Discrete Models of Active Media in Attached to The Activities of Cardiac Arrhythmia

Sergey Belyakin

doi:10.26717/bjstr.2019.22.003764

Abstract

The first theoretical study of cardiac arrhythmias was conducted in 1920-ies of the van - der - Pol and van - der - Mark, who proposed an electrical model of the heart...

Highlights

The first theoretical study of cardiac arrhythmias was conducted in 1920-ies of the van - der - Pol and van - der - Mark, who proposed an electrical model of the heart [1,2]
We draw an analogy between the results and pathological conditions of cardiac tissue
For example, consider the first pulse oscillator phase response curve (PRC), and the second – ABU, it can be found that some stable phase captures correspond to the observed pathologies in clinical practice

Summary

Introduction

The first theoretical study of cardiac arrhythmias was conducted in 1920-ies of the van - der - Pol and van - der - Mark, who proposed an electrical model of the heart [1,2]. For pic. the bifurcation diagram of the circle diffeomorphism on the parameter plane (b, a) is shown This diagram is divided into areas called language (or horns) of Arnold, which correspond to the sustainable capture phase ratio N/M (i.e., N cycles of the stimulator has M cycles of a nonlinear oscillator). It is possible to obtain phase capture regions with a different multiplicity, even at large values of ε and γ, the periodic behavior of the system with a capture of 1:2. Numerical analysis shows that with the growth of ε to a value of ~ 0.5, the area occupied by the resonance zonses becomes larger This leads to almost complete mixing of languages, so that it is possible to detect zones of different multiplicity in a sufficiently small neighborhood of almost any point (a, γ). The main result of this section is quite important for applications: for the systems described by the map (12), there are almost always such external influences, in which such systems will have a prescribed (pre-selected) dynamics

Conclusion

Summary