A THEORETICAL SOLUTION FOR THE FRICTIONLESS ROLLING-CONTACT OF CYLINDRICAL BIPHASIC ARTICULAR-CARTILAGE LAYERS

Previous studies have shown that interstitial fluid pressurization pla ys an important role in the load support mechanism of articular cartil age under normal step loading. These studies have demonstrated that in terstitial fluid pressurization decreases with time if the applied loa d is maintained constant. In the present study, a theoretical solution is obtained for another common loading of articular cartilage, namely the contact of surfaces in rolling motion. Pure rolling of symmetrica l frictionless cylindrical cartilage layers is analyzed under steady s tate. The linear biphasic model of Mow et al. [J. Biomech. Engng 102, 73-84 (1980)] is used to describe the mechanical response of articular cartilage. The solution of this contact problem reduces to simultaneo usly solving a set of four integral equations, akin to the dual integr al problem of elastic contact. It is found that the solution is depend ent on four non-dimensional parameters: R(h) = Vb/H(A)k, W/2 mu b, R/b , and v, where V is the surface velocity, b the cartilage thickness, H -A the aggregate modulus, mu the shear modulus, V Poisson's ratio, k t he permeability, R the radius of cylindrical surfaces, and W the appli ed load per unit cylinder length. For R(h) much less than 1, interstit ial fluid pressurization is found to be negligible, and all the applie d load is supported by the solid collagen-proteoglycan phase of the ti ssue, thus causing significant cartilage deformation. As R(h) increase s to a physiological level(R(h) similar to 10(4)), interstitial fluid pressurization may support more than 90% of the total applied load, sh ielding the solid matrix from high effective stresses and reducing mat rix strains and deformation. The protective effect of interstitial flu id pressurization is observed to increase with increasing joint congru ence (R/b); similarly, as the applied load (W/2 mu b) is increased, a greater proportion of it is supported by the fluid. In degenerative ca rtilage, R(h) may drop by one or more orders of magnitude, primarily a s a result of increased permeability. Thus, the protective stress-shie lding effect of interstitial fluid pressurization may become less effe ctive in diseased tissue, possibly setting a pathway for further tissu e degeneration.