A four-component mixture theory applied to cartilaginous tissues. Numerical modelling and experiments.

*(English)*Zbl 0966.92002
Eindhoven: TU Eindhoven, 116 p. (2000).

Mixture theory is applied to the numerical modeling of the cartilaginous discs which separate spinal vertebrae and to artificial hydrogels. Both exhibit swelling and shrinking. This behavior is caused by water bound to the charged solid skeleton of the tissue through an interplay of mechanical, electrical, and chemical mechanisms. The tissue is represented by a porous deformable medium saturated with a fluid in which positive and negative ions are dissolved. Hence the four components. A two-component theory involving only a solid and a fluid is also examined.

Tissue deformations, fluid and ion flows, fluid pressure, ionic concentrations, and electrical potentials are computed with the use of the four-component theory. The theory is derived from the balance equations and constitutive equations for a linear elastic solid medium described by Hooke’s law and from extended forms of Darcy’s law and Fick’s law for the fluid and ion fluxes, respectively. The results of the calculations are confirmed experimentally by measurements of deformations and electrical potentials of intervertebal discs and hydrogels as functions of time.

Tissue deformations, fluid and ion flows, fluid pressure, ionic concentrations, and electrical potentials are computed with the use of the four-component theory. The theory is derived from the balance equations and constitutive equations for a linear elastic solid medium described by Hooke’s law and from extended forms of Darcy’s law and Fick’s law for the fluid and ion fluxes, respectively. The results of the calculations are confirmed experimentally by measurements of deformations and electrical potentials of intervertebal discs and hydrogels as functions of time.

Reviewer: H.R.Hirsch (Lexington)

##### MSC:

92C10 | Biomechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

92-02 | Research exposition (monographs, survey articles) pertaining to biology |

92C05 | Biophysics |

92C35 | Physiological flow |