Calculation of the 3-D femoral component’s orientation in total hip arthroplasty using a trigonometric algorithm

The risk of dislocation after THA is reported to be 0.3%-10% over the last decades, in which malposition of the prosthetic components is considered an important factor^21,22,23. The orientation of a THA has been widely assessed on 2-D and 3-D images acquired with different imaging modalities, in different body positions, using a variety of definitions and conflicting terminology⁷. As of yet, no method for assessment of the 3-D orientation of the neck of the femoral component is available for uniform application to different imaging modalities and implant types.

This validation study demonstrates that the transverse orientation of the neck of the femoral component can be accurately assessed by combining the coronal and sagittal orientation of the neck of the femoral component, on for example biplanar radiographs (anterior–posterior and lateral), with a straightforward algorithm. This creates the opportunity for evaluation of femoral component orientation in 3-D, without the need for CT, and in the weight-bearing position. The method described in this proof-of-concept study can be applied to radiographs. Therefore, it could easily provide surgeons accurate feedback on the postoperative 3-D implant orientation and offers potential for comparison of the 3-D implant orientation across studies that used different modalities.

Practically, this method requires perfect orthogonal imaging of the implant and patient, thus traditional axiolateral/ crosslateral radiography of the proximal femur is insufficient^15,16. Innovative modalities such as biplanar radiography could easily provide such images with acceptable radiation exposure and costs for daily clinical practice. Non-orthogonal images could diminish the accuracy of the method. This could be easily controlled, by verification that both femoral heads overlap completely on the lateral radiograph. Furthermore, semi-automatic image processing to determine the exact center of the femoral head and axis of the neck may further reduce the error. To guarantee the theoretically excellent accuracy of a mathematical model, a strict protocol for image acquisition and processing is necessary in clinical practice. In case of non-orthogonal imaging and manual measurement of the coronal and sagittal orientation, the algorithm is still valid. However, it should be noted that the outcomes of calculated TV_F will be less accurate.

The orientation of the neck of the femoral implant was assessed in 3-D, by means of the three components of rotation relative to the scanning position, as well as relative to the mechanical femoral axis. The cranio-caudal, medio-lateral and antero-posterior translations, however, are not included in this assessment, since this is highly variable between individuals and implant types. According to a recent international consensus, the orientation parameters (CI, SI, TV) used in this study are defined in such a way that they are uniform and valid for the orientation of the neck of any type of femoral implant in THA surgery and any imaging modality. These parameters represent the basic 3-D orientation of the proximal part of the femoral implant that connects the proximal femur to the center of rotation of the acetabular cup, potentially very important for assessment of implant stability. Comparison of calculated TV_F and TV_F’ showed only small differences. This can be explained by minimal deviations of the mechanical axis of the femoral orientation to the scanning position and orientation of the scan. The long arm of the coronal and sagittal orientation of the mechanical femoral axis, with minimal impact on the proximal implant orientation is another explanation. Both TV_F and TV_F’ may be relevant in clinical practice, since the first can describe the functional orientation of the femoral implant in space, while the second describes the intrafemoral alignment.

The proposed algorithm can calculate TV_F in a valid and reliable way based on CI_F and SI_F, with excellent validity²⁴ (Table 2) and excellent and good intra- and inter-observer reliability respectively (Tables 4, 5). The mean absolute difference of our method was < 2° (Table 2), precise enough to enable its use in for the measurement of TV_F in daily clinical practice, where TV_F usually varies between -10° and 30°. Although Snijders et al. recommended careful use of the algorithm in cases in which two angles are approaching 0°¹⁸, use of MIP results in more precise measurements, which enables the use the algorithm even when both TV_F and SI_F are approaching 0°. Type of steel or head size had no impact on the validity of the algorithm, since only the neck-shaft of the prosthesis is used for calculations. The limited sample size of our study is a limitation of this study. The proof of concept of the mathematical algorithm will not change with a larger sample size, however there is a limitation in the measurement of reliability of our method.

The method described provides improvements for the evaluation of optimal femoral component positioning in THA, without a CT. This speeds up the process, allows for easily accessible postoperative feedback, gives better insight and offers great potential for future comparative studies. Additionally, this method could be cost effective and beneficial for patients safety, by reducing radiation exposure. The mean radiation exposure with our two biplane radiographs was 0.8 mSv, while conventional THA CT resulted in a mean of 10.6 mSv. Hence, with our method applied to biplane radiographs, a significant reduction in radiation exposure could be established. While very little is still known about the effect of the femoral component orientation, the described method can be of high relevance for defining the orientation of the femoral component uniformly. With this algorithm it is possible for clinicians to calculate the transverse femoral component alignment in THA patients when they assess implant position on a combination of conventional anterior–posterior and a lateral radiograph including the proximal femur. Furthermore, biplanar radiography techniques such as EOS^TM also allow for these analyses. Compared to 3-D imaging techniques, the biplanar radiographs are faster, cheaper part of the clinical routine and enables analysis in the upright position, with significantly lower radiation exposure. The presented method can act as the basis for new research studying the consequences of the femoral component orientation on implant stability.