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TECHNICAL PAPERS

Biaxial Mechanical Properties of the Native and Glutaraldehyde-Treated Aortic Valve Cusp: Part II—A Structural Constitutive Model

[+] Author and Article Information
Kristen L. Billiar

Department of Biomedical Engineering, University of Miami, Coral Gables, FL 33124

Michael S. Sacks

Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15261

J Biomech Eng 122(4), 327-335 (Mar 22, 2000) (9 pages) doi:10.1115/1.1287158 History: Received May 25, 1999; Revised March 22, 2000
Copyright © 2000 by ASME
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Figures

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Representative response of the components of deformation gradient tensor Fij1, κ1, κ2, and λ2, where subscripts 1 and 2 correspond to the circumferential and radial axes, respectively) during the loading phase of a biaxial test. Note the significant in-plane shear values (κ1 and κ2), which are plotted using a different scale.
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Mean stress–strain response of the AV cusps under equibiaxial tension for the native and 0 and 4 mmHg glutaraldehyde-treated tissue. Note the difference in the biaxial response between the 0 and 4 mmHg demonstrating how the state of collagen fiber crimp during fixation can influence the mechanical response.
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Stress–strain curves for six of the seven loading protocols for a 4 mmHg fixed specimen (open circles) and the simulated stress–strain curves (lines) using the optimal parameters (Table 1). The structural constitutive model demonstrated an excellent fit to the data, including the presence of large negative circumferential strains due to strong axial coupling. Although protocol five was not shown for clarity of presentation, it also demonstrated an equally good agreement between theory and experiment. Inset: biaxial testing protocols with the corresponding protocol numbers shown for reference.
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Simulation of the effect of misalignment of the biaxial test specimen to testing axes by setting μ=10 deg, demonstrating a large change in peak extensibilities, especially in the radial direction. This result underscores the need for complete deformation state analysis and compensation of small misalignments when studying highly aligned fibrous tissues such as the AV cusp.
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Effective fiber stress–strain curves calculated using Eq. (2) from 0 to 60 N/m and the A* and B values in Table 1. Native and 0 mmHg fixed tissue had relatively similar responses, whereas the loss of collagen fiber crimp by the application pressure during glutaraldehyde treatment clearly decreased the effective fiber compliance in the 4 mmHg fixed group. Also shown is the result for the 4 mmHg specimens re-analyzed with μ=0. Although smaller than the pressure fixation effects, this left shift in the stress–strain curve demonstrates how inaccuracies in the parameter values can be introduced when small misalignments are not accounted for when studying highly aligned fibrous tissues.
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Simulations using the structural model of the effect of σ on the equibiaxial stress–strain behavior. The insets provide a graphic representation of the fiber probability density distribution for each σ value: (a) σ=90 deg, approximately isotropic, (b) σ=35 deg, response qualitatively similar to bovine pericardium, (c) σ=20 deg, the circumferential strains are negative at low equibiaxial tensions, and (d) σ=10 deg, the material behavior is highly anisotropic. The dotted lines indicating zero strain are included to highlight ability of the model to simulate the crossover to negative strain observed in the pressure fixed cusps subjected to equibiaxial tension.
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A representative R(θ) distribution from an AV cusp fit to a dual Gaussian distribution using the methods of Sacks and Chuong 48. Here, the AV cusp fiber orientation distribution was principally composed of a highly aligned population (σ1=16 deg) and a broader distribution (σ2=44 deg). Although the fibers of both populations contribute to R(θ), the mechanical contribution of the fibers belonging to σ2 was negligible, supporting our assumption that the in-plane biaxial response can be modeled by a single highly aligned fiber population within the cusp.

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