An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies

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Abstract
The current investigation addresses advanced FE analyses of intact lumbar intervertebral discs. Human disc body units basically consist of a fluid filled cavity (nucleus pulposus) approximately at the disc center and surrounding annulus tissue reinforced by collagen fibers (annulus fibrosus). For the latter component a constitutive model is presented which accounts for nonlinear anisotropic stress response. In contrast to state-of-the-art material descriptions mostly used in the literature (linear elasticity), the current approach provides numerical accuracy in the finite strain regime. Thus, local strain and stress distributions in the annulus fibrosus can properly be determined. Because of the highly nonlinear stress response of the constitutive equations, nonlinear material parameters are required. Although tensile properties of the human annulus fibrosus can already be found in the literature, these material data are not suitable for the current concept as will be shown. The entire constitutive theory is therefore based on a new experimental procedure for the determination of local, nonlinear and anisotropic stress response in annulus tissue. The constitutive model proves its applicability in representative numerical examples. In contrast to state-of-the-art FE analyses, the results do not exhibit parasitic strain (and stress) distributions in annulus tissue under physiological loading conditions. Hence, the current approach seems to be very attractive for refined spinal implant design.