| The tibio-femoral joint has been mechanically modeled with two fixed kinematic axes of rotation, the longitudinal rotational axis in the tibia (LR axis) and the flexion-extension axis in the femur (FE axis). Several methods currently exist in the literature to approximate these axes of rotation; however, each has its limitations. Thus, the objective of this work was to develop a new method that incorporates a mathematical optimization that reduces the position and orientation errors in identifying both axes of rotation. The method was thoroughly validated both virtually and mechanically. The virtual axis finder identifies the axes in a two-step process: first, the LR axis is identified from pure internal-external rotation of the tibia and the FE axis is identified after the LR axis is known. The two-step process allows the coupled internal-external rotation that occurs during natural bending to be mathematically eliminated. Validation of the method was performed virtually with simulations of normal knee kinematics as well as mechanically with a two-rotational axis mechanism that modeled normal knee kinematics. Both validation techniques modeled roentgen stereophotogrammetric analysis (RSA) and 3D video based motion analysis. The orientation and position root mean square errors (RMSEs) for identifying the LR and FE axes with motion analysis (0.20°, 0.45mm, 0.20° and 0.11 mm, respectively) were smaller than with RSA (1.22°, 0.50 mm, 0.83° and 0.37 mm, respectively) with the virtual validation. Similarly, the orientation and position RMSEs for identifying the LR and FE axes with motion analysis (0.26°, 0.28 mm, 0.36° and 0.25 mm, respectively) were smaller than with RSA (1.04°, 0.84 mm, 0.82° and 0.32 mm, respectively) with the mechanical validation. Both measurement modalities produced satisfactory results; however, 3D video based motion analysis has smaller errors than RSA with in vitro, bone mounted markers. Because skin motion artifact was not included in the validations, applications of this method with in vivo conditions should either be used with RSA, or more work is required to assess the affect of skin motion artifact with 3D video-based motion analysis on the virtual axis finder. |
