The annulus fibrosus of the intervertebral disc is comprised of concentric lamella of oriented collagen fibers embedded in a hydrated proteoglycan matrix with smaller amounts of minor collagens, elastin, and small proteoglycans. Its structure and composition enable the disc to withstand complex loads and result in inhomogeneous, anisotropic, and nonlinear mechanical behaviors. The specific contributions of the annulus fibrosus constituent structures to mechanical function remain unclear. Therefore, the objective of this study was to use a structurally motivated, anisotropic, nonlinear strain energy model of annulus fibrosus to determine the relative contributions of its structural components to tissue mechanical behavior. A nonlinear, orthotropic hyperelastic model was developed for the annulus fibrosus. Terms to describe fibers, matrix, and interactions between annulus fibrosus structures (shear and normal to the fiber directions) were explicitly included. The contributions of these structures were analyzed by including or removing terms and determining the effect on the fit to multidimensional experimental data. Correlation between experimental and model-predicted stress, a Bland-Altman analysis of bias and standard deviation of residuals, and the contribution of structural terms to overall tissue stress were calculated. Both shear and normal interaction terms were necessary to accurately model multidimensional behavior. Inclusion of shear interactions more accurately described annulus fibrosus nonlinearity. Fiber stretch and shear interactions dominated contributions to circumferential direction stress, while normal and shear interactions dominated axial stress. The results suggest that interactions between fibers and matrix, perhaps facilitated by crosslinks, elastin, or minor collagens, augment traditional (i.e., fiber-uncrimping) models of nonlinearity. ß

Background 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, 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. Method of Approach Mechanical testing was performed with samples oriented along the circumferential, axial, and radial directions. Results For samples oriented along the radial direction, the toe-region modulus was 2.7X 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- to the linear-region of both nondegenerate and degenerate tissue. The shear fiber-matrix interaction contribution increased 125% with degeneration in the linear-region. Samples oriented along the radial and axial direction behaved similarly under uniaxial tension (modulus = 0.32MPa versus 0.37MPa), suggesting that uniaxial testing in the axial direction is not appropriate for quantifying the mechanics of a fiber reinforcement in the annulus. Conclusions In conclusion, the structurally motivated nonlinear, anisotropic hyperelastic constitutive model help to further understand the effect of microstructural changes with degeneration, suggesting that a remodeling in the subcomponents (i.e. the collagen fibers and FMI) may minimize the overall change in tissue mechanics with degeneration.

The current study predicted an optimal nucleus replacement of 1 to 4 MPa. An overly stiff implant could result in subsidence, which would preclude the benefit of disc height increase or restoration. Conversely, an overly soft implant could accelerate a degenerative cascade in the anulus.

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The intervertebral disc is comprised of complex components that provide the disc with nonlinear, viscoelastic and anisotropic mechanical properties. The annulus fibrosus (AF) is a highly organized structure composed of concentric layers of collagen fibers embedded in a proteoglycan matrix. The AF has a high tensile stiffness and supports the large loads encountered by the disc. Mathematical models are needed to interpret and elucidate the meaning of experimental measurements made in mechanical tests. Based upon the classic work of Spencer [1], the AF has been modeled as a fiber-induced anisotropic hyperelastic material [e.g.,2–6], using the principle invariants of the Green deformation tensor and structural tensors representing the collagen fiber populations. Contributions of other AF components to mechanical behaviors are less understood than the fibers or matrix and may include connections between collagens and proteoglycans that can be incorporated into models through fiber-matrix interactions [2–4]. The previous models, however, have not been applied to experimental data from both nondegenerate and degenerate tissue. Constitutive modeling applied to nondegenerate and degenerate AF may elucidate microstructural changes with degeneration, will be useful for finite element models [5], and provide targets for disc treatments, such as tissue engineered constructs [7].