A radial biphasic model for local cell-matrix mechanics in articular cartilage

Analytical and numerical solutions are presented for an interface problem that models deformation in the local cell-matrix unit (chondron) of articular cartilage. The cell and its protective pericellular matrix layer are modeled as isotropic biphasic continua deforming in small strain. A spherical geometry with purely radial deformation is assumed. Enforcement of the boundary and interface conditions results in an eigenvalue problem that is self-adjoint when the permeabilities of the cell and the layer are the same. In this case, a series solution of the interface problem is presented for a time-varying displacement prescribed at the boundary of the pericellular layer. The case of nonuniform permeability is considered via a numerical finite difference solution. The analytical and numerical solutions are used to conduct a parametric analysis of mechanical signal transmission due to an applied sinusoidal displacement. The dual role of the pericellular matrix as a mechanical signal transmitter and a protective layer is analyzed. For frequencies in the range 0-3Hz, transmission of transient-free radial displacement, solid stress, and strain are evaluated with varying pericellular stiffness and permeability in biphasic models of normal and osteoarthritic chondrons.