### Abstract

A one‐dimensional numerical model of potassium dynamics in the central nervous system is developed. The model incorporates the following physiological processes in computing spatial and temporal changes in extracellular K^{+} concentration, [K^{+}]_{o}: (1) the release of K^{+} from K^{+} sources into extracellular space, (2) diffusion of K^{+} through extracellular space, (3) active uptake of K^{+} into cells and blood vessels, (4) passive uptake of K^{+} into a cellular distribution space, and (5) the transfer of K^{+} by K^{+} spatial buffer current flow in glial cells. The following tissue parameters can be specified along the single spatial dimension of the model: (1) the volume fraction and tortuosity of extracellular and glial cell spaces, (2) the volume fraction of the cellular distribution space, (3) rate constants of active uptake and passive uptake processes, and (4) glial cell membrane conductance. The model computes variations in [K^{+}]_{o} and current flow through glial cells for three tissue geometries: (1) planar geometry (the retina and the surface of the brain), (2) cylindrical geometry (tissue surrounding a blood vessel), and (3) spherical geometry (tissue surrounding a point source of K^{+}). For simple sources of K^{+}, the performance of the model matches that predicted from analytical equations. Simulations of previous ion dynamics experiments indicate that the model can accurately predict ion diffusion and K^{+} current flow in the brain. Simulations of electroretinogram generation and K^{+} siphoning onto blood vessels suggest that unanticipated K^{+} dynamics mechanisms may be operating in the central nervous system.

Original language | English (US) |
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Pages (from-to) | 198-210 |

Number of pages | 13 |

Journal | Glia |

Volume | 1 |

Issue number | 3 |

DOIs | |

State | Published - 1988 |

### Keywords

- Astrocytes
- Computer model
- Glial cells
- Ion diffusion
- Potassium homeostasis
- Potassium spatial buffering

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## Cite this

*Glia*,

*1*(3), 198-210. https://doi.org/10.1002/glia.440010305