Unstable cardiac multi-spiral waves in a FitzHugh–Nagumo soliton model under magnetic flow effect

Conrad B. Tabi, Armand S. Etémé, Timoléon C. Kofané

Research output: Contribution to journalArticle

Abstract

This work deals with the stimulation of cardiac spiral waves in a two-dimensional FitzHugh–Nagumo model through modulational instability phenomenon in the presence of intracellular magnetic flux. The nonlinear generic model is firstly transformed into a two-dimensional complex Ginzburg–Landau equation with a small real damping term. Then, the latter is explored to perform the linear stability analysis and some modulational instability properties are derived and found to be modified with the change of either the magnetic coupling strength or the diffusion coefficient which are set as the control parameters. The bifurcation theory analysis is numerically performed, and the range of values of the stimulation parameter for which firing patterns emerge in cardiac media is well estimated. The recording of membrane potential as well as the magnetic flux as functions of time or spatial coordinates allows to picture some features such as time series, phase portraits and spatial patterns of membrane potential. As a result, diamond-shaped, squared-shaped and spiral-shaped waves are obtained. An elimination process of multi-spiral waves is proposed by exposing such patterns to an external magnetic flux. Thus, for suited values of parameters, the cardiac spiral waves are transmuted into target waves which obviously protect heart against harmful attacks such as ventricular tachycardia and fibrillation. Our results suggest that uncontrolled electromagnetic induction within cardiac tissue may be considered as the principal source of many heart injuries which are the first cause of mortality in the industrial world.

Original languageEnglish
JournalNonlinear Dynamics
DOIs
Publication statusAccepted/In press - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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