## 4 Discussion  
The use of flow diverting stents for treating cerebral aneurysms originated as a complementary technique to other endovascular treatments [6]. Successive clinical trials and experimental studies have shown that these devices are capable of reducing the intra-aneurysmal flow and of promoting the desired occlusion. Recent advances have produced the development of flexible, low porosity devices that have shown improved performances compared to the previous flexible, high porosity or rigid, low porosity stents. However, further study is still necessary for the development and the optimization of these devices as well as for the planning of the therapies. In this context, we have analyzed the performance of three flow diverting stents and the impact that these devices may have in different vessel geometrical configurations, which present variations of curvature and tortuosity in similar way as cerebral arteries. Notable curvature and high tortuosity characterize the geometries of these vessels. For this reason, high flexibility is desired for a FDS even if this aspect is not accompanied by the necessary porosity. High reported rates of successful FDS endovascular procedures generally indicate that the hemodynamic change induced by a FDS is responsible for the complete aneurysm occlusion. In the literature, it is assumed that a specific threshold should exist regarding the minimum necessary flow rate reduction that would promote thrombosis [10]. This threshold can be assessed by computational simulations that evaluate not only the reduction of flow but also the hemodynamical indices that could help to predict the recirculation of blood flow within the aneurysmic sac (such as the RRT and the OSI) and the risk of rupture (such as the TAWSS and the OSI) [46]. In the literature  
Figure 10: Histograms of the normalized area associated to the OSI of the aneurysm and of the artery (and stent) for V-bent, C-bent and S-bent vessel configurations. The depicted areas are normalized with respect to the area of whole geometry model. it is also stated that the value of OSI for ruptured aneurysms is higher than that for unruptured aneurysms [44]. The presented results show that the flow diverting devices increase the OSI at the dome when reducing porosity. This means that even if they promote a considerable flow reduction, they may still increase the risk of rupture. On the contrary, the porosity reduction promotes an increase of the RRT, which is desirable for guaranteeing the necessary occlusion. Previous studies have suggested the velocity or flow reduction as variables for predicting the FDS-induced desired thrombosis [9; 10; 16]. The structure of the flow has also been considered for assessing the local hemodynamics within the stented aneurysm [13; 16]. However, as demonstrated in the presented results and in those of other studies [6; 44] it is clear that the hemodynamic indices should be evaluated for having the entire picture on stenting effectiveness. The geometry of the artery in the presence of an aneurysm has been recognized to be crucial for assessing the flow characteristics and hence the effectiveness of the stent [13]. Higher vessel curvatures for example drastically reduces the capability of the stent to divert the flow [13]. The stent itself has also been found to strongly influence the arterial geometry [33]. Additionally, recent studies have shown that the vessel deformation induced by the flow diverting device may provide an unfavorable hemodynamic environment for thrombus formation [32]. For this reason, in this study we have analyzed and compared different geometrical configurations with and without the device. Even though the stented configuration shows a reduction of the flow within the aneurysm for the curved and the tortuous vessel, in comparison with the straight configuration analyzed in previous studies [28], its effectiveness is reduced. [PERSON] et al.