Control of Bifurcations of Skeletal Muscle Model Using Washout Filters in Periodic Paralysis and Myotonia Patients

Abstract

Abnormalities in the channels on the skeletal membrane are related to the tubular concentration of potassium and the proportion of non-inactivating sodium channels. In this work, we studied the muscle model approach to inherited disorders of channels. The muscle model was modified by reformulating the sodium current term in T-tubule membrane compartments. We investigated the stability criterion on the existence of bifurcation of the modified muscle model. The tubular concentration of potassium and the proportion of non-inactivating sodium channels are designated as the bifurcation parameters. To recover the ion channel disorder, the conditions of control for Hopf bifurcation in the muscle system were derived by using the Routh–Hurwitz theorem. We also designed a bifurcation controller in order to avoid instability in the muscle system at the bifurcation point. We added the linear controller in the method of washout filter to the muscle system. This study may have important clinical implications since some undesirable neural oscillations are very threatening as they occur in patients.