## 3 Results
### \({}^{166}\)Ho Versus \({}^{90}\)Y Monte Carlo Simulations  
To obtain a first comparison of the performance of the two radionuclides, only the MC simulations for each device have been considered for LS = 10%. To make the AD distributions of \({}^{90}\)Y and \({}^{166}\)Ho independent by the differences in the physical half-life of the two radionuclides, the ADr maps and the corresponding dose rate-volume histograms (DrVHs) (Figure 4) were computed. The ADr distribution of \({}^{166}\)Ho appears significantly more inhomogeneous compared to that of \({}^{90}\)Y, a fact supported by the HI, which is 3.5 for \({}^{90}\)Y and 6.3 for \({}^{166}\)Ho. This difference is due to the physical characteristics of the decay spectra of the two radionuclides, primarily the low-energy electron component of the \({}^{166}\)Ho spectrum, which is characterized by less energetic \(\beta^{-}\) decay spectra and discrete electrons [16]. The stronger inhomogeneity of the ADr distribution of \({}^{166}\)Ho implies a stronger correlation of the AD distribution with the anatomical density heterogeneity of the lung tissue. Impact on Clinical Decision-Making: From the \(\overline{AD}\) to the EBRT Dosimetric Constraints for \(D\)Vth  
All the results hereinafter presented are not intended to be for general application, given the strong dependence of the computations on the specific activity and density distributions of the evaluated case. Table 8 summarizes the results for the MC \(\overline{AD}\), the activity as high as safely administable (AHASA), and the maximum lung activity (MLA) to ensure that the \(\overline{AD}\) to the lungs does not exceed the 30 Gy threshold [7; 8] for the specific simulated case. The MLA was found to be nearly constant across all LS cases, at approximately 500 MBq, due to a negligible contribution of cross-irradiation from the hepatic region to the lungs. The AD maps were converted to BED maps using Equation (4), then to \(EQD_{2}\) maps, from which the DVHs were extracted. In this section, we attempt to simulate a clinical  
Figure 4: Example slices in the coronal view of the ADr maps (left) of \({}^{166}\)Ho (**a**) and \({}^{90}\)Y (**b**), along with the corresponding DrVHs (**c**), are shown for LS = 10%. The data demonstrate a different degree of inhomogeneity between the two radionuclides, due to the distinct physical characteristics of their decay spectra. evaluation of the LS = 10% reference phantom simulation as if treated with the prescribed activity (see Section 2.3). The \(\overline{AD}\) from the MC simulations was found to be 21.4 Gy for \({}^{90}\)Y at 1.8 GBq, and 35.3 Gy for \({}^{166}\)Ho at 5.7 GBq. This suggests that the treatment with \({}^{90}\)Y is safely administra \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Lung Shunt** & **MC \(\overline{AD}\) (Gy/GBq)** & **AHASA (GBq)** & **MLA (GBq)** \\ \hline
10\% & 6.2 & 4.88 & 0.49 \\
20\% & 12.0 & 2.50 & 0.50 \\
30\% & 17.9 & 1.67 & 0.50 \\
40\% & 23.9 & 1.26 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: MC \(\overline{AD}\) results for all the LS cases and the corresponding activity as high as safely administra  
table 16: HO results significantly exceed the reference constraint (see Table 4), confirming the need to reduce the administered activity. The DVHs of the \(\underline{EQD_{2}}\) maps are shown in Figure 5 along with the volumetric constraints from Table 4.  
For the simulated administered activities, \({}^{90}\)Y fully meets two constraints (\(V_{30}\) and \(V_{40}\)), while \(V_{20}\) compliance depends on the tissue T\({}_{\mu}\). Conversely, \({}^{166}\)Ho partially meets the \(V_{40}\) constraint, depending on the specific T\({}_{\mu}\). Neither radionuclide meets the \(V_{5}\) and \(V_{10}\) requirements. The probability of RP onset is graphically represented in Figure 6, along with the points for the LS = 10% case of \({}^{90}\)Y and \({}^{166}\)Ho for the maximum and minimum T\({}_{\mu}\) of LT.