Behavior of the voltage produced by an electrode in a membrane by means of the finite element method

Abstract

The spatial distribution of an electrical potential in a cell membrane subjected to an electric field was numerically obtained using an equivalent electrical circuit where the spatial variables that depend on the geometry are combined and an electrical circuit that relates the dynamics in the time of said excitation in four branches that represent the middle. It was observed that the potential decreases linearly in the geometry of the membrane due to the characteristics of the medium (sodium, potassium). On the other hand, the finite element method was developed for a two-dimensional domain that represents the geometry of a membrane, in such a way that it is possible to qualitatively analyze the behavior of the potential at any point of the membrane for an electrical pulse (electrode).

Finite element analysis of the voltage induced by a pair of electrodes in a cell membrane

“…Combinations of these test functions make it possible to approximate the answer to the differential equations by means of numerical analysis. Otherwise, the finite element method seeks the participation (contributions) of each of these test functions in such a way that the numerical solution approximates the analytical solution; the choice of test functions by means of the Galerkin approximation will consist of finding test functions that are close to the true (analytical) response [2].…”