Virtual Axis Finder: A New Method to Determine the Two Kinematic Axes of Rotation for the Tibio-Femoral Joint

The tibio-femoral joint has been mechanically approximated with two fixed kinematic axes of rotation, the longitudinal rotational (LR) axis in the tibia and the flexion-extension (FE) axis in the femur. The mechanical axis finder developed by Hollister et al. (1993, “The Axes of Rotation of the Knee,” Clin. Orthop. Relat. Res., 290, pp. 259–268) identified the two fixed axes but the visual-based alignment introduced errors in the method. Therefore, the objectives were to develop and validate a new axis finding method to identify the LR and FE axes which improves on the error of the mechanical axis finder. The virtual axis finder retained the concepts of the mechanical axis finder but utilized a mathematical optimization to identify the axes. Thus, the axes are identified 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 validation used virtual simulations of 3D video-based motion analysis to create relative motion between the femur and tibia during pure internal-external rotation, and flexion-extension with coupled internal-external rotation. The simulations modeled tibio-femoral joint kinematics and incorporated 1 mm of random measurement error. The root mean squared errors (RMSEs) in identifying the position and orientation of the LR and FE axes with the virtual axis finder were 0.45 mm and 0.20 deg, and 0.11 mm and 0.20 deg, respectively. These errors are at least two times better in position and seven times better in orientation than those of the mechanical axis finder. Variables, which were considered a potential source of variation between joints and/or measurement systems, were tested for their sensitivity to the RMSE of identifying the axes. Changes in either the position or orientation of a rotational axis resulted in high sensitivity to translational RMSE (6.8 mm of RMSE per mm of translation) and rotational RMSE (1.38 deg of RMSE per degree of rotation), respectively. Notwithstanding these high sensitivities, corresponding errors can be reduced by segmenting the range of motion into regions where changes in either position or orientation are small. The virtual axis finder successfully increased the accuracy of the mechanical axis finder when the axes of motion are fixed with respect to the bones, but must be used judiciously in applications which do not have fixed axes of rotation.