Application of Wiener-Hammerstein system identification in electrically stimulated paralyzed skeletal muscle modeling

Electrical muscle stimulation has demonstrated potential for restoring functional movement and for preventing muscle atrophy after spinal cord injury (SCI). Control systems used to optimize delivery of electrical stimulation protocols depend upon algorithms generated using computational models of paralyzed muscle force output. The existing skeletal muscle models are either not accurate or too complicated to implement for real-time control. In this paper, we propose a Wiener-Hammerstein system, Linear-Saturation-Linear (LSL) model, to model the skeletal muscle dynamics under electrical stimulus conditions. Experimental data from the soleus muscles of an individual with SCI was used to quantify the performance of the model. We demonstrate that the proposed Wiener-Hammerstein system is comparable to, in terms of model fitting, and outperforms, in terms of prediction, the Hill Huxley model, the most advanced and accurate model previously reported. On the other hand, the proposed LSL model is much simpler in terms of the structure and involves a much smaller number of unknown coefficients. This has substantial advantages in identification algorithm analysis and implementation including computational complexity, convergence and also in real time model implementation for control purposes.