On the fundamental fluid transport mechanisms through normal and pathological articular cartilage during function—I the formulation

Abstract

The fundamental fluid transport mechanisms associated with articular cartilage are important toward the understanding of the biomechanical processes involved in the physiology of normal and pathological synovial joints. Phenomenologically, articular cartilage is viewed as a mixture of two mechanically interacting continua, i.e. a solid matrix phase and a liquid phase composed of water. In synovial joints the liquid phase may be transported through the solid matrix by a direct pressure gradient as a result of the squeeze film action of synovial fluid during articulation and as a result of the consolidation of the solid matrix. The mechanically interacting mixture is composed of a solid. defined by an elastic internal energy function, and an incompressible liquid. The accompanying frictional resistance of relative motion is considered by a linear diffusive dissipation term. The equations of motion for each phase and the total mixture were derived from the extended Hamilton's Principle, where the Rayleigh dissipative resistance is considered as a generalized body force field. This procedure yields, as special cases, the classical Darcy's Law for the liquid transport due to direct pressure gradients, as well as Biot's consolidation equations for the liquid transport due to the dilatation of the solid phase.