A porous media model describing the inhomogeneous behaviour of the human intervertebral disc

Abstract

Due to the remarkable number of patients suffering from low back pain, a higher research interest is initiated regarding modern numerical simulation techniques. Herein, the Finite Element Method (FEM) in combination with an elaborated model has the potential to be the best choice aiding the design of new intervertebral disc (IVD) implants.As one of the most vulnerable parts of the human spine, the (IVD) belongs to the class of soft avascular cartilaginous tissues consisting of mostly ionized water (interstitial fluid) and collagen of type I and II embedded in an extracellular meshwork of charged protein compounds. More precisely, the type I collagen is organized in fiber bundles building a fiber‐reinforced ring, the anulus fibrosus (AF), which encloses a highly charged gelatinous core, the nucleus pulposus (NP).The purpose of this contribution is to utilize the established Theory of Porous Media (TPM) as a continuum‐mechanical framework for the modelling of the IVD. In this context, the TPM is perfectly suitable for the description of multi‐component continua with internal interactions and is proven to yield stable implementations within the mixed Finite Element Method (FEM). Following this, one succeeds in describing the electro‐chemomechanical couplings between the constituents as well as the viscoelastic and anisotropic properties of the extracellular matrix. Moreover, the fiber vectors, which represent the aligned collagen in a continuum‐mechanical sense, as well as the location‐dependent material parameters must be inhomogeneously distributed over the discretized IVD.