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Research Papers

A Structural Multi-Mechanism Damage Model for Cerebral Arterial Tissue

[+] Author and Article Information
Dalong Li

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261dal40@pitt.edu

Anne M. Robertson1

Department of Mechanical Engineering and Materials Science and McGowan Institute of Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA 15261rbertson@pitt.edu

1

Corresponding author.

J Biomech Eng 131(10), 101013 (Sep 17, 2009) (8 pages) doi:10.1115/1.3202559 History: Received November 29, 2008; Revised July 04, 2009; Published September 17, 2009

Early stage cerebral aneurysms are characterized by the disruption of the internal elastic lamina. The cause of this breakdown is still not understood, but it has been conjectured to be due to fatigue failure and/or by a breakdown in homeostatic mechanisms in the wall arising from some aspect of the local hemodynamics and wall tension. We propose to model this disruption using a structural damage model. It is built on a previously introduced nonlinear, inelastic multi-mechanism model for cerebral arteries (2005, “An Inelastic Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue,” Biomech. Model. Mechanobiol., 4(4), pp. 235–248), as well as a recent generalization to include the wall anisotropy (2009, “A Structural Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue,” Int. J. Solids Struct., 46(14–15), pp. 2920–2928). The current model includes subfailure damage of the elastin, represented by changes in the tissue mechanical properties and unloaded reference length. A structural model is used to characterize the gradual degradation, failure of elastin, and recruitment of anisotropic collagen fibers. The collagen fibers are arranged in two helically oriented families with dispersion in their orientation. Available inelastic experimental data for cerebral arteries are used to evaluate the constitutive model. It is then implemented in a commercial finite element analysis package and validated using analytical solutions with representative values for cerebral arterial tissue.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the reference configurations for the dual mechanism constitutive model with relevant kinematic variables drawn

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Figure 2

Comparison of the fit of two mechanical damage models to the data of Scott (14). For both models the elastin mechanism is modeled using a first order exponential (E-EXP1) strain energy function. The collage mechanisms is treated as either a two-fiber model (C-EXP2-2-fiber) or a disperse fiber model (C-EXP2-disp).

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Figure 3

Boundary conditions used in the two validation tests: (a) schematic of arterial strip under uniaxial stretch, (b) cyclically increasing displacement condition, and (c) step displacement boundary condition

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Figure 4

Comparison of two analytical solutions for the cyclic loading of increasing magnitude (Fig. 3). Results are compared for discrete elastin failure and mechanical damage based on the maximum equivalent strain (d0=d01). Elastin failure occurs at points B and A, respectively. Subsequent load cycles with only the collagen mechanism remaining follow load curve 1.

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Figure 5

Comparison of the analytical solutions for two types of mechanical damage of elastin under cyclic loading of increasing magnitude (Fig. 3). Results for damage based on the maximum equivalent strain are labeled d01 and those using the accumulated equivalent strain are labeled d02. Elastin failure occurs at points A and C, respectively. Subsequent load cycles with only the collagen mechanism remaining follow load curve 1.

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Figure 6

Comparison of the analytical and numerical solutions for cyclic mechanical damage of elastin with d0=d01. Elastin failure occurs at point A. Subsequent load cycles with only the collagen mechanism remaining follow load curve 1.

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Figure 7

Comparison of the analytical and numerical solutions for cyclic mechanical damage of elastin with d0=d02. Elastin failure occurs at point C.

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Figure 8

Comparison of the analytical and numerical solutions for elastin damage with d0=d03 for different choices of WSS and/or WSSG. As these quantities are increased, the elastin degradation occurs more rapidly.

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