Precision of distance determination using 3D to 2D projections: the error of migration measurement using X-ray images

The goal of this study has been to objectively and reliably estimate the precision of measuring 2D migration of hip prostheses. This is the distance change over time between the implant and the bone observable in X-ray images. To reach this goal, a generally valid scheme for determining the standard deviation of distance measurements in 3D to 2D projections has been worked out. The scheme was applied to four previously published methods for measuring the migration of the prosthetic cup using standard radiographs. Applying the scheme yields measures for the sensitivity of the migration measurement towards the relevant sources of error. Inserting previously published data for the amounts of the entering errors, the standard deviation of the migration measurement has been calculated numerically resulting in values up to several millimeters.