Mechanisms underlying a third-order parametric model of dynamic reflex stiffness

A parallel-cascade system identification method was used to identify the reflex contribution to dynamic ankle stiffness in both normal and spastic spinal cord injured (SCI) subjects. Reflex dynamics were estimated by the impulse response function between half-wave rectified velocity and reflex torque. Parametric models were fitted to these IRFs using non-linear, least-squares methods. A simple, second-order low-pass model described reflex dynamic stiffness well for normal subjects at low contraction levels. However, this model was inadequate for normal subjects, at high contraction levels, and for SCI subjects at all contraction levels. Good fits were obtained using a third-order model consisting of a second-order low-pass in series with a first order pole. We hypothesized that the third order model might arise from a “clonus-like” reflex activation that comprised several distinct bursts of activity. Simulation studies showed that this pattern of reflex activation in series with muscle dynamics gave an overall response which was described very well by a third order model. Sensitivity studies demonstrated the systematic dependence of the parameters of the third-order model on the interval between bursts of activation and their decay