An asymptotic solution for the contact of two biphasic cartilage layers

Abstract

This study addresses the hypothesis that interstitial fluid plays a major role in the load support mechanism of articular cartilage. An asymptotic solution is presented for two contacting biphasic cartilage layers under compression. This solution is valid for identical thin (i.e. epsilon = h'/a'0 << 1), frictionless cartilage layers, and for the 'early' time response (i.e. t' << (h')2/HAk) after the application of a step load. An equilibrium asymptotic solution is also presented (i.e.t'-->infinity). Here h' is the thickness, a'0 is a characteristic contact radius, HA is the aggregate modulus and k is the permeability of the cartilage layer. A main conclusion from this analysis is that the fluid phase of cartilage plays a major role in providing load support during the first 100-200 s after contact loading. Further, the largest component of stress in cartilage is the hydrostatic pressure developed in the interstitial fluid. For tissue fluid volume fraction (porosity) in the range 0.6 < or = phi f < or = 0.8, k = O(10(-15) m4/Ns) and HA = O(1 MPa), the peak magnitude of the principal effective (or elastic) stress may be as low as 14% of the peak hydrostatic pressure within the tissue, or the contact stress at the surface. In effect, the interstitial fluid shields the solid matrix from high normal stresses and strains. The asymptotic solution also shows that pressure-sensitive film measurements of intra-articular contact stress do not measure the elastic stress at the surface, but they rather provide a measure of the interstitial fluid pressure. Finally, this analysis provides strong support for the hypothesis that, if sudden loading causes shear failure within the cartilage-bone layer structure, this failure would take place at the cartilage-bone interface, and the plane of failure would be either parallel or perpendicular to this interface.