Linear Inverse Solutions: Simulations from a Realistic Head Model in MEG

Abstract

Distributed linear solutions are widely used in source localization to solve the ill-posed EEG/MEG inverse problem. In the classical approach based on dipole sources, these methods estimate the current densities at a great number of brain sites, typically at the nodes of a 3-D grid which discretizes the chosen solution space. The estimated current density distributions are displayed as brain electromagnetic tomography (BET) images. We have tested well known minimum norm solutions (MN, WMN, LORETA) and other linear inverse solutions [WROP, sLORETA, interference uniform, gain uniform, weight vector normalized (WVN), and a new solution named SLF (Standardized Lead Field)], using a MEG configuration (BTi Magnes 2500 WH with 148 axial magnetometers) and a realistic head model using BEM (Boundary Element Method). The solutions were compared in a noise-free condition and in the presence of noise using the classical dipole localization errors (DLE) together with a new figure of merit that we called max gain uniformity, which measures the capability of an inverse linear solution to show spots of activity with similar amplitudes on the brain electromagnetic tomographies when multiple dipole sources with similar moments are simultaneously active. Whereas some solutions (sLORETA, interference uniform and SLF) were capable of zero dipole localization errors in the noise-free case, none of them reached 100% of correct dipole localizations in the presence of a high level of Gaussian noise. The SLF solution, which has the advantage to be independent from any regularization parameter, presented the best results with the lowest max gain uniformities, with almost 100% of correct dipole localizations with 10% of noise and more than 90% of correct localizations with 30% of noise added to the data. Nevertheless, no solution was able to combine at the same time a correct localization of single sources and the capability to visualize multiple sources with comparable amplitudes on the brain electromagnetic tomographies.