A validation of the quadriphasic mixture theory for intervertebral disc tissue

The swelling and shrinking behaviour of soft biological tissues is described by a quadriphasic mixture model. In this model four phases are distinguished: a charged solid, a fluid, cations and anions. A description of the set of coupled differential equations of this quadriphasic mixture model is given. These equations are solved by the finite element method using a weighted residual approach. The resulting non-linear integral equations are linearized and solved by the Newton-Raphson iteration procedure. We performed some confined swelling and compression experiments on intervertebral disc tissue. These experiments are simulated by a one-dimensional finite element implementation of this quadriphasic mixture model. In contrast to a triphasic mixture model, physically realistic diffusion coefficients can be used to fit the experiments when the fixed charge density is relatively large, because in the quadriphasic mixture model electrical phenomena are not neglected