Three-dimensional orientation and location-dependent varying rules of radiographic angles of the acetabular cup

AimThe aim of this study is to demonstrate the varying rules of radiographic angles following varying three-dimensional (3D) orientations and locations of cup using an accurate mathematical model.MethodsA cone model is established to address the quantitative relationship between the opening circle of cup and its ellipse projection on radiograph. The varying rules of two-dimensional (2D) radiographic anteversion (RA) and inclination (RI) angles can be analyzed.ResultsWhen the centre of cup is located above X-ray source, with proper 3D RI/RA angles, 2D RA angle can be equal to its 3D counterpart, and 2D RI angle is usually greater than its 3D counterpart. Except for the original point on hip-centered anterior-posterior radiograph, there is no area on radiograph where both 2D RA and RI angles are equal to their 3D counterparts simultaneously.DiscussionThis study proposes an innovative model for accurately explaining how 2D RA/RI angles of cup are varying following different 3D RA/RI angles and location of cup. The analysis results provide clinicians an intuitive grasp of knowledge about 2D RA/RI angles greater or smaller than their 3D counterparts post-operatively. The established model may allow determining the effects of pelvic rotations on 2D radiographic angles of cup.