A Biphasic Model for Hip-Joint Replacement

The ball-and-socket geometry of the hip joint makes kinematic analysis of the joint motion relatively straightforward in comparison to other joints. The load-carrying surfaces of both ball and socket are covered with tough viscoelastic material known as cartilage. A number of lubrication theories have been proposed in the literature to account for the low coefficient of friction and low wear observed in healthy joints. The actual mechanism by which joints are capable of sustaining large repetitive loads with virtually no wear and with very little friction has not been fully understood. Therefore, analytical studies are presented for the understanding of the lubrication mechanism occurring in hip-joint replacements under restricted motion during standing or in the supporting phase during walking. The viscoelastic fluid has been considered to represent the synovial fluid in the fluid-film region. The problem described here has been analyzed in two regions (the porous matrix and the fluid-film region) separately along with suitable matching and boundary conditions at the interface. It has been concluded that the effect of the viscoelastic parameter for a particular gap is to increase the load capacity, indicating positive effects of the increase in concentration of suspended particles in the lubricant region. It has been observed that the coefficient of friction decreases with increasing values of the viscoelestic parameter. This is due to the fact that as the viscoelastic parameter increases, the concentration of hyaluronic acid molecules increases. It may also be noted from the results that the coefficient of friction decreases with increasing values of slip parameter. This shows that the slip velocity occurring at the porous boundary helps in maintaining normal functioning of human joints.