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Research Papers

# Theoretical and Uniaxial Experimental Evaluation of Human Annulus Fibrosus Degeneration

[+] Author and Article Information
Grace D. O’Connell

Department of Orthopaedic Surgery, University of Pennsylvania, 424 Stemmler Hall, Philadelphia, PA 19104-6081

Heather L. Guerin

Dawn M. Elliott1

Department of Orthopaedic Surgery, University of Pennsylvania, 424 Stemmler Hall, Philadelphia, PA 19104-6081delliott@mail.med.upenn.edu

1

Corresponding author.

J Biomech Eng 131(11), 111007 (Oct 21, 2009) (7 pages) doi:10.1115/1.3212104 History: Received August 05, 2008; Revised February 19, 2009; Published October 21, 2009

## Abstract

The highly organized structure and composition of the annulus fibrosus provides the tissue with mechanical behaviors that include anisotropy and nonlinearity. Mathematical models are necessary to interpret and elucidate the meaning of directly measured mechanical properties and to understand the structure-function relationships of the tissue components, namely, the fibers and extrafibrillar matrix. This study models the annulus fibrosus as a combination of strain energy functions describing the fibers, matrix, and their interactions. The objective was to quantify the behavior of both nondegenerate and degenerate annulus fibrosus tissue using uniaxial tensile experimental data. Mechanical testing was performed with samples oriented along the circumferential, axial, and radial directions. For samples oriented along the radial direction, the toe-region modulus was 2× stiffer with degeneration. However, no other differences in measured mechanical properties were observed with degeneration. The constitutive model fit well to samples oriented along the radial and circumferential directions $(R2≥0.97)$. The fibers supported the highest proportion of stress for circumferential loading at 60%. There was a 70% decrease in the matrix contribution to stress from the toe-region to the linear-region of both the nondegenerate and degenerate tissue. The shear fiber-matrix interaction (FMI) contribution increased by 80% with degeneration in the linear-region. Samples oriented along the radial and axial direction behaved similarly under uniaxial tension ($modulus=0.32 MPa$ versus 0.37 MPa), suggesting that uniaxial testing in the axial direction is not appropriate for quantifying the mechanics of a fiber reinforcement in the annulus. In conclusion, the structurally motivated nonlinear anisotropic hyperelastic constitutive model helps to further understand the effect of microstructural changes with degeneration, suggesting that remodeling in the subcomponents (i.e., the collagen fiber, matrix and FMI) may minimize the overall effects on mechanical function of the bulk material with degeneration.

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## Figures

Figure 1

Schematic showing the orientation of axial, circumferential, and radial samples taken from each disk

Figure 2

Representative experimental data (symbols) and model fit (solid line) to a nondegenerate and degenerate sample oriented along the radial direction. The nondegenerate tissue exhibited a nonlinear response, while the degenerate tissue exhibited a stiffer linear response. The constitutive model fit the experimental data well (solid line, R2=0.97).

Figure 3

Representative experimental data from a nondegenerate sample (circles) and a degenerate sample (triangles) oriented along the axial direction

Figure 4

Representative nondegenerate sample oriented along the circumferential direction with experimental data shown by the solid black circles and the model fit shown by the solid black line

Figure 5

Average stress contribution of the matrix (black), fibers (white), and shear fiber-matrix interactions (diagonal pattern) for (a) the toe-region and (b) the linear-region of nondegenerate and degenerate tissues oriented along the circumferential direction. Error bars represent the standard deviation,  ∗ denotes significance with respect to the toe-region stress contribution (p<0.05).

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