EEG/MEG error bounds for a static dipole source with a realistic head model

We derive Crameŕ-Rao bounds (CRBs) on the errors of estimating the parameters (location and moment) of a static current dipole source using data from electro-encephalography (EEG), magneto-encephalography (MEG), or the combined EEG/MEG modality. We use a realistic head model based on knowledge of surfaces separating tissues of different conductivities obtained from magnetic resonance (MR) or computer tomography (CT) imaging systems. The electric potentials and magnetic field components at the respective sensors are functions of the source parameters through integral equations. These potentials and field are formulated for solving them by the boundary or the finite element method (BEM or FEM) with a weighted residuals technique. We present a unified framework for the measurements computed by these methods that enables the derivation of the bounds. The resulting bounds may be used, for instance, to choose the best configuration of the sensors for a given patient and region of expected source location. Numerical results are used to demonstrate an application for showing expected accuracies in estimating the source parameters as a function of its position in the brain, based on real EEG/MEG system and MR or CT images.