Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli : A mathematical and numerical study
| Autor: | Kent-Andre Mardal, André H. Erhardt, Jakob Schreiner |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Potassium Channels
Cognitive Neuroscience Models Neurological Electroencephalography Article Cellular and Molecular Neuroscience symbols.namesake Seizures medicine Humans Bifurcation theory Nernst equation Computer Simulation Monodomain model Physics Neurons Electroshock medicine.diagnostic_test Dynamics (mechanics) Bidomain model Neuron–glia cell system Models Theoretical Seizure Sensory Systems Ordinary differential equation Nonlinear dynamics symbols Potassium Cellular model Reduction (mathematics) Biological system Extracellular Space Neuroglia Monodomain and bidomain model Algorithms Electroconvulsive therapy (ECT) |
| Zdroj: | Journal of Computational Neuroscience |
| ISSN: | 1573-6873 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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