Nonlinear identification of stretch reflex dynamics

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Abstract
The objective of this study was to use nonlinear identification techniques to study the dynamics of stretch reflexes in the human calf muscles (gastrocnemius-soleus). Stochastic perturbations of ankle position were applied while subjects maintained a constant, tonic contraction of gastrocnemius-soleus. Linear models of the relation between ankle velocity and the electromyographic (EMG) activity under these conditions typically accounted for less than 40% of the observed EMG variance. Nonlinear system identification techniques were then applied. The first- and second-order Wiener kernels were computed as the initial stage of this analysis. These did not provide an adequate description of system behavior; subsequent simulation studies showed that the major problem with the Wiener analysis was that the input spectrum was not adequately white. Nevertheless, the shape of the second-order Wiener kernel suggested that a Hammerstein structure consisting of a static nonlinearity followed by a dynamic linear system would be appropriate. Consequently, we used an iterative procedure for Hammerstein system identification to determine the form of the static nonlinearity and the associated linear dynamics. The resulting nonlinear model provided a much better description of the system's behavior than did the linear models (variance accounted for>60%). Furthermore, they confirmed our previous empirical findings; the static nonlinearity closely resembled a half-wave rectifier while the dynamics were typified by a pure delay and a velocity filter. The application of nonlinear identification techniques thus produced a much improved, physically meaningful model of stretch reflex behavior.

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