**Author details**

18 Will-be-set-by-IN-TECH

**Figure 14.** Isotopic (a) and anisotropic (b) component of the SEF reported in Eq. 18 for healthy (HAA)

parallel to the marked decrease in the isotropic stored energy for AAA tissues (as describe above), we can observed an increase of stiffness capturing the observed biaxial reduction in extensibility/distensibility in particular in the circumferential direction (see Fig. 10(g)). As mention in Sec. 1, in current clinical practise, the aortic diameter is the main feature that is used to predict the risk of rupture. The more reliable quantification of the rupture risk is provided by the RPI parameter of Eq. 15 (and similar), however, which stress (principal stress, circumferential stress or von Mises stress) and strength is still matter of controversy. Gaining an understanding of the mechanical properties of the AAA tissue therefore is of clinical significance. Due to the difficult to reliably predict abdominal aortic aneurysm expansion and rupture in individuals several clinical trials have been performed [25, 72]. At the same time, from the computational point of view, literature systematically reports the evidence to support the role of patient-specific biomechanical profiles in the management of patients with AAA both from imaging and FE approach [1, 13, 81]. In order to accurately predict the risk of rupture of AAA, is necessary to predict the AAA wall strength distribution and the material properties non-invasively. With regard to our work, our specific FE simulations (both deterministic and probabilistic), reveal the importance to define a more realistic geometrical shape by including also wall thickness regional variation. Several previous studies were devoted to the definition of the geometrical parameters that mainly influence the wall stress (Vorp et al. [83] and more recently Rodríguez et al. [62] found that wall stress is substantially increased by an asymmetric bulge in AAAs, just to cite but a few), but, to the best of our knowledge, this is the first structural study in which also the wall thickness is considered as variable. Figure 15 depicts results from two deterministic simulations extracted by the multivariate analysis: aneurysm with a large diameter and constant wall thickness (a) and FE model small diameter and a wall thickness reduction of 50% in the ventral area. The stress contour plot points out how the wall thickness reduction influence the maximum stress value

To conclude, there is, therefore, a pressing need to include patient specific regional variations to identify regions within AAAs that have the highest ratio of stress to strength. Future studies on patient-specific geometries of AAAs should consider the actual wall thickness. Moreover, the understanding the mechanical properties of the AAA wall will enhance our ability to design implants that can stay in place and/or protect the aneurysm wall from blood pressure.

and pathological (AAA) tissue.

and its localization.

Simona Celi *Institute of Clinical Physiology National Research Council IFC-CNR, Massa Fondazione Toscana CNR "G. Monasterio", Heart Hospital, Massa, Italy*

Sergio Berti *Fondazione Toscana CNR "G. Monasterio", Heart Hospital, Massa, Italy*
