Cargando…
Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study
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 th...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2020
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7242278/ https://www.ncbi.nlm.nih.gov/pubmed/32399790 http://dx.doi.org/10.1007/s10827-020-00746-5 |
_version_ | 1783537211299332096 |
---|---|
author | Erhardt, André H. Mardal, Kent-Andre Schreiner, Jakob E. |
author_facet | Erhardt, André H. Mardal, Kent-Andre Schreiner, Jakob E. |
author_sort | Erhardt, André H. |
collection | PubMed |
description | 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. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s10827-020-00746-5) contains supplementary material, which is available to authorized users. |
format | Online Article Text |
id | pubmed-7242278 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-72422782020-06-03 Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study Erhardt, André H. Mardal, Kent-Andre Schreiner, Jakob E. J Comput Neurosci Article 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. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s10827-020-00746-5) contains supplementary material, which is available to authorized users. Springer US 2020-05-12 2020 /pmc/articles/PMC7242278/ /pubmed/32399790 http://dx.doi.org/10.1007/s10827-020-00746-5 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Erhardt, André H. Mardal, Kent-Andre Schreiner, Jakob E. Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study |
title | Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study |
title_full | Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study |
title_fullStr | Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study |
title_full_unstemmed | Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study |
title_short | Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study |
title_sort | dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: a mathematical and numerical study |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7242278/ https://www.ncbi.nlm.nih.gov/pubmed/32399790 http://dx.doi.org/10.1007/s10827-020-00746-5 |
work_keys_str_mv | AT erhardtandreh dynamicsofaneurongliasystemtheoccurrenceofseizuresandtheinfluenceofelectroconvulsivestimuliamathematicalandnumericalstudy AT mardalkentandre dynamicsofaneurongliasystemtheoccurrenceofseizuresandtheinfluenceofelectroconvulsivestimuliamathematicalandnumericalstudy AT schreinerjakobe dynamicsofaneurongliasystemtheoccurrenceofseizuresandtheinfluenceofelectroconvulsivestimuliamathematicalandnumericalstudy |