**4. Discussion**

Using an anthropomorphic phantom filled with 90Y at clinically relevant activities placed on a respiratory motion platform, this investigation found that quiescent period respiratory gating leads to increased accuracy in measures of the activity concentration in both hot and cold features within a liver region. The study provided consistent results across a range of clinically relevant activities and at two contrast ratios, for two PET-CT scanners from different vendors. Our findings agree with expectations based on results from Siman et al. [19] who performed experiments using a less realistic phantom filled with a small amount of 18F on a single scanner. Although we found statistically significant increases in quantification accuracy, we note the data had high variance and the absolute gains from the application of quiescent period gating were moderate. The impact of the partial volume effect, seen by the difference in quantitative measures between smaller and larger spheres, was generally larger than the impact of applying the respiratory motion correction for the features analysed in this study (diameters ranging from 1 to 4 cm). This can be seen visually in Figures 4 and 5 but was also evidenced by the coefficients of the multi-linear regression. A decrease in sphere diameter of 1 cm led to a larger decrease in contrast recovery (−16%) compared to respiratory motion of 1 cm amplitude (−11% and −5% for uncorrected data and for quiescent period gating, respectively).

In this study, and in agreemen<sup>t</sup> with Hou et al. [16], we noted that the QUEST reconstruction for the Discovery 710 was not suitable for a voxel-level analyses. We considered images with relatively high noise to be unsuitable for estimation of the distribution of activity concentrations within a region. This reconstruction should hence not be used when a dose-volume histogram analysis is to be performed. The quantitative accuracy of the QUEST reconstruction was, however, acceptable when assessed using the background region in the stationary phantom acquisitions, with a percentage recovery coefficient of 104 ± 8%. As the QUEST images from the Discovery 710 were too noisy to be subjected to ACVH analysis our work focused on the BPL images for this scanner. A limitation of our study is that we only studied images with β = 1000 as chosen based on previous investigations [25]. In the case of a voxel level analysis aiming for accurate estimation of the distribution of activity concentrations (for accurate DVH generation), high β values that provide smoother images may be optimal [16]. Furthermore, our study investigated only one method of respiratory motion correction (device-driven quiescent period gating) without optimisation of the retained fraction, which was set at 50%. This method of correction

was chosen due to the relative simplicity and wide availability of the technique. The aim of our study was, however, not to optimise imaging parameters, but to demonstrate the extent to which respiratory motion degrades quantification accuracy, and the extent to which commonly used quiescent period gating can mitigate these effects. In this regard, our study shows that respiratory gating can be beneficial. Despite reducing the statistical quality of the images when discarding 50% of the coincidences, the application of gating was of net benefit with more accurate quantification of both VOI means and dosimetric measures such as AC80. However, we recognise the need for further investigations; for example, it would be useful from a practical point of view to define a minimum signal-to-noise ratio for the image (at the voxel level), below which the application of voxel-level dosimetric measures are not advised. Further development of methods for robust respiratory gating with retention of all (or most) counts in the case of 90Y PET is also needed. This is an ongoing area of research for 18F PET-CT imaging and the extension of methods, many of which use image registrations or other data-led techniques, to the case of low-count 90Y PET presents a variety of challenges. Without such techniques the justification for respiratory gating is tempered by the increase in image noise and the detrimental impact this has on voxel-level, DVH-type analyses. Increased smoothing or regularization of the image reconstruction (e.g., by increasing the β value in BPL) could compensate for the increased noise but at the expense of reducing spatial resolution. Although 90Y PET is challenging, we note that the current study did not utilise the most recent generation of long axial FOV, SiPM-based PET scanners. These offer significantly increased sensitivity through their extended axial coverage and reduced noise through improved time-of-flight capabilities, both of which make the newer scanners more suitable for gated 90Y PET. The image quality for gated studies is also expected to improve if higher activities are present in the scanner's FOV. This study investigated the range of activities encountered at both sites (up to 3.2 GBq).

The use of respiratory gating is becoming more common, and it is noteworthy that in this patient population the additional radiation dose from a respiratory gated CT is likely justified given the poor prognosis of patients referred for SIRT. While data-driven respiratory gating methods for both 90Y PET and CT are ye<sup>t</sup> to be robustly implemented in clinical practice, it may be appropriate to perform device-based gating of both the PET and the CT components of post-SIRT therapy PET-CT verification imaging. Accurate alignment of CT and PET images within the quiescent phase has been shown to be important for quantification using 18F and 68Ga PET-CT [28], and this is expected to apply equally to 90Y imaging.

As evidence mounts for a strong relationship between tumour dose and treatment response, the need for accurate dosimetry in SIRT also increases. While accurate dose estimation from pre-therapy imaging can be used to optimise treatment, post-therapy dosimetry can be used to verify the delivered dose and thus build the evidence base for the dose-response, allowing the treatment to be refined and to unravel the disease- and patient-related factors that may alter the dose thresholds for effective treatment.
