In the following, we report on (A) the proposed ODC-PET system geometry, (B) a simulation study of this system, and (C) the detector module design and its experimental evaluation.

A. system geometry

Considering the average size of a human torso and based on previous designs [29], the dimensions of the PET panels have been selected to be 256 \(\times\) 256 \(\times\) 12 mm3 each. The distance between the panels is not fixed and can be changed in the 200 to 300 mm range. Each one of the panels consists of a matrix of 4 \(\times\) 4 modules, and each module is built using small LYSO scintillator pixels of 2 \(\times\) 2 \(\times\) 12 mm3 each from TACrystal Co., Ltd, Taiwan. The LYSO pixels are arranged in 4 \(\times\) 4 matrixes of 8 \(\times\) 8 pixel elements each.

Each group of 4 \(\times\) 4 scintillation matrixes is coupled using optical grease (Saint-Gobain, BC-630 Silicone Grease) [47] to an array of 4 \(\times\) 4 AFBR-S4N44P164M BroadCom® SiPMs [48], each with an area of 4 \(\times\) 4 mm2. The SiPMs arrays are mounted on a Printed Circuit Board (PCB) designed explicitly for the project that allocates 4 \(\times\) 4 basic SiPM arrays to form a module of 64 × 64 mm2. The scintillator, module, and panel will be assembled identically to match and cover the sensitive surfaces of the SiPM detectors. Figure 1 provides drawings of the proposed system and the main components contained in 1 panel.

Fig. 1

From left to right, prototype detector element and components; detector module and components; and full panel detector. A sketch of the system being used as a torso imager is provided for a visual representation of the system

Regarding the detector block (scintillators & SiPMs) output signals, these are directly fed to the PETsys TOFPET2 ASIC boards, which are connected to the PETsys FEM acquisition card, and finally, to the PETsys data acquisition system (DAQ) for pre-processing. A total of 16 modules of 64 × 64 mm2 each, will be combined in a 4 × 4 matrix to form one panel of 256 × 256 mm2. Thus, a total of 32 modules are required to construct the two-panel system.

In the next stage of the project, it is planned to include a custom analog electronic readout between the SIPMs and the ASIC. The multiplexing readout is based on a previous design [49] and provides a reduction topology to shrink the number of signals to be digitalized in a ratio of 4 to 1. This is accomplished by merging the analog signals from the SiPMs allocated in the same row or column [41, 50]. Note that, after summation of the signals, there will be a common anode for all SiPMs belonging to one row (or column) thus allowing to preserve the rise time slope, which is key to achieve a significant reduction in crosstalk between the temporal channels of adjacent pixels and, thus, reduce the parasitic capacity of the connected SiPMs. Based on previous results with a semi-monolithic detector, see [49], we do not expect significant degradations in CTR performance. Finally, the multiplexed signals are connected to the PETsys chain.

Table 1 reports the number of elements needed to build the proposed ODC system with and without including the reduction readout topology.

Table 1 Number of elements needed to build the proposed ODC system with and without including the reduction readout topologyB. system simulations

To evaluate the expected performance of the double-panel design, simulations were performed using GATE v9.2 [51, 52]. The mechanical design of the system was based on previous studies [53, 54] aiming at ODC scanners. In this particular case, the aperture between panels can be adapted for different distance values to provide enough space for diverse patient sizes. In particular, the system has been simulated with panel distances of 200, 250, and 300 mm; these values have been selected since they are optimal for pediatric, standard-size, and plus-size patients, respectively. Figure 2a shows the simulated system with a phantom cylinder. This phantom is a solid cylinder composed of high-density polyethylene (0.95 g/cm3), the dimensions are 25 mm in diameter and 256 mm long.

Fig. 2

a Simulated geometry for the proposed ODC PET system based on two panels with variable distance. The simulated cylinder is also depicted. b Simulated geometry of the 4D PET, see [63]

In all simulations, the physics list “emstandard_opt4” was used, which is the list recommended for medical applications [55, 56] and, an energy blurring of 11% was included in the GATE code. Regarding the digitizer settings, the simulations include: TOF = 180 ps with an energy window of 357—613kev (30% below the photopeak for scatter correction and, 20% above the photopeak), and a coincidence windows of 5 ns. The simulations incorporate the main detector experimental components namely, optical coupling between the SiPMs and the Scintillation pixels (refractive index, n = 1.46), the treatment of the scintillator walls (polished surfaces + reflector/coating), air gap between elements.

For image reconstruction, a Maximum Likelihood Expectation Maximization (MLEM) algorithm was implemented [57], and an energy window in the range of 357 to 613 keV has been used. Detailed information regarding the MLEM software framework can be found in [58]. Also, TOF capabilities have been implemented in the reconstruction algorithm using the differences of timestamps of the coincidence events and binning the coincidence and scatter events in different histograms for each time bin [59]. During each MLEM iteration, a forward and backward projection for all the time bins was performed, weighting the system matrix considering the time boundaries in each bin [60]. Finally, scatter and attenuation correction have also been implemented in the reconstruction process to improve image quality [61]. For scatter correction, a double-energy window method was applied as detailed in [62], the events falling within the scatter window (± 30% at the photopeak level) were used to estimate the correction factor which is later used during the reconstruction. Regarding the attenuation correction, synthetic (simulated) μ-maps have been generated with the same dimensions and positions as all simulated phantoms and then, included in the MLEM reconstruction platform.

The sensitivity of the system has been calculated following the NEMA 2008 protocol [42] for the three mentioned panel distances (200, 250, and 300 mm).

Then, a study to find the number of time bins that maximize image quality was performed using a simulated image quality (IQ) NEMA NU-2 2008 phantom [42]. The NEMA IQ phantom has 50 mm length and 30 mm in diameter. It has two regions namely, rod-area (hot) and uniform-area that cover 20 mm and 30 mm axially, respectively. The rod-area contains cylinders of 1, 2, 3, 4, 5 mm in diameter and 20 mm in length. The uniform-area has two cold regions (filled with air and water) that occupy half of the axial plane (15 mm) and are of 8 mm in diameter. Thus, the total volume of the phantom is 35.3 cm3 and the active one is 35.32—Vcold = 35.2–1.5 = 33.8 cm3. In this simulation, the IQ phantom background was filled with a 5.3 kBq/ml activity and the hot rods with a 4:1 ratio. The IQ image was reconstructed with 20 iterations and a voxel size of 1 mm. A CTR value of 180 ps was selected since the targeted timing resolution for the system is < 200 ps. In particular, this selection was motivated by the fact that when we started the simulations, we only had data of two single collimated pixel elements with TiO2 coating. This pixel-to-pixel set-up yielded CTR values in the range of 170–187 ps FWHM depending on the acquisition conditions, and we felt confident at some point we will be reaching this value (after scaling up to a detector element and then to a module). Nevertheless, the Derenzo phantom analysis (explained in the following) was repeated but considering 200 ps CTR and no significant differences were observed in resolution.

The final reconstructed image of the phantom was also used to estimate the image Uniformity (see Eq. 2) and the Contrast Recovery Coefficients (CRC) (see Eq. 3).

$$Uniformity=100 \times \left(1-\frac_}_}\right)$$

(2)

$$CRC=100 \times \left(\frac_-_}_-_}\right)$$

(3)

For the analysis, the image slices covering the central 10 mm length of the IQ rods were averaged to obtain a single image slice of lower noise, and circular ROIs were drawn around each rod with a diameter that was twice the physical diameter of the rods. The maximum values in these ROIs were measured and calculated for both the non-TOF case and the TOF using 3, 5, 7, 9, and 11 time bins.

A simulation of a Derenzo phantom with rod diameters of 1.0, 1.2, 1.6, 2.4, 3.2, and 4.0 mm and an injected activity of 10 MBq was performed to assess image resolution. The simulation consisted on a 30 min long PET data acquisition and was reconstructed with 20 iterations and a 0.5 mm voxel size.

The reconstructed image was used to evaluate the accuracy in resolving rods in the Derenzo phantom using the Valley-to-Peak ratios (see Eq. 4). The Rayleigh criterion was applied to estimate the resolvability and, thus, the image spatial resolution of the proposed scanner; see equivalence 5 and reference [64].

$$\%Valley\;to\;Peak= 100 \times \left(\frac\right)$$

(4)

$$Rayleigh\;Criterion=0.735 (73.5\%)>Valley\;to\;Peak$$

(5)

B.1 imaging performance: conventional ring-shaped vs the proposed 2-panel ODC PET

The IQ and Derenzo phantom simulations detailed in Section. B have been repeated but using a conventional ring-PET. These results are compared with the ones reported by the 2-panel PET to verify the claim that including TOF information during the PET image reconstruction process partially compensates for the lack of angular projections and thus, systems like the proposed 2-panel PET can perform similarly to conventional ring-shaped PET in which all angular views are covered.

In particular, simulations of a brain-dedicated PET system have been used. The system is the so-called 4D PET, which consists on a conventional cylindrical scanner with a total of 320 semi-monolithic detectors arranged in 8 rings, see Figure 2b. The system defines an axial length of 200 mm and an internal diameter of 280 mm, and has 3D photon positioning and TOF capabilities. For specific details on the 4D-PET technology see reference [63].

Regarding image reconstruction, the same MLEM algorithm and the same settings than the ones used for the 2-panel ODC simulations have been implemented in the 4D PET case. Both non-TOF and TOF reconstructions are provided to validate the claim that including TOF capabilities during image reconstruction compensates for the missing angular projections. In the TOF reconstructions, CTR values (determined through the experimental evaluation of the modules [63]) of 350 ps and 180 ps FWHM have been used for the 4D PET and the ODC system, respectively. For the comparison, slices of the coronal and axial views of the phantoms, the source projection profiles of the smallest rods in the Derenzo phantoms of both systems, and the CRC values for the IQ phantom rods (non-TOF and ToF cases), are provided.

C. the prototype: detector element and module

Following the specifications described in the previous sections, a prototype detector element consisting of an 8 \(\times\) 8 matrix of LYSO pixels with sizes of 2 \(\times\) 2 \(\times\) 12 mm3 each, coupled to a matrix of 2 \(\times\) 2 AFBR-S4N44P164M BroadCom® SiPMs, was built.

Since the crystal surface finish and treatment play an important role regarding the transmission of the scintillation light to the photosensor and thus impacts CTR, spatial, and energy resolutions, two different crystal treatments were studied:

i.

All pixel elements have polished surfaces and are covered (except one of the 2 \(\times\) 2 mm2 faces, which is in contact with the photosensor) with an Enhanced Specular Reflective (ESR) foil. ESR are high reflectivity, mirror-like optical films. The selected ESR for the experiments has a reflectance of about 98.5% (VikuitiTM ESR film (3M, USA)) [43].

ii.

All pixel elements have polished surfaces and are coated (except the face in contact with the photosensor) with TiO2 white coat. The TiO2 is a type of coat composed of a titanium dioxide pigment mixed with water (soluble coat) [45], which acts as a diffuse reflector [65] and presents enhanced reflectivity for longer wavelength scintillators such as LYSO.

For the experimental evaluation, the setup consisted of one of the described detector prototypes but in which the 4 \(\times\) 8 crystals on the left side are covered with ESR, and the 4 \(\times\) 8 crystals on the right side are coated with TiO2, see Fig. 3. The SiPM outputs were connected to the PETsys DAQ and then sent to the workstation for analysis. A Python code was implemented for this purpose.

Fig. 3

Actual photos of reference and evaluation prototype detector. As can be seen in panel a the scintillation matrix includes the two treatments (TiO2 and ESR). b Photos of the experimental setup for coincidence measurements are shown indicating a label with the x- and y-axis orientations

To acquire coincide data, a reference detector based on a single 2 \(\times\) 2 \(\times\) 12 mm3 LYSO pixel coupled to a single SiPM was used. Both the evaluation and reference detectors were placed inside a black box to shield the modules from ambient light and were cooled down using compressed air. The detector (including the electronic board) temperature was kept in the range of 22 \(\pm\) 1 °C for all acquisitions.

Coincidence data was acquired by placing a 22Na source between the detectors; see the photos in panel (b) of Fig. 3. In the setup, the detector under evaluation was fixed on an XY table, and the reference one & source were sequentially moved simultaneously to evaluate both treatments.

Different combinations of these parameters were tested to determine the best PETSys threshold configuration [46] and best SiPM overvoltage (SiPMOV). In particular, the following values were considered: SiPMOV: [5, 9, 13], ThE: [15], Th1: [5, 11, 17, 23] and Th2: [5, 11, 17, 23]. A total of 48 combinations (for each treatment) were evaluated (see Table 2). Each acquisition lasted 20 min and was repeated three times to account for possible variances.

Table 2 SiPMOV and PETsys Threshold configuration combinations

These measurements were used to estimate the CTR and the relative photopeak gain, which is a good estimation of the light transfer to the photosensor and, thus, of the expected energy performance. Both the CTR and photopeak gain have been estimated as the Full-Width-At-Half-Maximum (FWHM) of the coincidence time difference between the evaluation and reference detectors and the energy spectra, respectively. The experimental errors have been calculated as the standard error calculated for three measurement trials and for each combination of parameters.

Once the surface treatment and the acquisition parameters that yield better performance were determined, two full modules, 64 \(\times\) 64 mm2 each, were mounted. Each component was carefully studied and mounted using custom-made holders for the scalability process.

Each module was built using four previous prototype detectors, i.e., 4 \(\times\) 4 matrixes of 8 \(\times\) 8 pixel elements each. All pixel elements were treated using TiO2 coating (see Section Results. B). Figure 4 shows the scaling-up process and the components used for constructing the modules.

Fig. 4

Photos showing the scaling-up process of the prototype detector to a full module. As depicted, the module comprises 16 scintillation blocks (64 LYSO pixels each) with TiO2 coat as treatment, 64 SiPMs, and 4 ASICs. A holder and black box were designed and 3D printed to ensure light shielding and to keep the temperature constant (using compressed air). Finally, a photo of the experimental setup for module evaluation (including PETsys DAQ) is shown

The two identical modules were placed inside a dark box, cooled down, and used to acquire coincidence data. The same non-collimated 22Na source was placed closer to one module between the detectors to increase the solid angle coverage and obtain a more homogeneous irradiation of one of the detectors. The Flood map was used to estimate the pixel resolvability and, thus, the expected spatial resolution. For CTR calculations, ROIs were drawn around clusters of 2 \(\times\) 2 scintillation pixels (1 SiPM, 4 \(\times\) 4 mm2) at five different random positions, namely: 1 \(\times\) corner (SiPM (1,1)), 2 \(\times\) lateral (SiPMs (2,6) and (14,14)), and 2 \(\times\) center (SiPMs (8,8), (10,9)). The acquired data was corrected for time-skew and, the coincidence events were energy filtered, only those coincidences falling within a ± 30% of the photopeak value were considered for CTR calculations. Then, the coincidence photon arrival time were histogram for each ROI and fitted using a Gaussian distribution, the total (module) CTR was finally estimated as the mean value of the CTRs for each ROI.