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

AIM: The 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.

METHODS: A 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.

RESULTS: When 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.

DISCUSSION: This 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.