Early Afterdepolarisations Induced by an Enhancement in the Calcium Current

Erhardt, André H.

doi:10.3390/pr7010020

Cited by 9 publications

(10 citation statements)

References 36 publications

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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%

Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli

2020

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In this paper, we investigate the dynamics of a neuron-glia cell system and the underlying mechanism for the occurrence of seizures. For our mathematical and numerical investigation of the cell model we will use bifurcation analysis and some computational methods. It turns out that an increase of the potassium concentration in the reservoir is one trigger for seizures and is related to a torus bifurcation. In addition, we will study potassium dynamics of the model by considering a reduced version and we will show how both mechanisms are linked to each other. Moreover, the reduction of the potassium leak current will also induce seizures. Our study will show that an enhancement of the extracellular potassium concentration, which influences the Nernst potential of the potassium current, may lead to seizures. Furthermore, we will show that an external forcing term (e.g. electroshocks as unidirectional rectangular pulses also known as electroconvulsive therapy) will establish seizures similar to the unforced system with the increased extracellular potassium concentration. To this end, we describe the unidirectional rectangular pulses as an autonomous system of ordinary differential equations. These approaches will explain the appearance of seizures in the cellular model. Moreover, seizures, as they are measured by electroencephalography (EEG), spread on the macro-scale (cm). Therefore, we extend the cell model with a suitable homogenised monodomain model, propose a set of (numerical) experiment to complement the bifurcation analysis performed on the single-cell model. Based on these experiments, we introduce a bidomain model for a more realistic modelling of white and grey matter of the brain. Performing similar (numerical) experiment as for the monodomain model leads to a suitable comparison of both models. The individual cell model, with its seizures explained in terms of a torus bifurcation, extends directly to corresponding results in both the monodomain and bidomain models where the neural firing spreads almost synchronous through the domain as fast traveling waves, for physiologically relevant paramenters. Keywords Nonlinear dynamics • Bifurcation theory • Neuron-glia cell system • Monodomain and bidomain model • Seizure • Electroconvulsive therapy (ECT) JS was supported by RCN no.273077.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli

2020

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“…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%

Dynamical analysis of early afterdepolarization patterns in a biophysically detailed cardiac model

Barrio

Martínez

Pueyo

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Arrhythmogenic early afterdepolarizations (EADs) are investigated in a biophysically detailed mathematical model of a rabbit ventricular myocyte, providing their location in the parameter phase space and describing their dynamical mechanisms. Simulations using the Sato model, defined by 27 state variables and 177 parameters, are conducted to generate electrical action potentials (APs) for different values of the pacing cycle length and other parameters related to sodium and calcium concentrations. A detailed study of the different AP patterns with or without EADs is carried out, showing the presence of a high variety of temporal AP configurations with chaotic and quasiperiodic behaviors. Regions of bistability are identified and, importantly, linked to transitions between different behaviors. Using sweeping techniques, one-, two-, and three-parameter phase spaces are provided, allowing ascertainment of the role of the selected parameters as well as location of the transition regions. A Devil's staircase, with symbolic sequence analysis, is proposed to describe transitions in the ratio between the number of voltage (EAD and AP) peaks and the number of APs. To conclude, the obtained results are linked to recent studies for low-dimensional models and a conjecture is made for the internal dynamical structure of the transition region from non-EAD to EAD behavior using fold and cusp bifurcations and maximal canards.

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“…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%

Analysis and simulation of a modified cardiac cell model givesaccurate predictions of the dynamics of the original one

Erhardt¹,

Solem²

2021

Preprint

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The 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to be a good approximation of the original one. As a consequence, one can extract fairly precise predictions of the behaviour of the original model from the bifurcation analysis of the modified model. Thus, the findings of bifurcations linked to complex dynamics in the modified model -like early afterdepolarisations (EADs), which can be precursors to cardiac death -predicts the occurrence of the same dynamics in the original model. It is shown that bifurcations linked to EADs in the modified model accurately predicts EADs in the original model at the single cell level. Finally, these bifurcations are linked to cardiac death at the tissue level by example.

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Early Afterdepolarisations Induced by an Enhancement in the Calcium Current

Cited by 9 publications

References 36 publications

Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli

Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli

Dynamical analysis of early afterdepolarization patterns in a biophysically detailed cardiac model

Analysis and simulation of a modified cardiac cell model givesaccurate predictions of the dynamics of the original one

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