The synergetic effect of pelvic rotation and X-ray offset on radiographic angles of the acetabular cup
- 55 Downloads
The objective of this study is to investigate the synergetic effect of the pelvic rotation and X-ray offset on the radiographic anteversion/inclination (RA/RI) angles of the acetabular cup using a mathematical model. A cone model for establishing the spatial relationship between a three-dimensional (3D) circle and its two-dimensional (2D) elliptical projection is utilized to quantify the relationship between the 3D RA/RI angles of the cup and their 2D counterparts with different types of pelvic rotations in pelvic/hip anteroposterior radiographs. The results reveal that the effect of inlet/outlet views on the 2D RA angle is similar to that of iliac/obturator views. The permissible ranges of pelvic rotation for the 2D RA angle with an acceptable bias are the 3D space formed by the limits of triple axial rotations. For a specified acceptable bias of the 2D RA angle, these ranges are almost equal between pelvic and hip radiographs. The combined inlet/obturator or outlet/iliac views can maintain the 2D RA angle of a pelvic radiograph within the same range of acceptable bias as that of a hip radiograph. For a 2D RA angle with an acceptable bias, the permissible range of pelvic rotation needs to be evaluated with equal attention in both radiographs.
KeywordsAcetabular cup 2D radiographic angle 3D radiographic angle Pelvic rotation X-ray offset
Total hip arthroplasty
The radius of the cup
- (o, p, q)
The coordinate of the X-ray beam source
- (x0, y0, z0)
The coordinate of the center of the cup
- [k1, i1, j1]
The normal vector of the cup before rotation
- [k, i, j]
The normal vector of the axis of the cup after rotation
- [l, m, n]
The normal vector of the space line
The x-axial rotation of the cup
The y-axial rotation of the cup
The z-axial rotation of the cup
Anonymous reviewers are appreciated very much for their help to improve this manuscript.
This study was partially funded by the Fundamental Research Funds for the Central Universities (FRF-TP-16-045A1).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- 6.Seradge H, Nagle KR, Miller RJ (1982) Analysis of version in the acetabular cup. Clin Orthop Relat Res 166:152–157Google Scholar
- 26.Yun HH, Murphy WS, Ward DM, Zheng G, Hayden B, Murphy SB (2019) Effect of pelvic tilt and rotation on cup orientation in standing anteroposterior radiographs. Hip Int 1120700019831665. doi: https://doi.org/10.1177/1120700019831665