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Spiral-generation mechanism in the two-dimensional FitzHugh-Nagumo system

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Abstract

Spiral waves are a mathematical concept that organizes spatio-temporal dynamics in dissipative, spatially extended biological, physical and chemical systems. They support a variety of important phenomena, such as re-entrant cardiac arrhythmias and spatial patterns in chemical reactions. In this paper we consider a two-dimensional (2D) disturbance wave that can make the pulse wave travel around the disturbance and generate a self-sustaining spiral wave. The use of a region temporarily refractory as a disturbance in format wave is a novel mechanism for generating activity in spiral shape. In addition, it is robust for a wide variety of refractory areas and geometry shapes. This situation models the appearance of abnormal electrical activity in the heart, where the disturbance is a cardiac tissue in damage. We present a Finite Element Method (FEM) scheme for the two-dimensional FitzHugh-Nagumo (FHN) system to simulate the spiral-generation mechanism in cardiac tissue. This scheme is based on the semi implicit Eyres algorithm and we present some numerical results to demonstrate the effectiveness and usefulness of the present technique.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her comments and suggestions which improved an earlier version of this work.

C. E.Rubio-Mercedes thanks to the Carolina Foundation for the financial support for the academic exchange at the University of Cádiz, Spain. G. Lozada-Cruz thanks to the Fundação de Amparo à Pesquisa do Estado de São Paulo, (FAPESP), grant 2015/24095-6, for the support.

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Authors and Affiliations

  1. Mathematics and Engineering Physics Programs, Mato Grosso do Sul State University (UEMS), Dourados, MS, Brazil

    C. E. Rubio-Mercedes

  2. Institute of Biosciences, Humanities and Exact Sciences, Department of Mathematics, São Paulo State University (UNESP), São José do Rio Preto, SP, 15054-000, Brazil

    G. Lozada-Cruz

  3. Departamento de Matemáticas, Facultad de Ciencias del Mar y Ambientales, Universidad de Cádiz, Puerto Real, 11510, Cádiz, Spain

    F. Ortegón Gallego

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  1. C. E. Rubio-Mercedes
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Correspondence to C. E. Rubio-Mercedes.

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Rubio-Mercedes, C.E., Lozada-Cruz, G. & Gallego, F.O. Spiral-generation mechanism in the two-dimensional FitzHugh-Nagumo system. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00725-1

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