## 3 Results  
In Table 1 the nominal and reconstructed activity concentrations of the liver compartment and spherical inserts considered in the AbdoMan phantom are reported, together with their relative deviations. The largest difference was found for the 40 mm diameter hollow sphere, most likely due to the intrinsic limitation in resolution of the SPECT system and the presence of partial volume effects (PVE) which result in an underestimated dose value (\(-26.4\%\)). In fact, the 40 mm hollow sphere is provided with a 25 mm solid inner representing the deposition of microspheres in a thin rim (i.e., 15 mm, comparable with the SPECT spatial resolution). As the VOI's volume exceeded the SPECT spatial resolution, the differences between the activity concentration drops, with deviations of \(-3.8\%\), \(+1.9\%\) and \(+1.0\%\) for the 20 mm, 40 mm sphere and liver compartment, respectively. As expected, the minor underestimation (\(-3.8\%\)) of the small 20 mm can be imputable to PVE. The quantitative accuracy is confirmed by visual inspection of the color wash dose maps reported in Figure 3 for the 40 mm sphere (Figure 3a, cyan circle) and the 40 mm hollow sphere (Figure 3b, red circle). Figure 3a shows a uniform dose distribution with minor blurring at the edge of the sphere due to spill-out effects. Figure 3b shows both the 40 mm hollow sphere and the 20 mm solid sphere. The apparent activity resulting inside the hollow sphere in Figure 3b is due to spill-out of counts from the object edges to the sphere core. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Abdom** & \(C_{nom}\) **(MBq/mL)** & \(C_{recon}\) **(MBq/mL)** & \(\Delta\)**(\%)** \\ \hline
20 mm sphere & 0.530 & 0.510 & \(-3.8\%\) \\
40 mm sphere & 0.530 & 0.540 & \(+1.9\%\) \\
40 mm hollow sphere & 0.530 & 0.390 & \(-26.4\%\) \\ Liver compartment & 0.103 & 0.104 & \(+1.0\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between nominal (\(C_{nom}\)) and reconstructed \(C_{recon}\) activity concentrations related to the AbdoMan phantom. Figure 4 shows the dose maps obtained by means of the two dose calculation methods: (a,d) DKM and (b,e) LDM at different slices of the AbdoMan phantom. In particular, the central section of the 40 mm sphere is reported in Figure 4a,b, while the 20 mm sphere and 40 mm hollow sphere are reported in Figure 4d,e. The quantitative comparison in terms of \(\gamma\)-map on the same slices considered are reported in Figure 4c,f. As shown, there are no regions of the map where the \(\gamma\)-index violates the imposed criteria. In particular, the 3D \(\gamma\)-index provided a passing rate of 100% and 99.9% for the criteria 2%-2 mm and 1%-1 mm, respectively, showing that the two dose methods resulted to be equivalent. In terms of dose difference between the SPECT absorbed dose obtained by means of LDM and DKM and related to the AbdoMan inserts and liver compartment, the results  
Figure 4: dose distributions for AbdoMan phantom reconstructed with xSPECT software using dose kernel method (**a,d**) and local energy deposition method (**b,e**) for two different slice’s location corresponding to the three investigated spheres. (**c,f**) \(\gamma\)-maps related to the slices considered. Figure 3: 3D dose distribution for the AbdoMan phantom visualized with MIM color wash tool for the liver section and the 40 mm spheres (**a**), the 20 mm and 40 mm hollow sphere with 25 mm insert (**b**). are reported in Table 2. Our results indicate that the xSPECT software in combination with dose kernel and local energy deposition methods is likely to provide satisfactory results, with differences estimates within 5% (20 mm and 40 mm hollow sphere) and 10% (40 mm sphere). Cumulative DVHs reported in Figure 5 were generated by means of the LDM and DKM. Recovery coefficients for our SPECT/CT system (0.86, 0.75 and 0.92 for the 40 mm, 20 mm and 40 mm hollow sphere, respectively) were used to account for partial volume effects [26].