Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue.

Geir Halnes,Daniel Keller,Ole A Andreassen,Klas H Pettersen,Gaute T Einevoll,Tuomo Mäki-Marttunen

doi:10.1371/journal.pcbi.1005193

Abstract

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

Highlights

The number of ions exchanged between neurons and the extracellular space (ECS) during a brief period of activity is typically too small to evoke significant changes in extracellular ion concentrations
When electrical potentials are measured in the extracellular space (ECS) of the brain, they are interpreted as a signature of neural signalling
We present a new computational model which explicitly models ion-concentration dynamics in the ECS surrounding a neural population, and which allows us to quantify the effect that diffusive currents have on the ECS potential

Summary

Introduction

The number of ions exchanged between neurons and the extracellular space (ECS) during a brief period of activity (i.e., due to the integration of synaptic input and generation of a few action potentials) is typically too small to evoke significant changes in extracellular ion concentrations. In models of short-term electrical signalling of neurons, the ion concentrations of the main charge carriers (e.g., K+, Na+, Cl-) are commonly assumed to remain effectively constant. This assumption often holds at longer time scales, due to the work done by neuronal and glial uptake mechanisms in maintaining ion concentrations close to baseline levels. Ion-concentration shifts in the ECS will change neuronal reversal potentials and firing patterns [9,10,11,12], and too large deviations from baseline levels can lead to pathological conditions such as hypoxia, anoxia, ischemia, epilepsy and spreading depression [9, 13,14,15]

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