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Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations

Author

Listed:
  • Roberto Barrio

    (IUMA and Departamento Matemática Aplicada, University of Zaragoza, E-50009 Zaragoza, Spain)

  • M. Angeles Martínez

    (IUMA and Departamento Matemática Aplicada, University of Zaragoza, E-50009 Zaragoza, Spain)

  • Lucía Pérez

    (Departamento Matemáticas, University of Oviedo, E-33007 Oviedo, Spain)

  • Esther Pueyo

    (I3A, University of Zaragoza, IIS Aragón and CIBER-BBN, E-50018 Zaragoza, Spain)

Abstract

In this study, we teased out the dynamical mechanisms underlying the generation of arrhythmogenic early afterdepolarizations (EADs) in a three-variable model of a mammalian ventricular cell. Based on recently published studies, we consider a 1-fast, 2-slow variable decomposition of the system describing the cellular action potential. We use sweeping techniques, such as the spike-counting method, and bifurcation and continuation methods to identify parametric regions with EADs. We show the existence of isolas of periodic orbits organizing the different EAD patterns and we provide a preliminary classification of our fast–slow decomposition according to the involved dynamical phenomena. This investigation represents a basis for further studies into the organization of EAD patterns in the parameter space and the involved bifurcations.

Suggested Citation

  • Roberto Barrio & M. Angeles Martínez & Lucía Pérez & Esther Pueyo, 2020. "Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:880-:d:365868
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    Cited by:

    1. Song, Jian & Liu, Shenquan & Wen, Qixiang, 2022. "Geometric analysis of the spontaneous electrical activity in anterior pituitary corticotrophs," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Ricardo López-Ruiz, 2022. "Mathematical Biology: Modeling, Analysis, and Simulations," Mathematics, MDPI, vol. 10(20), pages 1-2, October.

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