Long-range dependencies make the difference - Comment on "A stochastic model for EEG microstate sequence analysis"

The analysis of spontaneous resting state neuronal activity is assumed to give insight into the brain function. One noninvasive technique to study resting state activity is electroencephalography (EEG) with a subsequent microstate analysis. This technique reduces the recorded EEG signal to a sequence of prototypical topographical maps, which is hypothesized to capture important spatio-temporal properties of the signal. In a statistical EEG microstate analysis of healthy subjects in wakefulness and three stages of sleep, we observed a simple structure in the microstate transition matrix. It can be described with a first order Markov chain in which the transition probability from the current state (i.e., map) to a different map does not depend on the current map. The resulting transition matrix shows a high agreement with the observed transition matrix, requiring only about 2% of mass transport (1/2 L1-distance). In the second part, we introduce an extended framework in which the simple Markov chain is used to make inferences on a potential underlying time continuous process. This process cannot be directly observed and is therefore usually estimated from discrete sampling points of the EEG signal given by the local maxima of the global field power. Therefore, we propose a simple stochastic model called sampled marked intervals (SMI) model that relates the observed sequence of microstates to an assumed underlying process of background intervals and thus, complements approaches that focus on the analysis of observable microstate sequences.