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Research Papers

A Hyperelastic Constitutive Law for Aortic Valve Tissue

[+] Author and Article Information
Karen May-Newman1

Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182-1323kmn@kahuna.sdsu.edu

Charles Lam

Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182-1323

Frank C. P. Yin

Department of Biomedical Engineering, Washington University, St. Louis, MO 63130

1

Corresponding author.

J Biomech Eng 131(8), 081009 (Jul 06, 2009) (7 pages) doi:10.1115/1.3127261 History: Received October 27, 2008; Revised December 10, 2008; Published July 06, 2009

The objective of the present study was to perform biaxial testing and apply constitutive modeling to develop a strain energy function that accurately predicts the material behavior of the aortic valve leaflets. Ten leaflets from seven normal porcine aortic valves were biaxially stretched in a variety of protocols and the data combined to develop and fit a strain energy function to describe the material behavior. The results showed that the nonlinear anisotropic behavior of the aortic valve is well described by a strain energy function of two strain invariants, which uses only three coefficients to accurately predict the stress-strain behavior over a wide range of deformations. This structurally-motivated constitutive law has many applications, including computational modeling for clinical and engineering valve treatments.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 2

Biaxial testing of the aortic valve tissue was performed on individual valve leaflets. (a) Each leaflet was mounted to the four carriages of the biaxial testing apparatus with suture loops spanning a distance lx along the circumferential direction and ly along the radial direction. Four markers are placed in the central region of the leaflet defining dx by dy. (b) The carriages were controlled with a video feedback system that measured the position of the four central markers in real time.

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Figure 3

The response functions for one of the aortic leaflets tested (P32) were calculated from the experimental data collected during the constant invariant tests. Similar responses from additional valves tested led to the choice of a strain energy function that is an exponential function of the strain invariants I1 and α.

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Figure 4

Three protocols for each specimen were used to obtain the coefficients for the constitutive law shown in Eqs. 3,4. The data (shown with symbols: circles, circumferential direction; squares, radial direction) and corresponding fits (shown as overlaid solid lines) are shown for two different leaflets, P35 (left panels) and P44L2 (right panels).

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Figure 5

Predictions of the stress response for the same two leaflets illustrated in Fig. 4, P35 (left panels) and P44L2 (right panels). These predictions were made for protocols not used previously in the process of fitting the coefficients of the strain energy function. Experimental data are shown with symbols (circles, circumferential direction; squares, radial direction) and corresponding predictions shown as solid lines.

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Figure 6

Predictions of the stress-strain behavior of the average normal porcine aortic valve leaflet were made using the coefficients shown in Table 3. Experimental data are shown with symbols (circles, circumferential direction; squares, radial direction) and corresponding predictions shown as solid lines, showing excellent agreement.

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Figure 1

Anatomy of the aortic valve. (a) Cutaway view of the valve from the aortic side. (b) Side cross-sectional view of the aortic root, showing the valve in the closed and open states. (c) Diagram of a single aortic valve leaflet, showing the FM, CA, belly area (B), and the annular edge (AE). (From Ref. 1 with kind permission of Springer Science and Business Media).

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