*2.3. Background Variability*

Background variability (BV) was determined for all reconstructions obtained, based on count statistics in a manually drawn region of interest (ROI) in the background, extended over multiple slices. Care was taken to neither include voxels near the edge of the phantom nor near the hot spheres in order to avoid a bias in the background volume of interest (VOI) due to partial volume effects.

The BV was calculated by (2):

$$\text{BV} = \frac{\sigma\_{\text{VOI}}}{\mu\_{\text{VOI}}} \tag{2}$$

where σVOI is the standard deviation of the number of counts in the VOI and μVOI is the mean number of counts in the VOI.

#### *2.4. Activity Recovery Coefficients*

The recovery coefficient was used as measure for the ratio between the apparent activity concentration and the true activity concentration in a VOI. Ideally, the RC is equal to 1 for all sphere diameters. In general, the recovery coefficient will gradually decrease for smaller sphere diameters.

RCs were obtained semi-automatically. First, the spheres were identified visually in the PET image. Subsequently a box was manually defined around the maximum voxel value for each sphere. Each box was constructed to fully include a sphere without inclusion of voxels of other spheres. In addition, a background VOI was manually defined in such a way that the boundaries were neither close to the phantom wall nor to the spheres, to ensure homogeneity and avoid partial volume effects.

Next, the maximum voxel value in each box corresponding to a sphere was obtained. The measured ratio Rmeas,max between the maximum activity concentration Csphere,max in a sphere and the average activity concentration in the manually drawn background VOI Cbg,avg (equivalent to the T/B ratio in a patient scan, comparing maximum SUV to the background SUV), was defined as (3)

$$R\_{\text{meas, max}} = \frac{\mathbf{C}\_{\text{sphere, max}}}{\mathbf{C}\_{\text{bg, avg}}} \tag{3}$$

Using the location of the maximum voxel value of each sphere in the PET reconstruction, VOIs to determine the average voxel value in the sphere volume Csphere,avg were constructed automatically using a simple region growing algorithm including all voxels within a 3D isocontour at 50% of the maximum voxel intensity corrected for background [31]. These VOIs were used to calculate the measured ratio between the average activity concentration in the sphere and the background Rmeas,avg (equivalent to the T/B ratio in a patient scan, comparing mean SUV to the background SUV) (4).

$$\mathcal{R}\_{\text{meas, avg}} = \frac{\mathcal{C}\_{\text{sphere, avg}}}{\mathcal{C}\_{\text{big, avg}}} \tag{4}$$

The peak recovery coefficient RCpeak was also determined for each sphere by positioning a spherical contour with a 1.2 cm diameter such that the average voxel value within that sphere is maximized [3]. The measured ratio Rmeas,peak between the average activity concentration in the spherical VOI Csphere,peak and the background is equivalent to the SUVpeak in a patient scan (5):

$$R\_{\text{meas,peak}} = \frac{\mathcal{C}\_{\text{sphere,peak}}}{\mathcal{C}\_{\text{bg,avg}}} \tag{5}$$

As the actual ratio R between the activity concentration in the spheres and the activity concentration in the background compartments of the phantoms was known, RCmax, RCavg and RCpeak could be calculated by (6)–(8):

$$\text{RC}\_{\text{max}} = \frac{\text{R}\_{\text{meas, max}}}{\text{R}} \tag{6}$$

$$\text{RC}\_{\text{avg}} = \frac{\text{R}\_{\text{meas, avg}}}{\text{R}} \tag{7}$$

$$\text{RC}\_{\text{peak}} = \frac{\text{R}\_{\text{meas,peak}}}{\text{R}} \tag{8}$$

These RCs are therefore equivalent to the ratios between the observed maximum, average and peak T/B ratio and the true T/B ratio.

Statistical analysis was performed using a Student *t*-test for comparison of data in a single reconstruction and a paired *t*-test for assessment of differences between two reconstructions. A confidence level of 95% was used.

For each sphere, the RCavg values calculated in multiple acquisitions (1 min, 2 min and 5 min per bed position, each with a T/B ratio of 10:1 and 20:1) were averaged and the coefficient of variation (COV) was assessed. The optimal β value was chosen based on reproducibility, i.e., low COV, and detectability, i.e., high recovery and low background variability.
