Array Response Kernels for EEG and MEG in Multilayer Ellipsoidal Geometry

Abstract—We present forward modeling solutions in the form of array response kernels for electroencephalography (EEG) and magnetoencephalography (MEG), assuming that a multilayer el-lipsoidal geometry approximates the anatomy of the head and a dipole current models the source. The use of an ellipsoidal geom-etry 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 cor-responding to the head geometry and location of the source and sensors. This factorization allows the inverse problem to be ap-proached 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 el-lipsoidal geometry for the head is in average lower than the residual remaining when a spherical geometry is used for the same esti-mated dipole. Index Terms—Dipole source signal, electroencephalography (EEG), ellipsoidal head model, magnetoencephalography (MEG), N20 response, sensor array processing. I