## 3 Results
### The Impact of Revascularization on the Hemodynamics Parameters  
Figure 6 shows the impact of revascularization on the WSS distributions in the ACoAA. With the reduction of LICA stenosis degree, the high WSS region shifted from the left of the ACoAA dome towards the top, and the WSS magnitude on the dome's anterior region elevated as well. Figure 5: Impacts of revascularization on velocity vectors (**a**,**b**) and streamlines (**c**,**d**) in the anterior communicating artery aneurysm (ACoAA) at peak systolic. The pre-operative and post-operative results were shown in the left and right column, respectively. The TAWSS distributions of the cases are shown in Figure 7. The decreasing stenosis degree resulted in a reduction of overall TAWSS level and maximum TAWSS on the dome of the ACoAA. Table 3 listed the low TAWSS (\(<\)1.5 Pa) [27; 34; 35; 36; 37] and high TAWSS (\(>\)7 Pa) [38; 39; 40; 41] areas on the ACoAA dome. Compared with the sever stenosis case, a larger low TAWSS area and smaller high TAWSS area were observed in the case of reduced stenosis degree. The areas of low WSS and high WSS regions in the non-stenotic case were 32% larger and 67.6% smaller than that of the severe stenosis situation, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Cases**} & \multicolumn{2}{c}{**Area (mm\({}^{2}\))**} \\ \cline{2-3}  & **Low TAWSS** & **High TAWSS** \\ \hline Severe stenosis & 50 & 65 \\ Moderate stenosis & 72 & 28 \\ Mild stenosis & 69 & 18 \\ Non-stenotic & 66 & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Space-averaged TAWSS magnitude on the ACoAA. Figure 6: Impacts of revascularization on the wall shear stress (WSS) distribution of ACoAA at peak systolic. Figure 7: The distribution of time-averaged wall shear stress (TAWSS) on the ACoAA under different stenosis degrees: (**a**) non-stenotic, (**b**) mild stenosis, (**c**) moderate stenosis, (**d**) severe stenosis. Table 4 lists the specific magnitudes of the space-averaged TAWSS and maximum TAWSS on the ACoAA dome. In the non-stenotic case, the space-averaged TAWSS and maximum TAWSS magnitudes were 48.29% and 67.42% lower than that of the severe stenosis case, respectively. Figure 8 illustrated the OSI distributions on the ACoAA under different stenosis degrees. In the severe stenosis case, only small regions of high OSI (>0.2) were observed at the ACoAA neck of the affected side. With the decreasing stenosis degree, the high OSI regions migrated towards the ACoAA tip. Meanwhile, the blood supply from the affected side restored gradually with the decreasing LICA stenosis degree. The confluence of bilateral blood flow in the ACoAA resulted in more complex flow patterns, which elevated the flow instability and led to an increase in high OSI area as well as the average OSI magnitude on the ACoAA dome. The high OSI area and space-averaged OSI magnitude on the ACoAA dome of the non-stenotic case were 34 times and 2.85 times larger than that of the severe stenosis case, respectively. The space-averaged OSI magnitudes on the ACoAA dome of all cases were given in Table 5.  
Figure 9 illustrated RRT distribution on the ACoAA for each of the four cases. An elevation of the maximum RRT and space-averaged RRT on the ACoAA dome with the decreased stenosis degree was observed. Meanwhile, the high RRT region migrates from the ACoAA neck towards the tip. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**TAWSS Magnitude/Pa**} \\ \cline{2-5}  & **Severe Stenosis** & **Moderate Stenosis** & **Mild Stenosis** & **Non-Stenotic** \\ \hline Space-averaged & 7.02 & 4.03 & 3.57 & 3.63 \\ Maximum & _77.77_ & 40.91 & 24.27 & 25.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Space-averaged TAWSS magnitude on the ACoAA. Figure 8: The distribution of oscillating shear index (OSI) on the ACoAA under different degrees of stenosis: (**a**) non-stenotic, (**b**) mild stenosis, (**c**) moderate stenosis, (**d**) severe stenosis.