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Research Papers

Invariant-Based Anisotropic Constitutive Models of the Healthy and Aneurysmal Abdominal Aortic Wall

[+] Author and Article Information
C. A. Basciano

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910

C. Kleinstreuer1

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910; Department of Biomedical Engineering, North Carolina State University, Raleigh, NC 27695-7910ck@eos.ncsu.edu

1

Corresponding author.

J Biomech Eng 131(2), 021009 (Dec 10, 2008) (11 pages) doi:10.1115/1.3005341 History: Received April 18, 2008; Revised May 28, 2008; Published December 10, 2008

The arterial wall is a complex fiber-reinforced composite. Pathological conditions, such as aneurysms, significantly alter the mechanical response of the arterial wall, resulting in a loss of elasticity, enhanced anisotropy, and increased chances of mechanical failure. Invariant-based models of the healthy and aneurysmal abdominal aorta were constructed based on first principles and published experimental data with implementations for several numerical cases, as well as comparisons to current healthy and aneurysmal tissue data. Inherent limitations of a traditional invariant-based methodology are also discussed and compared to the models’ ability to accurately reproduce experimental trends. The models capture the nonlinear and anisotropic mechanical responses of the two arterial sections and make reasonable predictions regarding the effects of alterations in healthy and diseased tissue histology. Additionally, the new models exhibit convex and anisotropic monotonically increasing energy contours (suggesting numerical stability) but have potentially the inherent limitations of a covariant theoretical framework. Although the traditional invariant framework exhibits significant covariance, the invariant terms utilized in the new models exhibited limited covariance and are able to accurately reproduce experimental trends. A streamlined implementation is also possible for future numerical investigations of fluid-structure interactions in abdominal aortic aneurysms.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Ideal biaxial tension of a material with embedded fibers

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Figure 2

Finite element model of ideal biaxial loading

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Figure 3

((a) and (b)) Fit of the new HAA and AAA models to experimental data

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Figure 4

((a)–(c)) Energy contours for existing HAA and AAA models

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Figure 5

((a) and (b)) Energy contours for the new HAA and AAA models

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Figure 6

Verification of the model implementation for numerical programs

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Figure 7

Correlation between HAA and AAA models and biaxial experimental data from Vande Geest (7-8)

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Figure 8

Contours of the HAA and AAA models at an equibiaxial first PK stress of 100kPa

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Figure 9

Correlation between HAA model and pressure versus diameter data from Länne (20)

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Figure 10

Clinical relevance of the new models based on loading ratio

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