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

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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.

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Acknowledgements

The work by CBT is supported by the Botswana International University of Science and Technology under the Grant DVC/RDI/2/1/16I (25). I thank the Kavli Institute for Theoretical Physics (KITP), University of California Santa Barbara (USA), where this work was supported in part by the National Science Foundation Grant No. NSF PHY-1748958, NIH Grant No. R25GM067110, and the Gordon and Betty Moore Foundation Grant No. 2919.01.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana

    Conrad B. Tabi & Timoléon C. Kofané

  2. Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

    Armand S. Etémé

  3. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

    Timoléon C. Kofané

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  1. Conrad B. Tabi
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Tabi, C.B., Etémé, A.S. & Kofané, T.C. Unstable cardiac multi-spiral waves in a FitzHugh–Nagumo soliton model under magnetic flow effect. Nonlinear Dyn 100, 3799–3814 (2020). https://doi.org/10.1007/s11071-020-05750-z

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