Effects of Nonlinear Strain-Dependent Permeability and Rate of Compression on the Stress Behavior of Articular Cartilage

The compressive viscoelastic behavior of articular cartilage, a fiber-reinforced, porous, permeable solid matrix filled with water, is predominately governed by the flow of the interstitial water within the tissue and its exudation across the articular surface. The fluid flow is in turn governed by the permeability of the tissue and the loading imposed upon its surface. But for articular cartilage, the permeability depends nonlinearly on the strain: k = k_o exp(Me). Here, M is the nonlinear flow-limiting parameter and e is the dilatation. In this investigation, we studied the influence of M and R_o = k_oH_A / U˙h (where H_A is the elastic equilibrium modulus of the solid matrix, h is the tissue’s thickness and U˙ is the rate of compression applied onto the surface via a rigid, porous, free-draining filter) on the stress history of circular plugs of cartilage specimens attached to the bone. It was found that these two parameters have profound effects on the predicted compressive stress history. For very large R_o, the fluid flow effects become negligible. For small R_o and large M, large instantaneous compressive stresses several times larger than those observed at equilibrium are predicted. This amplification of compressive stress is due to the increase of importance of the relative fluid flow effect, i.e., R_o → 0, and nonlinear flow-limit effect, i.e., M > 0. Also, the theoretical curves predict that the rate of increase of stress initially decreases (convex) and finally becomes a constant. The results of our 5 percent offset compression experiments are in good agreement with the theoretical predictions.