Analysis of fluid and ion transport through a porous charged-hydrated biological tissue during a permeation experiment

Using our new triphasic mechano-electrochemical theory (Lai et al., 1991), we analyzed the transport of water and ions through a finite-thickness layer of charged-hydrated soft tissue (e.g., articular cartilage) in a one-dimensional steady permeation experiment. For this problem, we obtained numerically the concentrations of the ions, the strain field and the fluid and ion velocities inside when the specimen is subject to an applied mechanical pressure and/or osmotic pressure across the layer. The relationships giving the dependence of streaming potential and permeability on the negative fixed charge density (FCD) of the tissue were derived analytically for the linear case, and calculated for the nonlinear case. Among the results obtained were: 1) At a fluid pressure difference of 1 atm across the specimen layer, there is a 10% flow-induced compaction at the downstream boundary; 2) The flow-induced compaction causes the FCD to increase and the neutral salt concentration to decrease in the downstream direction; 3) While both ions move downstream, relative to the solvent (water), the anions (Cl^-) move with the flow whereas cations (Na⁺) move against the flow. The difference in ion velocities depends on the FCD, and this difference attained a maximum at a physiological FCD of around 0.2 mEq/ml; 4) The apparent permeability decreases nonlinearly with FCD, and the apparent stiffness of the tissue increases with FCD; and 5) The streaming potential has a maximum value at FCD within the physiological range.