## 4 Discussion
### Bland-Altman Plots  
The Bland-Altman analyses revealed that the deformable registration approach increased the volumes with regards to the manual one for all the delineated VOIs with a bias (LOA-; LOA+) of \(-25.6\) mL (\(-115.3\); \(64.2\)), \(-103.4\) mL (\(-403.4\); \(196.5\)), \(-76.5\) mL (\(-349.1\); \(196.1\)) for tumor, liver and NTL, respectively. These differences might be due to the dependence of the deformable registration algorithms on liver shape and tumor displacement, which could be strongly affected by the differences in the respiratory phase during the CT acquisition. On the contrary, as expected, the rigid registration kept the volumes almost the same. The slight differences in volume values could be due to the rounding effect in the rototranslation of the VOIs and to the different slice thickness between the CT images of our SPECT/CT and PET/CT systems (i.e., \(3.75\) mm and \(2.78\) mm, respectively). Accordingly, the average increase in V\({}_{\text{T,d}}\) and V\({}_{\text{NTL,d}}\) with respect to V\({}_{\text{T,m}}\) and V\({}_{\text{NTL,m}}\) (i.e., a negative bias in Figure 2b) is mirrored by a decrease in the absorbed mean doses of these VOIs. On the contrary, although the volumes are maintained by the rigid registration, a reduction of the D\({}_{\text{T,r}}\) and D\({}_{\text{NTL,r}}\) (i.e., a positive bias in Figure 3a,e) is observed. This is likely to be ascribed to the mispositioning of the VOIs when shape and volume are constrained by the rigid algorithm. For all the possible combinations in NTL mean absorbed dose (i.e., D\({}_{\text{NTL,m}}\) vs. D\({}_{\text{NTL,r}}\), D\({}_{\text{NTL,m}}\) vs. D\({}_{\text{NTL,d}}\) and D\({}_{\text{NTL,r}}\) vs. D\({}_{\text{NTL,d}}\)), the Bland-Altman analyses resulted in a maximum bias of \(2.3\) Gy [\(-8.8\);\(13.5\)]. These results were similar to the ones reported in [PERSON] et al. [15] for 10 HCC patients (i.e., \(0.9\) Gy (\(-7.4\); \(9.1\))) using a manually adjusted delineation in both pre- and post-treatment images. On the contrary, tumor mean absorbed dose showed larger biases and LOAs for all the possible combinations (i.e., D\({}_{\text{T,m}}\) vs. D\({}_{\text{T,r}}\), D\({}_{\text{T,m}}\) vs.D\({}_{\text{T,d}}\) and D\({}_{\text{T,r}}\) vs.D\({}_{\text{T,d}}\) were \(31.2\) Gy (\(-80.6\); \(143.0\)), \(41.7\) Gy (\(-70.1\); \(153.5\)) and \(10.5\) Gy (\(-37.1\); \(58.1\)), respectively) when compared to the same study (i.e., \(-5.8\) (\(-79.7\); \(68.2\))). These discrepancies are likely due to the different range of evaluated tumor volumes between the two investigated populations and to the VOI delineation/propagation methods. In particular, in our study tumor volumes ranged from \(1.3\) to \(1702.9\) mL, while in [PERSON] et al. they went from \(20\) to \(647\) mL, and the VOIs delineated on SPECT/CT images were copied on PET/CT images and adjusted by applying a threshold method to reproduce the same volume values. Moreover, [PERSON] et al. [26], using a rigid registration approach, reported that the mean difference for the NTL mean absorbed dose using \({}^{99m}\)Tc-MAA SPECT/CT and \({}^{90}\)Y PET/CT was \(2.1\) Gy (\(-1.2\); \(5.5\)), while the mean difference for the tumor was \(7.2\) Gy (\(-32.9\); \(47.3\)) in nine HCC patients (with volumes ranging from \(16\) to \(1760\) mL). These results showed a concordance between pre-treatment and post-treatment dosimetry better than the one reported in our study. The larger absorbed dose discrepancies experienced in our results could be due to the higher number of patients and tumor/liver shape and size variability. The Bland-Altman plots reported by [PERSON] et al. [17] showed that the variations between predicted and effective doses were markedly higher in the tumors than in the NTL, especially in lesions with major uptake.