## 2 Materials and Methods
Despite this important issue, very few contributions in scientific literature involve virtual models of the aortic tissues endowed with material hereditariness. The mainly used representation of the material mechanics is represented by a hyperelastic model [38] with free energy density, defined in terms of the strain tensor invariants, as in the Neo-Hookean, Ogden-Holzapfel, or more sophisticated materials models. In the present analysis, the FEM simulations have been carried out with the Neo-Hookean [46; 47] model for the aortic tissue, and it was implemented on ABAQUS (Dassault systemes) to reduce computational cost and, at the same time, to improve the accuracy of the simulation. The biomechanical characteristics of the patient-specific stent-graft involve two materials, one for the graft and the other for the stent: (i) the graft is the envelope of the device that represents the new lumen of the vessel, and that is constituted by a DACRON(tm) or polytetrafluoroethylene (PTFE) polymer, and (ii) the stent is composed of the stiffening struts, pre-knitted on the graft, which are represented by metallic rings with a 3D sinusoidal structure. In this study, the graft material has considered as DACRON, and its mechanical characteristics have been included for FSI analysis. The metallic structure of the stent, instead, has been considered to be constituted by Ni-Ti alloy. NiTinol is a shape memory alloy (SMA) that consists of an equiatomic amount of nickel and titanium. NiTinol is very popular in biomedical applications due to its remarkable super-elasticity, shape memory, biocompatibility, and corrosion resistance, as well as fatigue resistance and durability. NiTinol(tm) is a shape memory alloy that can be programmed to expand as soon as it is inserted into position and released, at a body temperature of 37 \({}^{\circ}\)C, assuming the dimensions of the vessel and remaining closed on itself at other temperatures; in this way, it is not necessary to use an expandable balloon to open the stent-graft once inserted. This represents the gold standard in cardiovascular applications. A typical stress-strain diagram of a Ni-Ti superelastic alloy is represented in Figure 1.  
We started modeling from the CT images Figure 2 of the AAA patient. The images were imported using the segmentation software Mimics 21.0 (Materialise), which allowed the two-dimensional and then three-dimensional reconstruction of the patient's aneurysm vessel Figure 3. Segmentation processes were applied both automatically and manually. Automatic operation was used to select the region of interest. These operations were based on the gray-scale of the CT images. The manual segmentation was then used to reduce the region of interest and to obtain an accurate mask. The accuracy of the vessel model therefore depended on the quality of the CT images, on the number of images available to the operator, and ultimately on the operator's ability to improve these manually by intervening in the automatic reconstruction process. The three-dimensional model of the patient's aorta used in CFD analysis was reconstructed by Mimics. Based on this, the stent-graft was realized by SolidWorks (Dassault Systemes), as shown in Figure 4. The rings of the stent have a circular section, and their size adapts to the  
Figure 3: Three-dimensional reconstruction of aneurismatic abdominal aorta. Figure 2: CT image of the sagittal, axial, and coronal plane of the patient. diameter of the graft. To perform CFD analyses, fluid models of the conventional graft and the patient-specific graft were also reconstructed using the software Soliworks, as shown in Figure 5. In detail, to reconstruct the conventional model, the graft was included in the aneurysm site. The three models were exported in _STL_ format for the next step.