## 4 Discussion
### Pre-Aneurysm State  
The contours presented for the TAWSS and pressure show that lesions formed in zones where these parameters had medium magnitudes, never in those with minimum values. As a comparison, the approximate value of the TAWSS in the healthy artery zone where the aneurysm was located (shown in Figure 22) was compared with the average value of the same parameter in the original aneurysm. Table 8 shows that, for all four cases, there was a reduction in the TAWSS when the aneurysm was present. Interestingly, for both ruptured cases, the reduction was approximately 75%, while for the unruptured cases, the reduction was lower, 45% for UG-1 and 33% for UG-2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Size Variation**} & \multicolumn{2}{c}{**Average von Mises Stress Difference [\%]**} \\ \cline{3-4}  & & **Diastole** & **Systole** \\ \hline \multirow{3}{*}{RG-2} & III & \(-\)19.5 & \(-\)17.2 \\  & II & \(-\)31.7 & \(-\)31.3 \\  & I & \(-\)17.1 & \(-\)15.6 \\ \hline \multirow{3}{*}{RG-3} & III & \(-\)17.1 & \(-\)21.8 \\  & II & \(-\)22.9 & \(-\)29.1 \\  & I & \(-\)11.4 & \(-\)10.9 \\ \hline \multirow{3}{*}{UG-2} & III & 28.0 & 25.0 \\  & II & 8.0 & 8.7 \\ \hline \multirow{3}{*}{UG-3} & III & 28.9 & 29.0 \\  & II & 7.9 & 9.7 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Percentage variation in the average von Mises stress at the aneurysm dome with respect to the original size.  
Figure 22: Location of the imported aneurysm and the TAWSS distribution: (**a**) RG-1, (**b**) UG-1, (**c**) RG-2, (**d**) UG-2.  
The reduction occurred because when the aneurysm was not present, the blood was in contact with the artery at a higher velocity than when the aneurysm occurred, because it needed to travel a longer path into the cavity. It was more difficult for the blood to flow, due to the change in direction and because there was blood with a lower velocity filling the cavity.  
[PERSON] et al. [38] clinically studied hemodynamic changes in aneurysms for four years, and the growth that was reported showed qualitatively similar geometric changes as in our investigation. The WSS decreased after growth, and for other hemodynamic characteristics, a large variability between the aneurysms was observed in the study population. [PERSON] et al. [39] reported that the pressure, velocity, and WSS decreased with the aneurysm size, increasing the rupture risk; they varied the aneurysm size considering a spherical aneurysm. Wall thickness heterogeneity affects the FSI results when modelling cerebral aneurysms [40], and the von Misses stress can be overestimated or underestimated using a constant aneurysm wall thickness, depending on the value used. The formation of paraclinoid aneurysms was reported near the location of high WSS and high strain in [41]; our results showed the same tendency in terms of TAWSS. [PERSON] et al. [41] also reported that the presence of the dura mater affected the FSI results. For CFD simulations of cerebral aneurysms, the rheology model is relevant. We used a non-Newtonian Casson model; the differences from the Newtonian blood model were more important in abdominal aortic aneurysms, and the effects of turbulence on WSS were negligible for the flow simulation of cerebral aneurysms [42].