The WT-PET design consists of two vertically positioned flat detector panels spaced 50 cm apart, each 70 cm wide and 106 cm high, as shown in Fig. 1. The AFOV (106 cm) is sufficient for simultaneous head and torso imaging, and total-body imaging can be achieved by sliding the panels down during an acquisition.

Schematic illustration of the (left) single BGO monolithic detector coupled with a 8 \(\times\) 8 SiPM array. (Right) The detector comprised two flat panels, each one consists of 14 \(\times\) 20 monolithic detectors with the possibility of performing the scan in the stand position

Given the flat panel design, the detectors can be positioned much closer to the patient, reducing the number of detectors. Moreover, the WT-PET scanner will use newly developed monolithic BGO detectors [18]. The scintillator blocks are 50\(\times\)50\(\times\)16mm\(^3\) in size and coupled to an 8\(\times\)8 array of SiPMs. A total of 14 \(\times\) 20 = 280 detectors are used per panel. The detectors provide a 2D spatial resolution of 1.3 mm full width at half maximum (FWHM), a DOI resolution of 2 mm FWHM and a coincidence time resolution (CTR) of 327 ps FWHM [18]. These are average (measured) values, with the effects of crystal scatter already included. The combination of fewer detectors and overall cost-efficient detector technology brings the price of the proposed WT-PET design close to the price of a standard PET/CT scanner.

The main system specifications and simulation parameters used for the WT-PET system are shown in Table 1, next to the Quadra-like TB-PET for comparison.

Simulation of PET acquisitions is done using the Geant4 Application for Tomographic Emission (GATE) Monte Carlo software [19, 20]. GATE includes coincidence sorting, producing the listmode (LM) data that is later used for image reconstruction. All simulations, except for count rate performance and spatial resolution measurements, are performed for 30 seconds of data acquisition, since that is the high-throughput scan time that is being aimed for in the WT-PET design. In the case of the Quadra-like TB-PET system, measurements are done both without a maximum ring difference cut (322 MRD), as well as with a cut of 85 rings applied (85 MRD) [21]. A coincidence time window (CTW) of 5 ns is chosen for the WT-PET, whereas the Quadra-like TB-PET uses a CTW of 4.7 ns. The digitizer in the GATE simulation of the investigated scanners used the alternative coincidence sorter (enabled with allDigiOpenCoincGate = true) and the “takeAllGoods” multiples policy. Note that the simulation of the Quadra-like TB-PET is based on the physical geometry of the scanner, but certain differences could remain between the simulation and experiment in terms of coincidence processing and image reconstruction.

For image reconstruction, a locally developed image reconstruction software written in C++, called Quantitative Emission Tomography Iterative Reconstruction (QETIR), is used. QETIR includes maximum-likelihood expectation maximization (MLEM) and ordered subset expectation maximization (OSEM) algorithms for iterative listmode reconstruction. QETIR, as a flexible image reconstruction software, can be used with various scanner configurations [11, 22, 23]. Depending on the purpose of the reconstruction, both TOF LM and non-TOF LM can be utilized. In this study, all reconstructions are done with TOF, using no subsets. No regularization is included, nor is any post-processing done on the final reconstruction.

We know the exact interaction point of the gamma photons with the scintillator from the GATE simulation. Note that in case of crystal scatter, GATE returns an energy-weighted interaction point, which is a good estimate for monolithic detectors since positioning is done based on the light spread. To obtain realistic results however, it is essential to smear this interaction point. For the case of the WT-PET, since it is equipped with DOI-capable monolithic detectors, the interaction point of the gamma photon within the BGO scintillation crystal is smeared with a Gaussian in 3D, as shown in Fig. 2. This is a fair approximation for the spatial resolution in a monolithic detector, except for interactions close to the edges or close to the SiPM array, where due to surface reflections or lack of light spread a certain bias may be introduced, asymmetrically degrading the resolution [12]. The values used for smearing are equal to the average detector spatial resolution in each direction, that is \(\sigma _ =0.55\) mm (2D spatial resolution of \(\sim\) 1.3 mm FWHM) and \(\sigma _ = 0.85\) mm (DOI resolution of \(\sim\) 2 mm). These are values obtained for the whole detector, so that the aforementioned discrepancies with the physical detector should average out. If the smearing would place the interaction point outside of the scintillator, the interaction point is instead placed on the very edge of the detector to disallow non-physical LORs. This will introduce some bias (which is not necessarily representative of the physical detector), but the frequency of such an occurrence is rather small given the detector volume relative to its spatial resolution.

As the Quadra-like TB-PET makes use of non-DOI-capable pixelated detectors, a different method of uncertainty in the interaction point is utilized. In this case, all the interaction points within a detector pixel are shifted to the central plane along the depth of the pixel, and are then uniformly randomized within that plane, as shown in Fig. 2.

(Left) A single monolithic detector utilized in the WT-PET system where the ground-truth interaction point of the gamma photon (red star) is smeared along the X, Y, and Z axes. (Right) Schematic illustration of the smearing applied to interaction points of gamma photons (red stars) within a single scintillation crystal pixel as the smallest detection unit in the Quadra-like TB-PET

To estimate the spatial resolution of the WT-PET and the Quadra-like TB-PET systems, six F-18 point sources with a diameter of 0.5 mm and an activity concentration of 15.28 MBq/ml are simulated according to the NEMA NU2-2018 guidelines [24,25,26]. Three points are located at the central transverse slice of the scanners (1, 10, and 20 cm in the radial direction), and another three at 3/8 of the AFOV. The aforementioned point sources were simulated in a warm background to account for the utilized iterative reconstruction algorithm. Due to the cylindrical geometry of conventional PET scanners, these coordinates provide an estimation of the spatial resolution for any angle around the scanner axis. Given the unique configuration of the WT-PET however, an additional series of six F-18 point sources with similar radial and axial arrangements are simulated, rotated 90 degrees around the scanner axis.

To better map the spatial resolution of the scanners under investigation, additional point sources outside of the NEMA guidelines are simulated along specific axes of the scanners, as shown in Fig. 3. In the case of the Quadra-like TB-PET, point sources are placed on the radial, axial, and diagonal (longest possible LOR) axes in steps of 5 cm. For the WT-PET, they are placed on the X, Y, Z, and diagonal axes, again in 5 cm steps. These additional sources were simulated in a cold background for both systems.

Image reconstruction is done with QETIR, based on true coincidences only using the MLEM algorithm (no subsets), 0.5\(\times\)0.5\(\times\)0.5 mm\(^3\) voxel dimensions and 10 iterations, with no spatial resolution modeling inside the reconstruction.

Schematic Illustration of point source locations for the WT-PET (left) and the Quadra-like TB-PET (right). For the WT-PET, the diagonal point sources (pink) are positioned in 3D toward the corner of one panel, while for the Quadra-like TB-PET, the symmetrical configuration results in diagonal point sources confined to the XZ plane

To evaluate the sensitivity of the WT-PET and the Quadra-like TB-PET, a 70-cm-long F-18 line source with an activity of 1 MBq is placed at the center of each scanner, as well as offset by 10 cm in the radial direction. The line source was surrounded by five concentric aluminum sleeves of the same length. Given the non-cylindrical configuration of the WT-PET system, the line source is offset along two different radial directions, once along the detector panels (X-axis) and once toward the detector panels (Y-axis). Since both the WT-PET and the Quadra-like TB-PET have an AFOV of 106 cm, all simulations are additionally repeated with a 106 cm line source.

The count rate performance of any PET system is essential to evaluate the impact of increasing count rates on image quality. Based on NEMA specifications, count rate simulations for the WT-PET design were performed with a 70-cm-long line source of F-18 in water, at a 4.5 cm offset from the axis of the tomograph, placed in a polyethylene cylinder of 20.3 cm diameter and 70 cm height. Due to the unique configuration of the proposed design, two different offset directions were considered, where the source was placed at \(X = 4.5\) cm (shifted laterally, parallel to the panels), and then at \(Y = 4.5\) cm (shifted toward one of the panels). For the Quadra-like TB-PET, one source placement at \(X = 4.5\) cm was sufficient, given the cylindrical configuration of the detectors. The activity of the line source ranged from 0.045 to 41 kBq/mL, with an acquisition time large enough to ensure that each simulation has a minimum of one million prompt counts. This is followed by analyzing the GATE output files where the true, scatter, and random coincidence counts were sorted based on the GATE tags of event ID and Compton interactions. According to NEMA standards, only data from the central 65 cm of the AFOV was considered, and a mask in the transaxial FOV was applied to set to zero all voxels located further than 12 cm from the center of the scanner. The noise equivalent count rate (NECR) represents an effective true count rate and is defined as:

$$\begin \textrm= \frac \end$$

(1)

where T, S, and R are the true, scatter and random coincidence count rates, respectively.

The scatter fraction (SF) measures the relative system sensitivity to scattered radiation. Based on NEMA, the same source and phantom specifications as the NECR study are used to evaluate the SF of both systems. The single slice rebinning (SSRB) algorithm was used for the scatter fraction analysis [27, 28]. The SF is defined as the ratio of scattered events to total events for a low enough count rate at which random rates are below 1% of the true rate [26, 29]. It is expressed as:

$$\begin \textrm=\frac \end$$

(2)

The image quality of the WT-PET and Quadra-like TB-PET is evaluated using the NEMA image quality (IQ) phantom. It comprises of six hot spheres with various diameters (10, 13, 17, 22, 28, and 37 mm) placed in a warm background. The sphere to background activity concentration ratio was 4:1 for both scanners, with a background activity of 5.3 kBq/cc.

To better investigate the impact of limited angle artifacts, additional IQ phantom simulations are performed for the WT-PET, all with two additional lesions (10 mm diameter spheres with 4:1 activity ratio), placed at the edge of the anterior and posterior surfaces of the IQ phantom, mimicking melanoma lesions. In a first study, the IQ phantom positioned at the center of the AFOV is compared to an IQ phantom placed at 1/8 of the AFOV. In a second comparison, we investigate the impact of different TOF values (200, 400, 600, and 800 ps) on the reconstruction. The total acquisition time in all the cases is 30 s.

QETIR is used for image reconstruction. The reconstruction is done based on true coincidences only using the MLEM algorithm (no subsets), 2\(\times\)2\(\times\)2 mm\(^3\) voxel dimensions and 10 iterations. For both scanners, sensitivity and ground-truth attenuation correction are applied. The quality of the reconstructed image is evaluated based on the contrast recovery coefficient (CRC) calculated using the methodology proposed by NEMA [30].