## 2 Materials and Methods
### CFD Modeling and Simulation  
#### 2.1.1 Generating the 3D Model of Geometry and the Volume Grid  
In the current study, a simplified geometry of an aneurysm located at the internal carotid artery was selected, because the flow diverters are more suitable for the treatment of these kinds of aneurysms. The simplified geometries with a straight parent artery give unrealistic results; therefore, adding an inclined section to the parent artery causes the velocity vector to have other components while turning in the bend, and enough flow enters the aneurysm as happens in real cases [4]. The schematic geometry is illustrated in Figure 2. The origin of the Cartesian coordinate system is located at the center of the inlet cross-section, so the mid-plane of the parent artery is located at z = 0. The diameters of the parent artery and aneurysm sac, and the spacing between the centerline of the inclined part and center of the aneurysm sphere are 4 mm, 10 mm, and 5 mm, respectively. More details about the dimensions can be found in reference [4]. Views 1 and 2, illustrated in Figure 2, are used for exploring the flow during navigation in the VR environment.  
Figure 1: Proposed workflow for visualization of CFD analysis data in VR environment.  
Figure 3 shows the generated 3D solid model of the braided stent with a length of 10 mm, where an intracranial aneurysm flow diverter by [PERSON] (Irvine) was selected [25]. The stent has a single wire thickness and is braided as per the study [13]. The strand thickness, external diameter, weave angle, and porosity of stent are 0.05 mm, 4 mm, 31.98\({}^{\circ}\), and 66.44%, respectively. In the current study, the number of stent wires was halved to 12 to display the phenomena in the VR environment much clearer.  
According to the study [26], instead of the whole stent, only the portion that was located at the aneurysm neck was used in numerical simulations for reduced computational time while having no considerable deviation from the flow behavior obtained with the full stent models. By doing so, the stent geometry was simplified, as shown in Figure 4. It is known that the positioning of the stent plays a major role in the effective treatment of the aneurysm. One of these positioning issues is related to the gap between the flow diverter and the parent artery wall that may create unfavorable conditions and increase the flow into the aneurysm. In order to investigate this effect, two cases were studied, the case with a 0.03 mm wall-stant gap, named \"With-Stent1,\" and the case named \"With-Stent2\" for which the gap has been clogged by a wall.  
Figure 3: Generated 3D model of stent.  
Figure 2: Generated 3D model of cerebral aneurysm—all dimensions are in millimeters.  
Seven slices were created as some important locations to report the contours of scalar variables, and they are illustrated in Figure 4. Slice 1 is located on the mid-plane of the geometry at z = 0, while Slices 2-6 are perpendicular to the artery wall. The equal-spaced slices of 3, 4, and 5 intersect the aneurysm, while slice 4 passes through the center of the aneurysm sphere. Slice 7 is parallel to the axis of the inclined artery and close enough to the artery-aneurysm interface to cover the near-neck phenomena.  
All geometries were generated in SOLIDWORKS, CAD software. The grids were generated using the ANSYS ICEM CFD software package. A nonuniform tetrahedral mesh was generated with a much finer grid close to the aneurysm neck and the wires of the stent. The number of grid elements ranged from 500,000 to 2,500,000 and were generated based on the grid independency test, and a compromise between the accuracy and computation time. The time step was 0.01 s. An example of the generated grid can be seen in Figure 5.