Summary: A number of beamformers have been introduced to localize neuronal activity using magnetoencephalography (MEG) and electroencephalography (EEG). However, currently available information about the major aspects of existing beamformers is incomplete. In the present study, detailed analyses are performed to study the commonalities and differences among vectorized versions of existing beamformers in both theory and practice. In addition, a novel beamformer based on higher-order covariance analysis is introduced. Theoretical formulas are provided on all major aspects of each beamformer; to examine their performance, computer simulations with different levels of correlation and signal-to-noise ratio are studied. Then, an empirical data set of human MEG median-nerve responses with a large number of neuronal generators is analyzed using the different beamformers. The results show substantial differences among existing MEG/EEG beamformers in their ways of describing the spatial map of neuronal activity. Differences in performance are observed among existing beamformers in terms of their spatial resolution, false-positive background activity, and robustness to highly correlated signals. Superior performance is obtained using our novel beamformer with higher-order covariance analysis in simulated data. Excellent agreement is also found between the results of our beamformer and the known neurophysiology of the median-nerve MEG response.

A mathematical model (sigma(omega) approximately equal to A omega alpha, where, sigma is identical with conductivity, omega = 2 pi f is identical with applied frequency (Hz), A (amplitude) and alpha (unit less) is identical with search parameters) was used to fit the frequency dependence of electrical conductivities of compact, spongiosum, and bulk layers of the live and, subsequently, dead human skull samples. The results indicate that the fit of this model to the experimental data is excellent. The ranges of values of A and alpha were, spongiform (12.0-36.5, 0.0083-0.0549), the top compact (5.02-7.76, -0.137-0.0144), the lower compact (2.31-10.6, 0.0267-0.0452), and the bulk (7.46-10.6, 0.0133-0.0239). The respective values A and alpha for the respective layers of the dead skull samples were (40.1-89.7, -0.0017-0.0287), (5.53-14.5, -0.0296 - -0.0061), (4.58-15.9, -0.0226-0.0268), and (12.7-25.3, -0.0158-0.0132).