Boundary integral formulation for the electrical response of a nerve to an extracellular stimulation
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Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
IEEE
Abstract
We present a two-dimensional boundary integral formulation of nerve impulse propagation. A nerve impulse is a potential difference across the cellular membrane that propagates along the nerve fiber. The traveling transmembrane potential is produced by the transfer of ionic species between the intra- and extra-cellular mediums. This current flux across the membrane-composed of conduction, diffusion and capacitive terms- is regulated by passive and active mechanisms that are highly complicated to describe mathematically from a microscopic point of view. Based on the Hodgkin and Huxley axon model, we propose a well-posed integral formulation based on a quasi-static approximation amenable to time-stepping schemes and discuss first results.
Description
Keywords
Mathematical model, Nerve fibers, Electric potential, Equations, Extracellular, Integral equations, Biomembranes