Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus

Accurate tissue stress predictions for the annulus fibrosus are essential f or understanding the factors that cause or contribute to disc degeneration and mechanical failure. Current computational models used to predict in viv o disc stresses utilize material laws for annular tissue that are not rigor ously validated against experimental data. Consequently, predictions of dis c stress resulting from physical activities may be inaccurate and therefore unreliable as a basis for defining mechanical-biologic injury criteria. To address this need we present a model for the annulus as an isotropic groun d substance reinforced with two families of collagen fibers, and an approac h for determining the material constants by simultaneous consideration of m ultiple experimental data sets. Two strain energy functions for the annulus are proposed and used in the theory to derive the constitutive equations r elating the stress to pure stretch deformations. These equations are applie d to four distinct experimental protocols and the material constants are de termined from a simultaneous, nonlinear regression analysis. Good agreement between theory and experiment is achieved when the invariants are included within multiple, separate exponentials in the strain energy function. (C) 1999 Elsevier Science Ltd. All rights reserved.