Axial Rotation of the Lower Limb Under Torsional Loading: II. Parameter Identification of a Dynamic System Model

In Part I of this two-part article, experiments that measured the response of the lower limb to dynamic, transient torsional loading applied at the boot/foot were described. Test variables included rotation direction, weight bearing, and joint flexion. For one of the three subjects tested, two approaches were explored for specifying parameters (that is, inertia, damping, stiffness) of a three-degree-of-freedom dynamic system model which best duplicated the measured response. One approach involved identification of linear parameters by means of optimization; the other approach entailed estimation. Parameter estimates, which included nonlinear, asymmetric stiffness functions, were derived from the literature. For both approaches, the efficacy of parameters was evaluated in terms of the resulting model's ability to duplicate the measured joint axial rotation. The optimization was undertaken to identify parameter dependence on test variables. Results indicate that, to a degree, parameter values are influenced by test variables. Results also indicate that the nonlinear, estimated model better approximates the experimental data than the linear, identified model.

In addition to identifying parameters of a three-degree-of-freedom model, parameters were also identified for a single-degree-of-freedom model where the motion variable was intended to indicate the rotation of the in vivo knee. It is concluded that the simpler model offers good accuracy in predicting both magnitude and time of occurrence of peak knee axial rotations. Model motion fails to track the measured knee rotation subsequent to the peak, however.