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Research Papers

Mechanical Stresses in Abdominal Aortic Aneurysms: Influence of Diameter, Asymmetry, and Material Anisotropy

[+] Author and Article Information
José F. Rodríguez1

Group of Structural Mechanics and Materials Modeling, Aragon Institute of Engineering Research (I3A), Torres Quevedo Building, María de Luna 3, Zaragoza 50018, Spain

Cristina Ruiz

Group of Structural Mechanics and Materials Modeling, Aragon Institute of Engineering Research (I3A), Torres Quevedo Building, María de Luna 3, Zaragoza 50018, Spain

Manuel Doblaré

Group of Structural Mechanics and Materials Modeling, Aragon Institute of Engineering Research (I3A), Torres Quevedo Building, María de Luna 3, Zaragoza 50018, Spainjfrodrig@unizar.es

Gerhard A. Holzapfel

Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology (KTH), Osquars backe 1, SE-100 44 Stockholm, Sweden

1

Corresponding author.

J Biomech Eng 130(2), 021023 (Apr 11, 2008) (10 pages) doi:10.1115/1.2898830 History: Received August 28, 2006; Revised September 24, 2007; Published April 11, 2008

Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Idealized geometric model of an AAA with parabolic-exponential shape. Ra denotes the radius of the artery, Ran the maximum radius of the aneurysm, Lan the length of the aneurysm, and e is the eccentricity between the aneurysm and the healthy artery.

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Figure 2

Geometric models of AAA for three values of FE=0,0.5,1.0 and for the extreme values for FR and FL (compare also with Table 1)

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Figure 3

Representative stress-stretch data for an AAA provided in Ref. 15, see Fig. 1 therein (symbols), and the anisotropic model 8 (solid curves)

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Figure 4

Representative stress-stretch data for an AAA provided in Ref. 15, see Fig. 1 therein (symbols), and the isotropic model 7 (solid curves)

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Figure 5

A typical finite element mesh used for the computations. The geometry corresponds to FR=2.75, FL=1.5, and FE=0.5.

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Figure 6

Orientation of collagen fibers in a hypothetical asymmetric aneurysm (FR=2.75, FL=1.5, FE=0.5). The fibers are oriented at an angle ϕ (given in Table 2) with respect to the circumferential direction of the artery.

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Figure 7

Contour plots of the maximum principal stresses in the aneurysmal wall for Cases 1 and 9 (see Table 1) and for three different values of FE: (a) isotropic stress response according to Eq. 7; (b) anisotropic stress response according to Eq. 8. The magnitude of the stress is given in kPa.

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Figure 8

Maximum principal stresses as a function of the three parameters FR, FL, FE: (a) FE=0.0; (b) FE=0.5; (c) FE=1.0. The dashed lines refer to the isotropic model 7, while the solid lines refer to the anisotropic model 8.

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Figure 9

Maximum principal stress fields in symmetric (FE=0.0) and asymmetric aneurysms (FE=1.0) with different relative lengths FL and for FR=2.75. Results were obtained with the anisotropic model 8.

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Figure 10

Element on which circumferential and longitudinal stresses were studied for both isotropic and anisotropic material models

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Figure 11

Isotropic circumferential stress versus anisotropic circumferential stress (Curves (a)–(c), and isotropic longitudinal stress versus anisotropic longitudinal stress (Curves (d)–(f)) as a function of parameters FR, FL, FE. The symbols refer to models with same FL: ◇, FL=1.5; ◻, FL=2.0; ○, FL=2.5.

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Figure 12

Circumferential stress distribution in the midsection of an aneurysm with FR=2.0, FL=2.0, and FE=1.0 for the isotropic and anisotropic model

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Figure 13

Longitudinal stress distribution in the midsection of an aneurysm with FR=2.0, FL=2.0, and FE=1.0 for the isotropic and anisotropic model

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Figure 14

Maximum principal stress for the isotropic versus the anisotropic model. Anisotropy appears to scale up the rupture risk indicator.

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