Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson’s ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4±14.3 MPa versus 5.6±4.7 MPa, outer versus inner sites) and the Poisson’s ratio $ν21$ (0.67±0.22 versus 1.6±0.7, outer versus inner), but not in the axial modulus (0.8±0.9 MPa) or the Poisson’s ratios $ν12$ (1.8±1.4) or $ν13$ (0.6±0.7). These properties were implemented in a linear anisotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for the AF as concentric and physically isolated lamellae may not be appropriate.