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DINAME2019
DINAME2019
Bifurcations from normal functioning to pathologies in heart rhythm dynamics using a three-coupled oscillator model
Submission Author:
Tiago Leite Pereira , DF , Brazil
Co-Authors:
Tiago Leite Pereira , Aline Souza de Paula, Augusto Luiz Cheffer de Melo, Marcelo Savi
Presenter: Tiago Leite Pereira
doi://10.26678/ABCM.DINAME2019.DIN2019-0151
Abstract
Heart functioning is a rich multiphysics problem involving muscular contractions, electric impulses and blood flows. Heart performs an essential physiological role and, due to that, several mathematical models were developed to describe and reproduce its behavior. Some of these models are related to the electrical impulse of the cardiac rhythm. The muscular contraction is accomplished by the Action Potential (AC), generated in the sinoatrial node, which spreads to the atrioventricular node and later to the His-Purkinje complex. Electrocardiogram (ECG) is a typical cardiac measu- rement that monitors depolarization and repolarization of the muscular cells. This paper investigates cardiac dynamics employing a model composed by three oscillators coupled by time delayed terms. Numerical simulations are carried out showing normal and pathological functioning, reproducing ECGs. Among pathological behaviors, simulations show atrial flutter, atrial fibrillation, ventricular flutter and atrial fibrillation. Nonlinear tools are employed to analyze system dynamics including Poincaré map, constructed by defining a proper plane in phase space, and Lyapunov exponents that are used to classify each behavior. Bifurcation diagrams are built showing the route from normal functioning to pathological ones.
Keywords
Nonlinear Dynamic, Cardiac Model, Chaotic Response, Fibrillation, Flutter
