Abstract
BACKGROUND: Femoral rotational alignment is a critical determinant of contact mechanics, kinematics, and long-term survivorship in total knee arthroplasty (TKA). Traditional techniques rely on anatomical landmarks, which exhibit substantial inter-patient variability and may not reliably optimize tibiofemoral load distribution. This study introduces a geometric, anatomy-independent framework using minimal surface theory (MST) to identify an energy-minimizing femoral rotational alignment based on curvature equilibrium rather than fixed bony reference axes. METHODS: A three-dimensional finite element model of the tibiofemoral articulation was constructed from computed tomography-derived anatomy. Posterior-stabilized TKA components were virtually implanted, and femoral rotation was varied from 5° internal to 5° external relative to the surgical transepicondylar axis. Simulations were performed at 0°, 45°, and 90° of flexion under a 700-N axial load. Willmore surface energy, mean contact pressure, peak shear stress, and contact area were quantified for each alignment. Sensitivity analyses evaluated robustness to posterior tibial slope (±3°) and insert conformity. RESULTS: Across all flexion angles and model conditions, the MST-derived minimum energy state occurred consistently at 2°-3° of external rotation. Compared with neutral alignment, this optimized orientation reduced Willmore energy by 38.6 %, mean contact pressure by 18.7 %, and peak shear stress by 30.8 %, while increasing contact area by 13.1 %. Internal malrotation resulted in abrupt curvature transitions, elevated stress concentrations, and reduced load-sharing capacity. Findings remained stable across sensitivity analyses, indicating that the energy-optimal configuration is reproducible and not dependent on specific anatomical landmarks. CONCLUSION: Minimal surface theory identifies a narrow and consistent external rotational target that optimizes congruence and reduces mechanical stress in TKA. This framework provides a mathematically grounded, anatomy-independent alternative to conventional landmark-based alignment strategies and may support future computational or robotic applications for patient-specific rotational planning. LEVEL OF EVIDENCE: Computational simulation study (Level V).