A nonlinear hyperelastic mixture theory model for anisotropy, transport, and swelling of annulus fibrosus.

A precise knowledge of the local mechanical and chemical environment around the nerve endings and disc cells in the annulus fibrosus will shed insight on understanding the mechanism of low-back pain and disc degeneration. It would also present an effective tool for the studies of the intervertebral disc structure-function relationship and provide guidance to disc tissue engineering. Experimental difficulties preclude the direct and simultaneous measurement of many of the important physical quantities, such as annulus pressurization, nutrient and electrolyte transport, and mechanical and swelling deformation. Considering that many of these quantities are coupled and that the annulus is highly anisotropic, interpretation of the results would be extremely challenging without an appropriate theoretical framework. In this study, we develop a nonlinear hyperelastic fiber-reinforced continuum mixture theory model for the annulus fibrosus. Special attention is given to the anisotropic nature of the annulus. On the basis of the lamella structure of annulus, and derived from a Helmholtz energy function, a locally transversely isotropic stress-strain relation is adopted for explicit representation of the collagen fiber orientations in general finite deformation situation. The exponential form of the Helmholtz energy function naturally reduces to the infinitesimal deformation form, and the equivalence between the current model coefficients and engineering elastic constants is established under the infinitesimal deformation. This model is able to describe the anisotropic finite and infinitesimal deformation, tension-compression nonlinearity, osmotic swelling, pressurization, electrical potential and current, and water and ion transports as well as the electroneutral nutrient (or growth factor) transport within the annulus.