The intervertebral disc is z cartilaginous structure which functions to support and distribute load and to provide motion and flexibility to the spine. The anulus fibrosus of the intervertebral disc consists of several lamellae in which the collagen fiber bundles are oriented at approximately 30° to the transverse plane, with the fiber angles in adjacent lamella alternating above and below the plane. The highly oriented structure of the anulus fibrosus gives rise to anisotropic material behaviors of the tissue.

In this study, a material model for fiber-induced anisotropy in the anulus fibrosus was proposed which described the solid matrix using an explicit representation of the collagen fiber orientations. A linear elastic strain energy formulation was proposed based on material and geometric parameters of the fibers and matrix. The engineering constants were experimentally determined in non-degenerate human lumber disc tissue by evaluating the stress-strain response at equilibrium for samples in five orientations and at two sites. The interlamellar fiber angle was measured.

At outer sites, the average linear moduli were 14.0, 0.7 and 0.4 MPa for samples which were oriented in the circumferential, axial and radial directions, respectively. At inner sites, the moduli were 4.6 and 1.0 MPa for samples oriented in the circumferential and axial directions. At outer sites, the Poisson's ratios ν₁₂, ν₁₃, ν₂₁, ν₂₃ and ν₃₁ were 1.7, 0.3, 0.6, 0.2 and 0.5, respectively. At inner sites the Poisson’s ratios ν₁₂, ν₁₃ and ν₂₁ were 1.6 ,0.8 and 1.4.

The fiber-induced anisotropic model and the experimentally measured engineering constants and fiber angles together provided a complete and unique representation of the material behaviors of the human anulus fibrosus in tension. Parametric studies were performed to determine the sensitivity of the material properties to the measured variation in the engineering constants. Model predictions were compared to independently measured values for model validation. The mechanisms underlying structure-function relationships in the anulus fibrosus were investigated by examining the distribution of the strain energy attributed to the different terms in the model. These results suggest that fiber-fiber interactions are important contributors to the material behaviors of the anulus fibrosus in tension.