Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

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.Author Summary: When electrical potentials are measured in the extracellular space (ECS) of the brain, they are interpreted as a signature of neural signalling. The relationship between the ECS potentials and the underlying neuronal processes is often studied with the aid of computer models. The ECS potential is typically assumed not to be affected by diffusive currents in the ECS, and existing models therefore neglect diffusion. However, there may be scenarios where this assumption does not hold. Here, 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. Using this model, we simulate a scenario where a population of pyramidal neurons is active over a long time, and produces large, but realistic concentration gradients in the ECS. In this scenario, diffusive currents are found to influence the ECS potential at frequency components as high as ten hertz. Unlike previously believed, we thus predict that there are scenarios where recorded local field potentials (LFPs) are likely to contain signatures not only of neural activity, but also of ECS diffusion.