Prediction of elastic deformation of acetabular cups and femoral heads for lubrication analysis of artificial hip joints

Fluid film lubrication analysis for artificial hip joints often requires the determination of the elastic deformation of the bearing surfaces of both the acetabular cup and the femoral head. This is generally not a trivial task, because of the complex spherical geometries and non-uniform structural supports due to the bone and cement involved. It is particularly important that an efficient numerical method is employed, with a reasonably small amount of computing time required. The normal elastic deformation of spherical bodies, with particular reference to the acetabular cup and the femoral head for artificial hip joints, was determined in the present study using the two-dimensional spherical fast Fourier transform (SFFT) technique. A cobalt-chromium alloy femoral head was considered, in combination with either an ultra-high molecular weight polyethylene acetabular cup fixed to a metallic (rigid) backing or a cobalt-chromium alloy cup fixed to an equivalent layer representing bone and cement. A representative pressure distribution was applied around both the central region of the cup and the anatomical position with a 45° inclination angle. The elastic deformation determined from the SFFT method was compared with that directly calculated from the finite element method, and excellent agreement was found when the pressure distribution was applied around the central region. Even when the pressure distribution was applied anatomically and extended to the edge of the cup, reasonably good overall agreement of the predicted elastic deformation was achieved. Furthermore, both the computing time and the storage space required for the SFFT method were significantly reduced, compared with the conventional direct summation method used by Jagatia and Jin.