EVALUATION OF THE UNCERTAINTY CONTRIBUTION CAUSED BY FORM DEVIATION IN THE ESTIMATION OF WEAR DEPTH AND VOLUMETRIC WEAR FROM EXPLANTED HIP JOINTS

In the retrieval analysis of explanted hip joints, the estimation of wear volume and visualization of wear pattern are commonly used to evaluate in-vivo performance. While many studies report wear volumes from explanted hips, it is important to understand the limitations of these estimates including the sources and magnitude of uncertainty of the reported results. This study builds on a previous uncertainty analysis by Carmignato et al. to quantify the magnitude of uncertainty caused by the assumption that the as-manufactured shape of an explanted hip component is a perfect sphere. Synthetic data sets representing idealized measurements of spheroidal explants (prolate, oblate and pinched) with a nominal diameter of 50 mm were generated. These data sets represent the shape and magnitude of form deviations observed for explanted hip components (Figure 1). Data were simulated for either unworn components or those with a known volume and magnitude of wear simulated to represent 5 µm penetration of a 49.90 mm femoral head into an acetabular cup (Table 1). The volume of wear and wear pattern were estimated using a custom Matlab script developed for analysis of metrology data from explanted hip joints. This script fits a least squares sphere to data points in unworn, as manufactured regions of the surface to estimate the as-manufactured shape of the component. The diameter of the best fit sphere, and wear volume were compared to the known wear depths and volumes from the synthetic datasets. The results showed that the Matlab script estimated a wear volume of up to 1.4 mm3 for an unworn cup with a radial deviation of 10 µm. The maximum error of 13.3 mm3 was for a pinched cup with wear at the pole. The complete results are shown in Table 2. In some cases with aspherical form deviations, the least squares sphere fitted to the synthetic data was displaced in the Z direction with respect to the origin of the spheroid and the radius of the least squares sphere was outside the range of the principal radii of the spheroid. For instance, in case 5, the center was shifted 22 µm vertically from the mathematical center. The results from this study show that the magnitude of uncertainty due to form deviations on wear volume varies depending on the shape and magnitude of the form deviations and in some cases was greater than 10 mm3. A further important finding is that in some instances, the diameter and center of the least squares sphere fitted to the unworn regions may not be consistent with the mathematical radius and center of the synthetic data. This may have important implications for the “reverse engineering” of the as-manufactured dimensions from worn explanted hip joints. Please contact authors directly for the figure: Figure 1 Graphical depiction of a) synthetic data set, b) deviation map of a hemispherical acetabular cup with simulated wear, c) deviation map of a prolate spheroid with simulated wear at rim with color bar set to ±5 microns, d) deviation map of pinched ellipsoid with simulated wear at 45 degrees from pole.