2019
DOI: 10.3390/pr7010020
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Early Afterdepolarisations Induced by an Enhancement in the Calcium Current

Abstract: 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 inve… Show more

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Cited by 10 publications
(10 citation statements)
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“…But this approach does not necessarily explain the complete behaviour of the system, cf. Erhardt (2019). However, our aim is to study the full system and its behaviour using numerical bifurcation analysis as in Erhardt (2018) and Tsaneva-Atanasova et al (2010).…”
Section: Introductionmentioning
confidence: 99%
“…But this approach does not necessarily explain the complete behaviour of the system, cf. Erhardt (2019). However, our aim is to study the full system and its behaviour using numerical bifurcation analysis as in Erhardt (2018) and Tsaneva-Atanasova et al (2010).…”
Section: Introductionmentioning
confidence: 99%
“…Finally, we address how and where EADs are created. Although the detailed process of EAD development is an open problem in the literature, some new dynamical system explanations have been recently introduced using low-dimensional models [16][17][18]39,45,46 where a new fast-slow decomposition of the models (two-slow one-fast rather than two-fast one-slow) allows to identify the key role of maximal canards on the creation of EADs (for more details on canard generation and theory, see Refs. 16, 17, and 39).…”
Section: Articlementioning
confidence: 99%
“…The main issue with several of the cardiac models of the form (1), from a mathematical point of view, is the requirement of a sufficiently smooth and regular ODE system in order to utilise theory such as bifurcation analysis. Bifurcation theory has already been widely utilised to investigate the dynamics of cardiac muscle cell models, see [18][19][20][21][22][23][24][25][26]. However, many of the existing detailed models are not smooth enough for the theory to be applied, see for example [27].…”
Section: On Modelling Cardiac Action Potentials and Related Issuesmentioning
confidence: 99%