Department of Orthopaedics, Chinese PLA General Hospital, Beijing, 100853, China.
Department of Orthopaedics, Beijing Tsinghua Changgung Hospital, School of Clinical Medicine, Tsinghua University, Beijing, 102218, China.
Med Biol Eng Comput. 2019 Nov;57(11):2359-2371. doi: 10.1007/s11517-019-02041-7. Epub 2019 Sep 9.
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. Graphical abstract The traditional methods for calculating the radiographic angles of the acetabular cup are based on the ellipse projection of the opening circle of the cup on radiographs. However, with varying locations of the X-ray source and pelvis rotations about different axes, the outline of this ellipse projection will change, and accordingly, the traditional method and calculating results will be inaccurate. In this study, a cone model for three-dimensional circle-to-two-dimensional ellipse projection is utilized to incorporate the effect of X-ray offset and quantify the relationships of the radiographic angles of the cup with the true orientation of the cup and pelvic rotations in either pelvic or hip anteroposterior radiographic situation.
本研究旨在利用数学模型探讨骨盆旋转和 X 射线外移对髋臼杯放射学前倾角/倾斜角（RA/RI）的协同作用。采用圆锥模型建立三维（3D）圆与其二维（2D）椭圆投影之间的空间关系，以量化不同类型骨盆旋转时骨盆/髋前后位 X 线片中髋臼杯 3D RA/RI 角与其 2D 对应角度之间的关系。结果表明，入口/出口位对 2D RA 角的影响与闭孔/髂骨位相似。对于 2D RA 角，在可接受偏差范围内，骨盆旋转的允许范围为三轴旋转极限形成的 3D 空间。对于特定可接受的 2D RA 角偏差，骨盆和髋部 X 线片之间的这些范围几乎相等。综合入口/闭孔或出口/髂骨位可以使骨盆 X 线片的 2D RA 角度保持在与髋部 X 线片相同的可接受偏差范围内。对于具有可接受偏差的 2D RA 角，需要在两张 X 线片中同等关注评估骨盆旋转的允许范围。
传统的髋臼杯放射学角度计算方法基于杯开口圆在 X 线片上的椭圆投影。然而，随着 X 射线源位置和骨盆围绕不同轴的旋转位置的变化，该椭圆投影的轮廓将会改变，相应地，传统方法和计算结果将变得不准确。在本研究中，采用三维圆到二维椭圆投影的圆锥模型来纳入 X 射线外移的影响，并量化杯的放射学角度与杯的真实方向和骨盆旋转之间的关系，无论是在骨盆还是髋部前后位 X 线片情况下。
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