# Effects of Sleep Deprivation on the Brain Electrical Activity in Mice
###### Abstract  
Sleep plays a crucial role in maintaining brain health. Insufficient sleep leads to an enhanced permeability of the blood-brain barrier and the development of diseases of small cerebral vessels. In this study, we discuss the possibility of detecting changes in the electrical activity of the brain associated with sleep deficit, using an extended detrended fluctuation analysis (EDFA). We apply this approach to electroencephalograms (EEG) in mice to identify signs of changes that can be caused by short-term sleep deprivation (SD). Although the SD effect is usually subject-dependent, analysis of a group of animals shows the appearance of a pronounced decrease in EDFA scaling exponents, describing power-law correlations and the impact of nonstationarity as a fairly typical response. Using EDFA, we revealed an SD effect in 9 out of 10 mice (Mann-Whitney test, \(p<0.05\)) that outperforms the DFA results (7 out of 10 mice). This tool may be a promising method for quantifying SD-induced pathological changes in the brain. d 2021 11 118  
complex dynamics of natural systems [16; 17; 18; 19; 20; 21; 22]. The traditional correlation function \(C(\tau)\) has two main restrictions, the first of which is the decay of \(C(\tau)\) with increasing time lag \(\tau\), which is fast for broadband random processes. The latter limits the ability to compute the scaling exponent describing long-range power-law correlations, because \(C(\tau)\) approaches zero and becomes comparable to computational errors for noisy datasets. The second restriction arises for time-varying dynamics, when the value of \(C\) is determined by two time moments \(t_{1}\), \(t_{2}\). Only for stationary processes there is a dependence on their difference \(\tau=t_{2}\) - \(t_{1}\), and the correlation function is described by one variable. Many natural processes do not satisfy this requirement, and the traditional approach is used under the assumption of quasistationarity for short segments of the dataset or after excluding the trend due to data filtering. The origin of nonstationarity differs. It can be caused by recording equipment failures or by transients between various system states. Otherwise, it appears due to internal slow dynamics with time scales comparable to the duration of the available datasets. In the latter case, we interpret part of the internal dynamics of a system with time-varying components as a trend. The advantage of DFA is the inclusion of data filtering (detrending) in the signal processing algorithm [14]. Moreover, this detrending is carried out for each time scale separately, which is important for inhomogeneous datasets. Another advantage is the transformation of the decreasing correlation function into a growing dependence of the root mean square (RMS) fluctuations of the signal profile around the local trend on the time scale, and the scaling exponent describing its power-law features is easier to estimate, especially in the region of long-range correlations [15]. The DFA has some limitations that were discussed in earlier studies [23; 24; 25; 26]. Despite the detrending procedure, nonstationarity influences the results, and data preprocessing is still important for analyzing complex systems using experimentally recorded signals [27]. In its original version [14; 15], the DFA considers one basic type of nonstationarity, namely, slow variations in the local mean value (trend). However, natural processes can include other types of time-varying behavior, e.g., repeated regular or random switching between system states, variations in energy, etc. The application of DFA can lead to misinterpretation of scaling exponents for inhomogeneous datasets, where segments with small and large RMS fluctuations can coexist, and their number affects the results. Several attempts have been made to modify the conventional method, such as multifractal DFA, which introduces a number of quantities instead of a single scaling exponent [28; 29].