Correction of acetabular cup orientation measurements for X-ray beam offset

It is important to achieve correct orientation of an acetabular cup in order to avoid impingement, dislocation and increased wear. Cup orientation is usually assessed from a pelvis radiograph in which the central X-ray beam has been focused on the pubic symphysis. However, the angular offset of this beam from a beam passing through the centre of the cup causes rotational artefact in the cup image. Three simple algorithms for correcting this 3D rotational artefact are proposed, and these were validated using 3D CAD techniques by simulating the X-ray focus, target point and film position, as well as cup orientation. The accuracy of the correction was assessed in different practical scenarios. Cup version could be corrected to within a few hundredths of a degree, and inclination to within 0.2 degrees , if the X-ray target position was accurately located. However, only a small error in the correction was incurred if this position was erroneously located by as much as 10mm. The error in correcting the rotation position about the axis of symmetry depended on the cup size and anteversion setting, and it varied sinusoidally according to the position of measurement. Generally, it was within any possible measurement error. For the largest cup size considered (60mm outer diameter), the error ranged between -0.4 degrees and 0.8 degrees at the highest anteversion setting (30 degrees ).