A Model to Study Time Lagged Interactions, Source Connectivity and Source Activities Using Multi-channel EEG

A computational model to examine time lagged interactions; identify number of interacting pairs of neuronal sources; and determine source activities from multi-channel EEG measurements is described. It is based on the imaginary part of the cross spectrum between the EEG channels. The imaginary part of the cross spectrum between the EEG channels provides the most suitable property that reflects the presence of interacting sources. The model assumes that not all sources are activated simultaneously and that there is a time lag amongst some of them. A new analytical expression derived for the imaginary part of cross spectrum between channels shows that it is different from the zero lag case. A method is then proposed to identify time lag interactions, by studying its variation as a function of frequency. Assuming pair wise interaction between sources, the model shows that simultaneous diagonalization at different frequencies of symmetric matrices formed by multiplying the anti-symmetric matrix of the imaginary part of cross spectrum with its transpose will provide information on the number of interacting source pairs as a function of frequency. The matrix that simultaneously diagonalizes all the symmetric matrices is identified as the mixing matrix. This can be used to obtain the source activities.