On the relation between EEG microstates and cross-spectra

Brain function as measured by multichannel EEG recordings can be described to a high level of accuracy by microstates, characterized as a sequence of time intervals within which the sign invariant normalized scalp electric potential field remains quasi-stable, concatenated by fast transitions. Filtering the EEG has a small effect on the spatial microstate scalp maps, but a large effect on the dynamics (e.g. duration, frequency of occurrence, and transition rates). In addition, spectral power has been found to be strongly correlated with microstate dynamics. And yet, the nature of the relation between spectra and microstates remains poorly understood. Here we show that the multivariate EEG cross-spectrum contains sufficient generative information for estimating the microstate scalp maps and their dynamics, demonstrating an underlying fundamental link between the microstate model and the multivariate cross-spectrum. Empirically, based on EEG recordings from 203 participants in eyes-closed resting state, their cross-spectral matrices were computed, from which stochastic EEG was generated. No significant differences were found for the microstate model (maps and dynamics) estimated from the actual EEG and from the stochastic EEG based solely on the cross-spectra. In addition, with the aim of quantifying the spatio-cross-spectral properties of the microstate model, we introduce here the topographic likelihood spectrum, based on the Watson distribution, which provides a frequency-by-frequency account of the contribution of a normalized microstate map to the normalized EEG cross-spectrum, independent of power. The topographic likelihood spectra are distinct for the different microstate maps. In a comparison between eyes-closed and eyes open conditions, they are shown to be significantly different in frequency specific patterns.