Radiographic stereometry for non-metal-backed acetubular cups: 3D wear estimation and related uncertainty

The aim of this work was to assess the 3D wear of non-metal-backed acetubular cups from two conventional digitized radiographs. The centers of the femoral head and the metal ring in the equatorial plane of the cup are located using 3D pose techniques for spheres and circles from sampled points in the images. The method used to locate these points of interest and also estimate their covariance is fully described in previous work. The covariance is used to decrease the bias of the pose estimation, while bootstrapping decreases its variance and gives access to the directions of minimal variability between the two centers for each image. These directions are used to produce the final distance after reconstruction. Results are compared with the 2D technique working on a single anteroposterior (AP) radiograph and assuming null lateral wear. Validation is performed on acetubular cups: (a) simulated by Monte-Carlo, (b) implanted on a pelvic model, and (c) acquired on patients just after arthroplasty. The accuracy in wear for simulation increases from about one to four hundredths of a millimeter as caudal and cranial absolute angulations decreases from 45° to 30°. It is more difficult to assess for real prostheses, but results are shown to lie within the manufacturer's dimensional tolerances. Globally, the access to the lateral wear is obtained at the expense of confidence in the global linear wear (0.06 mm), which is doubled with regard to 2D technique but still satisfying for clinical use, whereas the bias of the measurement is decreased.