Extracellular Stimulation and Ephaptic Coupling of Neurons in a Fully Coupled Finite Element-Based Extracellular–Membrane–Intracellular (EMI) Model

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 biophysical coupling between the extracellular (E) space, the cell membrane (M), and the intracellular (I) space. Here, we use a finite element–based Extracellular–Membrane–Intracellular (EMI) approach that solves a fully coupled system of equations to study extracellular stimulation and ephaptic coupling of cerebellar Purkinje neurons and neocortical layer 5 pyramidal neurons. These two archetypes differ substantially in morphology, ion-channel distribution, and firing behavior, and together span a range of neuronal properties. Specifically, we assess responses to extracellular stimulation while varying the distance to the stimulation source, the amplitude, and the frequency of the external current. We also investigate ephaptic interactions between neurons, and examine how the firing pattern of one neuron can be affected by the firing pattern of a neighboring neuron, how the rate of synchronization between neighboring neurons depends on cell distance and extracellular conductivity, and finally whether a neuron can directly trigger excitation in a neighboring neuron through ephaptic coupling. 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.