Array Response Kernels for EEG and MEG in Multilayer Ellipsoidal Geometry

We present forward modeling solutions in the form of array response kernels for electroencephalography (EEG) and magnetoencephalography (MEG), assuming that a multilayer ellipsoidal geometry approximates the anatomy of the head and a dipole current models the source. The use of an ellipsoidal geometry is useful in cases for which incorporating the anisotropy of the head is important but a better model cannot be defined. The structure of our forward solutions facilitates the analysis of the inverse problem by factoring the lead field into a product of the current dipole source and a kernel containing the information corresponding to the head geometry and location of the source and sensors. This factorization allows the inverse problem to be approached as an explicit function of just the location parameters, which reduces the complexity of the estimation solution search. Our forward solutions have the potential of facilitating the solution of the inverse problem, as they provide algebraic representations suitable for numerical implementation. The applicability of our models is illustrated with numerical examples on real EEG/MEG data of N20 responses. Our results show that the residual data after modeling the N20 response using a dipole for the source and an ellipsoidal geometry for the head is in average lower than the residual remaining when a spherical geometry is used for the same estimated dipole.

I. Introduction

Array processing methods have been developed to solve problems related to the localization of brain activity sources using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, and the solutions are useful in neurosciences and clinical applications [1], [2]. Solutions to the forward modeling problem in EEG/MEG consist of computing the electric potentials over the scalp and the magnetic field outside the head, respectively, given a current source within the brain. The forward model is necessary for solving the inverse problem (i.e., finding the current distributions using EEG/MEG measurements). Since solving the inverse problem often involves an iterative solution of the forward problem, it is important to have an efficient form for the analytical and numerical solutions of the forward problem in order to minimize the computational burden [3].