Estimation of the gain and threshold of the stretch reflex with a novel subspace identification algorithm

Reflex stiffness is often modeled as a Hammerstein system comprising a cascade of a static nonlinear element and a linear dynamic element. The nonlinearity is frequently modeled as a half wave rectifier so that changes in the reflex response can only be modeled by changes in the parameters of the linear element. This is an oversimplification since there are physiological mechanisms that could change both the threshold of the nonlinearity and the linear dynamics. This study explores the ability of a new subspace identification algorithm to distinguish changes in parameters of the nonlinear element from those of the linear element. Simulation studies demonstrate that the method does so very effectively even in the presence of substantial output noise. Pilot experiments in which the method was applied to stretch reflex EMG data revealed that both the threshold of the nonlinearity and the gain of the linear element change with muscle activation.