is shown at the top of the pixel and the anode is shown at the bottom of each pixel. In one embodiment of the present disclosure, a bias 15 may be supplied to the cathode via a bias circuit. The bias circuit is not shown in FIG. 1A. The bias circuit may include one or more capacitors and one or more resistors.

[0028] In one embodiment of the present disclosure, optical sensors 101 to 10 64 may be arranged in rows and columns. For example, the photosensor array 210 may be an 8x8 readout array. However, the readout array is not limited to 8x8 and may have other dimensions, such as 4x4 or 16x16. In some embodiments, the readout array may be an integer multiple of two. A two-dimensional array may be formed in a plane perpendicular to the longitudinal axis of the scintillator module. In one embodiment of the present disclosure, the photosensor 10 may be a silicon photomultiplier (SiPM). In other embodiments of the present disclosure, the photosensor 10 may be an avalanche photodiode (APD), a single-photon avalanche (SPAD), a photomultiplier tube (PMT), or a silicon avalanche photodiode (SiAPD). These are non-limiting examples of solid-state detectors that may be used. The number of photosensors 10 (pixels) in a device may be based on the application and size of the PET system. In FIG. 1A, the photosensor 10 is labeled "SiPM pixel." The two-digit number in the lower right corner of each pixel represents the pixel number. For example, "01" represents the first pixel and "64" represents the last pixel. The numbers are for illustration purposes only.

[0029] Figure 13 shows an example of a photosensor array 210 having an 8x8 configuration (8 rows and 8 columns). In Figure 13, not all of the photosensors are numbered as SiPM pixels "XX," where XX represents a number.

[0030] The optical sensors (SiPMs 01-08) are in the first row, the optical sensors (SiPMs 09-16) are in the second row, ..., the optical sensors (SiPMs 57-64) are in the eighth row (last row). The optical sensors (SiPMs 01, 09, 17, 25, 33, 41, 49, and 57) are in the first column, the optical sensors (SiPMs 02, 10, 18, 26, 34, 42, 50, and 58) are in the second column, ..., the optical sensors (SiPMs 08, 16, 24, 32, 40, 48, 56, and 64) are in the eighth column (last). Figure 13 also shows an exemplary arrangement of pseudo-prismatic segments of segmented pseudo-prismatic optical waveguide 200 superimposed on optical sensor 10. The photosensors 10 are individually indicated by lines, and the scintillator modules (crystals) are represented by dotted lines.

[0031] 1A, the cathodes of the optical sensors 10 are multiplexed (via integrators 30) to generate an energy readout channel. The signal is integrated by the integrators 30 to provide the energy for the event.

[0032] The specific optical sensors 10 multiplexed for a given energy channel are selected such that optical sensors 10 connected to the same segment of the segmented pseudoprismatic optical waveguide 200 are not multiplexed. For example, segment 1 1301 (as shown in FIG. 13 ) is associated with optical sensors (SiPMs) 01, 02, 09, and 10. Therefore, light may be provided between optical sensors (SiPMs) 01, 02, 09, and 10. According to embodiments of the present disclosure, these optical sensors may not be multiplexed. Similarly, segment 2 1302 is associated with optical sensors (SiPMs) 56, 63, and 64. Therefore, light may be shared between them. According to embodiments of the present disclosure, these optical sensors may not be multiplexed. Similarly, segment 3 1303 is associated with optical sensors (SiPMs) 61 and 62. Therefore, light may be shared between them. According to embodiments of the present disclosure, these optical sensors may not be multiplexed. The arrangement shown in FIG. 13 is similar to the arrangement shown in FIG. 3A.

[0033] 14 shows an example of a multiplexing pattern for light sensors 10 (the same pattern as in FIG. 1A) in which the multiplexed light sensors in each energy channel are not associated with the same pseudo-prismatic segment of the segmented pseudo-prismatic light guide. In the example, at least one light sensor 10 (pixel) is among the light sensors connected to the same energy channel.

[0034] For example, in energy channel (ASIC_Energy_01) 1001, photosensors 101, 103, 105, 107 are connected to the channel (for illustrative purposes, not all pixels / photosensors are specifically labeled with the reference number 10). Photosensors 102, 104, 106, 108 are not connected to energy channel (ASIC_Energy_01). In other aspects of the disclosure, photosensors 102, 104, 106, 108 may be connected to energy channel (ASIC_Energy_01) 1001, and photosensors 101, 103, 105, 107 may not be connected to energy channel (ASIC_Energy_01) 1001.

[0035] (ASIC_Energy_01) 1001 to (ASIC_Energy_08) 1008 may be referred to herein as row channels (which may be referred to herein as horizontal channels) because the photosensors in a row are each connected to the same channel.

[0036] (ASIC_Energy_09)1009~(ASIC_Energy_16)100 16 In this specification, the optical sensors in a column may be referred to as column channels (or vertical channels) because each optical sensor in a column is connected to the same channel. For example, in the energy channel (ASIC_Energy_09) 1009, the optical sensors 109, 10 25 , 10 41 , 10 57 are connected to the same energy channel. 17 , 10 33 , 10 49is not connected to the energy channel (ASIC_Energy_09) 1009. In another aspect of the present disclosure, the optical sensors 101, 10 17 , 10 33 , 10 49 may be connected to an energy channel (ASIC_Energy_09) 1009, and the optical sensors 109, 10 25 , 10 41 , 10 57 may not be connected to the energy channel (ASIC_Energy_09) 1009.

[0037] As noted above, the channels are connected such that adjacent pixels in any direction are not connected to the same energy channel.

[0038] In one aspect of the present disclosure, the subset of photosensors in a row connected to an energy channel is offset by a column from the subset of photosensors in an adjacent row connected to that energy channel. For example, photosensors 101, 103, 105, 107 connected to (ASIC_Energy_01) 1001 are in columns C1, C3, C5, and C7, respectively. Thus, photosensors 109, 109A, 109B, 109C, 109D, 109E, 109F, 109H ... 11 , 10 13 , 10 15 may not be connected to (ASIC_Energy_02) 1002, and the light sensors 10 in columns C2, C4, C6, and C8 10 , 10 12 , 10 14 , 10 16 may be connected to

[0039] In one aspect of the present disclosure, the subset of photosensors in a column connected to an energy channel is offset by a row from the subset of photosensors in the column row connected to that energy channel. 25 , 10 41 , 10 57are located in rows R2, R4, R6, and R8, respectively. 10 , 10 26 , 10 42 , 10 58 (In column C2) is (ASIC_Energy_10)100 10 , and the light sensors 102, 103 in columns R1, R3, R5, and R7 18 , 10 34 , 10 50 may be connected to

[0040] According to aspects of the present disclosure, the same optical sensors multiplexed for energy are also multiplexed to generate at least two timestamps, e.g., timing information. As shown in FIG. 1A, the anodes of the optical sensors are multiplexed for timing, and the multiplexed outputs for timing are labeled X01-X16 (551-555) in FIG. 1A. 16 , collectively 55). X01 through X16 can be inputs to the readout ASIC 405. In embodiments of the present disclosure, the anodes can be used because they are generally faster than the cathodes. The anodes are connected to at least two comparators 20 (two timestamps) within the readout ASIC 405. As shown in FIG. 1A, there are three comparators 20 associated with each energy channel. Each comparator 20 is associated with a different voltage threshold: V_th1, V_th2, and V_th3. The voltage thresholds can correspond to different numbers of photons. The same three voltage thresholds can be used for the comparators associated with the different energy channels ASIC_Energy_01 through ASIC_Energy_16 (collectively 100). When the multiplexed voltage exceeds the respective threshold, each comparator 20 outputs a transition (e.g., X01_T1, X01_T2, and X01_T3 for ASIC_Energy_01, ..., X16_T1, X16_T2, and X16_T3 for ASIC_Energy_16). The transition time for each comparator can be used as a timestamp.

[0041] In some embodiments of the present disclosure, the timestamps may be combined to determine timing parameters for events for a detection device (also referred to herein as a detection module). This timing parameter may then be used to determine the TOF between the coincident detection devices. The TOF may be determined by considering the difference (coincidence) between the timing parameters of two opposing detection devices. FIG. 15 shows two detection devices (e.g., detection module 1 1501 and detection module 2 1502) and a radiation source 1500 therebetween. The radiation source 1500 may be aligned with the center of the two detection devices. The coincidence time resolution (CTR) is a measure of the accuracy in repeated TOF measurements at the same location of the radiation source 1500 (jitter). The CTF is determined by considering the full width at half maximum (FWHM) of the distribution of TOFs at a given fixed location.

[0042] The CTR can be improved by using multiple timestamps. In some aspects, the use of multiple time points can improve the CTR through leading edge slope estimation or waveform estimation. The leading edge slope estimation or waveform estimation can be performed via machine learning. For example, a convolutional neural network (CNN) can be used, as described later.

[0043] In other embodiments, the connections to the readout ASIC 405 may be preserved, and the connected anode multiplexed output 55' may be used for the energy channel, as shown in FIG. 1B, for example, as ASIC_Energy_01'. The cathode multiplexed output 50' may be used for timestamps, for example, X01_T1', X01_T2', and X01_T3'. While FIG. 1B shows only one multiplexed energy channel (and associated timestamps) for discussion purposes, other channels may have the same configuration.

[0044] In other embodiments, the same terminal (e.g., anode or cathode) may be used for both energy and timing information. For example, as shown in FIG. 1C, the anode of optical sensor 10 may be multiplexed such that the same multiplexed output 55″ is connected to integrator 30 and comparator 20 to generate an energy channel, e.g., ASIC_Energy_01, and timestamps, e.g., X01_T1″, X01_T2″, and X01_I3″. As with FIG. 1B, FIG. 1C shows only one multiplexed energy channel (and associated timestamps) for discussion purposes, although other energy channels may have the same configuration.

[0045] The multiplexed outputs Y01-Y16 and the multiplexed outputs X01-X16 may be connected to a readout ASIC 405 (also referred to herein as the first processor). The readout ASIC 405 may include a comparator 20 and an integrator 30. When the output changes, the timing is recorded. The readout ASIC 405 may also include an analog-to-digital converter for digitizing the signal from the photosensor array 210 and a circuit for controlling the bias. The readout ASIC 405 may also include a communication interface for transmitting the digitized signal to a remote computer 400 (also referred to herein as the second processor) via a synchronization board 410. The synchronization board 410 synchronizes the readouts from different detector devices / readout ASICs in the PET system. While only one detector device is shown in the system shown in FIG. 2B, in practice there may be multiple detector devices connected to the synchronization board 410. The multiple detector devices may include opposing detector devices (detection modules 1 and 2) 1501 and 1502 shown in FIG. 15. Each detector device may have a 4 to 1 read multiplexing as described herein. Reflector 215 is omitted from Figure 2B. However, each detector device has a reflector 215.

[0046] FIG. 2A illustrates a particle detection device having a four-to-one scintillator module to photosensor coupling 202 according to an embodiment of the present disclosure. Each scintillator module 205 may be fabricated from lutetium-yttrium oxyorthosilicate (LYSO) crystal. The scintillator module 205 is not limited to LYSO; other types of crystals that emit photons in the presence of incident gamma rays, such as lutetium oxyorthosilicate (LSO), may be used. In FIG. 2A, the photosensor array is represented as a SiPM array 210. However, as noted above, the array is not limited to SiPMs. The scintillator module 205 contacts the surface of the SiPM array 210 at a first end. While FIG. 2A illustrates a space between the scintillator module 205 and the SiPM array 210, in practice, the scintillator module 205 is attached to the SiPM array 210 via optical adhesive or epoxy. The optical adhesive or epoxy does not alter or attenuate the path of particles or light (if any, the alteration is minimal). Space is shown to show particles moving from the first end of the scintillator module to the SiPM array (pixel). The scintillator module 205 contacts the surface of the segmented pseudo-prismatic light guide (PLGA 200) at the second end. A reflector 215 is disposed on top of the PLGA 200. In one embodiment of the present disclosure, the reflector 215 may comprise barium sulfate BaS04. In other embodiments, the reflector 215 may comprise other reflective materials. In one embodiment of the present disclosure, a reflector 215 may be used between each of the scintillator modules 205. The reflector 215 may also fill any space between segments of the segmented pseudo-prismatic light guide 200.

[0047] FIG. 3A shows a diagram of a segmented light guide and light sensor for a 4:1 scintillator module-to-light sensor coupling, with three different designs for the segmented pseudoprismatic light guide segments. The bottom left corner of the diagram is a plan view showing the relative placement of scintillator modules (2 x 2) per light sensor. Also referred to as "crystals" in FIG. 3A. For illustrative purposes, only a subset of the array is shown. Three different designs of pseudoprismatic segments, e.g., central pseudoprismatic 162, corner pseudoprismatic 166, and edge pseudoprismatic 168, are shown with different hashing. The central pseudoprismatic 162 and edge pseudoprismatic 168 are shown with hashing in opposite directions, while the corner pseudoprismatic 166 is shown with crossed hashing. The top right corner of FIG. 3A shows examples of three different designs (both cross-sectional and perspective views). The corner pseudoprismatic 166 may be in contact with a scintillator module 205 that is in contact with three different light sensors (three pixels). The edge pseudoprism 168 may be in contact with a scintillator module 205 that is in contact with two different photosensors (two pixels). The center pseudoprism 162 may be in contact with a scintillator module 205 that is in contact with four different photosensors (four pixels).

[0048] Two adjacent optical sensors are identified using 142 and 144 in FIG. 3A. As shown in FIG. 3A, the pseudo-prism has a substantially triangular outline. However, in other aspects of the present disclosure, the pseudo-prism may be substantially shaped as at least one of at least one prism, at least one anti-prism, at least one frustum, at least one cupola, at least one parallelepiped, at least one wedge, at least one pyramid, at least one frustum, at least one sphere, at least one rectangular prism... Examples of specific 3D shapes (five different shapes of segments) are shown in FIG. 3B. For example, the shapes may be 1) a rectangular prism, 2) a pyramid, 3) a combination of a rectangular prism and a pyramid, 4) a triangular prism, 5) a combination of a rectangular prism and a triangular prism, etc. A combination of a rectangular prism and a triangular prism is shown in FIG. 3A, where the rectangular prism forms the base of the triangular prism.

[0049] In one embodiment of the present disclosure, each pseudoprismatic segment of the segmented pseudoprismatic light guide 200 is offset from the photosensor. In some embodiments, the offset is due to the scintillator module. In this embodiment of the present disclosure (and with a 4:1 module to sensor coupling), each scintillator module may share light with other scintillator modules from different photosensors (pixels). For example, when a photon enters a pseudoprismatic prism (segment of the light guide) following a gamma ray interaction with the scintillator module 205, the photon (i.e., particle 300) is efficiently redirected by the geometry to an adjacent scintillator module (of a different pixel), increasing light sharing between photosensors (pixels).

[0050] FIG. 4 illustrates another example of a particle detection system according to an embodiment of the present disclosure. In FIG. 4, there is a 9-to-1 scintillator module-to-photosensor coupling. The photosensor 10 is connected to the readout ASIC 405 in the same manner as the 4-to-1 readout multiplexing 1 described above (shown in FIGS. 1A and 2B). As in FIG. 2B, the readout ASIC 405 is connected to the computer 400 via a synchronization board 410. The synchronization board synchronizes the readout from different detector devices / readout ASICs in the PET system. While only one detector device is shown in the system illustrated in FIG. 4, there are actually multiple detector devices connected to the synchronization board 410. The multiple detector devices may include opposing detector devices (detection modules 1 and 2) 1501 and 1502, as shown in FIG. 15. Each detector device has the 4-to-1 readout multiplexing 1 described herein. The reflector 215 is omitted from FIG. 4; however, each detector device does have a reflector 215. The computer 400 may include at least one processor, memory, and a user interface, such as a keyboard or display, which may be used by an operator to specify the reading interval or period.

[0051] In one embodiment of the present disclosure, each pixel (except the four corner pixels) may have nine scintillator modules 205. The corner pixels may have four scintillator modules. Figure 5 shows segments of a light guide. Similar to Figure 3A, segments with different designs are shown in the lower left with different hashing. The lower left portion of Figure 5 shows only a representative portion of the array 220. The solid lines around the group of scintillator modules or crystals in the lower left indicate the pixel (SiPM pixel), while the dashed lines indicate the module or crystal. Three different designs of pseudoprism segments, such as the central pseudoprism 162, the corner pseudoprism 166, and the edge pseudoprism 168, are shown with different hashing. The central pseudoprism 162 and the edge pseudoprism 168 are shown with hashing in opposite directions, while the corner pseudoprism 166 is shown with crossed hashing. In the 9x1 configuration, only the corner pixels may have 4x1 connections, so the profile of the corner pseudoprism 166 in the 9x1 configuration may differ from that in the 4x1 configuration. The right side of Figure 5 shows several different central pseudoprism positions relative to the pixels (and scintillator modules). Not all SiPM pixels (photosensors) are shown on the right side of Figure 5. In Figure 5, nine central pseudoprisms are shown to illustrate nine different first-order interaction scintillator modules (first-order interactions). For example, if the first-order interaction scintillator module is module 139 (the central scintillator module in the segment), the segment directs particles to four adjacent optical sensors / pixels 142, 144, 148, and 148. The "X" in Figure 5 refers to the first-order interaction scintillator module. Segments 132 and 134 may not be adjacent to each other, but appear adjacent in the drawing.

[0052] The corner pseudoprisms 166 in this configuration can redirect particles between the ends (three different photosensors / pixels) of a group of five scintillator modules (whose ends are in contact with the segments). The edge pseudoprisms in this configuration can redirect particles between the ends (two different photosensors / pixels) of five scintillator modules (whose ends are in contact with the segments).

[0053] In other configurations, even a corner photosensor / pixel 10 may be in contact with nine scintillator modules 205 .

[0054] In one aspect of the present disclosure, the scintillator module 205 may have a tapered end, as described in PCT Application No. US21 / 48880, entitled "Tapered Scintillator Crystal Modules And Methods Of Using The Same," filed September 2, 2021, the contents of which are incorporated by reference. The tapered end is a first end, e.g., a scintillator module / light sensor interface.

[0055] As noted above, the deterministic light sharing scheme induced by the segmented waveguide 200 ensures that inter-scintillator module light sharing occurs only between scintillator modules coupled to the same optically isolated pseudo-prismatic light waveguide, which enables the multiplexing herein to maintain high center-of-mass TOF and DOI and energy resolution.

[0056] FIG. 6 shows a flowchart of a method according to an embodiment of the present disclosure. For purposes of illustration, the functions described below are performed by a processor of the computer 400. At S600, the processor issues a command (via the synchronization board 410) to the readout ASIC 405 to read out signals from the optical sensor array. This may be in the form of a frame synchronization command. When the readout ASIC 405 receives the command, the readout ASIC 405 provides power to the optical sensor array 210. In some embodiments of the present disclosure, there is a switch that is controlled to close to provide bias. The readout ASIC 405 receives multiplexed signals Y01-Y16 50, respectively (via connections) for use with energy and X01-X16 55, respectively (via connections) for timing (or vice versa), or both. The multiplexed signals Y01-Y16 50 are integrated, digitized, synchronized (via the synchronization board 410) to obtain the respective energy channels, and transmitted to the computer 400. The multiplexed signals X01-X16 may be sent to comparators 20. Each comparator outputs a value for T1, T2, and T3, respectively, associated with each energy channel. The timing of the changes may be noted, digitized, and sent to computer 400. While FIG. 1A shows three comparators, the number of comparators is not limited to three. In some embodiments of the present disclosure, at least two comparators may be used.

[0057] In other aspects of the present disclosure, the outputs of the comparators may be combined through one or more logic gates before transmission to the computer. For example, the output from a first comparator may be sent to one logic gate, the output from a second comparator may be sent to a different logic gate, etc.

[0058] In one aspect of the present disclosure, the computer 400 includes a communication interface. In some aspects, the communication interface may be a wired interface.

[0059] At S605, the processor receives digitized signals from each of the energy channels ASIC_Energy 01 through ASIC_Energy 16 100 and timing signals, e.g., digitized outputs, from the comparators 20 (associated with each energy channel). In other embodiments, the processor may receive the digitized signals from outputs combined via logic gates. In some embodiments of the present disclosure, the digitized signals from each of the energy channels ASIC_Energy 01 through ASIC_Energy 16 100 are associated with a channel identifier so that the processor can recognize which digitized signal corresponds to which channel. The digitized signals may be stored in memory. In one embodiment of the present disclosure, the computer 400 has a preset mapping that identifies which pixels are connected (multiplexed) to each channel. The mapping may be stored in memory.

[0060] At 610, the processor may identify a subset of energy channels ASIC_Energy_01 through ASIC_Energy_16 that have the highest digitized signals for an event (for each event), e.g., the highest X energy. Each event is determined with respect to a time window. The event window begins with the first SiPM that senses a particle. The window is "open" for a set period of time, which may be a few nanoseconds. Particles detected within the window (from any SiPM) are grouped and considered to belong to the same event. In one aspect of the present disclosure, the number of associated energy channels may be based on the location of the event. For example, if the primary interaction is located in the center of the array (associated with the central pseudoprism 162), the number of associated energy channels may be four. The processor may identify the four energy channels with the top four digitized signals for the event. If the primary interaction is located in a corner pseudoprism 166, the processor may only need to identify the three energy channels associated with the top three digital outputs. If the first order interaction is located at the edge pseudoprism 168, the processor may only need to identify the two energy channels associated with the top two digital outputs.

[0061] When light sharing is optically separated by segments, the primary interacting optical sensor (pixel) can be determined from the relationship between the energy channel and the particular highest digitized signal. This relationship allows adjacent optical sensors to be uniquely identified based on the pattern of energy channels with the particular highest digitized signal. At S615, the processor may determine the primary interacting optical sensor (pixel). For example, if the primary interacting optical sensor is central, the processor may use the stored mapping to determine the relative positions of the identified four energy channels associated with the top four signals. This narrows the primary optical sensor down to four adjacent optical sensors / pixels (out of 16 possible sensors / pixels connected to the identified channels). For example, if the top four channels are energy channels ASIC_Energy_02, ASIC_Energy_03, ASIC_Energy_10, and ASIC_Energy_11, the processor may identify SiPM pixels 10, 11, 18, and 19 as adjacent optical sensors, e.g., adjacent pixels. The processor may then determine which of the four energy channels has the highest signal. The photosensor (out of the four narrowed-down adjacent photosensors) associated with the energy channel with the highest sensor is identified as the primary photosensor / pixel (primary interaction). For example, if the highest signal of the four energy channels is ASIC_Energy_03, the processor may determine that the primary interaction photosensor (pixel) is 19 (narrowed-down from 17, 19, 21, and 23 connected to ASIC_Energy_03).

[0062] If the primary interaction optical sensor is a corner, the processor may use the stored mapping to determine the relative positions of the identified three energy channels associated with the top three signals. In other embodiments, the processor may still use the four energy channels with the top four signals. This narrows the primary interaction optical sensor down to three adjacent optical sensors / pixels. The processor may then determine which of the three energy channels had the highest signal. The optical sensor (of the narrowed down three adjacent optical sensors) associated with the energy channel with the highest sensor is identified as the primary optical sensor / pixel (primary interaction).

[0063] If the primary interaction optical sensor is an edge optical sensor (associated with an edge pseudoprism), the processor may use the stored mapping to determine the relative positions of the identified two energy channels associated with the top two signals. In other embodiments, the processor may still use the four energy channels with the top four signals. This narrows the primary interaction optical sensor down to two adjacent optical sensors / pixels. The processor may then determine which of the two energy channels had the highest signal. The optical sensor (of the narrowed down two adjacent optical sensors) associated with the energy channel with the highest signal is identified as the primary interaction optical sensor / pixel.

[0064] At S620, the processor may determine the DOI. The DOI may be determined using the following formula:

[0065]

number

[0066] Pmax is the digitized value associated with the energy channel with the highest signal (highest energy) for the event, and P is the sum of the digitized signals associated with the identified subset of the event's energy channels, which can be calculated after subtracting Pmax, if necessary. Because the segment optically separates adjacent optical sensors associated with the segment, the sum is effectively the ratio of the energy associated with the primary interaction optical sensor to the sum of the energies of the adjacent sensors. Once the processor identifies the primary interaction optical sensors, it knows how many energy channels to add (up to M energy channels), for example, four for the center pseudoprism optical sensor, three for the corner pseudoprism optical sensors, and two for the edge pseudoprism optical sensors.

[0067] This ratio can then be converted to depth using the following formula: DOI=m*w+q (2) where m is the slope between DOI and w according to the best-fit linear regression model, and q is the intercept so that the DOI estimation starts at DOI=0 mm. The parameters m and q can be determined in advance for the scintillator module 205.

[0068] Thus, according to aspects of the present disclosure, the multiplexed energy signals may be used to determine the DOI and the primary interacting optical sensor without having to demultiplex the energy signals using demultiplexing techniques described herein, such as machine learning or lookup tables. In other aspects of the present disclosure, the DOI may be calculated after the multiplexed energy signals have been demultiplexed according to aspects of the present disclosure, and then calculated from the demultiplexed energy signals, where P is the digitized value associated with the optical sensor / pixel with the highest demultiplexed value, and p is the sum of all of the demultiplexed values ​​of each optical sensor / pixel.

[0069] In one aspect of the present disclosure, the primary interaction scintillator module may be estimated using the multiplexed energy signal based on the relative magnitudes of the top four energy channels. Using the example identified above, if the top four energy channels, ASIC_Energy_02, ASIC_Energy_03, ASIC_Energy_10, and ASIC_Energy_11, are determined, then the top-left scintillator module associated with SiPM19 may be estimated to be the primary interaction scintillator module, given the light-sharing scheme of the central light segment (e.g., pseudoprismatic). Using the relative magnitudes, the processor may identify primary photosensors (pixels), vertical / horizontal neighbors, and diagonal neighbors. Diagonal neighbors may have the lowest energy among the identified subset of energy channels. Horizontal / vertical neighbors may be close in energy, e.g., have approximately equal energy channel outputs. Adjacent photosensors identified using the subset of energy channels may be associated with the same segment (due to light sharing).

[0070] The primary interaction light sensor and primary interaction scintillator module may be estimated as described above due to scattering and noise, but the same may be determined after the energy signals in energy channel 100 are demultiplexed as described herein.

[0071] In S625, the processor may demultiplex the multiplexed energy signals from the energy channels 100 to the full photosensor resolution. For example, the processor may take the multiplexed energy signals from energy channels ASIC_Energy 01 through ASIC_Energy 16 100 and generate M×M energy channel information (the number of photosensors in the system), where M is the number of rows and columns. For example, for an 8×8 readout array, there are 64 demultiplexed energy channels.

[0072] In one embodiment of the present disclosure, the transformation is based on a pre-stored machine learning model. Generating the machine learning model is described in detail later with respect to Figures 7 and 8. Specifically, the processor may use the multiplexed energy signal as an input to retrieve the stored machine learning model and output corresponding 64 energy channels of the demultiplexed energy signal corresponding to an 8x8 array.

[0073] In other embodiments, the processor may use a stored lookup table that associates the multiplexed energy signal with a demultiplexed energy signal at full energy channel resolution. The lookup table may be created using experimental data acquired from non-multiplexed energy channels. For an 8x8 array, the lookup table may be created from 64 energy channels of experimental data obtained from multiple events. For example, data from 64 energy channels of an event is acquired. The multiplexed data may be generated by a processor (software-based multiplexing) that adds the same energy channels as shown in FIG. 1A to generate 16 energy channel data (with 4 additional energy channels). The 16 energy channel data is then associated with the 64 energy channel data for later use. This process can be repeated for multiple events to create multiple correspondences, for example, 16 energy channels from 64 energy channels. Subsequently, when the multiplexed data is obtained from the readout ASIC 405, the processor looks up the 64 energy channel data. The processor may select the 64 energy channel data that corresponds to the 16 energy channel data that is closest to the actually detected energy channel data. The closest may be defined as the minimum root mean square error or mean square error. However, other parameters may be used to determine the closest 16 energy channel data stored in the lookup table. In other aspects of the present disclosure, the processor may interpolate 64 energy channel data based on the difference between the stored closest 16 energy channel data sets (e.g., the two closest data sets).

[0074] At S630, the processor uses the demultiplexed energy signals (e.g., signals representing the energy from each optical sensor to calculate an energy-weighted average). The energy-weighted average may be calculated by the following formula:

[0075]

number

[0076]

number

[0077] In the above equation, x i and y i are the x and y positions of the ith readout photosensor (pixel), and p i is the digitized signal read by the ith photosensor (pixel), N is the total number of photosensors (pixels) in the photosensor array, and P is the sum of the digitized signals from all photosensors (pixels) for a single gamma ray interaction event.

[0078] In S635, the processor may determine a primary interaction scintillator module based on the energy-weighted average calculated for each scintillator module 205. The scintillator module 205 with the highest calculated energy-weighted average may be determined as the primary interaction scintillator module. The photosensor (pixel) associated with the scintillator module 205 with the highest calculated energy-weighted average may be determined as the primary interaction photosensor (pixel).

[0079] In other aspects of the present disclosure, for example, instead of determining all three features of the primary interaction optical sensor (pixel), the primary interaction scintillator module, and the DOI, the processor may determine one of the three features or any combination of features, for example, only at least one of the three features.

[0080] At S640, the processor determines timing parameters for the event (for the detection device). This timing parameter can later be used to determine the TOF between the detection devices (e.g., detection module 1 1501 and detection module 2 1502). The timing parameters can be determined based on a timestamp received from the readout ASIC 405. In one aspect of the present disclosure, because the primary interaction light sensor (pixel) can already be determined, the processor can use the timestamp associated with this energy channel to determine the timing parameters. The processor can retrieve the timestamp associated with this energy channel from memory. For example, once SiPM 19 is determined to be the primary interaction light sensor (pixel), the processor can retrieve X03_T1, X03_T2, and X03_T3 from memory. These timestamps were obtained from comparator 20 (rising edge detector). In some aspects, the processor can retrieve only X03_T1 because the primary interaction light sensor can typically have the earliest timestamp. In an aspect of the present disclosure, the processor may perform linear regression to determine timing parameters for the event using the retrieved timestamps, for example, X03_T1, X03_T2, and X03_T3. In another aspect of the present disclosure, the processor may retrieve a machine learning model to predict the TOF (timing offset between coincident detection devices) (e.g., detection module 1 1501 and detection module 2 1502).

[0081] The machine learning model may be based on a neural network. However, the machine learning model is not limited to a NN. Other machine learning techniques, such as state vector regression, may be used. In some aspects of the present disclosure, the neural network may be a convolutional neural network (CNN), which will be described later.

[0082] Using multiple timestamps may improve the resolution for CTR because it may eliminate jitter.

[0083] In other aspects, the processor may use a first, less determined timestamp to determine the timing parameter. In some aspects of the present disclosure, the first timestamp may be determined by combining the timestamp output from the comparator with a minimum voltage threshold via a logic gate. Further timestamps may be determined in the same manner.

[0084] In other aspects, the timing parameters may be determined prior to determining the primary interacting light sensor (pixel).

[0085] 7 illustrates a flowchart of an example of training and testing a machine learning model for use in transforming or demultiplexing energy channels according to an embodiment of the present disclosure. The generation of the machine learning model for use in transforming or demultiplexing energy channels may be performed on computer 400. In other embodiments, a different device may perform the generation of the model for use in transforming or demultiplexing energy channels, and the model may then be transmitted to computer 400.

[0086] Different machine learning models (for demultiplexing) may be used for different scintillator module / photosensor array configurations. For example, a first machine learning model (for demultiplexing) may be used for a 4 to 1 scintillator module to photosensor array combination, a second machine learning model (for demultiplexing) may be used for a 9 to 1 scintillator module to photosensor array combination (and a third machine learning model for a 16 to 1 combination).

[0087] Different machine learning models (for demultiplexing) may be used for different scintillator modules (dimensions). For example, for the same combination (e.g., a 4-to-1 scintillator module to photosensor array combination), different ML models (for demultiplexing) may be used for scintillator modules having a 1.5 mm × 1.5 mm × 20 mm vs. a 1.4 mm × 1.4 mm × 20 mm. To acquire training / test datasets, a particle detection device including an array of scintillator modules, a segmented optical waveguide, and a photosensor array (connected to a readout ASIC) may be exposed to a known particle source. Instead of being multiplexed according to aspects of the present disclosure via a connection to the readout ASIC, the photosensor array is connected to the readout ASIC via N connections, where N is the number of photosensors 10 in the photosensor array. The device may be exposed at different depths and over multiple events. Digitized signals from each channel (e.g., 64 channels) are recorded for each event in S700. This full channel resolution is used as the ground truth for evaluating the model (during testing).

[0088] In S705, a multiplexed energy signal may be generated by adding a preset number of energy channels for each event. In one embodiment of the present disclosure, the processor adds signals from the same optical sensor according to the multiplexing scheme shown in FIG. 1A to obtain a multiplexed signal. This is to simulate the hardware multiplexing described herein. For example, the processor may add signals from four optical sensors to reduce the number of energy channels to 16. The computer-based multiplexed signal may be stored in memory. In S710, the processor divides the computer-based multiplexed energy signal generated for each event into a training data set and a testing data set. In some embodiments, 80% of the computer-based multiplexed energy signal may be used for training, and 20% may be used for testing and validation. Other divisions, such as 75% / 25% or 90% / 10%, may also be used. In some embodiments, the division may be random.

[0089] The machine learning model (for demultiplexing) may be based on a neural network. However, the machine learning model is not limited to a neural network. Other machine learning techniques, such as state vector regression, may be used. In some aspects of the present disclosure, the neural network may be a convolutional neural network (CNN). Furthermore, in some aspects of the present disclosure, the CNN may be a shallow CNN with a U-NET architecture. Hyperparameters, including the number of convolutional layers, filters, and optimizers, may be iteratively optimized.

[0090] Figure 8 shows an example of a CNN with a U-NET architecture.

[0091] The U-Net consists of an input layer 800 containing multiplexed data (16x1 that can be reshaped into a 4x4x1 matrix before feeding it to the CNN). The input layer 800 can be followed by a series of 2D convolutions, such as 807 / 809 in Figure 8. Convolution layers 807 and 809 can have 32 different 4x4 matrices (also known as "filters").

[0092] The convolutional layers 807 / 809 may be followed by a max pooling layer 811 to reduce its 2D dimensions to 2x2, additional convolutional layers 813 / 815 with 64 filters each, and another max pooling layer 817 to reduce the 2D dimensions to 1x1. After being reduced to a 1x1 dimensional space, the matrix may go through several convolutional layers 819 / 821 with 128 filters each before going through an expansion pass to return it to its original 4x4 dimensions and complete the "U" shape.

[0093] The expansion path includes a series of upsampling convolutional layers 823 / 829, where features are merged with corresponding layers 825 / 831 of equal dimensions and convolutional layers 827 / 833 with 64 / 32 filters, respectively. The output layer 837 may be a convolutional layer with four filters to provide a 4x4x4 matrix, which may then be reshaped to correlate with the 8x8 readout array. All convolutional layers of the U-Net may have 2x2 filters with stride = 1, followed by a rectified linear unit (ReLU) activation function. Conceptually, the U-Net may be formulated to demultiplex a single 4x4 matrix (computer-based multiplexed signal) fed into the input layer into an 8x8 matrix (demultiplexed), which is equal to the number of optical sensors in the array. Note that the shape of the input layer (matrix dimensions) and the number of filters in the output layer may be modified based on the readout array being used. For example, the input matrix may be 16x1. Additionally, multiplexed input matrices with smaller dimensions may be used.

[0094] The model may be trained using a training dataset in S715, where the training dataset is input at 800. The model may be tested using a test dataset in S720, where the test dataset is input at 800. The optimizer may be a modified version of the Adam optimizer. The initial learning rate may be 1.0. The performance of the model may be evaluated using an evaluation parameter in S725. For example, the evaluation parameter may be mean squared error (MSE). However, the evaluation parameter is not limited to MSE.

[0095] Once the model is validated using the evaluation parameters, the model may be stored in memory (within computer 400) or transmitted to computer 400 at S730 for subsequent use.

[0096] FIG. 16 illustrates a flowchart of an example of training and testing a machine learning model for use in TOF prediction for a coincidence detection device (e.g., detection module 1 1501 and detection module 2 1502). In S1600, a dataset for training / testing may be obtained. In some embodiments of the present disclosure, the dataset may be obtained empirically using a known radiation source 1500 at a location between detection module 1 1501 and detection module 2 1502. The location of the radiation source 1500 may be controlled via a fine motor stage. In embodiments of the present disclosure, the increment between locations is controlled to be smaller than the expected CTR. In some embodiments, the increment may be smaller than a value that produces a 100 ps CTR. The range of travel of the radiation source 1500 may be 0-50 cm. At each location, multiple events may be detected. For example, the number of events may be 1,000. In other embodiments, the number of events may be 5,000. In other embodiments, the number of events may be 10,000. In an embodiment of the present disclosure, the radiation source 1500 may be for 511 KeV gamma ray absorption. For rising edge detection, at least two thresholds may be used.

[0097] In other embodiments, the training / testing dataset may be obtained by simulating events using parameters of the actual detection module, including the length, width, and height of the scintillator module, the optical response of the silicon photomultiplier tube at various single-photon time resolutions, e.g., a 4:1 coupling reflector filling between the scintillator modules, the optical sharing segment (shape), the known response of the scintillator module to 511 KeV gamma ray interactions, the size of the SiPM, and the efficiency of the scintillator module and SiPM.

[0098] In S1605, the dataset may be split into a training set and a testing set. In some embodiments, 80% of the acquired dataset may be used for training, and 20% may be used for testing and validation. Other splits may be used, such as 75% / 25% or 90% / 10%. In some embodiments, the split may be random. In some embodiments, the proportion of the dataset may be hidden and used for training validation to ensure that overfitting does not occur.

[0099] FIG. 17 illustrates an example of a CNN that can be used to predict TOF (output TOF) according to an embodiment of the present disclosure. The input may have one input layer. The input layer may include at least two timestamps per event from each of the coincidence detection devices, e.g., detection module 1 1501 and detection module 2 1502. As shown in FIG. 17, three timestamps (three thresholds) are used for each detection device. Therefore, the input layer is 1 @ 3 × 2 (three timestamps for two detection devices). The input layer feeds into a convolutional layer 1702. There are 64 filters in the convolutional layer 1702. The second convolutional layer 1704 has 128 filters. The filters may be 1 × 1 filters, with a step size of 1, and may have a rectified linear unit (ReLU) activation function. The CNN may also have two fully connected (dense) layers 1706 and 1708 with ReLU activation. The dense layer 1706 has 256 filters (weights), and the dense layer 1708 has 64 filters (weights). The output Toff (e.g., TOF) is output via a fully connected layer (dense layer 1710), which has one filter with linear activation.

[0100] The above model may be trained using a training dataset at S1610, where the training dataset is input at 1700. The above model may be tested using a test dataset at S1615, where the test dataset is input at 1700. Stochastic gradient descent (SGD) with a momentum term may be used to train the optimization with an initial learning rate of 0.01. The performance of the model may be evaluated using an evaluation parameter at S1620. For example, the evaluation parameter may be mean squared error (MSE). However, the evaluation parameter is not limited to MSE.

[0101] Once the model for predicting TOF using the evaluation parameters has been validated, the model may be stored in memory (in computer 400) or transmitted to computer 400 at S1625 for later use.

[0102] Testing and Simulation The multiplexing scheme described above and demultiplexing using a machine learning model to demultiplex the multiplexed energy channels were tested with both a 4:1 scintillator module to photosensor array combination and a 9:1 scintillator module to photosensor array combination.

[0103] The scintillator modules were fabricated using LYSO and coupled to an 8x8 SiPM array (the photosensor array) at one end and to the segmented pseudoprismatic optical waveguides described above at the other end. The scintillator module array for the 4:1 scintillator module / photosensor array coupling consisted of a 16x16 array measuring 1.4mm x 1.4mm x 20mm, while the scintillator module array for the 9:1 scintillator module / photosensor array coupling consisted of a 24x24 array measuring 0.9mm x 0.9mm x 20mm.

[0104] Standard flood data acquisition was obtained from both scintillator module arrays (and sensors) by uniformly exposing them with a 3 MBq Na-22 sodium point source (effective diameter 1 mm) located 5 cm apart (at different depths). To evaluate DOI performance, depth-collimated data were acquired at five different depths along the 20 mm scintillator module length (2, 6, 10, 14, and 18 mm) using lead collimation (1 mm pinhole). Data readout was facilitated using an ASIC (TOFPET2) and a FEB / D_v2 readout board (PETsys Electronics SA). Computer-based multiplexing was performed as described above to achieve 16 x 1 scintillator module to energy channel multiplexing for a 4:1 scintillator module-to-photosensor coupling, and 36 x 1 scintillator module to energy channel multiplexing for a 9:1 scintillator module-to-photosensor coupling.

[0105] Photopeak filtering using computer-based multiplexing was performed with an energy window of + / - 15% for each scintillator module. To exclude Compton scattering events at the photopeak, only events where the highest signal was more than twice the second signal were accepted.

[0106] Demultiplexing of the energy signals generated via computer-based multiplexing was performed using the method described above via machine learning (CNN using the U-Net architecture). U-Net training was performed using 80% of the total dataset. To ensure that overfitting had not occurred, 10% of the training dataset was retained and used for training validation. Adadelta, a modified version of the Adam optimizer, was used for training optimization.

[0107] Batch sizes of 500 and 1000 epochs were used for training. The training loss was calculated by taking the average difference between the model estimate and the ground truth value across all events in each epoch. The model was trained to reduce the loss between successive epochs until a global minimum was found. Model convergence was observed by plotting the training and validation loss curves as a function of epochs and verifying that they reached asymptotic behavior with approximately equal minima.

[0108] Figures 9A and 9B show a qualitative comparison of the actual energy signals output from each of multiple photosensors (without multiplexing) and predictions obtained from a machine learning model trained and tested on computer-based multiplexed energy signals from a 4:1 scintillator module-to-photosensor coupling using the multiplexing scheme (demultiplexing) described herein. The results appear similar. For example, as the comparison shows, complete scintillator module separation was achieved for all center, edge, and corner scintillator modules, regardless of whether computer-based multiplexing (channels per pixel) was used. U is on the x-axis, and V is on the y-axis.

[0109] FIG. 9C shows an example of a composite data set (computer-based multiplexed energy data) generated by adding four sensor outputs in a similar manner (multiplexing) as described above, with the sensor outputs read at full resolution (e.g., 64). FIG. 9D shows an example of a multiplexed data set generated from the readout of the multiplexed energy signals from the readout ASIC 405, which is connected to the sensor array 210 via the multiplexing scheme described above. Comparing FIGS. 9C and 9D, it can be seen that the data sets are very similar, but slightly different due to imperfect model convergence. FIGS. 9C and 9D show the mapping in U' and V' spaces performed to display the channels as squares.

[0110] 10A and 10B show a comparison of the DOI resolution of a particle detection system according to an embodiment of the present disclosure for a 4:1 scintillator module-to-photosensor combination with the DOI resolution of a related particle detection system for five different depths (2, 6, 10, 14, and 18 mm). The comparison is for a central photosensor in the photosensor array and another central photosensor in the photosensor array. In FIG. 10A, a "classical" calculation approach is used. In the classical approach, Equation 1 is calculated using the highest energy signal (photosensor- or pixel-based Pmax), and P is calculated from the sum of each energy channel (since there is no multiplexing, all 64 energy channel values ​​are added). In FIG. 10B, the DOI is calculated directly from the computer-based multiplexed energy signals. For example, Pmax was determined as the highest signal from 16 computer-based multiplexed energy signals, and P was determined from the sum of the highest four signals from the 16 computer-based multiplexed energy signals.

[0111] The DOI estimated distributions were similar for the non-multiplexed data (Figure 10A) and the multiplexed data (Figure 10B). The average DOI resolution across all measurement depths was 2.32 mm full width at half maximum (FWHM) for the non-multiplexed data (Figure 10A) and 2.73 mm FWHM for the multiplexed data (Figure 10B).

[0112] 11A and 11B show a qualitative comparison of the actual energy signals output from each of the multiple photosensors (without multiplexing) and the predictions obtained from a computer-based machine learning model trained / tested on multiplexed energy signals from a 9:1 scintillator module-to-photosensor coupling using the multiplexing scheme (demultiplexing) described herein. Excellent scintillator module separation was achieved in the center and edge scintillator modules, with comparable performance between the non-multiplexed data (FIG. 11A) and the multiplexed data (FIG. 11B).

[0113] 12A and 12B show a comparison of the DOI resolution of a particle detection system according to an embodiment of the present disclosure for a 9:1 scintillator module-to-photosensor combination with the DOI resolution of a related particle detection system for five different depths (2, 6, 10, 14, and 18 mm). The comparison is for a central photosensor in the photosensor array and another central photosensor in the photosensor array. In FIG. 12A, a "classical" calculation approach is used. In the classical approach, Equation 1 is calculated using the highest energy signal (photosensor- or pixel-based Pmax), and P is calculated from the sum of each energy channel (since there is no multiplexing, all 64 energy channel values ​​are added). In FIG. 12B, the DOI is calculated directly from the computer-based multiplexed energy signals. For example, Pmax was determined as the highest signal from 16 computer-based multiplexed energy signals, and P was determined from the sum of the highest four signals from the 16 computer-based multiplexed energy signals.

[0114] The DOI estimated distributions were similar for the non-multiplexed (Figure 12A) and multiplexed (Figure 12B) data. The average DOI resolution across all measurement depths was 3.8 mm full width at half maximum (FWHM) for the non-multiplexed data (Figure 12A) and 3.64 mm FWHM for the multiplexed data (Figure 12B).

[0115] The percentage errors of the CNN prediction for the energy-weighted averaging of the x and y coordinates were 2.05% and 2.15%, respectively, for a 4:1 scintillator module to light sensor combination, and 2.41% and 1.97% for a 9:1 scintillator module to light sensor combination. The percentage errors of the total energy detected per event for the multiplexed data following CNN prediction were 1.53% for a 4:1 scintillator module to light sensor combination, and 1.69% for a 9:1 scintillator module to light sensor combination.

[0116] The above tests demonstrate that differences in system performance using the described multiplexing scheme, as described herein, are minimized due to the deterministic light sharing resulting from the segmented pseudoprismatic optical waveguide. Note that observed differences may be a result of experimental conditions, such as using a 3 MBq Na-22 sodium point source (effective diameter 1 mm). Multiplexing provides data output from the photosensor array to the readout ASIC and connections. As the field transitions to DOI PET, minimizing data file size is particularly important, and depending on the readout scheme and DOI resolution (which determines the number of DOI bins), the number of effective lines of response (LOR) can increase by more than two orders of magnitude.

[0117] As mentioned above, using multiple timestamps per energy channel improves the CTR for the system. To demonstrate the improvement, events were simulated in software for two coincident detection modules. In the simulation, the energy channels were not multiplexed. However, because of light sharing, and because the multiplexing described above does not multiplex photosensors associated with the same pseudoprismatic segment, the CTR (and the respective timing in each module) should not be affected. Each detection module was simulated to have a 16 x 16 LYSO array. Here, each scintillator module was 1.5 mm x 1.5 mm x 20 mm. There was a 4:1 coupling. Each SiPM (pixel) was simulated to have dimensions of 3.2 mm x 3.2 mm. The segmented pseudoprismatic light guide described herein was used in the simulation. As described herein, the segmented pseudoprismatic light guide increases the light sharing ratio for all scintillator modules coupled to the same pseudoprismatic segment, thus introducing a depth-encoding signal. Reflective material between the scintillator modules was also included in the simulation.

[0118] 511 keV gamma-ray absorption was simulated as a spherical source (0.1 mm diameter) with an emission equal to the light yield of LYSO (approximately 27,000 photons / MeV). Events were dispersed based on the Beer-Lambert law for photoelectron absorption in lutetium versus depth in the scintillator. Energy deposition curves as a function of time were generated for each absorption and convolved with the photoresponse of a silicon photomultiplier tube at various single-photon time resolutions (SPTR = 10, 50, and 100 ps). An overall photopeak energy resolution of 10% was simulated.

[0119] The timestamps were generated based on three trigger thresholds (example voltage thresholds described herein) corresponding to the number of photons collected at the readout side (n = 5, 10, and 50 photons). The timestamps were generated based on uniformly distributed timing offsets (t) corresponding to the location offset from (0-50 cm). off = 0-1667 ps) (also referred to herein as TOF) was added to the timestamp from one of the two crystals for each coincident pair to simulate the actual movement of the radiation source between the coincidence detection modules.

[0120] While the ground truth DOI was known in the simulations, the DOI parameters used for CNN training and testing were calculated separately using an energy-weighted averaging method. Three separate simulations were performed to independently characterize the timing performance in these three regions: two center-matched crystals, two edge-matched crystals, and two corner-matched crystals. 60,000 events were simulated in each of the three cases for a total of 30,000 matched pairs per simulation.

[0121] For training, 100 epochs were used with a batch size of 20. The ground truth and CNN output t for each match pair in the test dataset offThe difference between the values ​​was calculated, and the standard deviation of the error distribution was calculated to characterize the CTR of the CNN. CNN performance accuracy was characterized by running each training case 10 times while reshuffling and redistributing the data between the training and test datasets, and calculating the mean and standard deviation of the CTR values ​​for each case.

[0122] The above-mentioned CNN (Fig. 17) uses TOF (T off ) were used to predict the CTR. Six different input layers were used: one timestamp, two timestamps, one timestamp with DOI correction, two timestamps with DOI correction, three timestamps, and three timestamps with DOI correction. Figure 18 illustrates the results table. The table is sorted by SPTR 100, 50, and 10, respectively. For each SPTR, six different input layers are shown. As can be seen, the CTR improves when two or three timestamps are used for one timestamp. For example, for an SPTR of 100, when one timestamp is used for the SiPM associated with the central pseudoprism 162, the CTR is 195 (SD of 2.3), but when two timestamps are used, the CTR is 136 (SD of 1.1), and when three timestamps are used, the CTR is even lower at 124 (SD of 1.5). Similar improvements are shown for other pseudoprism designs (corner or edge). When DOI correction is used (depth encoding is yes), the improvement is even more pronounced. As can be seen in Figure 18, the best result (highlighted) is with three timestamps and depth encoding is yes. Figure 18 shows a comparison with "classic CTR," which did not use TOF (depth encoding is no), calculated using machine learning and the difference in detected timestamps. To determine the contribution of TOF from DOI, a linear regression was performed between TOF and DOI with depth encoding, and its contribution was subtracted to obtain an accurate TOF estimate.

[0123] The terms "segment" and "pseudo-prismatic segment" are used interchangeably herein. The terms "segmented waveguide," "pseudo-prismatic optical waveguide," and "segmented pseudo-prismatic optical waveguide" are also used interchangeably herein.

[0124] As used herein, terms such as "a," "an," and "the" are not intended to refer to a singular entity only, but include a general class of which a particular example may be used for illustration.

[0125] As used herein, terms defined in the singular are intended to include terms defined in the plural, and vice versa.

[0126] References herein to "one aspect," "certain aspects," "some aspects," or "an aspect" indicate that the described aspect may include a particular feature or characteristic, but not all aspects necessarily include the particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same aspect. Furthermore, when a particular feature, structure, or characteristic is described in connection with an aspect, it is asserted that it is within the knowledge of one of ordinary skill in the art to affect such feature, structure, or characteristic in connection with other aspects, whether or not expressly described. For purposes of the following description, the terms "upper," "lower," "right," "left," "vertical," "horizontal," "top," "bottom," and derivatives thereof, shall refer to the device in relation to the floor and / or as oriented in the drawings.

[0127] Reference herein to any range of values ​​expressly includes each number subsumed within that range, including fractions and integers. By way of example, reference herein to the range "at least 50" or "at least about 50" includes integers such as 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, etc., and fractions such as 50.1, 50.2, 50.3, 50.4, 50.5, 50.6, 50.7, 50.8, 50.9, etc. In a further example, references herein to ranges "less than 50" or "less than about 50" include whole numbers such as 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, and fractions such as 49.9, 49.8, 49.7, 49.6, 49.5, 49.4, 49.3, 49.2, 49.1, 49.0.

[0128] The term "processor" as used herein may include a single-core processor, a multi-core processor, multiple processors located on a single device, or multiple processors in wired or wireless communication with each other and distributed over a network of devices, the Internet, or the cloud. Thus, as used herein, a function, feature, or instruction performed or configured to be performed by a "processor" may include the execution of a function, feature, or instruction by a single-core processor, the execution of collective or cooperative functions, features, or instructions by multiple cores of a multi-core processor, or the execution of collective or cooperative functions, features, or instructions by multiple processors, and each processor or core need not individually execute all functions, features, or instructions. For example, a single FPGA or multiple FPGAs may be used to implement the functions, features, or instructions described herein. For example, multiple processors may enable load balancing. In a further example, a server (also known as remote or cloud) processor may perform some or all functions on behalf of a client processor. The term "processor" also includes one or more ASICs, as described herein.

[0129] As used herein, the term “processor” may be interchangeable with the term “circuit.” The term “processor” may refer to, be a part of, or include processor hardware (shared, dedicated, or group) that executes code and memory hardware (shared, dedicated, or group) that stores code executed by the processor.

[0130] Furthermore, in some aspects of the present disclosure, a non-transitory computer-readable storage medium having electronically readable control information stored thereon is configured such that, when the storage medium is used in a processor, aspects of the functionality described herein are performed.

[0131] Furthermore, any of the above-mentioned methods may be embodied in the form of a program. The program may be stored in a non-transitory computer-readable medium and, when executed on a computing device (a device including a processor), is adapted to perform any of the aforementioned methods. Thus, a non-transitory tangible computer-readable medium is adapted to store information and to interact with a data processing facility or a computing device to execute the program of any of the above-mentioned embodiments and / or to perform the method of any of the above-mentioned embodiments.

[0132] A computer-readable medium or storage medium may be a built-in medium installed in a computer device body, or a removable medium detachably disposed from the computer device body. As used herein, the term computer-readable medium does not include a transitory electric or electromagnetic signal propagating through a medium (such as a carrier wave); therefore, the term computer-readable medium is considered tangible and non-transitory. Non-limiting examples of non-transitory computer-readable media include, but are not limited to, rewritable non-volatile memory devices (e.g., including flash memory devices, erasable programmable read-only memory devices, or masked read-only memory devices), volatile memory devices (e.g., including static random access memory devices or dynamic random access memory devices), magnetic storage media (e.g., including analog or digital magnetic tape or hard disk drives), and optical storage media (e.g., including CDs, DVDs, or Blu-ray discs). Examples of media incorporating rewritable non-volatile memory include, but are not limited to, memory cards, and media incorporating ROM, including, but not limited to, ROM cassettes. Additionally, various information about the stored images, such as property information, may be stored in any other format or provided in other ways.

[0133] The term memory hardware is a subset of the term computer-readable medium.

[0134] The described aspects and examples of the present disclosure are intended to be illustrative rather than limiting, and are not intended to represent all aspects or examples of the present disclosure. While basic novel features of the present disclosure as applied to various specific aspects of the present disclosure have been shown, described, and pointed out, it will also be understood that various omissions, substitutions, and changes in the form and details of the illustrated devices and their operation may be made by those skilled in the art without departing from the spirit of the present disclosure. For example, all combinations of elements and / or method steps that perform substantially the same function in substantially the same way to achieve the same results are expressly intended to be within the scope of the present disclosure. Furthermore, it should be recognized that structures and / or elements and / or method steps shown and / or described in connection with any disclosed aspect or aspect of the present disclosure may be incorporated into any other disclosed, described, or suggested aspect or aspect as a general matter of design choice. Moreover, various modifications and changes may be made, both literally and in their equivalents recognized in law, without departing from the spirit or scope of the disclosure, as set forth in the following claims. [Explanation of symbols]

[0135] 10 light sensors, SiPM pixels 101 Optical Sensor 102 optical sensor 103 Optical Sensor 104 optical sensor 105 optical sensor 106 optical sensor 107 optical sensor 108 optical sensors 109 optical sensor 10 10 Optical sensor 10 11 Optical sensor 10 12 Optical sensor 10 13 Optical sensor 10 14 Optical sensor 10 15 Optical sensor 10 16 Optical sensor 10 17 Optical sensor 10 18 Optical sensor 10 25 Optical sensor 10 26 Optical sensor 10 33 Optical sensor 10 34 Optical sensor 10 41 Optical sensor 10 42 Optical sensor 10 49 Optical sensor 10 50 Optical sensor 10 57 Optical sensor 10 58 Optical sensor 11 SiPM pixels 15 Bias circuit, bias 18 SiPM pixels 19 SiPM pixels 20 Comparator 30 Integrator 50 multiplexed outputs 50' Output 50'' output 100 Energy Channel 132 segments 134 segments 139 modules 142 optical sensors / pixel 144 optical sensors / pixel 148 optical sensors / pixel 162 Central pseudoprismatic 166 Corner Pseudo Prism 168 Edge Pseudo Prism 200 Segmented pseudo-prismatic optical waveguide, segmented optical waveguide, pseudo-prismatic optical waveguide 202 Optical Sensor Combination 205 Scintillator Module 210 Optical Sensor Array 210 SiPM array 215 Reflector 220 Array 400 Remote Computer, Computer 405 Readout ASIC 410 Sync Board 800 input layers 807 Convolutional Layer 809 Convolutional Layer 811 Max Pooling Layer 813 additional convolutional layers 815 additional convolutional layers 817 Max Pooling Layer 819 Convolutional Layer 821 Convolutional Layer 823 Upsampling Convolution Layer 825 layers 827 convolutional layers 829 Upsampling Convolutional Layer 831 layers 833 Convolutional Layer 837 Output Layer 1301 Segment 1 1302 Segment 2 1303 Segment 3 1500 radiation source 1501 Detection module 1, detection device 1502 detection module 2, detection device 1702 convolutional layers 1704 Second convolutional layer 1706 Dense layer 1708 Dense layer

Claims

1. a photosensor array comprising a first plurality of photosensors, each photosensor in the array corresponding to a pixel; a scintillator array comprising a second plurality of scintillator modules, the second plurality of scintillator modules being larger than the first plurality of photosensors, the scintillator modules contacting a respective photosensor at a first end of each of the scintillator modules; a segmented light guide comprising a plurality of pseudo-prismatic segments, the segmented light guide contacting second ends of the second plurality of scintillator modules, each pseudo-prismatic segment contacting a scintillator module in contact with at least two different photosensors, the at least two different photosensors being adjacent photosensors; Equipped with each pseudoprismatic segment configured to redirect particles between scintillator modules in contact with the respective pseudoprismatic segment; a third plurality of energy readout channels, a plurality of light sensors respectively connected to the energy readout channels, such that light sensors associated with the same pseudoprismatic segment are not connected to the same energy readout channel, and each energy readout channel has at least two timestamps associated therewith; For each energy readout channel, at least two comparators are connected to the plurality of photosensors for the same energy readout channel, each of the at least two comparators having a different threshold value; The particle detection system, wherein the timestamp is the time at which each comparator outputs a change based on a comparison with a respective threshold value.

2. The particle detection system of claim 1 , wherein the at least two timestamps are three timestamps.

3. The particle detection system of claim 1 , wherein the at least two comparators are connected to a respective anode of each of the plurality of optical sensors.

4. The particle detection system of claim 1 , wherein the at least two comparators are connected to a respective cathode of each of the plurality of optical sensors.

5. 2. The particle detection system of claim 1, wherein the third plurality of energy readout channels and the at least two comparators are connected to different terminals of the optical sensor.

6. 6. A particle detection system according to claim 1, wherein the number of said plurality of optical sensors connected to the same energy readout channel is four.

7. 7. A particle detection system according to any one of claims 1 to 6, wherein there is a 4:1 scintillator module to photosensor coupling.

8. 7. A particle detection system according to any one of claims 1 to 6, wherein there is a 9:1 scintillator module to photosensor coupling.

9. 9. A particle detection system according to claim 1, further comprising a first processor configured to bias the first plurality of optical sensors during a readout period and to receive outputs via the third plurality of energy readout channels and the at least two timestamps associated with each energy readout channel.

10. 10. The particle detection system of claim 9, further comprising a second processor in communication with the first processor, the second processor configured to determine timing parameters for an event based on the received at least two timestamps.

11. The particle detection system of claim 10 , wherein the timing parameter is based on a combination of the at least two timestamps.

12. The particle detection system of claim 10 , wherein the second processor is configured to determine a time of flight (TOF) difference between coincidence detection modules based on the timing parameters.

13. 13. The particle detection system of claim 10, wherein the second processor is further configured to determine at least one of a primary interaction pixel, a primary interaction scintillator module, or an interaction depth for the event.

14. 14. The particle detection system of claim 13, wherein the second processor is configured to select the at least two timestamps associated with the determined primary interaction pixel to determine the timing parameter.

15. 13. The particle detection system of claim 12, wherein the second processor is configured to determine the TOF using a machine learning model inputted with the at least two timestamps received from the coincidence detection module.

16. 12. A particle detection system according to claim 10 or 11, wherein the timing parameter is based on at least an earliest timestamp.

17. 12. A particle detection system according to claim 10 or 11, wherein the timing parameter is based on a linear regression analysis of the received at least two timestamps.

18. 18. A particle detection system according to claim 1, wherein the first plurality of photosensors are arranged in rows and columns, with adjacent photosensors in a row being connected to different energy readout channels and adjacent photosensors in a column being connected to different energy readout channels.

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