Time Evolution of Deformation in a Human Cartilage Under Cyclic Loading

Abstract

Recent imaging has revealed that in vivo contact deformations of human knee cartilage under physiological loadings are surprisingly large—typically on the order of 10%, but up to 20 or 30% of tibiofemora cartilage thickness depending on loading conditions. In this paper we develop a biphasic, large deformation, non-linear poroelastic model of cartilage that can accurately represent the time dependence and magnitude of cyclic cartilage deformations in vivo. The model takes into account cartilage tension–compression nonlinearity and a new constitutive relation in which the compressive stiffness and hydraulic permeability of the cartilage adjusts in response to the strain-dependent aggrecan concentration. The model predictions are validated using experimental test results on osteochondral plugs obtained from human cadavers. We find that model parameters can be optimised to give an excellent fit to the experimental data. Using typical hydraulic conductivity and stiffness parameters for healthy cartilage, we find that the experimentally observed transient and steady state tissue deformations under cyclic loading and unloading can be reproduced by the model. Steady state tissue deformations are shown to cycle between 10% (exudation strain) and 20% (total strain) in response to the cyclic test loads. At steady-state cyclic loading, the pore fluid exuded from the tissue is exactly equal to the pore fluid imbibed by the tissue during each load cycle.