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Detrended fluctuation analysis (DFA) is widely used to characterize long-range power-law correlations in complex signals. However, it has restrictions when nonstationarity is not limited only to slow variations in the mean value. To improve the characterization of inhomogeneous datasets, we have proposed the extended DFA (EDFA), which is a modification of the conventional method that evaluates an additional scaling exponent to take into account the features of time-varying nonstationary behavior. Based on EDFA, here, we analyze rat electroencephalograms to identify specific changes in the slow-wave dynamics of brain electrical activity associated with two different conditions, such as the opening of the blood–brain barrier and sleep, which are both characterized by the activation of the brain drainage function. We show that these conditions cause a similar reduction in the scaling exponents of EDFA. Such a similarity may represent an informative marker of fluid homeostasis of the central nervous system.
Natural systems often exhibit complex dynamics with long-range power-law correlations. To quantify this phenomenon, different variants of fluctuation analysis are used with detrended fluctuation analysis (DFA),1,2 representing a universal method that can be applied to both stationary and nonstationary time series. In many practical situations, however, nonstationarity cannot be eliminated by simply removing the slow variation in mean value. For such a case, we have recently proposed an extended method (EDFA), which estimates two scaling exponents: the first exponent is associated with the conventional DFA and the second exponent quantifies the impact of nonstationarity.3 Here, we use EDFA to identify informative markers of changes in electroencephalograms associated with two different factors, namely, open blood–brain barrier (BBB) and sleep, which are characterized by activated brain drainage function. By means of EDFA, we uncover that both factors, sound and sleep, cause similar changes in the low-frequency dynamics of electroencephalograms (EEG). These results offer a hint of the similarity of EEG dynamics related to distinct mechanisms of fluid drainage from the brain during sleep and after the BBB opening
