AN ASYMPTOTIC SOLUTION FOR THE CONTACT OF 2 BIPHASIC CARTILAGE LAYERS

This study addresses the hypothesis that interstitial fluid plays a ma jor role in the load support mechanism of articular cartilage. An asym ptotic solution is presented for two contacting biphasic cartilage lay ers under compression. This solution is valid for identical thin (i.e. epsilon=h'/a'(0) much less than 1), frictionless cartilage layers, an d for the 'early' time response (i.e. t' much less than (h')(2)/H(A)k) after the application of a step load. An equilibrium asymptotic solut ion is also presented (i.e. t' --> infinity). Here h' is the thickness , ab is a characteristic contact radius, H-A is the aggregate modulus and k is the permeability of the cartilage layer. A main conclusion fr om this analysis is that the fluid phase of cartilage plays a major ro le 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 f luid volume fraction (porosity) in the range 0.6 less than or equal to phi(f) less than or equal to 0.8, k = O(10(-15) m(4)/N s) and H-A = O (1 M Pa), the peak magnitude of the principal effective (or elastic) s tress may be as low as 14% of the peak hydrostatic pressure within the tissue, or the contact stress at the surface. In effect, the intersti tial fluid shields the solid matrix from high normal stresses and stra ins. The asymptotic solution also shows that pressure-sensitive film m easurements of intra-articular contact stress do not measure the elast ic stress at the surface, but they rather provide a measure of the int erstitial fluid pressure. Finally, this analysis provides strong suppo rt for the hypothesis that, if sudden loading causes shear failure wit hin the cartilage-bone layer structure, this failure would take place at the cartilage-bone interface, and the plane of failure would be eit her parallel or perpendicular to this interface.