Neural Network Modeling Of Electrically Stimulated Muscle Under Non-Isometric Conditions

This paper is concerned with developing a force-generating model of electrically stimulated muscle under non-isometric condition. Hill-based muscle models have been the most popular structure. This type of muscle model was constructed as a combination of different independent blocks (i.e., activation dynamics, force-length and force-velocity relations, and series elastic element). The model assumes that the force-length and the force-velocity relations are uncoupled from the activation dynamics. However, some studies suggest that the shapes of the active force-length and the active force-velocity curves change with the level of the activation. Moreover, the "active state" block of the Hill-type model has no physical interpretation. To overcome the limitation of the Hill-type model, we used the multilayer perceptron (MLP) with back-propagation learning algorithm and Radial Basis Function (RBF) network with stochastic gradient learning rule for muscle modeling, where the stimulation signal, muscle length, velocity of length perturbation, and past measured or predicted force constitute the input of the neural model, and the predicted force is the output. Two modes of network operation are of interest: a time-varying network which allows updating the parameters of network to continue after convergence, and a time-invariant neural network with parameters fixed after convergence. The results show that time-varying and time-invariant neural networks would be able to track the muscle force with accuracy up to 99.5% and 95%, respectively. In addition, the results show that the accuracy of muscle force prediction depends on the structure of neural network. The prediction accuracy of RBF network after 1000 training epochs is higher than that of MLP network after 5000 training epochs.