  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.
