## 3 Results
### NIL Case  
Several absorbed dose profiles for each subcase were extracted from different transversal slices. One example profile for the NUL-a case, presenting homogeneous liver and activity in three spherical regions and liver in concentration ratio 5:1, respectively, is reported in Figure 5. An image of voxel-by-voxel relative difference (RD) for the same slice from which the profile was selected is also reported in Figure 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(D_{gate}\) **(Gy)** & \(\mathbf{D}_{blinda}\) **(Gy)** & **RD (\%)** \\ \hline BS & 613 & 625 & \(-\)1.92 \\ MS & 588 & 604 & \(-\)2.65 \\ SS & 517 & 571 & \(-\)9.46 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Mean absorbed dose values for each sphere, calculated from the Gate image (\(D_{gate}\)) with a reduced workflow and from the application of the OLINDA/EXM factors (\(D_{blinda}\)). The relative difference (RD) is defined as \(\mathrm{RD}=\frac{D_{gate}-\overline{D}_{distab}}{D_{initd}}\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(D_{gate}\) **(Gy)** & \(D_{initd}\) **(Gy)** & **RD (\%)** \\ \hline
36.79 & 36.69 & 0.27 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison between average absorbed dose values to the liver, calculated from the Gate image (\(D_{gate}\)) and from the MIRD approach (\(D_{initd}\)) at the organ level. The relative difference (RD) is defined as \(\mathrm{=}\frac{\overline{D}_{gate}-\overline{D}_{mixed}}{D_{initd}}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(D_{gate}\) **(Gy)** & \(\mathbf{D}_{blinda}\) **(Gy)** & **RD (\%)** \\ \hline BS & 666 & 625 & 6.57 \\ MS & 558 & 604 & \(-\)7.62 \\ SS & 176 & 571 & \(-\)69.20 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Mean absorbed dose values for each sphere, calculated from the Gate image (\(D_{gate}\)) and from the application of the OLINDA/EXM factors (\(D_{blinda}\)). The relative difference (RD) is defined as \(\mathrm{RD}=\frac{\overline{D}_{gate}-\overline{D}_{initial}}{\overline{D}_{ initiald}}\).  
All the profiles selected for the NUL-a case showed a relative difference within 3% between the absorbed dose images calculated by MC simulation and convolution of voxel S-values. Relative differences for the entire liver confirmed that this result is valid for all liver slices, except for some boundary voxels, actually external to the liver and characterized by low dose values (less than few Grays).  
Absorbed dose profiles for the NUL-b case, presenting nonhomogeneous liver and nonuniform activity, are reported in Figures 6 and 7.  
Figure 5: Absorbed dose profile for the NUL-a case and comparison. (**a**) Absorbed dose image obtained with the MIRD scheme and absorbed dose profile selection; (**b**) absorbed dose image obtained with GATE and absorbed dose profile selection; (**c**) relative difference (RD) image for the whole slice; (**d**) comparison between absorbed dose profiles; (**e**) plot of the absorbed dose RDs for each voxel of the profile.  
Figure 6: Absorbed dose profile for the NUL-b case and comparison. (**a**) Absorbed dose image obtained with the MIRD schema and absorbed dose profile selection; (**b**) absorbed dose image obtained with GATE and absorbed dose profile selection; (**c**) relative difference (RD) image for the whole slice; (**d**) comparison between absorbed dose profiles; (**e**) plot of the absorbed dose RDs for each voxel of the profile.  
The relative differences between the absorbed dose images were up to 14% in the spherical regions, having a different density (1.200 g/cm\({}^{3}\)) as compared to the surrounding liver (1.050 g/cm\({}^{3}\)).