Raviart–Thomas-type sources adapted to applied EEG and MEG: implementation and results

Abstract

This paper studies numerically electroencephalography and magnetoencephalography (EEG and MEG), two non-invasive imaging modalities in which external measurements of the electric potential and the magnetic field are, respectively, utilized to reconstruct the primary current density (neuronal activity) of the human brain. The focus is on adapting a Raviart–Thomas-type source model to meet the needs of EEG and MEG applications. The goal is to construct a model that provides an accurate approximation of dipole source currents and can be flexibly applied to different reconstruction strategies as well as to realistic computation geometries. The finite element method is applied in the simulation of the data. Least-squares fit interpolation is used to establish Cartesian source directions, which guarantee that the recovered current field is minimally dependent on the underlying finite element mesh. Implementation is explained in detail and made accessible, e.g., by using quadrature-free formulae and the Gaussian one-point rule in numerical integration. Numerical results are presented concerning, for example, the iterative alternating sequential inverse algorithm as well as resolution, smoothness and local refinement of the finite element mesh. Both spherical and pseudo-realistic head models, as well as real MEG data, are utilized in the numerical experiments.