**3. Results**

The QUEST reconstruction for the Discovery 710 was found to be unsuitable for analyses at the voxel level and generation of an ACVH due to excessive noise. Hence, we focused our analysis on BPL images for this scanner.

The quantitative accuracy of the images determined from the background region in the stationary phantom acquisitions, expressed as the percentage recovery coefficient, was 100.0 ± 7% and 98.2 ± 4% (mean ± standard error) for the GE Discovery 710 (using BPL reconstruction) and the Siemens Biograph mCT, respectively. This verifies that the phantom filling and scanner calibrations were accurate for 90Y. The quantification accuracy of the background region is presented in Figure 1.

A simple multi-linear model gave a reasonable fit to the recovery coefficients from the hot spheres, with the multiple correlation coefficient equalling 0.81 and the adjusted coefficient of determination being 0.65. The coefficients of the model were significantly different from zero for motion amplitude (*p* < 0.001) and motion correction (being on or off, *p* = 0.003). There was a dependence on the scanner (*p* < 0.001) and unsurprisingly on the sphere diameter (*p* < 0.001), the contrast (*p* < 0.001) and the phantom activity (*p* < 0.001). The model parameters confirmed an increased contrast recovery (+16% per cm) with increasing sphere diameter over the tested range of 1–4 cm. The application of 1–1.5 cm motion reduced the contrast ( −11% per cm) which was partly compensated by motion correction being applied (+6.1% on average).

The paired-samples two-tailed *t*-test confirmed that the mean contrast recovery with quiescent period gating was significantly higher than without gating. For the Biograph mCT, the mean recovery coefficent, from all studies including motion and for all six VOI, was 55% without motion correction compared to 59% with respiratory gating (*p* = 0.007). For the Discovery 710, the corresponding values were 50% increasing to 55% with gating (*p* = 0.003). Similar findings were found when examining the AC80 values from the four hot spheres, where for the Biograph mCT the mean value of AC80 was 25% without motion correction compared to 29% with respiratory gating (*p* < 0.001). For the Discovery 710, the mean AC80 values were 23% and 29% for uncorrected motion and with respiratory gating respectively (*p* < 0.001).

**Figure 1.** The quantification accuracy from the seven background regions in images from the Discovery 710 and Biograph mCT when the phantom was static. Error bars represent standard errors.

Example 90Y PET images are shown in Figure 2, where the improvement in contrast provided by gating is apparent at the expense of increased noise.

**Figure 2.** PET images (coronal slices) from the phantom with and without motion applied. The upper row of images is from the Discovery 710. The lower row is from the Biograph mCT. The grey scale maximum equals the true activity concentration in the hot spheres, with minimum at zero. The activity concentration ratio between the spheres and background was 8:1. For each scanner the images show a similar slice of the phantom while stationary, while in motion but without correction, and while in motion with quiescent period respiratory gating. The motion amplitude was 10 mm. The total activity in the phantom was 1.8 GBq for the Discovery and 1.9 GBq and Biograph. The slice contains the 40 mm insert with 25 mm cold core, as well as a 20 mm diameter sphere.

Averaged ACVHs are presented in Figure 3, for the case of the stationary and moving phantom with and without quiescent period gating. The recovery of the 90Y activity within

the spherical inserts is presented in Figure 4 for which data are grouped by scanner and contrast ratio, with the presented data being the average of the tests performed at similar contrast ratios. The impact from the partial-volume effect for the different spheres is provided by the no-motion data, which is seen alongside the results for respiratory motion and respiratory motion with gating. The AC80 values extracted from the ACVHs are similarly presented in Figure 5.

**Figure 3.** Activity concentration volume histograms for the 30 mm sphere. Each figure part shows the results for no motion, and when motion is present (10–15 mm amplitudes) either with or without quiescent period gating. Data are presented as the average ACVH for this sphere from the four phantom experiments on each scanner. (**a**) Discovery 710 (BPL reconstruction); (**b**) Biograph mCT.

**Figure 4.** Contrast recoveries for different sphere diameters and types. Each figure part shows the results for no motion, and when motion is present (10–15 mm amplitudes) either with or without quiescent period gating. Combined datasets from four phantom experiments on each scanner. (**a**) Discovery 710 (BPL reconstruction); (**b**) Biograph mCT.

**Figure 5.** AC80 from different sphere diameters. Each figure part shows the results for no motion, and when motion is present (10–15 mm amplitudes) either with or without quiescent period gating. Combined datasets from four phantom experiments on each scanner. (**a**) Discovery 710 (BPL reconstruction); (**b**) Biograph mCT.
