A Jaszczak phantom (Model ECT/DLX/P, Data Spectrum Corporation, Durham, USA) was used to qualitatively evaluate spatial resolution and image quality. It is illustrated in Fig. 1. The Jaszczak phantom features cold rods (4.8 mm, 6.4 mm, 7.9 mm, 9.5 mm, 11.1 mm, and 12.7 mm in diameter) and spheres (9.5 mm, 12.7 mm, 15.9 mm, 19.1 mm, 25.4 mm, and 31.8 mm in diameter) surrounded by an activity-filled background compartment (0.3 mol hydrochloric acid (HCl)). PET measurements of the Jaszczak phantom are common for the analysis of spatial resolution and enable a visual assessment of the separability of the cold rods. However, focal hot spots cannot be imitated as in real patient data with the Jaszczak phantom. We additionally determined the spatial resolution semiquantitatively using the NEMA PET body phantom (PTW Freiburg), as shown in Fig. 1. The NEMA PET body phantom allows hot spot imaging of spheres of different sizes (10 mm, 13 mm, 17 mm, 22 mm, 28 mm, and 37 mm in diameter) at different sphere-to-background contrast ratios.
All PET measurements were performed on a digital Biograph Vision PET/CT system (Siemens Healthineers). Following a low-dose CT (120 kVp, 78 mAs, spiral pitch factor of 1.5, 512 × 512 matrix with a pixel size of 0.98 mm × 0.98 mm) used for attenuation correction of the subsequent PET scan, the PET data were acquired in the list mode over a single bed position, covering an axial field of view (FoV) of 26 cm . The duration of the PET data acquisition of the Jaszczak phantom filled with 18F-FDG was determined based on the recommendations in the NEMA NU 2-2018 protocol for the characterization of image quality . In the corresponding measurements with the NEMA PET body phantom, the standards in clinical routine according to the German Guideline for 18F-FDG PET/CT in oncology were used as a reference . The duration of the acquisition of the 68Ga-HCl and 64Cu-HCl PET data was adjusted to that of the 18F-FDG-PET data. The respective actual activity concentration in the phantom at the timepoint of imaging and the decay probability of the nuclides (Table 1) were taken into account to achieve similar count statistics between scans with different nuclides. PET data were reconstructed according to the standards in our clinical routine for 18F-FDG using an ordered subset expectation maximization (OSEM) 3D iterative reconstruction algorithm with 6 iterations and 5 subsets (6i5s), applying PSF and ToF (TrueX algorithm) with an image matrix size of 440 × 440, resulting in a voxel size of (1.65 × 1.65 × 1.5) mm3. No postfiltering was applied (all-pass filter). Reconstructions were performed with attenuation correction and relative scatter correction.
Qualitative evaluation of spatial resolution using the Jaszczak phantom
The background compartment of the Jaszczak phantom was filled with 18F-FDG, 68Ga-HCl, or 64Cu-HCl aiming at an activity concentration of 5.3 kBq/mL .
The acquisition duration of the Jaszczak phantom filled with 18F-FDG, 68Ga-HCl, or 64Cu-HCl was 546 s, 611 s, or 2629 s, respectively. PET/CT scans of the Jaszczak phantom were analyzed visually to determine spatial resolution. In each PET/CT scan, the narrowest rods and spheres that were still distinguishable from one another were determined visually.
Semiquantitative evaluation of spatial resolution and image quality using the NEMA PET body phantom
The NEMA PET body phantom was filled with 18F-FDG, 64Cu-HCl, or 68Ga-HCl. According to the recommendations in the NEMA NU 2–2018 protocol, we aimed at an activity concentration of 5.3 kBq/ml in the background compartment and a sphere-to-background activity concentration ratio of approximately 4:1 or 8:1 . The actual activity concentrations at the timepoint of imaging differed slightly from the target and are specified in Table 2. The phantom was also scanned after wrapping it in gel cooling packs 1 cm thick containing propylene glycol to simulate attenuation and scatter conditions comparable with those in an obese patient. The acquisition durations of all PET/CT scans of the NEMA PET body phantom are specified in Table 2.
Spatial resolution was evaluated semiquantitatively according to Hofheinz et al.  using the software Rover (version 3.0.60 h, ABX, Radeberg, Germany). Briefly, the resolution was determined based on the analysis of radial activity profiles of the homogeneously filled phantom spheres and the assessment of the FWHM of the PSF in the reconstructed images. PSF was modeled by a 3D Gaussian function, and FWHM was determined by applying the method described in detail in . This method is based on fitting the analytic solution for the radial activity profile of a homogeneous sphere convolved with a 3D Gaussian function to the reconstructed data. In this process, the full 3D vicinity of each sphere is evaluated by transforming the data to spherical coordinates relative to the center of the sphere. The analytic solution has five parameters: signal (true activity within the sphere), background level, FWHM of the PSF, sphere radius, and wall thickness of the spherical inserts. The radius and wall thickness of the spheres were fixed to their known values. The remaining three parameters were determined by nonlinear least-squares fitting. With this method, the spatial resolution can be determined at a finite background as well as for extended objects. Therefore, it allowed us to study the size and contrast dependence of the resolution. Note that this method assumes a Gaussian PSF, which is never exactly the case. However, the method still leads to a reasonable approximation of the spatial resolution as long as the slope at the object boundary (signal decline) is modeled correctly by the fit function. The means and standard deviations of the FWHM of all six spheres were compared between PET measurements with different nuclides.
Image quality was evaluated semiquantitatively using Rover (version 3.0.60 h, ABX, Radeberg, Germany). Three uniform background volumes of interest (VOIs) of at least 61 ml volume were delimited as illustrated in Additional file 1: Fig. S1A. According to , a 3D isocontour at 50% of the maximum pixel value was used for the segmentation of each sphere, taking into account the activity concentration in the background of the phantom. For each sphere, the mean, maximum, and peak recovery coefficients (RCmean, RCmax, and RCpeak, respectively) were determined as the ratio of the measured mean, maximum, or peak SUV of the VOI to the actual activity concentration in the phantom sphere at the timepoint of imaging. SUVpeak was determined as the mean SUV of a 12-mm-diameter spherical region around the maximum voxel, considering only voxels within the 3D isocontour of the sphere . The actual activity concentration was determined as the amount of activity filled in the phantom (measured with an activity meter, which was calibrated for the nuclide and syringe used to fill the phantom with the radioactivity) divided by the volume of the phantom compartment. The means and standard deviations of the RC values of all six spheres were compared.
Image noise, called percent background variability in the NEMA NU 2-2018 protocol , was calculated as the coefficient of variation within each of the three background VOIs (CoVBG). The mean CoVBG values of the three VOIs were compared between PET images of different nuclides.
The contrast between each sphere and the background (contrast recovery coefficient (CRC)) was calculated according to the definitions in the NEMA NU 2-2018 protocol . The means and standard deviations of the CRC of all spheres were compared between PET images.
The contrast–noise ratio (CNR) was calculated as the difference in SUVmean between each sphere and the background divided by the standard deviation of the activity concentration in the background compartment. The means and standard deviations of the CNRs of all spheres were compared between PET images.
According to the NEMA NU 2-2018 protocol , the relative count error in the lung insert of the NEMA PET body phantom was determined as the ratio of the average number of counts in a cylindrical VOI with a 30 mm diameter in the lung insert of the phantom not filled with radioactivity relative to the average number of counts within the three VOIs placed in the activity-filled phantom background.
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