A MICROCONTINUUM MODEL OF ELECTROKINETIC COUPLING IN THE EXTRACELLULAR-MATRIX - PERTURBATION FORMULATION AND SOLUTION

A microcontinuum model is formulated to describe electrokinetic transduction interactions and transport in the extracellular matrix (ECM) in terms of microscopic structural and compositional parameters. A unit cell technique is used in which the ECM is modeled as an ordered array of charged solid cylinders surrounded by a diffuse double layer. Under physiological conditions, the Debye length is on the order of the relevant microstructural dimensions of the ECM. Hence, the model includes the effects of overlapping diffuse double layers and the associated electrokinetic coupling within the bulk of the unit cell. A system of coupled differential equations is developed to describe electrokinetic coupling within the unit cell. This governing system is cast in dimensionless form, introducing two dimensionless groups whose relative order of magnitude suggests a perturbation analysis. The perturbation expansion of the governing system shows that the electromechanical coupling perturbs both the fluid flow and ion concentrations to the same order. The system is solved using the numerical grid generation technique in conjunction with the finite difference method. Model parameter values were chosen to describe the ECM of articular cartilage and similar connective tissues. Reasonable agreement between theory and experiment was found for the strain dependence of the hydraulic permeability k(11), the magnitude of k(22), and the magnitude and ionic strength dependence of k(e) = k(21)/k(22). (C) 1994 Academic Press, Inc.