Extracellular stimulation and ephaptic coupling of neurons in a fully coupled finite element-based...

The extracellular potential surrounding neurons is of great importance: it is measured to interpret neural activity, it underpins ephaptic coupling between neighboring cells, and it forms the basis for external stimulation of neural tissue. These phenomena have been studied for decades, both experimentally and computationally. In computational models, variants of the classical cable equation for membrane dynamics and an electrostatic equation for the extracellular field are the most common approaches. Such formulations however, typically decouple the governing equations and therefore neglect the bidirectional coupling between the extracellular (E) space, the cell membrane (M), and the intracellular (I) space.

We use a finite element-based Extracellular-Membrane-Intracellular (EMI) approach that solves a fully coupled system to study extracellular stimulation and ephaptic coupling in detailed models of cerebellar Purkinje neurons and neocortical layer 5 pyramidal neurons. We vary the distance to the stimulation source, the amplitude, and the frequency of an external current, and we simulate two-cell configurations to assess ephaptic spike-timing effects, synchronization, and the possibility of direct ephaptic action potential triggering.

We find that weak sinusoidal stimulation induces subthreshold membrane oscillations that follow the stimulus frequency, and that constant or sinusoidal extracellular stimulation modulate spike rates and spike timing in a manner that depends on stimulation strength and distance. In two-cell simulations, we find that Purkinje neurons synchronize ephaptically in a distance-and extracellular-conductivity-dependent manner, and that pyramidal neuron spike timing is altered by a neighboring firing cell. Direct ephaptic triggering requires markedly reduced extracellular conductivity relative to bulk values.

The results provide quantitative insight into extracellular field-mediated neural coupling and how externally applied fields, such as those used in deep brain stimulation, interact with single-neuron biophysics. The results support the view that ephaptic interactions between neurons are more plausibly expressed as spike-timing modulation and synchronization than as direct excitatory triggering under physiological conditions.