Calculation of impingement-free combined cup and stem alignments based on the patient-specific pelvic tilt.

Proper cup alignment is crucial in total hip arthroplasty for reducing impingement risks, dislocations and wear. The Lewinnek "safe zone" is often used in clinical routine. This safe zone does not consider functional aspects and dislocation can occur even when the cup is oriented within the safe zone. Functional safe zones based on the hip range of motion (ROM) were introduced but are not commonly used in clinical routine. The reason might be that these methods are time-consuming due to complex simulations. A relatively fast method based on analytical mathematical formulas was proposed, but it is difficult to consider arbitrary motion. This work introduces an efficient algorithm for calculating a patient-specific target zone based on the target ROM which can consider any set of motions. The method is based on matrix transformations and trigonometric formulas. The resulting target zone which contains all impingement-free cup orientations is dependent on the patient-specific pelvic tilt, the 3D angular neck and stem orientation within the femur, and the technical prosthesis ROM. This method could be integrated into computer-assisted preoperative planning and intra-operative navigation tools. As pelvic tilt and stem orientation influence the optimal cup orientation they need to be acquired from the patient to derive a patient-specific ROM-based target zone.