Error bounds for EEG and MEG dipole source localization

General formulas are presented for computing a lower bound on localization and moment error for electroencephalographic (EEG) or magnetoencephalographic (MEG) current source dipole models with arbitrary sensor array geometry. Specific EEG and MEG formulas are presented for multiple dipoles in a head model with 4 spherical shells. Localization error bounds are presented for both EEG and MEG for several different sensor configurations. Graphical error contours are presented for 127 sensors covering the upper hemisphere, for both 37 sensors and 127 sensors covering a smaller region, and for the standard 10-20 EEG sensor arrangement. Both 1- and 2-dipole cases were examined for all possible dipole orientations and locations within a head quadrant. The results show a strong dependence on absolute dipole location and orientation. The results also show that fusion of the EEG and MEG measurements into a combined model reduces the lower bound. A Monte Carlo simulation was performed to check the tightness of the bounds for a selected case. The simple head model, the low power noise and the few strong dipoles were all selected in this study as optimistic conditions to establish possibly fundamental resolution limits for any localization effort. Results, under these favorable assumptions, show comparable resolutions between the EEG and the MEG models, but accuracy for a single dipole, in either case, appears limited to several millimeters for a single time slice. The lower bounds increase markedly with just 2 dipoles. Observations are given to support the need for full spatiotemporal modeling to improve these lower bounds. All of the simulation results presented can easily be scaled to other instances of noise power and dipole intensity.