A model of cardiac tissue as an excitable medium with two interacting pacemakers having refractory time

Abstract

A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase.

Polynomial Model of Two Interacting Pacemakers Taking into Account the Time of Refractoriness

“…This corresponds to the situation when the limiting behavior of the display depends on the initial phase difference of the oscillators x 0 [6]. For figure 4 the circle map constructed for some values of a and γ is given [6]. It kind of confirms that with increasing γ the system dynamics becomes more complicated, and the display ceases to be monotonous, and it appears the intervals with the slope, a large 1.…”

“…The dynamics of the system thus becomes multistable. This corresponds to the situation when the limiting behavior of the display depends on the initial phase difference of the oscillators x 0 [6]. For figure 4 the circle map constructed for some values of a and γ is given [6].…”

“…assuming in (10) δ = 0. For figure 5a the regions of phase captures in parametric space (a, γ) obtained as a result of numerical investigation are presented [6,8]. In this figure, the color gamut is much richer (visualization was carried out using Matlab R2007b, and the equations were solved using Microsoft Visual Studio C++ 2010 Professional (x64)).…”