Conversion of the Sagittal Functional Safe Zone to the Coronal Plane Using a Mathematical Algorithm: The Reason for Failure of the Lewinnek Safe Zone.

Abstract

Ante-inclination (AI) of the cup is a key component of the combined sagittal index (CSI) for predicting joint stability after total hip arthroplasty (THA). We aimed to (1) validate a mathematical algorithm relating AI to radiographic anteversion (RA), radiographic inclination (RI), and pelvic tilt (PT); (2) convert the AI criterion of the CSI into the coronal functional safe zone (CFSZ) and explore the influences of standing-to-sitting pelvic motion (PM) and pelvic incidence (PI) on the CFSZ; and (3) attempt to locate a universal cup orientation that always fulfills the AI criterion of the CSI for all patients. In the first phase, a phantom pelvis was designed to simulate a range of PT values, and an acetabular cup was implanted with different RA, RI, and PT settings using a robot-assisted technique and scanned using the EOS imaging system. The second phase involved patient radiographs. We enrolled 100 patients who underwent robot-assisted THA from April 2019 to December 2019, and EOS images before THA and at the 12-month follow-up were recorded. The AI was measured on a lateral radiograph; this angle was used as the reference and compared with the calculated AI to assess the accuracy of the algorithm. Linear regression was conducted to explore the relationship between the size of the CFSZ and the values of PM and PI. We calculated the intersection of the CFSZs of the patients to find a universal cup orientation (RA and RI) for the CSI. The algorithm was accurate according to both the phantom study and patient radiographs using PT at the time of follow-up, with mean absolute errors (MAEs) of 1.5° (width of 95% confidence interval [CI], 2.2°) and 2.8° (width of 95% CI, 3.0°), respectively. However, the preoperatively predicted AI had an MAE of 9.0° (width of 95% CI, 10.5°). In patient subgroups with lower PM or PI, the sizes of the CFSZ and of its intersection with the Lewinnek safe zone were significantly smaller (p < 0.017). No universal cup orientation existed to fulfill the CSI criteria for all patients or for any of the PM or PI subgroups. The target orientation for the cup in THA should be individualized. Our validated algorithm may serve as a quantitative tool for the patient-specific optimization of cup AI on the basis of the functional safe zone. The Lewinnek safe zone fails because it cannot predict the functional orientation of the cup. The concept of a universal safe zone of cup orientation should be abandoned and replaced by a patient-specific surgical target.