Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries
Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentia...
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2020-03-01
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doaj-b1ab3ae3967d4a98953241b62fca3d922020-11-25T02:38:28ZengFrontiers Media S.A.Frontiers in Neuroinformatics1662-51962020-03-011410.3389/fninf.2020.00011506706Finite Element Simulation of Ionic Electrodiffusion in Cellular GeometriesAda J. Ellingsrud0Andreas Solbrå1Andreas Solbrå2Gaute T. Einevoll3Gaute T. Einevoll4Gaute T. Einevoll5Geir Halnes6Geir Halnes7Marie E. Rognes8Department for Scientific Computing and Numerical Analysis, Simula Research Laboratory, Oslo, NorwayCentre for Integrative Neuroplasticity, University of Oslo, Oslo, NorwayDepartment of Physics, University of Oslo, Oslo, NorwayCentre for Integrative Neuroplasticity, University of Oslo, Oslo, NorwayDepartment of Physics, University of Oslo, Oslo, NorwayFaculty of Science and Technology, Norwegian University of Life Sciences, Ås, NorwayCentre for Integrative Neuroplasticity, University of Oslo, Oslo, NorwayFaculty of Science and Technology, Norwegian University of Life Sciences, Ås, NorwayDepartment for Scientific Computing and Numerical Analysis, Simula Research Laboratory, Oslo, NorwayMathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modeling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.https://www.frontiersin.org/article/10.3389/fninf.2020.00011/fullfinite elementelectrodiffusionion concentrationscell membraneephaptic couplingKNP-EMI |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ada J. Ellingsrud Andreas Solbrå Andreas Solbrå Gaute T. Einevoll Gaute T. Einevoll Gaute T. Einevoll Geir Halnes Geir Halnes Marie E. Rognes |
spellingShingle |
Ada J. Ellingsrud Andreas Solbrå Andreas Solbrå Gaute T. Einevoll Gaute T. Einevoll Gaute T. Einevoll Geir Halnes Geir Halnes Marie E. Rognes Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries Frontiers in Neuroinformatics finite element electrodiffusion ion concentrations cell membrane ephaptic coupling KNP-EMI |
author_facet |
Ada J. Ellingsrud Andreas Solbrå Andreas Solbrå Gaute T. Einevoll Gaute T. Einevoll Gaute T. Einevoll Geir Halnes Geir Halnes Marie E. Rognes |
author_sort |
Ada J. Ellingsrud |
title |
Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries |
title_short |
Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries |
title_full |
Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries |
title_fullStr |
Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries |
title_full_unstemmed |
Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries |
title_sort |
finite element simulation of ionic electrodiffusion in cellular geometries |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Neuroinformatics |
issn |
1662-5196 |
publishDate |
2020-03-01 |
description |
Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modeling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting. |
topic |
finite element electrodiffusion ion concentrations cell membrane ephaptic coupling KNP-EMI |
url |
https://www.frontiersin.org/article/10.3389/fninf.2020.00011/full |
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