title: Analytical and empirical fluctuation functions of the EEG microstate random walk - Short-range vs. long-range correlations.
abstract: We analyze temporal autocorrelations and the scaling behaviour of EEG microstate sequences during wakeful rest. We use the recently introduced random walk approach and compute its fluctuation function analytically under the null hypothesis of a short-range correlated, first-order Markov process. The empirical fluctuation function and the Hurst parameter H as a surrogate parameter of long-range correlations are computed from 32 resting state EEG recordings and for a set of first-order Markov surrogate data sets with equilibrium distribution and transition matrices identical to the empirical data. In order to distinguish short-range correlations (H ≈ 0.5) from previously reported long-range correlations (H > 0.5) statistically, confidence intervals for H and the fluctuation functions are constructed under the null hypothesis. Comparing three different estimation methods for H, we find that only one data set consistently shows H > 0.5, compatible with long-range correlations, whereas the majority of experimental data sets cannot be consistently distinguished from Markovian scaling behaviour. Our analysis suggests that the scaling behaviour of resting state EEG microstate sequences, though markedly different from uncorrelated, zero-order Markov processes, can often not be distinguished from a short-range correlated, first-order Markov process. Our results do not prove the microstate process to be Markovian, but challenge the approach to parametrize resting state EEG by single parameter models.
authors.affiliation: Epilepsy Center Rhein-Main, Goethe University Frankfurt am Main, Schleusenweg 2-16, Frankfurt am Main 60528, Germany; Department of Neurology and Brain Imaging Center, Goethe University Frankfurt am Main, Schleusenweg 2-16, Frankfurt am Main 60528, Germany. Electronic address: fredericvon.wegner@kgu.de.
authors.forename: F
authors.initials: F
authors.lastname: von Wegner
authors.affiliation: Department of Neurology and Brain Imaging Center, Goethe University Frankfurt am Main, Schleusenweg 2-16, Frankfurt am Main 60528, Germany; Department of Neurology, University Hospital Kiel, Schittenhelmstrasse 10, Kiel 24105, Germany.
authors.forename: E
authors.initials: E
authors.lastname: Tagliazucchi
authors.affiliation: Department of Neurology and Brain Imaging Center, Goethe University Frankfurt am Main, Schleusenweg 2-16, Frankfurt am Main 60528, Germany.
authors.forename: V
authors.initials: V
authors.lastname: Brodbeck
authors.affiliation: Department of Neurology and Brain Imaging Center, Goethe University Frankfurt am Main, Schleusenweg 2-16, Frankfurt am Main 60528, Germany; Department of Neurology, University Hospital Kiel, Schittenhelmstrasse 10, Kiel 24105, Germany.
authors.forename: H
authors.initials: H
authors.lastname: Laufs
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D004569:Electroencephalography / Q000379:methods*; D006801:Humans; D008390:Markov Chains; D015233:Models, Statistical; D015203:Reproducibility of Results; D012146:Rest / Q000502:physiology; D012680:Sensitivity and Specificity; D013223:Statistics as Topic; D055815:Young Adult
keywords: EEG; Hurst parameter; Long-range correlations; Markov process; Microstates; Resting state; Scaling