Mechanical behavior of annulus fibrosus: a microstructural model of fibers reorientation

Experimental uniaxial tensile tests have been carried out on annulus tissue samples harvested on pig and lamb lumbar intervertebral discs. When subjecting the samples to loading cycles, the stress-strain curves exhibit strong nonlinearities and hysteresis. This particular behavior results from the anisotropic microstructure of annulus tissue composed of woven oriented collagen fibers embedded in the extracellular matrix. During uniaxial tension, the collagen fibers reorient toward the loading direction increasing its global stiffness. To describe this behavior, we propose a heuristic two-dimensional rheological model based on three mechanical and one geometrical characteristics. The latter one is the fibers orientation angle becoming the key parameter that govern the macroscopic mechanical behavior. The experimental results are used to identify the physical properties associated with the rheological model, leading to an accurate representation of the stress-strain curve over a complete loading cycle. In this framework, the fibers reorientation can solely account for the rigidity increase while the hysteresis is associated with liquid viscous flows through the matrix. Based on this representation, unusual coupling effects between strains and fluid flows can be observed, that would significantly affect the cell nutrients transport mechanisms.