Biorheology and fluid flux in swelling tissues. II. Analysis of unconfined compressive response of transversely isotropic cartilage disc

Abstract

The response of a cartilage disc to unconfined compressive loading under small deformations is analyzed. The cartilage is considered as a transversely isotropic bicomponent (solid-fluid) tissue. Concentration effects (commonly termed osmotic pressure) are accounted for. The tissue’s permeability is taken to be isotropic. Its concentration force is assumed to vary linearly with volume.

The analysis shows that if the tissue’s fibrous structure is taken into consideration, then the instantaneous response to a step loading depends on the tissue’s elasticity and on its concentration force. The subsequent creep response, under commonly used experimental conditions, has a time constant which depends on the concentration force and permeability, but independent of its elastic response. The equilibrium volume is predicted to depend only on the concentration force. Where data is available it confirms the model’s predictions.

It is concluded from the present analysis that inclusion of concentration effects and the tissue’s fibrous structure has significant consequences in terms of the relative roles of the collagen fibers (solid) vs. the ground substance (fluid) in the response of the cartilage to compressive loading.