Knee model of hydrodynamic lubrication during the gait cycle and the influence of prosthetic joint conformity

Background  The influence of the total joint components’ elastic deformation on lubrication is generally accepted, but little is known about the influence of joint conformity under hydrodynamic lubrication based on fluid film interposition. The aim of this study was to evaluate induced pressure and stresses in the knee under fluid film lubrication during the stance phase of walking under various joint conformity conditions. Methods  A theoretical two-dimensional (2D) geometric model of knee prosthesis contact, with Dirichlet boundary conditions at both edges, and with a conformity index (CI) of 0, 0.3, 0.5, 0.6, 0.7, 0.8, 0.9, 0.92, 0.94, 0.96, 0.98, 0.99, 0.995, and 1.0, was used to calculate the spatiotemporal lubricant flow on a synovial fluid rheological model. With the instantaneous load as a source term, the Reynolds lubrication equation was subsequently solved following a finite volume approach in two dimensions and three dimensions. Results  Conformity strongly influenced the peak pressure, from 47 MPa with CI = 0 to 1.4 MPa with CI = 1, with a definite behavior change from CI = 0.96. The role of hydrodynamic lubrication was restricted to early steps of the stance phase. With CI < 0.96, there was a smooth maximum pressure decrease with increasing CI. In contrast, the maximum pressure fell abruptly with conformity > 0.96. Conclusion  The present model suggested the limited modifying effect of hydrodynamic lubrication in total knee replacement systems. However, its role during the early stance phase, coupled with high conformity, helps significantly to decrease compressive stresses on the polyethylene, fostering the beneficial effect of high conformity in a mixed lubrication regime. This beneficial effect may also be of great interest in total knee replacement systems based on materials with less deformation.