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Open AccessArticle

Early Afterdepolarisations Induced by an Enhancement in the Calcium Current

Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway
Processes 2019, 7(1), 20; https://doi.org/10.3390/pr7010020
Received: 20 November 2018 / Revised: 20 December 2018 / Accepted: 29 December 2018 / Published: 4 January 2019
(This article belongs to the Special Issue Methods in Computational Biology)
Excitable biological cells, such as cardiac muscle cells, can exhibit complex patterns of oscillations such as spiking and bursting. Moreover, it is well known that an enhancement in calcium currents may yield certain kind of cardiac arrhythmia, so-called early afterdepolarisations (EADs). The presence of EADs strongly correlates with the onset of dangerous cardiac arrhythmia. In this paper we study mathematically and numerically the dynamics of a cardiac muscle cell with respect to the calcium current by investigating a simplistic system of differential equations. For the study of this phenomena, we use bifurcation theory, numerical bifurcation analysis, geometric singular perturbation theory and computational methods to investigate a nonlinear multiple time scales system. It will turn out that EADs related to an enhanced calcium current are canard–induced and that we have to combine these theories to derive a better understanding of the dynamics behind EADs. Moreover, a suitable time scale separation argument determines the important and sensitive system parameters which are related to the occurrence of EADs. View Full-Text
Keywords: nonlinear dynamics; multiple time scales; geometric singular perturbation theory; bifurcation analysis; canard-induced EADs; calcium current nonlinear dynamics; multiple time scales; geometric singular perturbation theory; bifurcation analysis; canard-induced EADs; calcium current
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Erhardt, A.H. Early Afterdepolarisations Induced by an Enhancement in the Calcium Current. Processes 2019, 7, 20.

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