A nonlinear anisotropic continuum model of human annulus fibrosus mechanical behavior

The intervertebral discs permit motion and distribute the large and complex loads of the spine. The annulus fibrosus of the intervertebral disc is comprised of a ring of layered, angled fibers embedded in a hydrated matrix of aggregated proteoglycans, with smaller amounts of minor collagens, elastin, and small proteoglycans. This structure and composition enable the intervertebral disc to withstand loads in tension, torsion, compression, shear and bending, and result in inhomogeneous, anisotropic, and nonlinear mechanical behaviors. The specific contributions of each of the annulus fibrosus structural constituents to overall mechanical function remain unclear. Therefore, the objective of this study was to predict the contribution of annulus fibrosus structures to overall mechanical function using a combination of experimental testing and mathematical modeling. Annulus fibrosus samples were tested in 3 orientations in uniaxial tension. A multi-dimensional stress-strain dataset was collected and mechanical properties were measured. Additionally, load-induced fiber-reorientation was measured using a novel application of Fast Fourier Transform. Reorientation was found to be affine. A structurally motivated, finite deformation, anisotropic, nonlinear, hyperelastic model was developed for orthotropic annulus fibrosus. Terms to describe fibers, matrix, and interactions (shear and perpendicular to the fiber directions) between annulus fibrosus structures were explicitly included in the model. The effect of these terms on the simultaneous fit to multi-dimensional experimental data was determined by comparing R2 goodness-of-fit, model parameters, and Pearson correlation coefficients. The contribution of each structural term to overall tissue stress was calculated. It was found that both shear and perpendicular interaction terms were necessary to accurately model multi-dimensional behavior. Fiber stretch and shear interactions dominated the contributions to circumferential direction stress, while perpendicular and shear interactions dominated axial stress. The results reported here suggest that interactions between fibers and matrix play an important role in annulus fibrosus mechanical behaviors like nonlinearity and anisotropy and contribute to overall tissue load-bearing