The NEMA IEC image quality phantom was filled with 9.61 MBq of Zr-89, giving an activity concentration of 9.35 kBq/ml and 0.92 kBq/ml in the spheres and background compartments respectively. This activity was chosen to be clinically representative. A typical activity of Zr-89 administered for PET-CT is of the order of tens of MBq of activity, administered days prior to the scan. The acquisition duration per bed is expected to be slightly longer than F-18 PET to account for the lower coincidence rate. For example, in the clinical study by Kirchner et al., which optimised a BSREM algorithm, for clinical images the mean activity in a whole body (WB) PET image was 14 MBq, with the mean acquisition duration per bed position of 6.9 min [13].

All six spheres were filled hot with the ratio of activity concentration in the spheres to the background set at 10:1 [15, 16]. A 60-minute acquisition was acquired on a time-of-flight (TOF) PET-CT scanner (GE Discovery 710 [LYSO block detector, 64 slice CT scanner]). The original scan was divided into three 20-minute acquisitions to provide three repeats for each data point, due to the relatively long half-life of Zr-89 there was no significant difference in count statistics between each acquisition. Within each 20-minute acquisition, the list-file data was retrospectively re-binned into acquisitions of length 2, 3, 4, 5, 7.5, 10, 15 and 20 min. Reconstruction was performed using BSREM (varying beta from 500 to 9000) and OSEM. This gave a total of 450 reconstructed images. The beta range was selected based on previous BSREM evaluation and optimisation work in literature for different radioisotopes with a higher lowest value to reflect the higher noise characteristics expected in Zr-89 images (compared to F-18 and Y-90) [3, 4, 6]. Although not optimised, the OSEM reconstruction parameters were chosen to be the same as those used in previous work by J. Kirchner et al. to enable comparison with their work (2 iterations, 16 subsets, 6.4 mm gaussian filter, heavy z-axis filtering with all manufacturer corrections applied (CT-based attenuation, scatter, point-spread-function (SharpIR) and TOF)) [13]. This reconstruction is also very similar to that found to be optimal by Christian et al. for a GE D710 scanner (2 iterations, 24 subsets, 7.0 mm Gaussian Filter, point-spread-function (SharpIR)) [18]. Reconstructed images had voxel dimensions of 2.73 × 2.73 × 3.27 mm, with an in-plane matrix size of 256 × 256 and 47 slices. Example images and horizontal count rate profiles are shown in Fig. 1 for a range of acquisition durations and beta values.

A selection of 12 phantom images (out of 450 reconstructed images). A horizontal profile through the centre of the phantom (37 mm sphere, lung insert and 17 mm sphere) is overlaid in red on each image to aid visualisation of the noise. Each profile is normalised to the maximum signal in the image on which it is overlaid. Image noise is visibly decreased as acquisition duration and beta increase, however, the quantitation in small volumes worsens, as shown in the decreased profile peak height through the 17 mm sphere. The upper window limit is set at 70% of maximum image signal for each image. No temporal change in the activity distribution was observed in the hour of data acquired

An imageJ script was written to measure Contrast Recovery Coefficient (CRC) (Eq. 1) and Background Variability (BV) (Eq. 2) for all sphere sizes following the NEMA-NU 2-2018 image quality protocol [19]. Further metrics were also calculated for comparison, for quantitative comparison the recovery coefficient for the mean and maximum signal in the volume RCMEAN and RCMAX were measured. For comparison of noise and quantifying image quality the contrast-to-noise-ratio (CNR) and signal-to-noise-ratio (SNR) were calculated. As per the NEMA-NU 2-2018 protocol, twelve background regions were drawn around the phantom and replicated over five slices centred on the central sphere slice. Regions were drawn on axial CT reference image and transferred to the registered PET images.

$$C_=\:\frac_}_}-1}_}_}-1}*100$$

(1)

$$CNR_j=\:\frac_}_}$$

(5)

$$SNR_j =\:\frac_}_}$$

(6)

Where CH, j is the average measured activity concentration within a region of interest for the sphere j on the central sphere slice. CB, j is the average measured background activity concentration over 60 regions of interest of the same size (12 regions drawn around the phantom and replicated over five slices centred on the central sphere slice). aH and aB are the known activity concentrations, in the sphere and background compartments respectively. SDj is the standard deviation of counts over the 60 background regions. The RCmean, CNR and SNR are varying combinations of the same parameters as used in the CRC and BV metrics. Figures 3 and 4 are provided here for completeness and to enable comparison to other papers in future where different metrics may be used. The primary analysis in this work focuses on CRC and BV as they are standardised quantitative values for the NEMA IEC phantom and represent the key characteristics shown by the other values discussed.

Contrast Recovery Coefficient (CRC) and Background Variability (BV) for BSREM against regularisation parameterbeta as compared to OSEM for 2, 5 and 20-minute acquisition durations. The shaded horizontal lines in each plot show the OSEM measurement (mean ± standard error) for the equivalent acquisition duration for comparison

Recovery coefficient for the mean and maximum signal for each sphere size, over three acquisition durations (2, 5 and 20 min). The shaded horizontal lines in each plot show the OSEM measurement (mean ± standard error) for the equivalent acquisition duration for comparison

The code used was validated on F-18 NEMA image quality phantom images. Consistent analysis and region definition were used between all reconstructions for each sphere size. The method of region generation samples the data without interpolation for edge voxels (the region definition is binary with voxels either included or excluded from the total ROI). This results in small variations in the proportion of the sphere volume included in the ROI between different sphere sizes. Therefore, results were compared within each sphere size, with general trends taken over the range of sphere sizes.

The mean and standard error of the mean was calculated for CRC and BV for each reconstruction protocol from three repeats taken from the three sequential 20-minute datasets.