Wear of polyethylene cups in total hip arthroplasty: a parametric mathematical model

This paper presents a parametric mathematical model of the head-cup wear coupling in total hip arthroplasty (THA). The model evaluates the dependence of acetabular volumetric wear upon the characteristic parameters of patient and hip prosthesis. Archard's law is assumed to calculate the wear coupling behaviour. The wear factor is taken from pin-on-disc wear tests as a function of materials and finishing of the articular joint. The forces acting on the hip joint are taken from experimental data found in the literature whilst the load distribution is calculated under the hypotheses of perfectly rigid ideal wear coupling. The sliding distance is obtained by combining the three elementary displacements -- due to rotations around the three axes -- at the generic bearing surface location. The simulations show that the polymeric wear volume per step cycle decreases ranging from fast walking speeds to low running speeds, it increases linearly with patient body weight and with femoral head diameter, it decreases slightly for positive variations of the socket inclination angle and it increases exponentially with femoral head roughness. The volumetric wear rate per year calculated for a standard reference patient is 5.8 mm3. The relevant iso-wear maps show a marginal pattern with the maximum located near the cup superior borderline. At the instant of peak load, the iso-stress maps show a paracentral pattern with the maximum superior to the cup polar point, and the iso-sliding distance maps show a marginal pattern with two maxima located near the cup's superior and inferior borderlines.