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to direct their research toward examining posterior wall stress for clinical relevance. One of the first studies to apply the finite element analysis (FEA) to determine the AAA wall stress was the study of [37] who concluded that FEA has a potential of becoming a crucial tool in the study of vascular mechanics. Their study was followed by extensive research in the area of numerically predicted AAA wall stress that continues even at present. However, limitations of this study include the use of idealized models with regular structures and evenly distributed wall stress.

In 1998, Vorp et al. [38] published a study on the influence of maximum diameter and aortic aneurysm asymmetry on mechanical wall stress. They investigated the effects of asymmetry on 3D stress distribution in the wall of AAA and refuted the critical diameter criterion suggesting that all AAAs with the same diameter have the same risk of rupture. They generated 10 virtual computer models with commercial software (Pro‐Engineer v. 16.0; Parametric Technology Waltham, Mass) according to two protocols. In the first protocol, five models were generated with constant maximum diameter parameter (6 cm) while asymmetry β varied from 0.3 to 1.0. In the second protocol, asymmetry was kept constant β = 0.4 while maximum diameter parameter varied from 4 to 8 cm. The results confirmed that both parameters had the influence on the increase and decrease in the wall stress in the different sections of the aneurisms and that aneurysm rupture was caused by a gross mechanical failure of the aortic wall which occurs when wall stress exceeds the strength of the tissue. It was also concluded that maximum stress occurs on the posterior wall for small AAAs (≤5), while for larger AAAs peak stress is on the anterior surface. Although it pioneered in proving the effects of asymmetry, the study was performed on virtual models, so potential limitations assuming that AAA wall is homogenous, isotropic, and linearly elastic with small strains and uniform thickness have to be taken into account when analyzing real AAA models.

      Venkatasubramaniam et al. [10] refuted traditional views that relate aneurysm size to the risk of rupture. They conducted a comparative study of aortic wall stress in ruptured and non‐ruptured aneurysms with an aim to prove the importance of wall stress when predicting the risk of rupture in individual patients. Namely, the study included computed tomography (CT) scans of 27 patients (12 ruptured and 15 non‐ruptured AAA), predominantly males. Using the finite element method, they calculated wall stress using the geometry of AAA, the material properties of the aortic wall, and the forces and constraints acting on the wall. The material properties were used from a previously validated mathematical model by [39–41]. ANSYS 6.1 program (ASN Systems Ltd, Cannonsburg, USA) was utilized for the analysis and post‐processing while the von Mises stress was used to evaluate the state of the aneurysms. There were no important differences in the mean diameter between two groups (6.8 cm for non‐ruptured and 7.6 cm for ruptured, P > 0.1) and there were two aneurysms that ruptured at small diameters of 5.0 and 5.7 cm. The authors concluded that AAA that ruptured or went on to rupture had significantly higher peak stress (mean 1.02 MPa) compared with non‐ruptured (mean 0.62 MPa). Moreover, systolic blood pressure was also significantly higher in ruptured AAA. Noting that 45 and 65 mm diameter AAAs can have the same stress, they emphasized the role of the shape and asymmetry of the aneurism including the anterior and superior limits. They also demonstrated that wall stress can be calculated from a routine CT scan and that it may be a better predicator of AAA risk of rupture than diameter alone on the individual basis. On the other hand, the study assumed a uniform AAA wall thickness of 2 mm and did not take into account the effect of thrombus on wall stress.

      In 2006, Vande Geest et al. [42] developed a biomechanics‐based rupture potential index (RPI) that became a useful rupture prediction tool. Namely, the RPI predetermined the wall strength on a patient‐specific basis by utilizing experimental tensile testing and statistical modeling. The tissue strength was calculated by taking parameters such as age, sex, smoking status, family history of AAA, normalized diameter, and the maximum thickness of the ILT into account. Then, the wall stress was predicted with FEA. Although the authors reported that the RPI has a potential to identify high rupture risk of AAA better than diameter or peak wall stress (PWS) alone, their approach still requires validation before it can be introduced into clinical setting.

In the study conducted by Scotti et al. [43], 10 idealized models of AAA were used, generated with the CAD software ProEngineer Wildfire (Parametric Technology Corporation, Needham, MA) [44] together with an additional non‐aneurismal model as control in order to assess the significance of an arbitrary estimated peak fluid pressure (117 mmHg) compared with nonuniform pressure resulting from a coupled FSI. The models differed in the degree of asymmetry and wall heterogeneity and the FEA was used to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics. Each model contained fluid and solid domain and was analyzed with static pressure‐deformation analysis together with FSI. The Navier–Stokes equations were used as governing equations for homogeneous blood flow, while for computational solid stress (CSS) analysis, only the solid domain was considered. The results exhibited that a realistic fluid pressure distribution to the inner AAA wall (instead of an arbitrary peak systolic pressure) resulted in at least 20% higher wall stress, despite wall thickness heterogeneity. Additionally, maximum AAA wall stress increased with asymmetry although the computational model included blood flow.

      Finol and Ender [45, 46] used a Spectral Element Method with three‐step time splitting scheme for the semidiscrete formulation of the time‐dependent terms in the momentum equations for axisymmetric two‐aneurysm abdominal model. This methodology has been widely used for the Direct Numerical Simulation of transitional flows with fast‐evolving temporal phenomenon and complex geometries.

      Multi‐scale models for AAA are considered constitutive models for vascular tissue, where collagen fibers are assembled by proteoglycan cross‐linked collagen fibrils (CFPG‐complex) and reinforce an otherwise isotropic matrix (elastin). There is multiplicative kinematics for the straightening and stretching of collagen fibrils. Mechanical and structural assumptions at the collagen fibril level define a piece‐wise analytical stress–stretch response of collagen fibers.

      The concept of multi‐scale constitutive model performs integration at the material point for macroscopic stress which takes into account micro plane concept incorporated in the finite element modeling (FEM) [47, 48].

      Zhang et al. [49] used multi‐scale and multi‐physical models for understanding disease development and progression, and for designing clinical interventions. They investigated multi‐scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, and personalized and precision medicine in cardiology with examples in arrhythmia and heart failure.

      FSI describes the wave propagation in arteries driven by the pulsatile blood flow. These problems are complex and challenging due to the high nonlinearity of the problem. The nonlinearity exists in the fluid equation but also in the structure displacement which modifies the fluid domain and generates geometrical nonlinearities as well [50].

Some authors used the generalized string model as the structure of blood flow in compliant vessels and arteries [50–56]. Causin et al. [57] described this string model as a structural model derived from the theory of linear elasticity for a cylindrical tube with small thickness. Nobile and Vergara [56] emphasized that the generalized string model neglects bending as well. Čanić et al. [58–61] claimed that there are no analytical results which are able to prove the well posedness of FSI problems without assuming the structure model that includes the higher‐order derivative terms, capturing the viscoelastic behavior. For blood flow, there is a strong added mass effect issue in which the fluid and structure have comparable densities.

      All the above studies demonstrate the importance of biomechanical modeling of AAA by using FEM approach with and without FSI and nonlinear wall deformation. This mechanical approach provides an additional understanding of potential indicators of rupture risk.

1.4 Experimental Testing to Determine Material Properties

      Experimental tests are used to determine the mechanical properties of AAA. In‐vivo measurements are based on the imaging modality. For in‐vivo measurements, the main difficulty is to accurately determine the true force and the displacement distribution for the aorta wall. For isolating samples

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