Improved mathematical model of the wear of the cup articular surface in hip joint prostheses and comparison with retrieved components

Abstract

Abstract

This paper presents an analytical model of the cobalt-based alloy-ultra-high molecular weight polyethylene (UHMWPE) wear coupling. Based on a previous model in which the cup wear volume over a gait cycle (WG) was calculated under the simplifying assumption of an ideal rigid coupling, the current version proposes a more realistic wear simulation. All three components of the hip loading force were considered for the contact pressure calculation and all three components of the hip motion were taken into account for the sliding distance calculation. The contact pressure distribution was calculated on the basis of the Hertzian theory for the elastic contact of two bodies with non-conforming geometrical shapes. The wear factor was taken from hip simulator wear tests. The calculated WG is 67 × 10⁻⁶mm³ for a standard reference patient. The parametric model simulations show that WG increases linearly with the patient weight, femoral head diameter and surface roughness. It increases non-linearly to a maximum and decreases to an asymptotic value with increasing cup/head clearance and with cup isotropic elastic modulus. The cup orientation in the pelvis affects only slightly the total amount of WG whereas it is the dominant factor affecting the shape of the wear distribution. The iso-wear maps show paracentral patterns at low cup inclination angles and marginal patterns at higher inclination angles. The maximum wear depth is supero-posterior when the cup is in neutral alignment and supero-anterior at increasing anteversion angles. Complex patterns with a combination of paracentral and marginal wear were obtained at specific clearance values and cup orientations. The results of the simulations are discussed in relation to the wear distribution measured on the articular surface of 12 UHMWPE components retrieved from failed hip joint prostheses, after a period of in situ functioning.