### Abstract

Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant—at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

Original language | English (US) |
---|---|

Article number | 27 |

Journal | Frontiers in Computational Neuroscience |

Volume | 11 |

DOIs | |

State | Published - Apr 24 2017 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cable equation
- Ephaptic coupling
- Extracellular potential
- Membrane potentials
- Numerical modeling

### ASJC Scopus subject areas

- Neuroscience (miscellaneous)
- Cellular and Molecular Neuroscience

### Cite this

*Frontiers in Computational Neuroscience*,

*11*, [27]. https://doi.org/10.3389/fncom.2017.00027

**An evaluation of the accuracy of classical models for computing the membrane potential and extracellular potential for neurons.** / Tveito, Aslak; Jæger, Karoline H.; Lines, Glenn T.; Paszkowski, Łukasz; Sundnes, Joakim; Edwards, Andrew G.; Māki-Marttunen, Tuomo; Halnes, Geir; Einevoll, Gaute T.

Research output: Contribution to journal › Article

*Frontiers in Computational Neuroscience*, vol. 11, 27. https://doi.org/10.3389/fncom.2017.00027

}

TY - JOUR

T1 - An evaluation of the accuracy of classical models for computing the membrane potential and extracellular potential for neurons

AU - Tveito, Aslak

AU - Jæger, Karoline H.

AU - Lines, Glenn T.

AU - Paszkowski, Łukasz

AU - Sundnes, Joakim

AU - Edwards, Andrew G.

AU - Māki-Marttunen, Tuomo

AU - Halnes, Geir

AU - Einevoll, Gaute T.

PY - 2017/4/24

Y1 - 2017/4/24

N2 - Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant—at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

AB - Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant—at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

KW - Cable equation

KW - Ephaptic coupling

KW - Extracellular potential

KW - Membrane potentials

KW - Numerical modeling

UR - http://www.scopus.com/inward/record.url?scp=85018366333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018366333&partnerID=8YFLogxK

U2 - 10.3389/fncom.2017.00027

DO - 10.3389/fncom.2017.00027

M3 - Article

AN - SCOPUS:85018366333

VL - 11

JO - Frontiers in Computational Neuroscience

JF - Frontiers in Computational Neuroscience

SN - 1662-5188

M1 - 27

ER -