## Materials and Methods
### Numerical Analysis  
The computational meshes were generated using the commercial software Ansys ICEM CFD, Version 16.0 (ANSYS Inc., Canonsburg, PA, USA). Due to the complexity of the geometry in the presence of stents, the grids were composed of unstructured tetrahedral elements. Finer mesh with smaller tetrahedral elements were used to resolve the stent struts (see Figure 3). To ensure independent results from the mesh element size, a mesh independency study was carried out by using the mesh convergence criterion based on the WSS and the intra-aneurysmal velocity. In particular, we considered it as converged if the mesh results in WSS and velocity profiles within 2.5% from the finest tested mesh [21]. Convergence was reached with an element size around the stent strut of 0.015 mm and a global tetrahedral element size of 0.3 mm. The total number of mesh elements ranged from \(0.4\times 10^{6}\) to \(12\times 10^{6}\) elements for both untreated and treated models. Unsteady CFD simulations for both \begin{table}
\begin{tabular}{c c c c} \hline  & **Thickness (mm)** & **Length (mm)** & **Diameter (mm)** \\ \hline
**STENT BS** & 0.4 & 40 & 4.75 \\
**STENT 1** & 0.1 & 40 & 4.75 \\
**STENT 2** & 0.1 & 40 & 4.75 \\ \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the flow diverting stents used. Figure 2: Mesh patterns of the considered FDSs with different porosities (90, 80, and 70%). From the left to the right are STENT BS, STENT 1 and STENT 2.  
treated and untreated geometrical models were carried out on the commercial software Ansys CFX, Version 16.0 (Ansys Inc., Canonsburg, PA, USA). Notably, in many previous studies of computational hemodynamics of cerebral aneurysm, the blood is simplified of being a Newtonian fluid, which may not be always true [11; 37]. For improvement, in the present study we took the rheology of a non-Newtonian fluid into account by employing the constitutive model in which the dynamic viscosity decreases as the shear rate increases. In particular, we used the Carreau-Yasuda model that has been demonstrated as more appropriate than the Newtonian model for low shear rates [37; 38]. The constitutive equation of the Carreau-Yasuda model is given by [39; 40; 41]:  
\[\mu=\mu_{\infty}+(\mu_{0}-\mu_{\infty})\left[1+\left(\lambda\dot{\gamma} \right)^{q}\right]^{\frac{q-1}{q}} \tag{1}\]  
where \(\mu_{0}=0.056\) is the viscosity at zero shear rate expressed in \([Pa\cdot s]\), \(\mu_{\infty}=0.00345\) is the viscosity for an infinite shear rate expressed in \([Pa\cdot s]\), \(\lambda=3.313\) is the relaxation time expressed in \([s]\), \(n=2\) is the power exponent and \(a=0.64\) is the Yasuda exponent [39]. The blood density was set to 1050 kg/m\({}^{3}\). The vessel wall was assumed to be rigid with a no-slip boundary condition. A flow rate waveform was used as the inlet and outlet conditions, since the model is not compliant. In particular, a time-dependent velocity waveform in an intracranial aneurysmatic cerebral artery was taken from literature [42]. This waveform was adapted to our models for computing the mass flow at the inlet. The obtained waveform that represents a time-dependent mass flow was imposed at the inlet and at the outlet of the model, which were extended to ensure fully developed flow in the region near the stent and the aneurysm. The resultant time dependent mass flow is represented in Figure 3a). Cardiac cycles of 1 s were discretized in time steps of 0.001 s. The main variables such as velocity and pressure were set initially to zero for facilitating convergence. To reduce the effect of initial transients at the beginning of the computation, three complete cardiac cycles were computed and data from the last one was stored for subsequent analysis [19; 21]. Typically, the results could be influenced by the convergence obtained at the beginning of the simulations and by the initialization of the variables (either automatic or user-defined). Computing three consecutive cardiac cycles assures a convergent solution and transient-independent results.