Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments

Abstract

Articular cartilage is a biphasic material composed of a solid matrix phase (∼ 20 percent of the total tissue mass by weight) and an interstitial fluid phase (∼ 80 percent). The intrinsic mechanical properties of each phase as well as the mechanical interaction between these two phases afford the tissue its interesting rheological behavior. In this investigation, the solid matrix was assumed to be intrinsically incompressible, linearly elastic and nondissipative while the interstitial fluid was assumed to be intrinsically incompressible and nondissipative. Further, it was assumed that the only dissipation comes from the frictional drag of relative motion between the phases. However, more general constitutive equations, including a viscoelastic dissipation of the solid matrix as well as a viscous dissipation of interstitial fluid were also developed. A constant “average” permeability of the tissue was assumed, i.e., independent of deformation, and a solid content function Vs/Vf (the ratio of the volume of each of the phases) was assumed to vary with depth in accordance with the experimentally determined weight ratios. This linear, nonhomogeneous theory was applied to describe the experimentally obtained biphasic creep and biphasic stress relaxation data via a nonlinear regression technique. The determined intrinsic “aggregate” elastic modulus, from ten creep experiments, is 0.70 ± 0.09 MN/m2 and, from six stress relaxation experiments, is 0.76 ± 0.03 MN/m2. The “average” permeability of the tissue is (0.76 ± 0.42) × 10−14 m4 /N•s. We concluded that the large spread in the permeability coefficients is due to the assumption of a constant deformation independent permeability. We also concluded that 1) a nonlinearly permeable biphasic model, where the permeability function is given by an experimentally determined empirical law: k = A(p) exp [α(p)e], can be used to describe more accurately the rheological properties of articular cartilage, and 2) the frictional drag of relative motion is the most important factor governing the fluid/solid viscoelastic properties of the tissue in compression.