Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus.

The physical properties of the annulus fibrosus are critical to the intervertebral disc's biomechanical function; alterations with degeneration and aging can contribute directly to joint dysfunction and pain. A constitutive model that links the mechanical structure of the annulus to its material properties is important for many bioengineering purposes. To this end, we developed a strain energy function with separate terms to represent the matrix, the fibers, and the interactions between the constituents. Additionally, we measured the tensile and compressive stress-strain response of the annulus in the circumferential direction. We simultaneously applied the strain energy function to these new data and to data from a wide range of experimental protocols reported in the literature. By choosing experimental protocols that use an unloaded reference configuration, we developed a comprehensive formulation for the multiaxial annular elastic behavior. As a partial validation, this formulation predicted experimental results that were not included in model parameter specification. We anticipate that this constitutive formulation will be useful for computational simulations of the disc's biomechanical response and for elucidating structure-function relationships of the annulus fibrosus.