Nonlinear Dynamic Waves In Electromechanical Excitable Biological Media
Free (open access)
R. N. Miftakhov & M. W. Vannier
A mathematical model of electromechanical conjugation in a longitudinal smooth muscle layer of the gut is formulated. The general assumptions of the model are based on electrophysiological and mechanical experimental data demonstrating slow oscillatory activity (at the resting state) and spiking activity (at the excited state) with concurrent development of active forces of contraction-relaxation. The myogenic syncytium is considered as a continuum of weakly connected oscillators. Strong connections among oscillators are provided by an intermittent fast propagating wave of depolarization along the syncytium. The description of electrical behavior of each oscillator is based on Hodgkin-Huxley formalism. Electromechanical coupling concludes intracellular calcium dependent mechanisms of force generation. Passive relaxation forces are mainly due to the elastic properties of the collagen and elastin fibers. The dynamics of the propagating nonlinear electromechanical wave of contraction-relaxation is studied numerically. The results demonstrate good qualitative and quantitative agreement with the results of physiological experiments.