An Anisotropic Hyperelastic Model Applied to Nondegenerate and Degenerate Annulus Fibrosus

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].