Knee Joint Secondary Motion Accuracy Improved by Quaternion-Based Optimizer With Bony Landmark Constraints

Skin marker-based motion analysis has been widely used in biomechanical studies and clinical applications. Unfortunately, the accuracy of knee joint secondary motions is largely limited by the nonrigidity nature of human body segments. Numerous studies have investigated the characteristics of soft tissue movement. Utilizing these characteristics, we may improve the accuracy of knee joint motion measurement. An optimizer was developed by incorporating the soft tissue movement patterns at special bony landmarks into constraint functions. Bony landmark constraints were assigned to the skin markers at femur epicondyles, tibial plateau edges, and tibial tuberosity in a motion analysis algorithm by limiting their allowed position space relative to the underlying bone. The rotation matrix was represented by quaternion, and the constrained optimization problem was solved by Fletcher’s version of the Levenberg–Marquardt optimization technique. The algorithm was validated by using motion data from both skin-based markers and bone-mounted markers attached to fresh cadavers. By comparing the results with the ground truth bone motion generated from the bone-mounted markers, the new algorithm had a significantly higher accuracy (root-mean-square (RMS) error: $0.7±0.1deg$ in axial rotation and $0.4±0.1deg$ in varus-valgus) in estimating the knee joint secondary rotations than algorithms without bony landmark constraints (RMS error: $1.7±0.4deg$ in axial rotation and $0.7±0.1deg$ in varus-valgus). Also, it predicts a more accurate medial-lateral translation (RMS error: $0.4±0.1mm$⁠) than the conventional techniques (RMS error: $1.2±0.2mm$⁠). The new algorithm, using bony landmark constrains, estimates more accurate secondary rotations and medial-lateral translation of the underlying bone.