An optimization algorithm for human joint angle time-history generation using external force data

A mathematical model is presented that estimates joint kinematics and kinetics using measured external resultant loads and readily available parameters. The musculo-skeletal system was represented by a planar three degrees of freedom open kinematic chain. Information extraction was limited to the flexion-extension function of ankle, knee, and hip during quasi-planar motor tasks. Starting from plausible first approximation kinematics, other kinematic functions are iteratively generated by an optimization algorithm and corresponding ground reaction loads are calculated through inverse dynamics. Kinematic coordinates are represented using B-splines and modified by manipulating the control points. The iterative procedure stops and provides the final kinematic and kinetic estimates when a similarity criterion between estimated and measured ground reaction components is satisfied. The model structure was elaborated upon and the algorithm parameters optimized for robustness and accuracy using a benchmark motion in a simulation exercise. The maximal root mean square difference over time between estimated and benchmark quantities was approximately 1% of the peak to peak value for ground reaction components and intersegmental couples, and 6% for joint angles.