The effect of ionic diffusion on extracellular potentials in neural tissue

In computational neuroscience, it is common to use the simplifying assumption that diffusive currents are negligible compared to Ohmic currents. However, endured periods of intense neural signaling may cause local ion concentration changes in the millimolar range. Theoretical studies have identified scenarios where steep concentration gradients give rise to diffusive currents that are of comparable magnitude with Ohmic currents, and where the simplifying assumption that diffusion can be neglected does not hold. We here propose a novel formalism for computing (1) the ion concentration dynamics and (2) the electrical potential in the extracellular space surrounding multi-compartmental neuron models or networks of such (e.g., the Blue-Brain simulator). We use this formalism to explore the effects that diffusive currents can have on the extracellular (ECS) potential surrounding a small population of active cortical neurons. Our key findings are: (i) Sustained periods of neuronal output (simulations were run for 84 s) could change local ECS ion concentrations by several mM, as observed experimentally. (ii) For large, but realistic, concentration gradients, diffusive currents in the ECS were of the same magnitude as Ohmic currents. (iii) Neuronal current sources could induce local changes in the ECS potential by a few mV, whereas diffusive currents could could induce local changes in the ECS potential by a few tens of a mV. Diffusive currents could thus have a quite significant impact on ECS potentials. (v) Potential variations caused by diffusive currents were quite slow, but could influence the comparable to those induced by Ohmic currents up to frequencies as high as 7Hz.