## 3 Results
### Patient Studies  
Correlation and Agreement between Absorbed Dose Distributions Derived from Spect and Pet Images  
Figure 4 shows the results of the voxelwise PCC and ICC between the ADD derived from SPECT-MAA and PET-MS images computed on the liver reference volume. Two outliers were observed (P10_12 and P12_14) and excluded in this analysis. The median of the PCC was 0.69, and the mean was 0.64 with range of 0.52-0.81. Regarding the ICC estimate, a moderate to good agreement was obtained (median 0.67, mean 0.62, range 0.52-0.80). Considering the mean AD in PTV and NLV from all treatments, the PCC was 0.80 and 0.98, respectively, and the ICC was 0.79 and 0.97, respectively. Thus, the agreement of the mean AD between the SPECT-MAA- and the PET-MS-based ADD computed on the liver ROI was good to excellent. The results of the \(\gamma\)-index PR computed on four liver ROI are presented in Figure 5.  
The highest values of the patients' \(\gamma\)-index PR were obtained with the less conservative 15%/15 mm conditions, which were above 90% in all patient studies. Considering a 10 mm DTA (approximately the spatial resolution of the SPECT) and a 10% DD, \(\gamma\)-index PR values above 90% were obtained. This showed that the predictive power of the ADD based on SPECT-MAA compared to the ones based on PET-MS was good. Optimization of the activity to be administered. In 11 out of 16 treatments, the objective function (OF) converged for a maximum in the range considered acceptable (administered activity between 0 and 12 GBq) both for the SPECT-MAA- and PET-MS-derived ADD (Table 4). For these 11 treatments, the agreement of the estimated activities was very high, with an ICC of 0.96 (\(p<0.001\)), with no statistically significant difference between the optimal activities estimated based on the SPECT-MAA and PET-MS (paired Wilcoxon signed-rank test, \(p\) = 0.86). Figure 6 shows example graphs of the OF optimization, in this case, for P1_1. The OF optimization of the P4_4 and P14_16 showed quite different results when the SPECT-MAA or the PET-MS ADD were considered. Possibly, the two administrations (i.e., MAA and MS) were performed in different liver sites, and/or the patient's liver anatomy changed significantly between the planning and treatment day. The OF optimiza  
Figure 4: Boxplot of the voxelwise PCC and ICC between the SPECT-MAA and PET-MS based ADD computed on the liver reference volume of each patient. The two green diamonds correspond to the mean. The circles containing red plus sign are considered/taken as outliers. tion did not converge within the range of the activity test values in the P9_11, P11_13, and P13_15, interestingly indicating the high selectivity of the administrations to the PTV. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pn_t** & **Administered** & **SPECT-MAA Estimated** & **PET-MS Estimated** \\
**Activity (MBq)** & **Optimal Activity (MBq)** & **Optimal Activity (MBq)** \\ \hline P1\_1 & 2750 & 2598 & 2594 \\ \hline P2\_2 & 3347 & 3748 & 4009 \\ \hline P3\_3 & 3961 & 6239 & 8518 \\ \hline P4\_5 & 4231 & 10,662 & 9423 \\ \hline P5\_6 & 4305 & 4397 & 3397 \\ \hline P6\_7 & 2814 & 2274 & 2281 \\ \hline P7\_8 & 5604 & 8094 & 8481 \\ \hline P8\_9 & 1537 & 4898 & 4505 \\ \hline P8\_10 & 4227 & 2219 & 2450 \\ \hline P10\_12 & 1992 & 1471 & 1380 \\ \hline P12\_14 & 4481 & 8675 & 8539 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Administered and estimated optimal activities based on SPECT-MAA and on PET-MS for each of the 11 treatments, with OF converging for a maximum between 0 and 12 GBq. Figure 5: Boxplots with the distributions of the \(\gamma\)-index PR considering seven DD/DTA test conditions in four liver ROI: (**a**) _liver_ref_, (**b**) liver, (**c**) PTV, and (**d**) NLV. The red plus sign are considered/taken as outliers. Two example tables with detailed information regarding the estimated ADD based on the pre-treatment SPECT-MAA as a function of the activity to be administered are shown in Supplementary Materials.