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Research Papers

A Structural Model of the Venous Wall Considering Elastin Anisotropy

[+] Author and Article Information
Rana Rezakhaniha1

Hemodynamics and Cardiovascular Technology Laboratory (LHTC), School of Life Sciences, Institute of Bioengineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 15, CH-1015 Lausanne, Switzerlandrana.rezakhaniha@epfl.ch

Nikos Stergiopulos

Hemodynamics and Cardiovascular Technology Laboratory (LHTC), School of Life Sciences, Institute of Bioengineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 15, CH-1015 Lausanne, Switzerland

1

Corresponding author.

J Biomech Eng 130(3), 031017 (May 06, 2008) (11 pages) doi:10.1115/1.2907749 History: Received March 19, 2007; Revised January 23, 2008; Published May 06, 2008

The three-dimensional biomechanical behavior of the vascular wall is best described by means of strain energy functions. Significant effort has been devoted lately in the development of structure-based models of the vascular wall, which account for the individual contribution of each major structural component (elastin, collagen, and vascular smooth muscle). However, none of the currently proposed structural models succeeded in simultaneously and accurately describing both the pressure-radius and pressure-longitudinal force curves. We have hypothesized that shortcomings of the current models are, in part, due to unaccounted anisotropic properties of elastin. We extended our previously developed biomechanical model to account for elastin anisotropy. The experimental data were obtained from inflation-extension tests on facial veins of five young white New Zealand rabbits. Tests have been carried out under a fully relaxed state of smooth muscle cells for longitudinal stretch ratios ranging from 100% to 130% of the in vivo length. The experimental data (pressure-radius, pressure-force, and zero-stress-state geometries) provided a complete biaxial mechanical characterization of rabbit facial vein and served as the basis for validating the applicability and accuracy of the new biomechanical model of the venous wall. When only the pressure-radius curves were fitted, both the anisotropic and the isotropic models gave excellent results. However, when both pressure-radius and pressure-force curves are simultaneously fitted, the model with isotropic elastin shows an average weighted residual sum of squares of 8.94 and 23.9 in the outer radius and axial force, respectively, as compared to averages of 6.07 and 4.00, when anisotropic elastin is considered. Both the Alkaike information criterion and Schwartz criterion show that the model with the anisotropic elastin is more successful in predicting the data for a wide range of longitudinal stretch ratios. We conclude that anisotropic description of elastin is required for a full 3D characterization of the biomechanics of the venous wall.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the experimental setup

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Figure 2

Schema of (a) the ZSS, (b) the ZLS of a vessel, and (c) the choice of the coordinate system

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Figure 3

Experimental diameter-pressure and longitudinal force-pressure data of the rabbit facial veins at different stretch ratios. Error bars denote standard deviations.

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Figure 4

Longitudinal stress versus circumferential stretch for different longitudinal stretch ratios

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Figure 5

Longitudinal stress versus longitudinal stretch for different circumferential stretch ratios

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Figure 6

Fit of the experimental pressure-radius (top row) and pressure-longitudinal force (bottom row) curves by the isotropic and anisotropic model under 115% of in vivo longitudinal stretch ratio. Column (a) shows the fit of the isotropic model when only the radius-pressure data are used to fit the data. Column (b) shows the fit of the isotropic model when both the radius-pressure and force-pressure curves are fitted. Column (c) shows the fit of the model with anisotropic elastin properties when fitted to both pressure-radius and pressure-force data.

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Figure 7

Fit of the original isotropic SEF to the entire experimental data set, including three different stretch ratios. The top row shows the radius-pressure data and the lower row the longitudinal force-pressure data.

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Figure 8

Fit of the new anisotropic SEF to the entire experimental data set, including three different stretch ratios. The top row shows the radius-pressure data and the lower row the longitudinal force-pressure data.

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