A New Method to Make 2-D Wear Measurements Less Sensitive to Projection Differences of Cemented THAs

Abstract

Wear curves from individual patients often show unexplained irregular wear curves or impossible values (negative wear). We postulated errors of two-dimensional wear measurements are mainly the result of radiographic projection differences. We tested a new method that makes two-dimensional wear measurements less sensitive for radiograph projection differences of cemented THAs. The measurement errors that occur when radiographically projecting a three-dimensional THA were modeled. Based on the model, we developed a method to reduce the errors, thus approximating three-dimensional linear wear values, which are less sensitive for projection differences. An error analysis was performed by virtually simulating 144 wear measurements under varying conditions with and without application of the correction: the mean absolute error was reduced from 1.8 mm (range, 0–4.51 mm) to 0.11 mm (range, 0–0.27 mm). For clinical validation, radiostereometric analysis was performed on 47 patients to determine the true wear at 1, 2, and 5 years. Subsequently, wear was measured on conventional radiographs with and without the correction: the overall occurrence of errors greater than 0.2 mm was reduced from 35% to 15%. Wear measurements are less sensitive to differences in two-dimensional projection of the THA when using the correction method.

Appendix 1

The correction method uses the underlying mechanism of differences in 2-D projected distances with varying positions of two objects in space to construct a 3-D linear wear approximation [17]. The following formula is used for correction of the raw wear measurement assuming the second radiograph to be the true plane of wear:

$$ {\text{corrected wear}} = {\text{v1}} \times {\text{cosine}}{\text{ }}{\upbeta}/{\text{cosine}}{\text{ }}\upalpha - {\text{v2}} $$

where v1 is the distance between the two reference points on the first (direct postoperative) radiograph, v2 is the distance between the reference points on the second radiograph, α is the opening angle of the cup on the first radiograph, and β is the opening angle of the cup on the second radiograph used for the wear measurement. The opening angles are calculated with the following formula: opening angle = arcsine (minor axis/major axis).

This formula should be applied to the vectoral component of wear occurring perpendicular to the long axis of the projected metal contrast wire. The component of wear occurring parallel to this axis should not be changed. The total linear wear is then calculated by taking the square root of the sums of the quadratic values of the adjusted vector perpendicular to the major axis and the unadjusted vector parallel to the major axis of the ellipse.