Erratum to radiographic assessment of the cup orientation after total hip arthroplasty: a literature review.

[This corrects the article DOI: 10.21037/atm.2019.12.150.].

Radiographic assessment of the cup orientation after total hip arthroplasty: a literature review.

Optimal acetabular cup orientation is of substantial importance to good long-term function and low complication rates after total hip arthroplasty (THA). The radiographic anteversion (RA) and inclination (RI) angles of the cup are typically studied due to the practicability, simplicity, and ease of interpretation of their measurements. A great number of methods have been developed to date, most of which have been performed on pelvic or hip anteroposterior radiographs. However, there are primarily two influencing factors for these methods: X-ray offset and pelvic rotation. In addition, there are three types of pelvic rotations about the transverse, longitudinal, and anteroposterior axes of the body. Their effects on the RA and RI angles of the cup are interactively correlated with the position and true orientation of the cup. To date, various fitted or analytical models have been established to disclose the correlations between the X-ray offset and pelvic rotation and the RA and RI angles of the cup. Most of these models do not incorporate all the potential influencing parameters. Advanced methods for performing X-ray offset and pelvic rotation corrections are mainly performed on a single pelvic AP radiograph, two synchronized radiographs, or a two-dimensional/three-dimensional (2D-3D) registration system. Some measurement systems, originally developed for evaluating implant migration or wear, could also be used for correcting the X-ray offset and pelvic rotation simultaneously, but some drawbacks still exist with these systems. Above all, the 2D-3D registration technique might be an alternative and powerful tool for accurately measuring cup orientation. In addition to the current methods used for postoperative assessment, navigation systems and augmented reality are also used for the preoperative planning and intraoperative guidance of cup placement. With the continuing development of artificial intelligence and machine learning, these techniques could be incorporated into robot-assisted orthopaedic surgery in the future.

The synergetic effect of pelvic rotation and X-ray offset on radiographic angles of the acetabular cup.

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.

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.

A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty.

We established a mathematical method to precisely calculate the radiographic anteversion (RA) and radiographic inclination (RI) angles of the acetabular cup based on anterior-posterior (AP) pelvic radiographs after total hip arthroplasty. Using Mathematica software, a mathematical model for an oblique cone was established to simulate how AP pelvic radiographs are obtained and to address the relationship between the two-dimensional and three-dimensional geometry of the opening circle of the cup. In this model, the vertex was the X-ray beam source, and the generatrix was the ellipse in radiographs projected from the opening circle of the acetabular cup. Using this model, we established a series of mathematical formulas to reveal the differences between the true RA and RI cup angles and the measurements results achieved using traditional methods and AP pelvic radiographs and to precisely calculate the RA and RI cup angles based on post-operative AP pelvic radiographs. Statistical analysis indicated that traditional methods should be used with caution if traditional measurements methods are used to calculate the RA and RI cup angles with AP pelvic radiograph. The entire calculation process could be performed by an orthopedic surgeon with mathematical knowledge of basic matrix and vector equations.