Bifurcation analysis of a certain Hodgkin-Huxley model depending on multiple bifurcation parameters
type: Item
instance of: scholarly article
title: Bifurcation analysis of a certain Hodgkin-Huxley model depending on multiple bifurcation parameters
zbMATH Open document ID: 1407.37120
author: André H. Erhardt
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: In this paper, we study the dynamics of a certain Hodgkin-Huxley model describing the action potential (AP) of a cardiac muscle cell for a better understanding of the occurrence of a special type of cardiac arrhythmia, the so-called early afterdepolarisations (EADs). EADs are pathological voltage oscillations during the repolarisation or plateau phase of cardiac APs. They are considered as potential precursors to cardiac arrhythmia and are often associated with deficiencies in potassium currents or enhancements in the calcium or sodium currents, e.g., induced by ion channel diseases, drugs or stress. Our study is focused on the enhancement in the calcium current to identify regions, where EADs related to enhanced calcium current appear. To this aim, we study the dynamics of the model using bifurcation theory and numerical bifurcation analysis. Furthermore, we investigate the interaction of the potassium and calcium current. It turns out that a suitable increasing of the potassium current adjusted the EADs related to an enhanced calcium current. Thus, one can use our result to balance the EADs in the sense that an enhancement in the potassium currents may compensate the effect of enhanced calcium currents.
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 92B05
zbMATH DE Number: 6994634
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: bifurcation analysis
zbMATH Keywords: ion current interactions
describes a project that uses: MATCONT
MaRDI profile type: Publication
full work available at URL: math6060103
OpenAlex ID: W2808130444
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Wikidata QID: Q129683651
DOI: 10.3390/MATH6060103
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description: scientific article; zbMATH DE number 6994634