A finite element method framework to model extracellular neural stimulation.

Objective. Increasing complexity in extracellular stimulation experiments and neural implant design also requires realistic computer simulations capable of modeling the neural activity of nerve cells under the influence of an electrical stimulus. Classical model approaches are often based on simplifications, are not able to correctly calculate the electric field generated by complex electrode designs, and do not consider electrical effects of the cell on its surrounding. A more accurate approach is the finite element method (FEM), which provides necessary techniques to solve the Poisson equation for complex geometries under consideration of electrical tissue properties. Especially in situations where neurons experience large and non-symmetric extracellular potential gradients, a FEM solution that implements the cell membrane model can improve the computer simulation results. To investigate the response of neurons in an electric field generated by complex electrode designs, a FEM framework for extracellular stimulation was developed in COMSOL. Approach. Methods to implement morphologically- and biophysically-detailed neurons including active Hodgkin-Huxley (HH) cell membrane dynamics as well as the stimulation setup are described in detail. Covered methods are (a) development of cell and electrode geometries including meshing strategies, (b) assignment of physics for the conducting spaces and the realization of active electrodes, (c) implementation of the HH model, and (d) coupling of the physics to get a fully described model. Main results. Several implementation examples are briefly presented: (a) a full FEM implementation of a HH model cell stimulated with a honeycomb electrode, (b) the electric field of a cochlear electrode placed inside the cochlea, and (c) a proof of concept implementation of a detailed double-cable cell membrane model for myelinated nerve fibers. Significance. The presented concepts and methods provide basic and advanced techniques to realize a full FEM framework for innovative studies of neural excitation in response to extracellular stimulation.
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