Fatigue and non-fatigue mathematical muscle models during functional electrical stimulation of paralyzed muscle

Electrical muscle stimulation demonstrates potential for preventing muscle atrophy and for restoring functional movement after spinal cord injury (SCI). Control systems used to optimize delivery of electrical stimulation protocols depend upon the algorithms generated using computational models of paralyzed muscle force output. The Hill-Huxley-type model, while being highly accurate, is also very complex, making it difficult for real-time implementation. In this paper, we propose a Wiener-Hammerstein system to model the paralyzed skeletal muscle under electrical stimulus conditions. The proposed model has substantial advantages in identification algorithm analysis and implementation including computational complexity and convergence, which enable it to be used in real-time model implementation. Experimental data sets from the soleus muscles of fourteen subjects with SCI were collected and tested. The simulation results show that the proposed model outperforms the Hill-Huxley-type model not only in peak force prediction, but also in fitting performance for force output of each individual stimulation train.