  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.
