EFFECTS OF FIXED CHARGES ON THE STRESS-RELAXATION BEHAVIOR OF HYDRATED SOFT-TISSUES IN A CONFINED COMPRESSION PROBLEM

The 1-D confined-compression stress-relaxation behavior of a charged, hydrated-soft tissue was analyzed using the continuum mixture theory d eveloped for cartilage (Lai et at, 1991). A pair of coupled nonlinear partial differential equations governing the displacement component u( s) of the solid matrix and the cation concentration c(+) were derived. The initial-boundary value problem, corresponding to a ramp-displacem ent stress-relaxation experiment was solved using a finite-difference method to obtain the complete spatial and temporal distributions of st ress, strain, interstitial water pressure (including osmotic pressure) , ion concentrations, diffusion rates and water velocity within the ti ssue. Using data available in the literature, it was found that: (1) t he equilibrium aggregate modulus of the tissue (as commonly used in th e biphasic theory) consists of two components: the Donnan osmotic comp onent and the intrinsic matrix component, and that these two component s are of similar magnitude. (2) For the rate of compression of 10% in 200 s, during the compression stage, the fluid pressure at the imperme able boundary supports nearly all the load, while near the free-draini ng boundary, both the matrix stiffness and the fluid pressure support a substantial amount of the load. (3) Equivalent aggregate modulus and equivalent diffusive coefficient used in the biphasic theory can be f ound, which predict essentially the same stress relaxation behavior. T hese equivalent parameters for the biphasic model embody the FCD effec t of the triphasic medium. The internal fluid pressure predicted by th e two models are however different because of osmotic effects. (4) Pea k stress at the end of the compression stage is higher for a tissue wi th higher FCD. We have obtained the strain, stress, flow, pressure and ion concentration fields inside the tissue. Some representative resul ts of these fields are presented: These fields are essential for deter mining the local variations of mechanical, electrical and chemical env ironments around cells necessary for the understanding of the mechano- electrochemical signal transduction processes required for the control of biologic functions. (C) 1998 Elsevier Science Ltd. All rights rese rved.