Abstract
Multi-directional motion at the ball-socket interface of a hip replacement joint has been discovered as a fundamental feature that determines the magnitude of wear for ultra-high molecular weight polyethylene (UHMWPE). The present study considers the wear of UHMWPE moving along a circular path with a uniform angular change rate of the velocity vector defined by the curvature of the sliding circle. It is apparent the as the sliding circle radius increases the motion is approaching more towards linear tracking. Therefore, wear rate per unit sliding distance would decrease with increasing the slidng circle radius. However, the sliding distance per cycle increases linearly with the radius of the circle, which would cause a proportional increase in the wear rate per cycle. We hypothesize that these two opposing effects on wear with respect to the changing radius of the sliding circle would cancel out each other leading to wear rate per cycle being independent of sliding distance.
Experiments were conducted on a hip simulator with a biaxial rocking motion that results in a circular sliding path at the polar region of the acetabular cup that experiences the highest contact stresses and wear. The radius of the sliding circle, r, depends solely on the radius of the femoral ball, R, and the biaxial rocking angle, a, such that r=Rsina. Two tests were conducted. The first test was run under standard conditions with a constant biaxial rocking angle of +/−23 and head diameters ranging between 28 mm and 44 mm. Acetabular components were machined from virgin non-crosslinked UHMWPE with inner diameters matching those of the femoral heads. For the 28 mm bearing, the cups were of standard hemispherical geometry. The larger cups were truncated by various degrees so that the nominal contact area remained exactly the same as that of the standard 28 mm hemispherical components. The second test was run with the standard 28 mm components and various biaxial rocking angles: +/−10, +/−15, +/−20 and +/−23. Both tests were run for a total duration of 2 million cycles with diluted alpha-serum as a lubricant and physiologic loading (peak load: 2450N) as described by Paul.
Volumetric wear at 2 million cycles for both tests are summarized in Figure 1. Fig. 2 shows a graphic representation of the total volumetric wear (DV) as a function of the sliding circle radius (r). Total volumetric wear is independent of the head diameter (2R), the biaxial-rocking angle (a) and the sliding circle radius (r). The total volumetric wear is proportional to the number of cycles and independent of the sliding distance per cycle. The clinically observed wear rate-ball diameter relationship, therefore, is not attributed to variations in sliding distance per walking step with differing ball head sizes.
For the same nominal contact area between a ball and a socket, the total volumetric wear of UHMWPE is independent of the ball diameter, the biaxial rocking angle and the sliding circle radius. In other words, the total volumetric wear is proportional to the number of cycles and independent of the sliding distance per cycle.
