A finite difference method to solve the forward problem in electroencephalography (EEG)

In this paper, a three-dimensional finite difference method to solve the forward problem in electroencephalography is developed. The aim is to compute the electric potential in the whole head. hree-dimensional conservative difference schemes are defined on a regular grid for elliptic equations with strongly discontinuous coefficients. For each scheme, the error of approximation is estimated by making some assumptions on surface locations with respect to the grid. These assumptions are due to a lack of knowledge of the real discontinuity surfaces. Numerical results allow the comparison of the accuracy of the different schemes when surfaces do not satisfy the previously mentioned assumptions, which is the case in most real-life applications. Such applications will be discussed in conclusion.