Confidence limits of dipole source reconstruction results

Equivalent dipole models are widely used in electro-encephalo-graphic (EEG) and magneto-encephalo-graphic (MEG) source reconstruction. Despite their point-like definition, the best-fit solutions have a certain probability volume depending on the source position and orientation as well as on the actually used sensor set-up and the signal-to-noise ratio (SNR). In order to avoid the misleading impression of exact localization results, a measure of the SD of the dipole localization is desirable.

This measure can be obtained by performing a deviation scan around the best-fit positions, where the explainable field is determined and compared to the best-fit field. Using a linear approximation, confidence ellipsoids can then be computed and their axes and volumes can be determined by relating the field differences to the noise of the measured data. Test-dipoles inside of a 3 spherical shells volume conductor model were used to simulate EEG- and MEG-data with sources of known positions, orientations, and noise levels. Confidence ellipsoids were computed for these test-dipole solutions and deviation scans around the best-fit dipole positions were performed in order to compare the size and the shape of the confidence ellipsoids with the real error-hypersurface. SDs of repeated dipole localizations at different depths were computed to show the validity of the linear approximation over the whole eccentricity range.

The size of the axes of the confidence ellipsoids is inversely proportional to the SNR of the measured data, thus the confidence volume is inversely proportional to the third power of the SNR. Good agreement between SDs of repeated dipole localizations and the confidence ellipsoids was found for both EEG- and MEG-cases.

The new method adds a new and important dimension to dipole source reconstruction results by characterizing their reliability. It is also very helpful in deciding how many dipoles are necessary to explain the measured data, since superfluous dipoles exhibit rather large confidence volumes.