Simulating NEMA characteristics of the modular total-body J-PET scanner—an economic total-body PET from plastic scintillators

Positron emission tomography (PET) is a well established diagnostic method enabling detection of a tissue pathology on a molecular level before it evolves to the functional or morphological abnormalities (McKenney-Drake et al 2018, Schmall et al 2019). Currently, routine PET imaging with devices of about 20 cm axial field-of-view (AFOV) (Grant et al 2016, Van Sluis et al 2019), in a single bed position, enables the diagnosis of individual organs only, and the diagnosis of the whole-body requires a combination of series of sequential images obtained from many patient positions in the scanner, thus only a time-dependent scan of the total-body is available (Houshmand et al 2015). With the advent of the total-body PET (TB-PET), precision medicine will be enhanced with a new toolbox that allows for the simultaneous molecular imaging of the whole human body, providing concurrent imaging of metabolic rate in near and distant organs (Cherry et al 2017, 2018, Badawi et al 2019, Efthimiou 2020, Jones 2020, Karp et al 2020, Moskal and Stępień 2020, Surti et al 2020a, 2020b, Vandenberghe et al 2020, Zhang et al 2020). Thanks to the high sensitivity, TB-PET enables the extreme reduction of the whole-body imaging duration or the lessen of the radiopharmaceutical dose (Majewski 2020), thus opening perspectives for application of PET to the wider group of patients (e.g. children Nardo et al (2020)) or patients suffering from systemic diseases (Yamashita et al 2014, Nakajima et al 2017, McKenney-Drake et al 2018, Borja et al 2020, Vandenberghe et al 2020). By the introduction of uExplorer, the first total-body PET, to the clinical practice (Badawi et al 2019) it was demonstrated (Zhang et al 2019, 2020) that in addition to the static standardized uptake value images, TB-PET may also deliver a kinetic model based parametric imaging of all tissues in the body, simultaneously. These new capabilities open promising prospects for quantitative improvements of diagnostic and prognostic assessments of e.g. oncological, cardiological and neurological diseases (Majewski 2020).

Yet, the high costs of the TB-PET scanner based on LYSO crystal scintillators, estimated to around $ 10 million or more (Cherry et al 2018), is a serious obstacle to the widespread use of this modality in clinical practice, including the medical research clinics. Therefore, reducing the cost of TB-PET production has become one of the important challenges taken by many research groups, and constitutes one of the hot research topics in this field. The considered solutions include: reduction of scintillator thickness (Surti et al 2013, 2020a), reduction of number of detectors by arranging them in sparse configuration (Zhang et al 2019, Zein et al 2020, Zhang and Wong 2017) or taking advantage of the Cherenkov light to improve timing properties with BGO crystals (Brunner and Schaart 2017, Gonzalez-Montoro et al 2017, Zhang and Wong 2017, Cates and Levin 2019, Kwon et al 2019, Gundacker et al 2020). In order to take advantage of the Compton scattering there is also an ongoing research aiming at combining standard PET tomography with Compton cameras (Grignon et al 2007, Donnard et al 2012, Lang et al 2012, Oger et al 2012, Lang et al 2014, Thirolf et al 2015, Hamidreza et al 2017, Aya et al 2017, Kuramoto et al 2017, Kenji et al 2020, Mizuki et al 2020, Yoshida et al 2020).

LYSO crystals account for about 50% of the total costs of the TB-PET scanner, while the rest of the costs comes mainly from readout electronics and SiPMs. An application of BGO crystals may reduce costs of the scintillators only by a factor of about 2 (Vandenberghe et al 2020). Thus, as it was argued in reference (Moskal and Stępień 2020), that the reduction of crystal thickness or exchange of the LYSO by BGO crystals will not lead to a sufficiently significant reduction of production costs. Therefore, one of the promising, economic solution for the construction of the TB-PET scanner is the exchange of the expensive crystals to cost-effective plastic scintillator strips arranged axially, further on referred to as Jagiellonian PET (J-PET) (Moskal et al 2011, 2014, 2015, 2016a, Niedźwiecki et al 2017, Moskal and Stępień 2020, Sharma et al 2020b, 2020a). The costs of components for the total-body plastic J-PET are expected to be about 5 times less than the crystal-based total-body PET (Moskal and Stępień 2020).

Table 1 compares basic properties of plastic scintillator with BGO and LYSO crystals which are currently used in PET detectors. The much higher density of crystals with respect to plastics, and the more effective registration of annihilation photons, can be compensated by the multi-layer geometry (Moskal et al 2016a) possible with the axial arrangement of plastic strips with the readout at the ends (Moskal et al 2014). The significantly lower light attenuation in plastic with respect to crystals (e.g. plastic scintillator BC-480 is characterized by 7 and 18 times longer light attenuation length compared to BGO and LYSO crystals, respectively) enables the effective light transport even up to 2 m long plastic strips. Moreover the negligible fraction of photo-electric effect for the interaction of 511 keV photons in plastic scintillators does not preclude the possibility of the scatter fraction (SF) reduction. When using plastic scintillators the scattering in the patient may be suppressed based on the measurement of the energy deposition due to the Compton interaction (Moskal et al 2014, 2016a).

Total-body J-PET (TB-J-PET) may constitute an economic alternative for the crystal TB-PET scanners, since plastic scintillators are more than an order of magnitude less expensive than BGO crystals, and plastic PET with axially arranged scintillator strips reduces also significantly costs of readout electronics and SiPMs. The reduction of the electronics cost may be achieved due to the fact that the readout (except the wavelength shifters (WLS) strips) is placed at the ends of the cylindrical detector compared to the coverage of the cylinder surface in case of the radially arranged blocks of crystal PET detectors (Moskal and Stępień 2020). Prospects and clinical perspectives of TB-J-PET imaging using plastic scintillators were recently described in Moskal et al (2019a), (2019b), Moskal and Stępień (2020). Prospects for fundamental physical questions can be found in Kamińska et al (2016), Moskal et al (2016b), (2018), Hiesmayr and Moskal (2019), Gajos (2020). In this article we assess the performance characteristics of TB-J-PET constructed from plastic scintillator strips. The spatial resolution (SR), sensitivity (S), SF, noise equivalent count rate (NECR) and image quality (IQ) for the TB-J-PET are estimated according to the National Electrical Manufacturers Association NEMA NU 2-2018 standards (NEMA 2018) by using Geant4 Application for Tomographic Emission (GATE) (Jan et al 2004, 2011, Sarrut et al 2014, 2021) and the dedicated analysis software developed by the J-PET group (Kowalski et al 2018, Krzemień et al 2020). We assess NEMA characteristics for few TB-J-PET configurations. Transaxial field-of-view with diameter of 78.6 cm is assumed for all studied geometries, while AFOV of 200 cm (total-body) and 140 cm (head and torso) is considered. In addition, the influence on the result due to the unknown depth-of-interaction (DOI) is studied comparing results obtained assuming: (i) an ideal case that the true interaction point is known, (ii) a case when the DOI is not known, and (iii) assuming the resolution for the determination of DOI (full width at half maximum (FWHM)) is equal to FWHM (DOI) = 10 mm. Moreover studies of SR as a function of maximum allowed axial distance between the interaction points (the maximum accepted oblique angle of the line-of-response (LOR)) were also conducted.

In the section Materials and methods (section 2) we define the geometry and structure of the TB-J-PET scanner, properties of the materials constituting the detector and the assumed temporal and SRs. This section describes also briefly the methods of how the NEMA characteristics are evaluated. Next, results of simulations and analysis are presented in the section Results (section 3), which is followed by the Discussion (section 4) section including comparison of TB-J-PET characteristics to the performance characteristics of current clinical solutions and the total-body crystal-based PET scanners, in particular to the total-body uExplorer (Cherry et al 2017, Zhang et al 2017, Cherry et al 2018, Badawi et al 2019) and PennPET Explorer (Karp et al 2020) systems. While the NEMA norms were designed for PET systems with small AFOV, they may not be adequate for the total-body PET scanners with AFOV exceeding 70 cm long phantoms and emission sources required by the NEMA NU 2-2018 (NEMA 2018). Therefore, in the Discussion section the results obtained according to the NEMA norm are compared to the values obtained for the longer sources with lengths of 140 and 200 cm.

Plastic scintillators (1.021.06 g cm⁻³) (Eljen Technology https://eljentechnology.com/images/technical_library/Physical_Constants_Plastic.pdf , Crystals https://crystals.saint-gobain.com ) are about 7 times less dense than LYSO crystals (7.07.4 g cm⁻³) (Mao et al 2013) and the linear attenuation coefficient for the 511 keV photons is much higher for LYSO and BGO (μ = 0.83 cm⁻¹ and μ = 0.96 cm⁻¹, respectively) than for plastic scintillator (μ = 0.096 cm⁻¹) (see table 1). This implies that in a single scintillator layer with thickness of 2–3 cm (typical thickness of scintillators used in PET (Conti 2009, Vandenberghe et al 2020)) most of annihilation photons hitting the detector are interacting in case of LYSO and BGO (81%–92% and 85%–94%, respectively) but only about a quarter (17%–25%) in case of plastic scintillators. Therefore, in case of TB-J-PET the registration efficiency is increased significantly by the application of multi-layer detection system with an effective total thickness larger than 3 cm in the case of two layers, see figure 1, e.g. for 2–3 cm thick layers the registration efficiency would be about 44%.

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2.1. Detector system configuration

2.2. Spatial and temporal resolution

In order to take into account the detector spatial and temporal resolution the simulated time and axial position of photons' interactions were smeared according to a Gaussian distribution. In case of axial resolution the FWHM of 5 mm of the Gaussian was assumed. Such a resolution is expected when applying a layer of WLS strips arranged perpendicularly to the scintillator strips (Smyrski et al 2014, 2017, Kowalski et al 2018).

For the estimation of the influence of the uncertainty of DOI reconstruction three scenarios are considered: (i) ideal case with DOI known from the simulations, (ii) standard case when DOI is estimated as center of the scintillator in the transaxial cross section, and (iii) assuming that the resolution of the determination of DOI can be approximated by the Gaussian function with a FWHM = 10 mm.

The expected values of coincidence resolving time (CRT) expressed as FWHM were estimated using a simulation method described in Moskal et al (2016a) and assuming that detector is built from BC-408 scintillators with a photon absorption length of 380 cm (table 1). Figure 2 presents the dependence of expected CRT value as a function of the AFOV for the case of unknown DOI in scintillators with thickness of 1.5 cm (solid line with dots), 3 cm (dotted line) and for the ideal case with known DOI (solid line). For the estimation presented in this article CRT values obtained for the 3 cm thickness with unknown DOI were used, which represents the worst case scenario.

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In order to account for the time resolution of the detector system, a simulated time of annihilation photon's interaction was smeared according to the Gaussian distribution corresponding to CRT = 190 ps and CRT = 240 ps for AFOV of 140 cm and 200 cm, respectively.

2.3. Simulation tools

2.4. Image reconstruction method

3D bin-mode filter-back-projection (FBP) with re-projection (FBP3DRP), implemented in Software for tomographic image reconstruction (STIR) (Thielemans et al 2012, Khateri et al 2019), was employed in our earlier works (Shopa et al 2017, Kowalski et al 2018, Moskal et al 2020). It is, however, impractical for 2-layer 2 m long J-PET due to the limitations of the geometries that the STIR framework supports: both multi-layer and continuous scintillators cannot be defined. Therefore, as a temporary solution, positions of scatterings inside scintillator strips (hits) are remapped onto a virtual single cylindrical layer in transverse plane and onto discrete rings along axial direction. Such procedure, though, may impose additional distortion and worsen axial resolution, undermining the benefits of re-projection at the same time (see the discussion in Shopa et al (2017)).

Alternatively, we developed a time-of-flight (TOF) FBP algorithm (TOF FBP), based on the idea presented in Conti et al (2005). Projection data is weighted twice: with a filter in frequency space and during back projection for each TOF bin. One could also define a more general, non-bin definition based on the summation over LORs. The reconstructed image f for an arbitrary voxel v is estimated using back-propagation operator ${ \mathcal B }$ as:

$$\begin{eqnarray}&&f({\boldsymbol{v}})=\sum _{i=1}^{{N}_{\mathrm{LOR}}}{f}_{i}({\boldsymbol{v}})=\sum _{i=1}^{{N}_{\mathrm{LOR}}}{ \mathcal B }{p}_{i}^{F},\end{eqnarray} \tag{ 1 }$$

where each filtered projection element

$$\begin{eqnarray}&&{p}_{i}^{F}\equiv {p}_{i}^{F}(s,\phi ,\zeta ,\theta ,t)={{ \mathcal F }}^{-1}\{W({\nu }_{s}){ \mathcal F }\left[{p}_{i}(s,\phi ,\zeta ,\theta )\right]\}\cdot h(t-{t}_{i}).\end{eqnarray} \tag{ 2 }$$

s, ϕ, θ, ζ are coordinates in projection domain of sinograms p_i (Bailey et al 2005), ${ \mathcal F }$ and ${{ \mathcal F }}^{-1}$ are 1D Fourier and inverse Fourier transform operators, respectively, which serve to operate between space domain (projection coordinate s) and frequency domain (coordinate ν_s ). W(ν_s ) is the ramp filter, i denotes the index of LOR, h(t) is TOF kernel and t_i is the temporal parameter which defines the position of annihilation along LOR. For each (ith) coincidence, the dimensionality of p^F _i is reduced from ${{\mathbb{R}}}^{5}$ to ${{\mathbb{R}}}^{2}$, since only s and t are not fixed, i.e. ${p}_{i}^{F}\equiv {p}_{i}^{F}(s,{\phi }_{i},{\zeta }_{i},{\theta }_{i},t)$.

The sum in equation (1) requires multiple integration over every LOR, which could be time consuming. Besides, TOF normalisation is essential, because each back-projection ${ \mathcal B }{p}_{i}^{F}$ is not made over the entire image plane, but is restricted by h(t) kernel instead. However, this can be ignored for the case of 1 mm NEMA source, since it is definitely smaller than the minimal sampling for the displacement coordinate s. Furthermore, formula (1) can be redefined directly in image space as asymmetrical three-component kernel: one along LOR, which represents TOF function h(t), second—along Z-axis, reflecting the uncertainty of hit position, and the third—as image-domain ramp filter, which operates on transverse plane along the direction, orthogonal to LOR. In this work, we shall use Gaussian definition for TOF and Z components, as it proved to be consistent with FBP3DRP and was successfully tested on both multi-layer and 2 m long scanners (Moskal et al 2020, Shopa 2020).

Each resulting image was additionally corrected by the sensitivity map of the TB-J-PET, generated beforehand in GATE using Monte Carlo method. For comparison, selected data for 140 cm long scanner were reconstructed using FBP3DRP. Since STIR operates with single layer geometries only, in the latter case hits were projected on ideal single layer cylindrical scanner. Furthermore, each strip was axially divided into 256 discrete sections—maximal value allowed for 1-byte representation of axial coordinate, set in SAFIR (Becker et al 2017)—a STIR extension which we employed for the conversion of data into suitable Interfile format. Each voxel of the reconstructed image for the STIR FBP3DRP had dimensions of 1.50 mm along x and y axes and 2.73 mm along the z axis. For our TOF FBP implementation a voxel had dimensions of 1.56 mm along x and y axes and 2.59 mm along the z axis.

Comparison of reconstruction results obtained using FBP3DRP and TOF FBP, for 140 cm long tomograph and the point source placed in position of (1, 0, 0) cm is presented in figure 3.

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The outcomes are fairly consistent with each other. Therefore, further on, for the estimation of SR we will use the TOF FBP which enables image reconstruction with multi-layer geometry without necessity of remapping interaction points onto single layer.

2.5. NEMA-NU2-2018 norm

2.5.1. Spatial resolution

The standard, approved for the estimation of SR by National Electrical Manufacturers Association (NEMA) (NEMA 2018), defines point-like source for the measurements and its positioning inside PET scanner: three transverse locations (x = 1 cm, 10 cm and 20 cm) and two axial—at the centre and at 3/8 of AFOV. The SR (point spread function—PSF) is defined as a FWHM of the reconstructed image, calculated for each direction separately. For the image reconstruction the TOF FBP method was utilised as explained above in section 2.4.

2.5.2. SF and NECR

SF of the PET scanner quantifies the sensitivity of the detector to scattered radiation. It is expressed as a ratio between the rates of scattered coincidences and the sum of scattered and true coincidences: ${SF}=\displaystyle \frac{S}{S+T}$. It is measured (or simulated) for relatively low source activity, such that the contribution of accidental coincidences is negligible.

NECR is the characteristic that shows the influence of scattered and random coincidences on the performance of the scanner as a function of the source activity and it is a measure of the effective sensitivity of the scanner (Conti 2009). The NECR is defined as: ${NECR}=\displaystyle \frac{{T}^{2}}{T+S+R}$, where T stands for the rate of true coincidences, S–scattered coincidences, R–random (accidental) coincidences.

For both SF and NECR, simulated phantom is a solid cylinder made of polyethylene with an outside diameter equal to 20.3 cm and length 70 cm. Parallel to the axis of the cylinder, a hole with diameter 0.64 cm is drilled in a radial distance 4.5 cm from the axis of the phantom. A line source insert is also made of polyethylene and it is a tube with the inside diameter 0.32 cm and outside diameter 0.48 cm. The tube may represent known activity and be placed inside the hole of the phantom.

In presented studies, two methods of estimating SF and NECR were used. The first one is based on the 'true' Monte Carlo information about the photons' propagation that is saved in the GATE output file. Having this information it is possible to judge if a coincidence is true, scattered or accidental.

On the other hand, in real measurements not all information about the photons' propagation is available. Because of that, we apply also a second method as proposed in the NEMA norm, which is based on the analysis of sinograms.

2.5.3. Sensitivity

The sensitivity of a positron emission tomograph is expressed as the rate of true coincidence events T normalized to the total activity A of the source. In order to calculate sensitivity, a linear 1 MBq source of back-to-back gamma photons with length of 70 cm was simulated along the axis of the scanner in the centre of the AFOV.

2.5.4. Image quality

In order to estimate the IQ, simulation of the IEC phantom with cold and hot spheres was performed with the 140 cm long AFOV detector. The phantom was positioned in the center of the AFOV. IQ was calculated based on regions of interest (ROIs) located in two cold and four hot spheres described in NEMA norms (NEMA 2018). Hot spheres of 10 mm (Sphere 10), 13 mm (Sphere 13), 17 mm (Sphere 17) and 22 mm (Sphere 22) diameter, and cold spheres of 28 and 37 mm diameter were simulated. The hot spheres were filled with the activity concentration of 4 times higher than the background region. All spheres centres were positioned in the same transaxial plane located 70 mm from the phantom lid. The 180 mm long cylinder of 51 mm diameter was positioned in the center axis of the phantom. Injection of the 53 MBq of (18)F-FDG dissolved in water was simulated. The scan time was set to 500 s.

In post-processing, positions of interaction points in scintillators were smeared with the FWHM of 5 mm (along axis of the detecting chamber), while the TOF resolution was set to 135 ps (FWHM). All the simulations were performed with GATE (Sarrut et al 2014, 2021).

The field of view of the scanner was set to 50 × 50 × 130 cm³. The voxel size was 2.5 mm³ isotropic. Only true coincidences were taken into reconstruction and their number was about 219 mln. The images were reconstructed with the LM-TOF-MLEM algorithm with the CASTOR (version 3.1) toolkit (Thibaut et al 2018). Twenty iterations were used. In the reconstruction, sensitivity and attenuation corrections were included.

Two IQ evaluation metrics were calculated: contrast recovery coefficient (CRC) and background variability (BV). In order to calculate aforementioned parameters, circular ROI was defined on each hot sphere. Furthermore, 12 circular ROIs were also defined on the phantom background. Then, they were replicated to four transaxial slices ± 1 cm and ± 2 cm resulted in 60 ROIs defined in the phantom background for each sphere in total. The CRC for each hot sphere with diameter d was calculated as follows:

$$\begin{eqnarray}&&{CRC}=\displaystyle \frac{{C}_{H,d}/{C}_{B,d}-1}{4-1},\end{eqnarray} \tag{ 3 }$$

where C_H,d was the mean counts in the hot sphere and C_B,d was the mean of the background ROI counts and 4 in delimiter stands for the true activity ratio between hot spheres and phantom background. The BV for each sphere with diameter d was calculated as follows:

$$\begin{eqnarray}&&{BV}=\displaystyle \frac{{S}_{d}}{{C}_{B,d}},\end{eqnarray} \tag{ 4 }$$

where S_d was the standard deviation of the background ROI counts.

2.6. Extension of NEMA norm for TB-PET scanners

3.1. Spatial resolution

In order to calculate SR, TOF FBP reconstruction was utilised as explained in section 2. Example images of point-like sources reconstructed with TOF FBP for the J-PET scanner with AFOV = 140 cm are presented in figures 4 and 5. It is visible that achievable SR is in the order of 5 mm. Axial SR (figure 4) improves with the axial distance from the center of the scanner, while the spatial radial resolution worsens with the distance from the scanner axis (figure 5). The values of FWHM and FWTM are given in tables 2–4.

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Table 2. Spatial resolution, expressed as FWHM and FWTM of PSF, determined for AFOV of 140 and 200 cm assuming an ideal case that DOI is known.

AFOV	Source position		FWHM (mm)			FWHM (mm)			Voxel dimensions (mm)
140 cm		1	3.8	3.4	4.8	6.3	5.5	10.1	1.56	2.59
	0	10	3.5	3.4	4.5	5.9	5.6	8.6
		20	3.8	3.6	4.6	6.1	5.9	8.8
	52.5 (3/8 AFOV)	1	4.2	3.8	5.8	6.7	6.3	9.3
		10	3.8	3.7	5.5	6.5	6.4	8.3
		20	4.0	4.0	5.5	6.5	6.6	8.5
200 cm		1	3.7	3.3	4.9	6.1	5.4	10.2	1.56	2.59
	0	10	3.4	3.2	4.5	5.7	5.4	8.7
		20	3.7	3.4	4.7	6.0	5.7	9.0
	7.5 (3/8 AFOV)	1	4.2	3.7	5.9	6.8	6.1	9.7
		10	3.8	3.7	5.6	6.4	6.3	8.4
		20	4.0	3.9	5.6	6.4	6.5	8.6

In table 2 the PSF values are shown for the idealized case of known DOI. The result indicates that in the center of the scanner, even with the relatively large scintillators cross section of 6 mm times 30 mm, FWHM values of PSF are equal to 3.3 mm, 3.7 mm and 4.9 mm for the TB-J-PET scanner, for radial, tangential and axial directions, respectively.

Table 3 presents results obtained assuming that DOI is unknown, and the center of the scintillator in the transversal plane is taken as a position of photon interaction. In this case, in the center of the scanner, the FWHM values of PSF, achievable for the assumed geometry, are equal or better than 5 mm (radial,tangential) for both AFOV = 140 cm and AFOV = 200 cm. In case of axial PSF the FWHM values of about 7.1 and 7.8 mm are obtained.

Table 3. Spatial resolution, expressed as FWHM and FWTM of PSF, determined for AFOV of 140 and 200 cm assuming that DOI is not known. For the case of AFOV = 200 cm results for the reconstruction with the limited axial distance between hits ${\rm{\Delta }}{Z}_{\max }$ are also presented.

AFOV	Source position		FWHM (mm)			FWHM (mm)			Voxel dimensions (mm)
140 cm		1	4.9	4.8	7.1	8.2	8.1	19.3	1.56	2.59
	0	10	6.2	4.8	7.2	10.5	7.9	18.4
		20	10.3	5.0	7.6	15.3	8.3	18.0
	52.5 (3/8 AFOV)	1	4.9	4.9	6.3	8.5	8.5	11.1
		10	6.0	4.8	6.2	10.3	8.0	10.6
		20	9.6	5.0	6.7	14.9	8.4	12.5
200 cm	0	1	4.8	4.8	7.8	8.3	8.0	23.3	1.56	2.59
	10	6.4	4.8	7.8	10.7	7.8	21.1
		20	10.5	5.0	7.9	15.5	8.2	21.3
	7.5 (3/8 AFOV)	1	4.9	4.8	6.7	8.6	8.2	13.7
		10	6.2	4.8	6.8	10.4	8.0	12.8
		20	9.4	5.0	7.1	14.9	8.5	14.7
200 cm ΔZmax = 30 cm	0	1	5.0	4.9	5.4	8.6	8.4	10.8	1.56	2.59
	10	6.1	4.9	5.2	10.3	8.2	10.0
		20	9.5	5.1	5.5	14.8	8.8	10.3
	75.0 (3/8 AFOV)	1	4.9	4.9	6.2	8.6	8.4	10.8
		10	6.0	4.9	6.1	10.1	8.3	10.0
		20	9.2	5.2	6.2	14.7	9.0	10.5
200 cm ΔZmax = 110 cm	0	1	4.9	4.8	7.2	8.3	8.1	19.2	1.56	2.59
	10	6.3	4.8	7.3	10.7	7.8	18.1
		20	10.4	5.0	7.7	15.5	8.2	19.0
	75.0 (3/8 AFOV)	1	4.9	4.8	6.7	8.6	8.2	13.8
		10	6.2	4.8	6.8	10.4	8.0	12.8
		20	9.4	5.0	7.1	14.9	8.5	14.7

Table 3 also shows results of SR estimated limiting axial (oblique) angle of LOR. Following (Zhang et al 2017) the test was performed restricting maximal axial distance ΔZ_max between each pair of hits to 30 and 110 cm. Obtained results indicate that the axial PSF improves from 7.8 to 7.2 mm with limiting axial acceptance distance ΔZ_max to 110 cm, and it improves further to 5.4 mm for ΔZ_max= 30 cm.

Finally the PSF values for the TB-J-PET were determined assuming that DOI can be reconstructed with the resolution described by the Gaussian function with FWHM of 10 mm (table 4). In principle, the WLS layer can allow for determination of DOI (Moskal and Smyrski 2018), yet this solution was not yet tested experimentally. The result presented in table 4 shows an improvement of radial, tangential and axial values of PSF with respect to the case when the DOI is unknown. Specifically the tangential SR is improved, and it is lower than 4 mm for all positions defined in the NEMA norm.

Table 4. Spatial resolution, expressed as FWHM and FWTM of PSF, determined for AFOV of 140 and 200 cm assuming that DOI is determined with the resolution of FWHM(DOI) = 10 mm.

AFOV	Source position		FWHM (mm)			FWHM (mm)			Voxel dimensions (mm)
140 cm		1	4.3	3.8	7.2	6.8	6.2	18.8	1.56	2.59
	0	10	4.8	3.8	6.6	8.1	6.2	15.4
		20	6.6	3.8	6.3	12.0	6.2	13.7
	52.5 (3/8 AFOV)	1	4.3	3.9	6.2	6.9	6.5	10.9
		10	4.8	3.9	6.0	8.3	6.4	9.8
		20	7.0	3.8	6.2	12.5	6.3	10.6
200 cm	0	1	4.3	3.8	7.6	6.9	6.2	22.5	1.56	2.59
	10	4.8	3.8	7.1	8.2	6.2	17.8
		20	6.6	3.8	6.7	12.0	6.2	16.0
	75.0 (3/8 AFOV)	1	4.3	3.8	6.6	7.0	6.4	13.3
		10	4.8	3.9	6.4	8.3	6.4	11.4
		20	6.8	3.8	6.5	12.3	6.4	12.2

3.2. SF and NECR

As it was described in section 2.5.2 both SF and NECR were estimated using two different methods. In the case of method based on sinograms, the detecting chamber is divided into 1 cm slices and a sinogram is calculated for each slice. After alignment and processing (see figure 6) the number of true coincidences (T) was disentangled from scattered and random (S + R) according to the prescription given in the NEMA norm (see lower panel of figure 6).

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To calculate SF and NECR based on the information available from the Monte Carlo simulations, firstly the rates of subsequent types of coincidences were calculated. These rates for true, detector-scattered, phantom-scattered and accidental coincidences are shown in figure 7 as a function of the activity concentration, calculated as the total source activity divided by the phantom volume. The determined rates were used to calculate the SF and the NECR as a function of the activity concentration. Results for SF and NECR are presented in table 5 and figure 8, respectively. The SF amounts to about 36% when using a standard length (recommended by NEMA-NU-2018 norm) of the phantom and source. There is no significant difference between obtained SF values for two studied lengths of the detector. Yet, the differences between SF values calculated with two methods are significant. It is due to the differences in the data selection. Narrower data cut in case of sinograms limits the number of false coincidences taken into account. A similar effect, namely that the SF obtained when using sinograms is smaller than the one obtained using true Monte Carlo method, was also observed in Yang and Peng (2015).

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Table 5. Scatter fraction determined for TB-JPET with AFOV of 140 and 200 cm. Results obtained based on sinograms and on true Monte Carlo are presented. Table includes estimations done for source and phantom length (SL) of 70, 140 and 200 cm.

Method	AFOV = 140 cm	AFOV = 200 cm
Sinograms, SL = 70 cm	35.6%	36.2%
True MC, SL = 70 cm	54.2%	54.3%
Sinograms, SL = 140 cm	37.4%	37.6%
True MC, SL = 140 cm	58.4%	58.2%
Sinograms, SL = 200 cm	38.2%	38.0%
True MC, SL = 200 cm	60.0%	59.9%

The NECR characteristics are presented in figure 8. Like in case of SF, the method based on the analysis of sinograms provides different values for NECR than obtained when using a true Monte Carlo method. The result obtained according to the methodology required by the NEMA-NU2-2018 norm (NEMA 2018) is shown in the right panel of figure 8. The maximum value of NECR for a standard length of the phantom is equal to 630 kcps (550 kcps) and is achieved at about 30 kBq cc⁻¹ (25 kBq cc⁻¹) for AFOV of 200 cm and 140 cm respectively. The longer the phantom, the lower value of activity concentration for which the NECR peak is obtained.

3.3. Sensitivity

Determined values of sensitivities are summarized in figure 9 showing the sensitivity profiles grouped according to the length of the detector. The value of sensitivity determined at the centre of the tomograph amounts to 38 cps kBq⁻¹ and 32 cps kBq⁻¹ for AFOV of 200 cm and 140 cm, respectively. Results for AFOV of 140 cm and SL of 200 cm were omitted.

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3.4. Image quality

In figure 10 exemplary reconstructed NEMA IEC images are presented for 5th iteration of TOF-MLEM in axial (left), coronal (middle) and sagittal (right) view. All the spheres could be easily distinguished from the background.

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CRC versus BV plots for hot spheres are presented in figure 11. All cases shown, typical trade-off between the CRC and BV parameters. The greatest value of CRC is observed for the biggest sphere (Sphere 22) and the lowest for Sphere 10. Values of the BV started from 0.02 and increased with the number of iterations.

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The performance characteristics presented in the above section were determined applying the prescription given in the NEMA-NU2-2018 norm (NEMA 2018). This norm requires estimations of SF and NECR using 70 cm long linear source and the scatter phantom of the same length. Such length was adjusted formerly to the short AFOV PET scanners being much shorter than 70 cm. In this article we considered total-body PET scanners with the AFOV of 140 and 200 cm and therefore, in addition to NEMA standards we performed estimations of the performance characteristics also for the source and phantom length of 140 and 200 cm. Table 5 indicates that while increasing the length of the phantom from 70 cm to 140 cm and 200 cm, the SF increases only slightly from 35.6% (36.2%) to 37.4% (37.6%) and 38.2% (38%), respectively for AFOV of 140 cm (200 cm). In turn, the maximum of NECR value (figure 8) is decreasing from 550 kcps (630 kcps) to 420 kcps (540 kcps) and 320 kcps (450 kcps) when increasing the phantom and source lengths from 70 cm to 140 cm and 200 cm, respectively for AFOV of 140 cm (200 cm).

The SR was determined for the ideal case when the DOI is known, for the cases when it is reconstructed with the precision of FWHM(DOI) = 10 mm and when it is unknown. In general we observed that in the center of the considered TB-J-PET scanner the radial and tangential resolution is better than 4.9 mm independent of the scenario and that the axial resolution varies between PSF = 4.8 mm (for the ideal case) and PSF = 7.8 mm (for the unknown DOI). In the case when DOI is determined with the uncertainty of 10 mm the radial SR varies between 4.3 mm (at the center) to 6.3 mm at the most distant NEMA defined point. The tangential resolution is equal to about 3.9 mm for all positions and axial PSF varies between 6.4 and 7.6 mm.

In table 6 the characteristics simulated for the double layer TB-J-PET are compared with the state-of-the-art PET scanners and the first TB-PET systems.

The SR estimated for the TB-J-PET (built from strips with 6 mm times 30 mm cross section) is equal to 4.8 mm transversal and 7.6 mm axial. Obtained results show that the SR depends significantly on the DOI resolution and can be improved down to PSF = 3.7 mm (transversal) and 4.8 mm (axial) when improving the DOI reconstruction precision. Thus the values of the SR expected for the TB-J-PET are comparable with the resolution of current clinical PET scanners.

The value of SF of 36.2% obtained for the TB-J-PET is in the range of typical SFs for other systems. The NECR is by 3.5–5 times larger with respect to standard PET and 2.4 times lower than of uExplorer.

The sensitivity in the center of the scanner is higher by 1.7–3.9 times with respect to current PET systems and lower by a factor of 4.6 and 1.4 with respect to uExplorer and PennPET Explorer, respectively. Yet, the sensitivity of TB-J-PET may be further increased by adding a third detection layer.

Reconstructed images of the NEMA IEC phantom and the CRC versus BV curves shows that good quality images could be obtained with the total body J-PET setup. However, the impact of other effects (point spread modelling, post-reconstruction filtering, different reconstruction algorithms, other corrections etc) have to be further carefully investigated.

In case of the total-body scan, the figure of merit (TB-FOM), a measure of the whole-body sensitivity, can be expressed as the rate of events registered and selected for the image reconstruction per rate of photons emitted from the whole-body. Taking into account an approximately triangular shape of the sensitivity profile, in the case of the 200 cm long source TB-FOM can be approximated as TB-FOM = 0.5 times S(@ 0cm) times AFOV / 200 cm. Comparing values of TB-FOM shown in table 6 one can infer that the sensitivity for the total-body scan (TB-FOM) of the J-PET is by factor of 12.6–8 larger with respect to TB-FOM of the current clinical PET scanners (in agreement with estimations presented in articles (Moskal and Stępień 2020, Vandenberghe et al 2020)), and it is by factor of 4.4 less than TB-FOM of uExplorer.

Performance characteristics of the total-body J-PET scanner (TB-J-PET) built from plastic scintillators were estimated according to the NEMA NU 2-2018 standards (NEMA 2018). The calculations were performed by means of the GATE simulation package (Jan et al 2004, 2011, Sarrut et al 2014, 2021) and the J-PET software analysis tools (Kowalski et al 2018, Krzemień et al 2020). For the TB-J-PET a double layer geometry with plastic strips with dimensions of 6 mm times 30 mm was assumed. The strips are arranged in modules forming 24-sided polygon with the inner diameter of 78.6 cm.

The performed simulations indicated that for the TB-J-PET with AFOV = 200 cm a SR of PSF = 3.7 mm (transversal) and PSF = 4.9 mm (axial) is achievable. The NECR peak of 630 kcps is expected at 30 kBq cc⁻¹ activity concentration, and the sensitivity at the center amounts to 38 (cps kBq⁻¹). The SF is estimated to 36.2%.

The values of SF and SR are comparable to those obtained for the clinical PET scanners as well as to the first total-body uExplorer PET. However, the NECR is by factor of about 4 larger with respect to standard PET systems. Moreover, the TB-J-PET sensitivity for the whole-body scan (TB-FOM) is by a factor of 12.6–8 larger with respect to current clinical PET systems with AFOV in the range from 16 cm to 26 cm, and by a factor of about 4.9 less than of uExplorer PET.

Though the whole-body sensitivity increase of the TB-J-PET is less than the one of uExplorer it is still a significant improvement with respect to the current 16–26 cm long PET systems (and can still be increased by adding a third detection layer). This makes J-PET an economic and alternative technology for the construction of the total-body PET systems. The cost of the TB-J-PET is expected to be a factor of 5 lower with respect to the LYSO based TB-PET systems (Moskal and Stępień 2020). This is mainly due to the application of the axially arranged long strips of plastic scintillators with readout at the edges, instead of the detectors built from radially arranged blocks of heavy scintillator crystals, thus reducing significantly not only the cost of scintillators but also the number of SiPMs and electronics channels. In addition to the discussed advantages, the mechanical robustness of plastics with respect to crystals allows for making the plastic total-body scanner lightweight, modular and portable, thus making TB-J-PET a promising cost-effective solution for the broad clinical applications of total-body PET scanners.

Sensitivity, SF and NECR were obtained not only for standard NEMA sources and phantoms with 70 cm length but also for longer ones with lengths of 140 and 200 cm equal to the length of scanners investigated in this article. We propose that the NECR characteristic should be redefined and the characteristic should be presented not for activity concentration but activity concentration normalized by the length of the phantom or just for the total activity used.

The authors acknowledge technical and administrative support of A. Heczko, M. Kajetanowicz and W. Migdał. This work was supported by the National Centre for Research and Development through grant INNOTECH-K1/IN1/64/159174/NCBR/12, the Foundation for Polish Science through the TEAM POIR.04.04.00-00-4204/17 programes, the National Science Centre of Poland through grants no. 2017/25/N/NZ1/00861, 2019/35/B/ST2/03562, the Ministry of Science and Higher Education through grants no. 6673/IA/SP/2016, 7150/E-338/SPUB/2017/1, the Austrian Science Fund through grant no. FWF-P26783 and the Jagiellonian University via project CRP/0641.221.2020. JB acknowledges the support of InterDokMed project no. POWR.03.02.00-00-I013/16.

The authors have no relevant conflicts of interest to disclose.