## 3 Results
### Patient Analysis Results  
The mean percentage dose differences between VSV and MC were found to be 7.0 \(\pm\) 0.8%, 4.1 \(\pm\) 2.9% and 6.7 \(\pm\) 1.4% for water-equivalent structures: Liver, H-L and Tumor, respectively. For air-equivalent structures, the mean percentage dose differences were found to be \(-\)61.2 \(\pm\) 7.7% for the Lung L and \(-\)61.1 \(\pm\) 6.2% for both Lung R and Lungs. Considering the L-L Edge structure, the percentage mean dose differences between VSV and MC were \(-\)50.8 \(\pm\) 5.3%. The box plots of the percentage differences between VSV and MC results are shown in Figure 3. Passing-Bablok regression plots for the agreement assessment between the VSV method and MC one for each water-equivalent structure extracted from the patient analysis are shown in Figure 4 and display a mean slope for these structures equal to 1.07 \(\pm\) 0.01.  
Figure 5, instead, shows Passing-Bablok regression plots for the agreement evaluation between the VSV method and MC one for each air-equivalent structure extracted from the patient analysis, displaying a mean slope equal to 0.39 \(\pm\) 0.01. The L-L Edge structure is  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Setup Simulation** & **Structures** & **MIM \({}^{90}\)Y-SurePlan MAD** & **Torch MAD** \\  & & **[Gy]** & **[Gy]** \\ \hline \multirow{4}{*}{1} & Lungs & 0.22 & 0.50 \\  & L–L Edge & 4.60 & 8.90 \\  & Liver & 62.11 & 61.40 \\ \hline \multirow{4}{*}{2} & Lungs & 6.86 & 23.10 \\  & L–L Edge & 10.89 & 27.40 \\ \cline{1-1}  & Liver & 62.79 & 62.50 \\ \hline \hline \end{tabular}
\end{table}
Table 2: MAD values extracted from phantom analysis for selected VOIs by using MIM and Torch, respectively.  
Figure 2: An axial view with phantom liver and lungs compartments showing the differences between Setup 1 and 2 when using MIM \({}^{90}\)Y-SurePlan (**a**,**c**) and Torch (**b**,**d**).  
also included in Figure 5, with a regression slope of 0.49. More details about Passing-Bablok regression analysis results are listed in Table 3.  
Figure 4: Passing–Bablok regression for comparison of MAD values between VSV method and MC one for water-equivalent structures (**a**) Liver, (**b**) H–L, and (**c**) Tumor.  
Figure 3: Box plots of percentage differences between MAD calculated using the VSV method and MC one for selected VOIs.  
Figure 5: Passing–Bablok regression for comparison of MAD values between VSV method and MC one for air-equivalent structures (**a**) Lung R, (**b**) Lung L, (**c**) Lungs, and (**d**) L–L Edge.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structures** & **Fit Parameters** & **Value** & \
\begin{tabular}{c} **Lower Confidence** \\ **Interval** \\ \end{tabular} &
\begin{tabular}{c} **Upper Confidence** \\ **Interval** \\ \end{tabular} \\ \hline \multirow{2}{*}{Liver} & Intercept & 0.230 & \(-\)0.326 & 0.595 \\  & Slope & 1.063 & 1.055 & 1.080 \\ \hline \multirow{2}{*}{Healthy Liver} & Intercept & \(-\)0.440 & \(-\)0.910 & \(-\)0.141 \\  & Slope & 1.075 & 1.053 & 1.097 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Passing–Bablok regression analysis results reporting for each fitting parameter (intercept and slope) the relative lower and upper confidence interval.