Radiographic measurement of acetabular cup version and rotation - Validation of algorithms to correct for X-ray target offset on pelvic radiographs

摘要

Objectives: Simple, accurate algorithms to correct version and rotation measurements for X-ray offset at the pubic symphysis will be presented. Background: Incorrect orientation of the acetabular cup during total hip surgery can result in postoperative impingement, a reduced range of motion, dislocation and increased wear [1, 2]. Computer image guided systems can improve the accuracy of orientation of the cup, and postoperative radiographic measurement of cup orientation [4, 6] may be used to verify the accuracy of placement [3]. However, the resulting measurements are erroneous because the X-ray beam is offset at the pubic symphysis. Published correction methods involve either an empirically derived graph [5] or a complex "back projection" algorithm requiring image analysis techniques [3]. Our technique is simple and will correct radiographic measurements of version and rotation (about the polar axis) of a plastic acetabular cup having an equatorial/polar marker wire. Method: The algorithms were validated using a 3-D CAD system. Two circles, representing combined equatorial and polar wire markers of a 40mm diameter cup, were created on the CAD screen. A point representing the X-ray focus was situated 850mm above the circles and at an infero-medial position representing the pubic symphysis target point. A series of lines was drawn from the focus to points around the equatorial circle (representing X-rays) and these were projected on to a plane 150mm below the circle centre (representing the X-ray plate). The coordinates of the intersections of these lines with the plane were read into custom software which fitted an ellipse (representing the radiographic wire marker image) to the points. Lines from the focus to two points on the circle (representing the cup baseline) were also projected on to the plane in order to assess the change in inclination. All points taken manually were "snapped" into position so the coordinates of these points were "exact". The circles were set at different combinations of "radiographic" version and rotation in 5 degrees increments up to 30 degrees and the co-ordinate data was analyzed using custom software. Version was calculated from the ratio of minor to major diameters of the elliptic image of the "wire". Rotation was calculated from the position of the intersection of one side of the polar "wire" with the equatorial "wire" [6]. Correction algorithms required only the x-y co-ordinates of the X-ray target in relation to the elliptic image centre, the X-ray focus to cassette height and the calculated/measured inclination of the elliptical image.