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

Femoral component orientation plays a key role in implant stability and therefore the success rate of total hip arthroplasty. To date, this topic has been studied using various definitions and a variety of imaging modalities and protocols. The aim of this study is a proof of concept that a new algorithm can be used to describe the femoral component's 3D orientation on the three orthogonal anatomical planes and relative to its mechanical axis using input from two orthogonal planes. CT scans of 18 patients with a total of 22 hip arthroplasties were collected. From these, orthogonal coronal and sagittal projections of the complete femur were acquired in the scanning position (MIPs) and relative to the femoral mechanical axis (corrected MIPs). On these images, the orientation of the neck of the femoral component in space and relative to the femoral axis, respectively, was measured by coronal inclination (CI_F), sagittal inclination (SI_F) and transverse version (TV_F). With the algorithm, TV_F was also calculated based on CI_F and SI_F. Differences between measured and calculated TV_F and intra- and inter-observer reliability were evaluated using intra-class correlation coefficients (ICC). The error of non-orthogonal imaging (85° angle between the sagittal and coronal reconstructions) was tested on a third series of MIPs. The ICC between the calculated TV_F and manually measured TV_F, in space and relative to the femoral axis, was 0.98 for both with median absolute differences of 1.3 and 1.5°. For non-orthogonal images this was 0.70 with a median absolute difference of 5°. ICCs for intra-observer and inter-observer reliability for the calculated TV_F values were 0.98 and 0.88, respectively. With this algorithm the transverse orientation of the neck of the femoral component can be assessed in space and relative to the mechanical femoral axis by combining its sagittal and coronal orientation. As long as the imaging visualizes two orthogonal planes, the orientation of an implant can be assessed in 3-D, regardless of the imaging modality.