Trigonometric Algorithm Defining the True Three-Dimensional Acetabular Cup Orientation Correlation Between Measured and Calculated Cup Orientation Angles

Background: Acetabular cup orientation plays a key role in implant stability and the success of total hip arthroplasty. To date, the orientation has been measured with different imaging modalities and definitions, leading to lack of consensus on optimal cup placement. A 3-dimensional (3D) concept involving a trigonometric description enables unambiguous definitions. Our objective was to test the validity and reliability of a 3D trigonometric description of cup orientation. Methods: Computed tomographic scans of the pelvis, performed for vascular assessment of 20 patients with 22 primary total hip replacements in situ, were systematically collected. On multiplanar reconstructions, 3 observers independently measured cup orientation retrospectively in terms of coronal inclination, sagittal tilt, and transverse version. The angles measured in 2 planes were used to calculate the angle in the third plane via a trigonometric algorithm. For correlation and reliability analyses, intraobserver and interobserver differences between measured and calculated angles were evaluated with use of the intraclass correlation coefficient (ICC). Results: Measured and calculated angles had ICCs of 0.953 for coronal inclination, 0.985 for sagittal tilt, and 0.982 for transverse version. Intraobserver and interobserver reliability had ICCs of 0.987 and 0.987, respectively, for coronal inclination; 0.979 and 0.981, respectively, for sagittal tilt; and 0.992 and 0.978, respectively, for transverse version. Conclusions: The 3D concept with its trigonometric algorithm is a valid and reliable tool for the measurement of cup orientation. Clinical Relevance: By calculating the transverse version of cups from coronal inclination and sagittal tilt measurements, the trigonometric algorithm enables a 3D definition of cup orientation, regardless of the imaging modality used. In addition, it introduces sagittal tilt that, like pelvic tilt, rotates around the transverse axis.