Fatigue and Non-Fatigue Mathematical Muscle Models During Functional Electrical Stimulation of Paralyzed Muscle

Electrical muscle stimulation demonstrates potential for restoring functional movement and for preventing muscle atrophy after spinal cord injury (SCI). To optimize delivery of electrical stimulation protocols, an accurate and easy-to-implement mathematical skeletal muscle model is essential. The existing models are either accurate but complex, making them hard to implement, such as the Hill-Huxley-type model, or simple but inaccurate, such as second order model. In this paper, we propose a Wiener-Hammerstein system to model the paralyzed skeletal muscle dynamics under electrical stimulus conditions. The proposed model has substantial advantages in identification algorithm analysis and implementation including computational complexity and convergence. Experimental data sets were collected on soleus muscles under 15 Hz frequency stimulation for fourteen subjects with SCI. 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.