Efficacy of Hammerstein models in capturing the dynamics of isometric muscle stimulated at various frequencies

Abstract

Functional electrical stimulation (FES) can be employed more effectively as a rehabilitation intervention if neuroprosthetic controllers contain muscle models appropriate to the behavioral regimes of interest. The goal of this thesis is to investigate the performance of one such model, the Hammerstein cascade, in describing isometric muscle force. We examine the effectiveness of Hammerstein models in predicting the isometric recruitment curve and dynamics of a muscle stimulated at fourteen frequencies between 1 to 100Hz. Explanted frog plantaris longus muscle is tested at the nominal isometric length only; hence, the muscle's force-length and force-velocity dependences are neither assumed nor ascertained. The pilot data are fitted using ten different models consisting of various combinations of linear dynamics with polynomial nonlinearities. Models identified using data with input stimulation frequencies of 20Hz and lower generate an average RMS error of 12% and are reliably stable (87 of 90 simulations). Between 25 to 40Hz, the average error generated by the estimated models is 10%, but the estimated dynamics are less stable (16 of 30 simulations). Above 40Hz, linear and Hammerstein nonlinear models fail to consistently generate stable dynamic estimates (11 of 30 simulations), and errors are large (eRMs = 44%).

(cont.) Simulations also suggest Hammerstein models found iteratively do not perform much better than linear dynamic systems (in general, eRMS = 10 to 15%). In addition, simulations using iterated nonlinearities generate RMS errors that are comparable to those simulations using a fixed nonlinearity (both about 16%). These preliminary results warrant further investigation into the limits of Hammerstein models found iteratively in the identification of isometric muscle dynamics.