3D-Simulation of Electrical Activity at Cell Membranes, Interacting with Self-Generated and External Electric Fields

The electric activity of neurons creates extracellular potentials. These fields act back onto the neurons, contributing to synchronization of population activity. External fields are therapeutically used for neuro-stimulation. The mutual interaction between fields and membrane-currents is not captured by today's concepts of cellular electrophysiology, as those are based on isolated membranes in infinite, isopotential extracellular space. Even the direct influence of fields is not correctly represented by the commonly used activating function. While a reduced set of Maxwell's equations can be used to couple membrane currents and electric fields, this approach is rarely taken because adequate computational tools are missing. We present a computational method that implements this set of equations. It allows simulation under realistic conditions: sub-micron cell morphology, various ion channel properties and distributions and a conductive, non-homogeneous space. An implicit solver preserves numerical stability even for large time-steps, limited only by the development of membrane potentials. This allows simulation times of minutes instead of weeks, even for complex problems. The extracellular fields are accurately represented, including secondary fields, which originate at inhomogeneities of the extracellular space. We present a set of instructive examples.View Large Image | View Hi-Res Image | Download PowerPoint Slide