{"id":127,"date":"2015-11-18T00:00:00","date_gmt":"2015-11-17T23:00:00","guid":{"rendered":"http:\/\/semmelweis.hu\/psychophysiology\/weiss-b-clemens-zs-bodizs-r-halasz-p-comparison-of-fractal-and-power-spectral-eeg-features-effects-of-topography-and-sleep-stages-brain-res-bull-84-6-359-75-2011\/"},"modified":"2019-01-23T18:33:51","modified_gmt":"2019-01-23T17:33:51","slug":"weiss-b-clemens-zs-bodizs-r-halasz-p-comparison-of-fractal-and-power-spectral-eeg-features-effects-of-topography-and-sleep-stages-brain-res-bull-84-6-359-75-2011","status":"publish","type":"post","link":"https:\/\/semmelweis.hu\/psychophysiology\/2015\/11\/18\/weiss-b-clemens-zs-bodizs-r-halasz-p-comparison-of-fractal-and-power-spectral-eeg-features-effects-of-topography-and-sleep-stages-brain-res-bull-84-6-359-75-2011\/","title":{"rendered":"Weiss B, Clemens Zs, B\u00f3dizs R, Hal\u00e1sz P: Comparison of fractal and power spectral EEG features: Effects of topography and sleep stages. Brain Res Bull 84(6):359-75 (2011)"},"content":{"rendered":"\n\n\n
\n

<\/a>DOI:10.1016\/j.brainresbull.2010.12.005<\/a><\/p>\n

B\u00e9la Weissa<\/sup>, Zs\u00f3fia Clemensb<\/sup>, R\u00f3bert B\u00f3dizsc,d<\/sup>, P\u00e9ter Hal\u00e1sza<\/sup><\/p>\n

a<\/sup>Faculty of Information Technology, P\u00e1zm\u00e1ny P\u00e9ter Catholic University, Pr\u00e1ter u. 50\/a, 1083 Budapest, Hungary
\nb<\/sup> National Institute of Neuroscience, Amerikai \u00fat 57, 1145 Budapest, Hungary
\nc<\/sup> Institute of Behavioural Sciences, Semmelweis University, Nagyv\u00e1rad t\u00e9r 4, 1089 Budapest, Hungary
\nd<\/sup>HAS\u2013BME Cognitive Science Research Group, Stoczek u. 2, ST. Building, III\/311, 1111 Budapest, Hungary<\/em><\/small><\/p>\n

Corresponding author: Tel.: +36 1 886 4753; fax: +36 1 886 4724. E-mail address: #mailto# var addy7868 = ‘weiss’ + ‘@’; addy7868 = addy7868 + ‘itk’ + ‘.’ + ‘ppke’ + ‘.’ + ‘hu’; # (B. Weiss)
\n<\/em><\/small><\/em><\/small>
\nReceived: 22 July 2010
\nReceived in revised form: 30 November 2010
\nAccepted: 7 December 2010<\/p>\n

<\/small><\/address>\n

ABSTRACT<\/h3>\n

Fractal nature of the human sleep EEG was revealed recently. In the literature there are some attempts to relate fractal features to spectral properties. However, a comprehensive assessment of the relationship between fractal and power spectral measures is still missing. Therefore, in the present study we investigated the relationship of monofractal and multifractal EEG measures (H and D) with relative band powers and spectral edge frequency across different sleep stages and topographic locations. In addition wetested sleep stage classification capability of these measures according to different channels.We found that cross-correlations between fractal and spectral measures as well as between H and D exhibit specific topographic and sleep stage-related characteristics. Best sleep stage classifications were achieved by estimating measureD in temporal EEG channels both at group and individual levels, suggesting that assessing multifractality might be an adequate approach for compact modeling of brain activities.<\/p>\n

Keywords<\/h3>\n

Fractal analysis; Power spectral analysis; Topography; Cross-correlation; Sleep stage classification<\/p>\n

1. Introduction <\/strong><\/p>\n

With advent of relatively cheap and high performance personal computers sophisticated and computation demanding time series analysis methods became available to a broad brain research community. Application of chaos theory and non-linear time series methods gave a deeper insight into brain dynamics reflected by EEG signals. For a comprehensive recent review on non-linear analysis of EEG we refer to ref. [90]. This approach relies on a transition from the time domain to the phase space and generation of trajectories for EEG time series using different embedding techniques. Inferences about brain dynamics were drawn by estimating different characteristics of trajectory attractors using measures such as the correlation dimension D2, the fractal dimension Df, the largest Lyapunov exponent L1, etc. Early results were promising and suggested a deterministic nature of brain dynamics with a rather low-dimensional chaotic behavior in physiological and pathological conditions that could not be revealed using simple linear methods such as power spectral analyses. Filtered noise, however,can mimic the signatures of deterministic chaos [77]. This latter finding necessitated a revision of results obtained by non-linear techniques. Surrogate data analyses [83] did not entirely support early results on the low-dimensional chaotic behavior of the brain. This was in agreement with the finding that the relatively high complexity of the EEG signals does not allow a reliable dissociation of its waxing and waning oscillations exceeding 2\u201315 s from that of the filtered white noise [14,69,89]. As a consequence alternative approaches were developed including novel non-linear and stochastic time series analysis methods.
\nFractality is a common property in nature [65] which may originate from self-organized criticality (SOC) [4\u20136] of the particular system of interest. Unlike deterministic approaches aimed at finding low-dimensional chaos, the SOC framework allows for describing the high-dimensional character of the dynamics and the presence of stochastic effects [58]. SOC is a phenomenon characterizing systems that might arrive at a critical state (phase transition) without any tuning of a specific parameter [6]. The proof of presence of SOC requires a demonstration of spatio-temporal long-range correlations and power-law scale-free (also called selfsimilar or fractal) fluctuations [4]. Scale-free behavior means that no characteristic scales dominate the dynamics of the underlying processes. It also reflects a tendency of complex systems to develop correlations that decay more slowly and extend over larger distances in time and space than the mechanisms of the underlying processes would suggest [4,7,8,58]. The long-range correlations build up through local interactions until they extend throughout the entire system. After this stage, the dynamics of the system exhibit power-law scaling behavior and the underlying process operates in a critical state [5,6]. A critical state is a regime of a system where opposing forces are balanced. In the nervous system such a balance might be represented by the relationship between excitation and inhibition, which is known to be important for the transfer of information [85] and for the sustained neuronal activity [87]. Neural network simulations demonstrated that the presence of long-range spatio-temporal correlations is beneficial for the optimal transfer of information since these correlations represent an optimal compromise between high susceptibility to perturbations and stability in the system [10,17].
\nSeveral features of neural networks are consistent with SOC, such as a large number of elements (neurons) interacting with each other in a nonlinear way (e.g. presence of threshold for spiking), a possibility to change and save connectivity between the elements (e.g. via synaptic plasticity), absence of any special parameter tuning, and spatio-temporal dynamics obeying power-law statistics [58,68]. Despite of these common properties of neural networks and SOC systems, several studies revealed power-law neural fluctuations that do not necessarily reflect self-organized critical states of brain [9,80,81]. For example, B\u00e9dard et al. [9] have shown that fractal property of local field potentials recorded from cat parietal cortex does not rely on critical states, but rather stems from filtering properties of the extracellular media. All these results indicate a more general nature of fractality that could be used as a descriptor of structural and functional properties of the brain during different conditions.
\nFractal geometry of brain structures [49,70] as well as powerlaw spatio-temporal properties of neuronal activities have been revealed. Although the spatial power spectral density (PSDx) of scalp EEG recordings might deviate from the ideal power-law scalefree behavior [34], the PSDx of epipial EEG conforms to it [33]. Temporal long-range correlations were observed at different levels of the brain electrical activity hierarchy in different species and during different conditions. For example, Lowen et al. revealed that individual ion channel currents show long-term correlation and possess fractal properties [62]. Considering spike trains in extracellular recordings, long-term correlations were found among interspike intervals of the medullary sympathetic neurons in cats [56]. Spasic et al. showed that the fractal dimension of local field potentials of anaesthetized rats changes significantly after unilateral discrete injury [88]. Fractal exponent of EEG activity in the Gallotia galloti lizard decreased with the increment of temperature from 25 \u25e6C to 35\u25e6C [35].
\nThe exact values of fractal measures may be related to biophysical mechanisms and the neural architecture underlying oscillations. However, given the uncertainties related to the estimation of these measures [15,16,36,42,47,48] it might be more reasonable to compare the variances of features for different conditions. In line with this, a series of human studies revealed differences in the fractal measures between specific conditions. A study by Linkenkaer- Hansen et al. [58] showed that mu and alpha oscillations scale similarly, but beta oscillations have a significantly smaller scaling exponent compared to these two latter oscillations during eyes-closed state. Another study showed that long-range temporal correlations are stronger in the eyes-closed condition as compared with the eyes-open condition [67]. In the study of Nikulin and Brismar [68] largest exponent values for alpha and beta oscillations were found during the eyes-closed condition in the occipital and parietal areas. Fractal dimension was found to be significantly higher for drowsy EEG compared to the wake state [13]. Increased sensory input [59] or high level of alertness [75] was shown to disrupt long-range temporal correlations. Several studies addressed self-similarity of sleep EEG [1,53\u201355,63,74,86,95]. Generally, most of these studies reported higher scaling exponents and thus stronger long-range temporal correlations for deeper sleep stages. It was also indicated that brain electrical activities are more complex than they could be completely described by a single scaling exponent [63,95]. In a previous study [95] we provided a detailed topographic analysis of temporal fractal measures during different vigilance states. In the present study we extended the characterization of self-similarity properties by a comprehensive topographic comparison of multifractal and monofractal measures with each other and with power spectral measures, and also examined their sleep stage classification capabilities.<\/p>\n

2. Materials and methods<\/strong><\/p>\n

2.1. Subjects and EEG recordings<\/em><\/p>\n

Twenty-two healthy subjects with no sleep disturbances, free of drugs and medications as assessed by an interview and questionnaires on sleeping habits and health participated in the study (age: 17\u201355 years, mean\u00b1S.D.: 31\u00b19 years, 11 males and 11 females). The study was approved by the ethical committee of the Semmelweis University and subjects gave written informed consent to participation. Sleep was recorded in the sleep laboratory for two consecutive nights. The timing of lights off was determined by the subjects, and morning awakenings were spontaneous. On average subjects spent 462.39\u00b169.01 (mean\u00b1S.D.) minutes in sleep during the second night. Sleep was recorded by standard polysomnography, including electroencephalography (Fp1, Fp2, F3, F4, Fz, F7, F8, C3, C4, Cz, P3, P4, T3, T4, T5, T6, O1 and O2 electrodes), electrooculography (EOG), bipolar submental electromyography (EMG) and electrocardiography (ECG). EEG electrodes were referenced to the contralateral mastoid. Midline EEG electrodes were referenced to the right mastoid. Impedance of the EEG electrodes was kept below 5 k. Signals were collected, pre-filtered, amplified and digitized at a sampling rate of fs = 249 Hz using the 30 channel Flat Style SLEEP La Mont Headbox with implemented second order filters at 0.5 Hz (high pass) and 70 Hz (low pass) as well as the HBX32-SLP 32 channel preamplifier (La Mont Medical Inc., USA). Additionally, a 50Hz digital notch filtering was performed by means of the DataLab acquisition software (Medcare, Iceland).<\/p>\n

2.2. EEG processing<\/em><\/p>\n

Pre-processing and feature estimation were accomplished in a self-developed EEG visualization and processing toolbox under Matlab2009b (MathWorks, Natick, MA,USA). Statistical analyses were performed using STATISTICA (StatSoft, Inc., Tulsa, OK, USA) and Matlab2009b.<\/p>\n

2.2.1. Pre-processing<\/em>
\nAlthough hardware filtering had been applied during EEG recording, some artifacts remained. Thus, we first performed software filtering on the raw EEG recordings with Butterworth IIR filters (eight order 0.3\u201370 Hz band-pass and 50 Hz notch with a quality factor Q= 45). To avoid phase distortion, we used the built-in filtfilt( ) function of the Matlab for zero-phase digital filtering. For all subjects a hypnogram was prepared according to the Rechtschaffen and Kales standard [78] using 20 s long epochs. To compare the analyzed EEG features during different sleep stages 90 epochs of 20 s length were selected from sleep stages NREM2, NREM4 and REM (30 min\/stage) for all subjects. Selection included segments without artifact contamination only.<\/p>\n

2.2.2. Fractal analysis<\/em>
\nMonofractal and multifractal properties of the selected EEG epochs were evaluated by estimation of the self-similarity parameter H (also called Hurst exponent or Hurst parameter) and the range of fractal spectra (D), respectively. To estimate H, we applied the rescaled adjusted range based approach, while D was approximated by estimation of generalized dimensions spectra. The brief description of the applied methods can be found in the following subsections. For detailed information on selection of estimation methods and parameter settings we refer to [95].<\/p>\n

2.2.2.1. Estimation of the Hurst exponent.<\/em>
\nThe stochastic process X(t) with continuous parameter t is self-similar with the self-similarity parameterHif the distribution of the rescaled process c\u2212H<\/sup>X(ct) is the same as the distribution of X(t), where c>0 is arbitrary [64]. H is widely used to assess monofractality, scale-free properties and the degree of long-range temporal correlations of time series.When 0 < H < 0.5, an increase in the process is more probably followed by a decrease (anti-persistence) and vice versa, the process is considered to have short-range dependence. If H= 0.5, observations of the process are uncorrelated. When 0.5 < H < 1, an increase in the process is more probably followed by an increase and a decrease is more probably followed by a decrease (persistence), the process is considered to have long-range dependence [1,12,44,47,64].
\nBasically two kinds of homogenous self-similar (see also the first paragraph of Section 2.2.2.2) signals exist: fractional Gaussian noises (fGn) and fractional Brownian motions (fBm). fGn processes are considered to be stationary with a constant mean value and constant variance over time, while fBm\u2019s exhibit non-stationary property with a time-dependent variance. fGn and fBm signals are interconvertible. Taking the differences between neighboring elements of an fBm time series one might create an fGn signal, while by cumulative summation of fGn elements one can generate a motion process. The corresponding fBm and fGn signals are characterized by the same H<\/em>. Self-similarity of a time series is also reflected in their power spectrum. The power versus frequency relationship is given by P(f)\u221df\u2212K<\/em><\/sup>, where K<\/em> is called spectral or fractal exponent. Depending on the type of a fractal signal the relationship between H<\/em> and K<\/em> is given by H<\/em>= (K<\/em> + 1)\/2, \u22121< K <\/em>< 1 for fGn and H<\/em>= (K<\/em> \u22121)\/2, 1< < 3 forfBm[26]. Similarly,H<\/em> is linearly related to the detrended fluctuation analysis exponent [71,72] as H<\/em>= \u03bb for fGn signals and H<\/em>= \u03bb\u22121 in case of fBm processes. Additionally, the Hurst exponent is also related to the widely used fractal dimension as H<\/em>=2\u2212Df [25,41], where Df refers to the fractal dimension of a one dimensional Brownian motion X(t) in the X\u2013t plane. Although many approaches are available for the estimation ofHnone of these can be generally considered as an ideal one because of differences of fGn and fBm signals [24\u201326,76] and doubts related to the estimation of non-linear parameters from time series of finite length [15,16,36,42,47,48]. Like in our previous study [95] for the estimation of H<\/em> we used the rescaled adjusted range or R\/S statistics based method [12,44,64].We implemented this method keeping in mind the stationarity properties of the analyzed EEG segments and the fact that this method is applicable to stationary fGn processes or to differenced fBm signals only. Here we provide a short description of this approach, for further details we refer to [95]. Let X(n) be a discrete time series. The partial sum process is defined as
\n
\nThe sample variance of the process X can be obtained using
\n
\nThe adjusted range is given by
\n
\nwhere
\n
\n
\nThe R\/S statistics or the rescaled adjusted range is defined by
\n
\nIn [64] it was proven that for self-similar processes the expected value of R\/S(n) is proportional to nH<\/sup>, i.e.
\n
\nas n\u2192\u221e, where CH is a positive constant and H is the self-similarity parameter of the process. Using this power-law relationship the Hurst exponent can be estimated by:
\n<\/p>\n

2.2.2.2. Estimation of multifractal spectra. <\/em>
\nHomogenous self-similar time series can be described by a single scale-free exponent. These signals are also called monofractal time series. Additionally, heterogeneous multifractal time series showing self-similarity only in local ranges of the structure also exist. Their scale-free property varies in time. Hence they should be decomposed into many sub-sets and characterized by different exponents. This can be carried out by estimation of fractal spectra. Using the Alfr\u00e9d R\u00e9nyi\u2019s generalized entropy, a continuous spectrum of generalized dimensions (also called R\u00e9nyi dimensions or fractal spectrum) Dq<\/sub> can be defined, where \u2212\u221e\u2264q\u2264\u221e[79]. A commonmethod for estimation of fractal spectra is the box-counting technique. In this study we applied a box-counting approach that is based on estimation of the moments of signal amplitude distribution and was also used in [51,95]. One reason for choosing this method is that a previous study [28] revealed a promising sleep stage classification performance of entropy of amplitudes (ENA), a measure that is closely related to the amplitude distribution of time series. In our case Dq<\/sub> is defined as follows:
\n
\n\u03b4V is the bin width or box length. The partition function can be obtained using
\n
\nwhere b(\u03b4V) denotes the number of non-overlapping bins
\n
\nVmax<\/sub> and Vmin<\/sub> are themaximumand minimum values of EEG signals recorded during measurements, respectively. \u03a7i<\/sub>(q,\u00a0\u03b4V) = pq<\/sup>i<\/sub> is a weighted measure that represents the percentage of EEG values that falls into the ith bin, and q is the moment or weight of the measure. If ni<\/sub> is the number of EEG values in the ith bin and N is the total number of the samples, than the probability that the signal falls into the ith bin of length \u03b4V is:
\n
\nSome of the Dq<\/sub> values are known under different names and widely used in the field of time series analysis. D0<\/sub> is the Hausdorff-Besicovitch or fractal dimension. For q = 1 one should use
\n
\nwhere the numerator is the well-known Shannon\u2019s entropy and can be related to ENA applied in [28]. D2 is called correlation dimension.
\nThe range of fractal spectra is defined as \u0394D= max(Dq<\/sub>)\u2212min(Dq<\/sub>), where max(Dq<\/sub>) =D\u2212\u221e<\/sub>, min(Dq<\/sub>) =D\u221e<\/sub>, i.e., \u0394D=D\u2212\u221e<\/sub> \u2212D\u221e<\/sub>, since Dq<\/sub> is a monotonically decreasing function. \u0394D is a measure of multifractality, indicates deviation from monofractal. Larger \u0394D indicates multifractality, while smaller \u0394D indicates that the analyzed system tends to possess the monofractal property.<\/p>\n

2.2.3. Power spectral measures (PSMs)<\/em>
\nTo assess the relationship between fractal measures and power spectral properties of sleep EEG signals, we estimated the relative power of widely used frequency bands (RBPs). Relative powers were used instead of absolute ones in order to avoid the effect of variation of total power across subjects. To describe spectral properties in a more compact way, we calculated the spectral edge frequency (fse<\/sub>) since this measure can be considered as a clinically well-established EEG measure for monitoring sleep cycles and depth of anesthesia [28,37,38,61].
\nBefore estimation of power spectral EEG features, Hanning windowing was applied to the selected epochs to damp out the frequency leakage, i.e., the Gibbs phenomenon that originates from truncation of time series. From these windowed time series the power spectra P(f) were obtained using the Fast Fourier Transformation (FFT) with frequency resolution f = 0.152 Hz and range [0Hz, fs<\/sub>\/2Hz]. The relative power of the B frequency band can be calculated from a power spectrum as follows:
\n<\/p>\n

where PT<\/sub> is the total power of the time series, PB<\/sub> is the total power of the B<\/em> frequency band, fi<\/sub> = (i\u22121)\u0394f<\/em> with a maximal value of fs<\/sub>\/2 when i =N, Bub<\/sub> and Blb<\/sub> are indices corresponding to the upper and lower boundary frequencies of the B band, respectively. The analyzed bands were as follows: SO: (0.5\u20131] Hz, \u03b4: (1\u20134] Hz, \u0398: (4\u20138] Hz,\u03b1: (8\u201311] Hz, \u03c3 : (11\u201316] Hz, \u03b2: (16\u201330] Hz, \u03b3: (30\u201370] Hz. These frequency bands are thought to represent specific EEG patterns. Slow oscillations (SOs) were assessed separately from delta band activity given their distinct characteristics [3,66].
\nThe spectral edge frequency was defined as the frequency up to which SEP% of the total power of the [0Hz, fcse<\/sub> Hz] frequency range is accumulated:
\n<\/p>\n

In this study SEP and cut-off f<\/em>cse<\/sub> frequency parameters were set to 95% and 70 Hz, respectively. According to Eq. (14) and the nature of sleep EEG, lower f<\/em>se<\/sub> values can be predicted for deeper sleep stages since during these states the power spectrum is biased towards lower frequencies.<\/p>\n

2.3. Statistical analysis<\/em><\/p>\n

2.3.1. Topographic distribution of EEG measures across different sleep stages<\/em>
\nNormality of the estimated features was tested using the Shapiro-Wilk W test, while the homogeneity of variances was evaluated with the Levene test. Since not all of the estimated measures matched normality and homogeneity in each channel we evaluated the effect of sleep stages using the non-parametric one-way Kruskal\u2013Wallis analysis of variances (ANOVA). Individual medians of the estimated measures were grouped using the independent variable \u201cSTAGE\u201d having factors levels NREM4, NREM2 and REM. Pair-wise comparison of sleep stages was carried out with rank post-hoc test. To test differences between bilateral symmetric scalp locations we used the Wilcoxon matched pairs test for each measure and sleep stage. For this purpose eight symmetrical channel pairs (Fp1\u2013Fp2, F7\u2013F8, F3\u2013F4, C3\u2013C4, T3\u2013T4, T5\u2013T6, P3\u2013P4, O1\u2013O2) and an additional midline channel pair (Fz\u2013Cz) were formed.<\/p>\n

2.3.2. Cross-correlation analysis<\/em>
\nCross-correlations were calculated between locations for all estimated measures (inter-site correlations) and between the measures at each location. Specifically, comparisons were carried out between monofractal and multifractal measures as well as between fractal and power spectral features. Spearman\u2019s correlation coefficients were calculated in all cases using individual medians of particular EEG measures. Sleep stages were considered separately as well as together.<\/p>\n

2.3.3. Hierarchical clustering <\/em>
\nEffect of topography was analyzed by hierarchical clustering of channels for all three sleep stages. Z-score standardization of the individual medians was carried out for all measures and channels separately. Hierarchical channel cluster trees were generated by pairing eight similarity measures (Euclidean distance (euc); standardized Euclidean distance (seu); Mahalanobis distance (mah); city block metric (cit); Minkowski metric (min); cosine distance (cos); correlation distance (cor); Chebychev distance (che)) with seven linkage methods (unweighted average distance (ave); centroid distance (cen); furthest distance (com); weighted center of mass distance (med); shortest distance (sin); inner squared distance (war); weighted average distance (wei)). Performance of each combination was assessed by calculation of the cophenet correlation coefficient (CCC). We selected the similarity-linkage pair with highest CCC value to cluster the channels into four and nine clusters. The 4-cluster analysis was aimed to reveal possible groupings of neighbor EEG channels and thus forming e.g. anterior, posterior, central, lateral or similar clusters. The 9-cluster analysis was applied to assess whether symmetrical EEG channels (see Section 2.3.1) also cluster together.
\nClustergrams were generated for measure and channel clustering using group level medians (medians of individual medians) of all measures in all channels. Standardization of features was performed across channels. Clustergrams, enclosing heat maps and dendrograms were examined for sleep stages separately. Hierarchical channel cluster trees were generated using the cosine similarity metric and the unweighted average linkage method. Measure dendrograms were constructed applying the Euclidean distance as a similarity measure and the unweighted average method for linkage. Channel clustering was also carried out based on the two fractal measures as well as combining the seven relative band powers.<\/p>\n

2.3.4. Linear discriminant analysis <\/em>
\nClassification of sleep stages was performed with linear discriminant analysis (LDA) using all features and all channels separately both at individual and group levels. At the individual level 3\u00d790 estimated values were used for each subject, while 22\u00d73\u00d790 values were considered at the group level. After a 10-fold cross-validation procedure the accuracy of classifications was assessed with Kappa analysis of the confusion (also called error) matrices.<\/p>\n

2.3.4.1. Confusion matrix.<\/em>
\nA confusion matrix C is a k\u00d7k quadratic matrix, where k is the number of classes. Columns of C stand for the reference data (classification performed by the human expert in this case) and rows denote the classified data (LDA classification in this case). Hence, Cij = nij is a count of EEG segments classified by the human expert into the jth class but classified to the ith class using LDA. For an example see Table 1 that presents the confusion matrix obtained by LDA classification of sleep stages usingD measure in the Cz channel of a representative subject #16. The number of segments classified to the i<\/em>th class using LDA is
\n<\/p>\n

while
\n<\/p>\n

is the total number of segments classified to the j<\/em>th sleep stage by the human expert. Let pi,j<\/sub> denote the proportion of samples in the i<\/em>, jth cell of C, corresponding to ni,j<\/sub><\/em>:
\n<\/p>\n

where n is the total number of the analyzed EEG segments. Furthermore, marginals pi+<\/sub><\/em> and p+j<\/sub><\/em> can be defined by
\n<\/p>\n

and
\n<\/p>\n\n\n\n\n\n\n\n\n\n\n
Table1<\/strong>
\nConfusion matrix obtained for LDA classification of sleep stages using estimated D values in the Cz channel of a representative subject #16.<\/td>\n<\/tr>\n
\u00a0<\/td>\nHEC(reference)<\/td>\nni+<\/sub><\/td>\n<\/tr>\n
NREM4<\/td>\nNREM2<\/td>\nREM<\/td>\n\u00a0<\/td>\n<\/tr>\n
LDAC<\/td>\nNREM4<\/td>\n87<\/td>\n0<\/td>\n0<\/td>\n87<\/td>\n<\/tr>\n
 <\/td>\nNREM2<\/td>\n3<\/td>\n76<\/td>\n9<\/td>\n88<\/td>\n<\/tr>\n
 <\/td>\nREM<\/td>\n0<\/td>\n14<\/td>\n81<\/td>\n95<\/td>\n<\/tr>\n
n+j<\/sub><\/td>\n <\/td>\n90<\/td>\n90<\/td>\n90<\/td>\n\u00a0<\/td>\n<\/tr>\n
The corresponding values area sfollows: \u02c6K=0.85, \u02c6var(\u02c6K)=7.25\u00b710\u22124 and OA=90.37%. HEC: classification carried out by the human expert; LDAC: classification performed by linear discriminant analysis.<\/small><\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

2.3.4.2. Kappa analysis. <\/em>
\nThe Kappa analysis is a technique used to statistically test whether two confusion matrices are significantly different. The result of Kappa analysis is a KHAT statistic\u00a0\u02c6K, an estimate of Kappa that is a measure of classification accuracy or agreement. It is based on the difference of the actual agreement (the major diagonal of the error matrix) and the chance agreement (indicated by the row and column totals, i.e. marginals). If the actual agreement is<\/p>\n

<\/p>\n

and the chance agreement is defined as
\n<\/p>\n

the estimate of Kappa is given by
\n<\/p>\n

The variance of Kappa is as follows:<\/p>\n

<\/p>\n

where<\/p>\n


\n
\n<\/p>\n

and
\n<\/p>\n

\u02c6K\u00a0can take values from the range [\u22121, 1]. However, positive values are expected\u00a0since there should be a positive correlation between classifications performed by\u00a0the human expert and LDA. Landis and Koch characterized the possible ranges for\u00a0KHAT into three groups [52]: a value greater than 0.80 (i.e., >80%) represents strong\u00a0agreement; a value between 0.40 and 0.80 (i.e., 40\u201380%) represents moderate agreement\u00a0and a value below 0.40 (i.e., <40%) represents poor agreement. As it can be\u00a0seen in Table 1, a strong agreement (\u02c6K = 0.85) between classifications performed by\u00a0the human expert and LDA was found using the \u0394D measure in the central channel\u00a0of subject #16.
\nIt was shown that the Kappa analysis overestimates the proportion of randomness\u00a0and thus underestimates the classification accuracy [18,19]. Therefore, where\u00a0applicable, we also provide the most widely used classification performance measure,\u00a0the overall accuracy
\n<\/p>\n

For the particular confusion matrix presented in Table 1 with \u02c6K = 0.85, the\u00a0corresponding overall accuracy was 90.37%.<\/p>\n

The fact that the \u02c6K statistic is asymptotically normally distributed provides a\u00a0means for testing the significance of \u02c6K for a single confusion matrix to determine if\u00a0the agreement between the classification performed between the human expert and\u00a0LDA is significantly grater than zero, i.e., LDA performs better that than a random\u00a0classifier. The test statistic is expressed by:
\n<\/p>\n

Given the null hypothesis H0<\/sub> : K = 0, and the alternative H1<\/sub> : K \u2260 0, H0 is rejected\u00a0if Z \u2265 Z\u03b1<\/sub>\/2, where \u03b1\/2 is the confidence level of the two-tailed Z test.<\/p>\n

Moreover, there is a test to determine whether two confusion matrices are\u00a0significantly different. This provide us the opportunity to compare classifications\u00a0performed using different EEG features and channels. Let \u02c6K1<\/sub> and \u02c6K2<\/sub> ( var(\u02c6K1<\/sub>)\u00a0and var(\u02c6K2<\/sub>) )\u00a0denote the estimates of the \u02c6K statistic (estimates of variances) for confusion\u00a0matrices #1 and #2, respectively. The test statistic in this case is defined\u00a0as<\/p>\n

<\/p>\n

Z is standardized and normally distributed. Given the null hypothesisH0<\/sub> : K1 \u2212K2 =0,\u00a0and the alternative H1<\/sub> : K1 \u2212K2 \u2260 0, H0 is rejected if Z \u2265 Z\u03b1\/2.
\nFinally, in addition to computing statistics for an entire confusion matrix, it may\u00a0be useful to look at the agreement of individual classes. Individual class accuracy can\u00a0be tested using the conditional Kappa coefficient. The estimates of the conditional\u00a0Kappa coefficient and its variance for the ith class are given by
\n
\nand
\n<\/p>\n

respectively. The same comparison tests available for the Kappa coefficient apply to\u00a0this conditional Kappa for an individual class. For more details and comparison of\u00a0Kappa analysis to other methods we refer to [18,19].<\/p>\n

3. Results<\/strong><\/p>\n

3.1. <\/em>Distribution of EEG measures across vigilance states and <\/em>topographic locations<\/em><\/p>\n

Topographic distributions of group level medians for the three\u00a0sleep stages as well as their differences are shown in Fig. 1. Results\u00a0obtained for the fractal measures were in agreement with those\u00a0presented in [95]. Namely, highest H values emerged frontally during\u00a0all sleep stages, while the minimum was found during REM\u00a0in the central zone. A HNREM4<\/sub> >HNREM2<\/sub> >HREM<\/sub> trend was present\u00a0across the whole head surface. Measure \u0394D, showed an opposite\u00a0trend: DREM<\/sub> >DNREM2<\/sub> >DNREM4<\/sub>. Minima of \u0394D could be\u00a0found in the fronto-central region during all sleep stages, while\u00a0higher values were observed in the posterior circumferential channels.\u00a0Salient H<\/em> difference peaks that occurred for sleep stage pairs\u00a0NREM4-REM and NREM2-REM could not be observed in the case\u00a0of \u0394D. Power spectral measures also exhibited expected topography.\u00a0Relative band powers of slow activities (SO and \u03b4 bands)\u00a0were higher for NREM4 than NREM2 as well as for NREM2 than\u00a0REM. Generally, PSOr<\/sub> showed amore even topographic distribution\u00a0when compared to P\u03b4r<\/sub> in all sleep stages. Across all sleep stages the\u00a0minimum of PSOr<\/sub> occurred at the vertex during REM sleep. Frontal\u00a0regions exhibited slightly higher values of PSOr<\/sub> compared to other\u00a0regions during NREM2 and REM. During NREM4 higher PSOr<\/sub> values\u00a0occurred bilaterally in the fronto-temporal region and in C4,\u00a0P4, O2 channels. P\u03b4<\/sub>r<\/sub> exhibited higher values in the fronto-central\u00a0channels during NREM4 and NREM2 and in the central region during\u00a0REM sleep. Generally, faster activities (above 4 Hz) showed an\u00a0opposite trend with lower relative band power values for deeper\u00a0sleep stages. During NREM4 relatively even topographic distributions\u00a0were found for faster activities. During NREM2 higher values\u00a0appeared in the posterior region, showing maxima in the parietal\u00a0channels for P\u03b4<\/sub>r<\/sub>. REM sleep revealed a more diverse topography\u00a0of faster activities. Maximum of theta activity was found centrally.\u00a0Highest values in the \u03b1 and \u03c3 bands occurred in posterior channels.\u00a0Finally, relative power of \u03b2 and \u03b3 frequency bands peaked\u00a0in temporal channels. Spectral edge frequency showed lower values\u00a0for deeper sleep stages as it was conjectured from Eq. (14).\u00a0Slightly higher values of fse<\/sub> were present in posterior channels\u00a0during NREM4 and NREM2, while during REM higher values were\u00a0located in temporal channels.<\/p>\n

Comparing sleep stages using one-way Kruskal-Wallis ANOVA\u00a0revealed highly significant (p < 0.00001) differences for all measures\u00a0in all channels except for the relative power of the \u03b4 band.\u00a0For detailed results see the supplementary Table S1. The level of\u00a0significance for P\u03b4r<\/sub> varied across channels between p < 0.01 and\u00a0p < 0.00001. Pair-wise comparison of sleep stages using the rank\u00a0 post-hoc test resulted in most significant differences between\u00a0sleep stages NREM4 and REM for all measures and channels\u00a0with the exception of P\u03c3r<\/sub>. This latter measure exhibited highest\u00a0significance values between NREM4 and NREM2 in fronto-centroparietal\u00a0channels (F3, Fz, F4, C3, Cz, C4, P3 and P4). In general,\u00a0least or non-significant differences were observed between sleep\u00a0stages NREM2 and REM. Comparison between NREM4 and NREM2\u00a0revealed significant values for all measures with the exception of\u00a0the relative \u03b4 band power which reached significancy in F3, C3, P3\u00a0and P4 channels only.<\/p>\n

<\/p>\n

Fig. 1. <\/strong>Topographic distribution of group level medians (medians of individual medians) for the analyzed sleep stages and differences of these medians between sleep stages.\u00a0Relative band powers are denoted by the labels of the corresponding frequency bands.<\/p>\n

3.1.1. Interhemispheric comparisons<\/em><\/p>\n

As expected, Wilcoxon matched pairs test revealed (Table 2)\u00a0more significant differences for the non-symmetric Fz\u2013Cz channel\u00a0pair as compared with the other symmetric channel pairs. Out of\u00a0the 30 cases (10 measures\u00d73 stages) the Fz\u2013Cz channel pair exhibited\u00a019 significant values. Regarding the symmetric channel pairs\u00a0most significant differences were found for channel pairs P3\u2013P4\u00a0(10 cases) and O1\u2013O2 (8 cases), while least significant differences\u00a0appeared for the frontal channel pairs Fp1\u2013Fp2 (2 cases), F7\u2013F8 (4\u00a0cases) and F3\u2013F4 (4 cases). In posterior channel pairs more significant\u00a0results occurred during deeper sleep stages while in frontal\u00a0channel pairs the least significant differences were found during\u00a0sleep stage NREM4. Most significant interhemispheric differences\u00a0occurred for relative powers of delta and beta frequency bands (7\u00a0cases for both out of total 24 = 3 sleep stages\u00d78 symmetrical channel\u00a0pairs). For P\u03b4<\/sub>r <\/sub>significant cases were distributed similarly across\u00a0sleep stages, while P\u03b2r<\/sub> revealed the most (5 cases) significant differences for NREM2 sleep. PSOr<\/sub> resulted in 4 significant cases, all\u00a0during NREM4. By contrast, no significant interhemispheric differences\u00a0were found for P\u03b3r<\/sub> in this sleep stage. No gross tendencies\u00a0were observed for P\u03b1r<\/sub> and P\u03c3r<\/sub> across sleep stages and locations,\u00a0however, there were some significant results. Compact EEG features\u00a0(H,\u0394D and fse<\/sub>) altogether revealed a lownumberof significant\u00a0results: 5, 4 and 0 significant cases for NREM4, NREM2 and REM,\u00a0respectively.
\nConsidering all 10 measures NREM2 (20 cases) and NREM4 (17\u00a0cases) revealed twice more significant differences as compared to\u00a0REM sleep (8 cases out of total 80 = 10 measures\u00d78 symmetrical\u00a0channel pairs).<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Table2<\/strong>
\nResults of the Wilcoxon matched pairs test.<\/td>\n<\/tr>\n
M<\/td>\nS<\/td>\nChannelpair<\/td>\n<\/tr>\n
 <\/td>\n <\/td>\nFp1Fp2<\/td>\nF7F8<\/td>\nT3T4<\/td>\nT5T6<\/td>\nO1O2<\/td>\nF3F4<\/td>\nC3C4<\/td>\nP3P4<\/td>\nFzCz<\/td>\nSC<\/td>\n<\/tr>\n
H<\/td>\nN4<\/td>\n>x<\/td>\n>x<\/td>\n>1<\/td>\n<x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<1<\/td>\n>3<\/td>\n2<\/td>\n<\/tr>\n
N2<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n>3<\/td>\n0<\/td>\n<\/tr>\n
R<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>3<\/td>\n0<\/td>\n<\/tr>\n
\u0394D<\/td>\nN4<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n>1<\/td>\n>x<\/td>\n>x<\/td>\n<3<\/td>\n1<\/td>\n<\/tr>\n
N2<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<1<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<1<\/td>\n>x<\/td>\n2<\/td>\n<\/tr>\n
R<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n0<\/td>\n<\/tr>\n
SO<\/td>\nN4<\/td>\n<x<\/td>\n>1<\/td>\n>x<\/td>\n<x<\/td>\n<3<\/td>\n>x<\/td>\n<3<\/td>\n<2<\/td>\n<x<\/td>\n4<\/td>\n<\/tr>\n
N2<\/td>\n>x<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>3<\/td>\n0<\/td>\n<\/tr>\n
R<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>3<\/td>\n0<\/td>\n<\/tr>\n
\u03b4<\/td>\nN4<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>1<\/td>\n>1<\/td>\n>x<\/td>\n2<\/td>\n<\/tr>\n
N2<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n>2<\/td>\n>1<\/td>\n<x<\/td>\n>x<\/td>\n2<\/td>\n<\/tr>\n
R<\/td>\n>1<\/td>\n>2<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>1<\/td>\n>x<\/td>\n>x<\/td>\n<1<\/td>\n3<\/td>\n<\/tr>\n
\u03b8<\/td>\nN4<\/td>\n<x<\/td>\n<x<\/td>\n<1<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n<3<\/td>\n1<\/td>\n<\/tr>\n
N2<\/td>\n<x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n<1<\/td>\n<3<\/td>\n<2<\/td>\n2<\/td>\n<\/tr>\n
R<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n>1<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n1<\/td>\n<\/tr>\n
\u03b1<\/td>\nN4<\/td>\n<x<\/td>\n<x<\/td>\n<1<\/td>\n>x<\/td>\n>1<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n2<\/td>\n<\/tr>\n
N2<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<2<\/td>\n<2<\/td>\n<x<\/td>\n2<\/td>\n<\/tr>\n
R<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n>x<\/td>\n<4<\/td>\n0<\/td>\n<\/tr>\n
\u03c3<\/td>\nN4<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>2<\/td>\n>x<\/td>\n>x<\/td>\n>2<\/td>\n<3<\/td>\n2<\/td>\n<\/tr>\n
N2<\/td>\n<1<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n>1<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n<4<\/td>\n2<\/td>\n<\/tr>\n
R<\/td>\n<x<\/td>\n>x<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<1<\/td>\n<2<\/td>\n1<\/td>\n<\/tr>\n
\u03b2<\/td>\nN4<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n>1<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<4<\/td>\n1<\/td>\n<\/tr>\n
N2<\/td>\n<x<\/td>\n<1<\/td>\n<2<\/td>\n<x<\/td>\n>x<\/td>\n<1<\/td>\n<1<\/td>\n<1<\/td>\n<4<\/td>\n5<\/td>\n<\/tr>\n
R<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n>1<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n1<\/td>\n<\/tr>\n
\u03b3<\/td>\nN4<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n>x<\/td>\n>x<\/td>\n<4<\/td>\n0<\/td>\n<\/tr>\n
N2<\/td>\n>x<\/td>\n<1<\/td>\n<x<\/td>\n<2<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n<1<\/td>\n<2<\/td>\n3<\/td>\n<\/tr>\n
R<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<2<\/td>\n<1<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n2<\/td>\n<\/tr>\n
fse<\/td>\nN4<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>2<\/td>\n<x<\/td>\n<1<\/td>\n>x<\/td>\n<2<\/td>\n2<\/td>\n<\/tr>\n
N2<\/td>\n<x<\/td>\n<x<\/td>\n<1<\/td>\n<1<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<3<\/td>\n2<\/td>\n<\/tr>\n
R<\/td>\n>x<\/td>\n>x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n<x<\/td>\n>x<\/td>\n0<\/td>\n<\/tr>\n
All<\/td>\nN4<\/td>\n0<\/td>\n1<\/td>\n3<\/td>\n0<\/td>\n5<\/td>\n1<\/td>\n3<\/td>\n4<\/td>\n7<\/td>\n17<\/td>\n<\/tr>\n
N2<\/td>\n1<\/td>\n2<\/td>\n2<\/td>\n3<\/td>\n1<\/td>\n2<\/td>\n4<\/td>\n5<\/td>\n7<\/td>\n20<\/td>\n<\/tr>\n
R<\/td>\n1<\/td>\n1<\/td>\n0<\/td>\n2<\/td>\n2<\/td>\n1<\/td>\n0<\/td>\n1<\/td>\n5<\/td>\n8<\/td>\n<\/tr>\n
AS<\/td>\n2<\/td>\n4<\/td>\n5<\/td>\n5<\/td>\n8<\/td>\n4<\/td>\n7<\/td>\n10<\/td>\n19<\/td>\n45<\/td>\n<\/tr>\n
\n

M: measure, relative band powers are denoted by the labels of the corresponding frequencybands; S: sleepstage; SC: number of symmetrical channel pairs (the midline Fz\u2013Cz channel pair not included) that resulted significant differences; All: number of measures that revealed significant differences summed for sleep stages NREM4 (N4), NREM2 (N2) and REM (R) separately as well as considering all sleep stages (AS) together. The > (<) sign denotes greater (smaller) group level medians in the electrodes above the left hemisphere and Fz and it is followed by the significance level sign: x(notsignificant), 1 (p<0.05), 2 (p<0.01), 3 (p<0.001), 4 (p<0.0001).<\/small><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

3.2. Cross-correlation analysis<\/em><\/p>\n

3.2.1. Inter-site correlations
\n<\/em>In Fig. 2 the 35 strongest inter-site correlations (p < 0.05) are\u00a0denoted by black lines drawn between the appropriate locations\u00a0for all 10 EEG measures and for each sleep stage separately as well\u00a0as together (also see Supplementary video Inter_site_correlations.avi\u00a0for different number of inter-site correlations). Considering all\u00a0sleep stages together highest inter-site correlations were observed\u00a0centrally (F3, Fz, F4, C3, Cz, C4, P3, P4) for all features except for\u00a0the relative power of the band where highest correlations were\u00a0found intrahemispherically. Sleep stages were characterized by different\u00a0topography in inter-site correlation maps. In general, power\u00a0spectral measures (except for P\u03b3r<\/sub>) showed strongest correlations\u00a0between anterior channels during NREM4. During NREM2 and REM\u00a0highest correlations were observed more posteriorly. P\u03b3r<\/sub> exhibited\u00a0higher correlations within than between hemispheres during\u00a0NREM4 and NREM2, a tendency which was not true for REM. Compared\u00a0to the topographic properties of the above spectral measures,\u00a0H<\/em> exhibited an opposite trend with higher posterior correlations\u00a0during NREM4 and higher anterior correlations during NREM2 and\u00a0REM. At the same time \u0394D did not reveal such differences between\u00a0sleep stages. In agreement with previous results presented in [95]\u00a0\u0394D showed higher inter-site correlations compared to H<\/em>.<\/p>\n

<\/p>\n

Fig. 2. <\/strong>Highest 35 inter-site correlations denoted by black lines drawn between the\u00a0appropriate locations. Spearman\u2019s correlation coefficients were calculated considering\u00a0all sleep stages together (column ALL) as well as separately. Only significant\u00a0(p < 0.05) correlations are depicted. Lowest presented correlation values can be\u00a0found above the topographic maps. Relative band powers are denoted by the labels\u00a0of the corresponding frequency bands.<\/p>\n

3.2.2. Cross-correlation of measures<\/em><\/p>\n

3.2.2.1. Cross-correlation between the fractal measures<\/em>.
\nWhen all\u00a0sleep stages were considered together strong negative crosscorrelations\u00a0(p < 0.00001) between H<\/em> and \u0394D were found with\u00a0weakest correlations in the occipital zone (Fig. 3). Evaluating sleep\u00a0stages separately one could observe stronger and more significant\u00a0correlation values for deeper sleep stages. During NREM4 lower\u00a0values were found in the occipital and the fronto-polar regions.\u00a0During NREM2 weakest correlations were found posteriorly. REM\u00a0sleep showed non-significant negative correlations in the circumferential\u00a0channels and non-significant but positive correlation in\u00a0the F3, Fz, and F4 channels.<\/p>\n

<\/p>\n

Fig. 3.<\/strong> Spearman cross-correlations between H and \u0394D considering all sleep stages\u00a0together as well as separately. Significant values (p < 0.05) are denoted on the left\u00a0side of the color bars using the following notations: no sign (none of the values are\u00a0significant); only + (all values are significant); + with a dash (only values below the\u00a0dash are significant).<\/p>\n

3.2.2.2. Cross-correlation between fractal and power spectral measures.<\/em>
\nResults of cross-correlation analyses between fractal and\u00a0power spectral measures are summarized in Fig. 4. Generally, a positive cross-correlation was observed between H and slower brain\u00a0activities (SO and \u03b4 bands), while faster activities (above 4 Hz)\u00a0were negatively correlated with the monofractal measureH. Higher\u00a0and more significant correlations were found for deeper sleep\u00a0stages. Overall, the strongest positive correlation was revealed for\u00a0the relative power of the SO band, while the strongest negative\u00a0correlation was found for the relative power of the theta band.\u00a0Generally, weaker correlations appeared in the anterior channels\u00a0during NREM4. During NREM2 stronger correlations (positive for\u00a0the SO and negative for the \u03b8 band) were found in the anterior\u00a0region while faster activities (\u03c3,\u00a0\u03b2, and\u00a0 \u03b3\u00a0\u00a0bands) exhibited weakest\u00a0correlations with H<\/em> in posterior channels. During REM stronger\u00a0positive correlation between slow activities (SO and \u03b4 bands) and\u00a0H was found in the temporal and occipital channels while faster\u00a0activities were negatively correlated with the monofractal measure\u00a0H. Above the \u03b8 band stronger negative correlations were present\u00a0in the circumferential channels decreasing around the vertex and\u00a0even switching to positive correlation values in the case of \u03b1 and \u03b3\u00a0bands.<\/p>\n

Generally, correlations between \u0394D and RBPs exhibited relationships\u00a0with a sign opposite to that found for measure H. Namely,\u00a0\u0394D was negatively correlated with slow (SO and \u03b4) while positively\u00a0correlated with faster (above 4 Hz) activities. Similarly to\u00a0H, more significant values appeared for deeper sleep stages. Compared\u00a0to H, correlations of \u0394D with slow activities were weaker\u00a0and less significant. Highest positive correlation values between\u00a0\u0394D and P\u0398<\/sub>r<\/sub> were found in the anterior channels regardless of sleep\u00a0depth. Relative power of alpha and sigma bands exhibited strongest\u00a0positive correlations with \u0394D in the temporal channels. P\u03b2r<\/sub> and\u00a0P\u03b3r <\/sub>showed strongest positive correlations with \u0394D around the Fz\u00a0channel during NREM4, while the nadirs of these correlations were\u00a0found during REM sleep in the same region.
\nInspection of cross-correlation maps between spectral edge frequency\u00a0and the fractal measures indicated that these correlations\u00a0reflect contribution of certain frequency bands in a compact way,\u00a0such as in the case of the correlation between fse<\/sub> and H during\u00a0NREM4 where the minimum of correlations was found frontally.
\nTo estimate the contribution of single frequency bands to the\u00a0overall variation of compact measures, one must bear in mind that\u00a0certain band powers are also correlated [11]. To control for this\u00a0effect, we performed multiple linear regression (MLR) analyses\u00a0with relative band powers as predictors and compact EEG measures\u00a0as response variables. At this point we analyzed sleep stages\u00a0together and only those channels where best classifications were\u00a0predicted based on supplementary Table S1 and previous results\u00a0presented in [95]. Thus, for H MLR was carried out in channel Cz\u00a0with a result
\n<\/p>\n

and statistics F(7, 58) = 200.99, p < 0.00001, Std . Err . Est . = 0.01,\u00a0R = 0.98, R2<\/sup> = 0.96, adjusted R2 = 0.96. For \u0394D MLR was performed\u00a0considering the T4 channel. The obtained result was\u00a0
\n<\/p>\n

with statistics F(7, 58)\u00a0= 77.54, p < 0.00001, Std . Err . Est . = 0.12,\u00a0R = 0.95, R2<\/sup> = 0.9, adjusted R2<\/sup> = 0.89. Finally, contribution of different\u00a0frequency bands to the spectral edge frequency was tested in\u00a0channel T6 with the result
\n<\/p>\n

and the following statistics F(7, 58) = 360, p < 0.00001,\u00a0Std . Err . Est . = 1.23, R = 0.99, R2<\/sup> = 0.98, adjusted R2<\/sup> = 0.97. Coefficients\u00a0of relative band powers were standardized and their\u00a0standard errors were provided in brackets. Only coefficients with\u00a0stars above them were significant with notation: ** (p < 0.01), ***\u00a0(p < 0.001), **** (p < 0.0001) and ***** (p < 0.00001).<\/p>\n

<\/p>\n

Fig. 4. <\/strong>Spearman cross-correlations between fractal and power spectral measures (PSMs). The left panel depicts results obtained for H. Cross-correlations between \u0394D and\u00a0PSMs are presented in the right panel. Sleep stages were considered together (columns denoted by ALL) as well as separately. Significant values (p < 0.05) are marked on the\u00a0left side of the color bars using the following notations: no sign (none of the values are significant); only + (all values are significant); + with a dash (only values above\/below\u00a0the dash are significant). Relative band powers are denoted by the labels of the corr esponding frequency bands.<\/p>\n

3.3. Clustering of channels and measures<\/em><\/p>\n

Hierarchical channel cluster trees were generated for all three\u00a0sleep stages and all EEG features separately using the best similarity\u00a0and linkage combinations. Visual inspection of the dendrograms\u00a0revealed both common and distinct channel clusters across sleep\u00a0stages (see e.g. Fig. 5 for measure \u0394D). For statistical evaluation\u00a0channels were clustered into 4 and 9 clusters, respectively\u00a0(supplementary Table S2).<\/p>\n

<\/p>\n

Fig. 5.<\/strong> Dendrograms of EEG channels obtained using the multifractal measure\u00a0\u0394D. Hierarchical cluster trees were generated applying the best similarity\/linkage\u00a0(Sim\/Lin) methods according to the cophenet correlation coefficient (CCC). For the\u00a0abbreviation of Sim\/Lin methods see Section 2.3.3.<\/p>\n

As can be seen in Table S2 and Table 3, the 9-cluster analysis\u00a0showed that most EEG features revealed proximity of symmetrical\u00a0channels in the frontal region and during NREM4. As compared,\u00a0during REM the symmetric channels were clustered together more\u00a0posteriorly and circumferentially. Regardless of the sleep stage\u00a0most of the measures (6\u20139 out of 10) indicated the proximity of\u00a0F3\u2013F4, C3\u2013C4 and P3\u2013P4 channels. The non-symmetrical Fz and Cz\u00a0channels clustered together in much less cases. A more detailed\u00a0examination of data in supplementary Table S2 unveiled that Fz\u00a0tended to cluster with frontal F3 and F4 channels, while Cz mostly\u00a0formed common clusters with the central channels C3 and C4. With\u00a0regard to P\u03b3r<\/sub> symmetric channels did not cluster together during\u00a0NREM4 and NREM2 sleep stages but did so in REM sleep.<\/p>\n\n\n\n\n\n\n\n\n\n\n
Table 3<\/strong>
\nNumber of measures that indicated common clusters for channel pairs based on results of the 9-cluster analysis presented in supplementary Table S2.<\/td>\n<\/tr>\n
Sleep stage<\/td>\nChannel pair<\/td>\n<\/tr>\n
Fp1Fp2<\/td>\nF7F8<\/td>\nT3T4<\/td>\nT5T6<\/td>\nO1O2<\/td>\nF3F4<\/td>\nC3C4<\/td>\nP3P4<\/td>\nFzCz<\/td>\nSC<\/td>\n<\/tr>\n
NREM4<\/td>\n6<\/td>\n2<\/td>\n0<\/td>\n0<\/td>\n0<\/td>\n9<\/td>\n9<\/td>\n6<\/td>\n1<\/td>\n32<\/td>\n<\/tr>\n
NREM2<\/td>\n5<\/td>\n0<\/td>\n0<\/td>\n0<\/td>\n2<\/td>\n7<\/td>\n7<\/td>\n7<\/td>\n3<\/td>\n28<\/td>\n<\/tr>\n
REM<\/td>\n1<\/td>\n1<\/td>\n2<\/td>\n1<\/td>\n3<\/td>\n9<\/td>\n7<\/td>\n7<\/td>\n5<\/td>\n31<\/td>\n<\/tr>\n
Alls<\/td>\n12<\/td>\n3<\/td>\n2<\/td>\n1<\/td>\n5<\/td>\n25<\/td>\n23<\/td>\n20<\/td>\n9<\/td>\n91<\/td>\n<\/tr>\n
SC denotes sums across symmetrical channel pairs (the midline Fz\u2013Cz channel pair not included), while Alls indicates sums across sleep stages.<\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In the 4-cluster analysis, where all measures were considered\u00a0separately, a rather uneven clustering of channels was found.\u00a0Notably, in almost all cases there were channels (typically the circumferential\u00a0ones such as: Fp1, Fp2, O1, O2, T5, T6) that formed\u00a0individual clusters because of their large distance from the remaining\u00a0EEG derivations. At the same time, several topographic features\u00a0revealed by the above analyses could be verified. For example, highest\u00a0P\u03c3r<\/sub> values in parietal channels during NREM2 (Fig. 1) were\u00a0reflected in a separate cluster formed by P3 and P4 channels. As\u00a0another example disconnection of the hemispheres during NREM4\u00a0with regard to the relative power of the \u03b3 band (Fig. 2) was also\u00a0supported by forming separate clusters over left and right hemispheres.<\/p>\n

Hierarchical clustering of channels was also carried out using\u00a0all measures together to minimize the effect of \u201coutlier\u201d channels\u00a0and to assess topography of overall brain dynamics. Performing\u00a04-cluster analysis of hierarchical channel cluster trees (Fig. 6)\u00a0revealed symmetric channel clusters for all sleep stages (Table 4).\u00a0In general, separate clusters were formed by anterior, central, temporal\u00a0and posterior channels. Topographic boundaries of these\u00a0clusters slightly varied across sleep stages.<\/p>\n\n\n\n\n\n\n\n\n\n\n
Table 4<\/strong>
\nClustering of EEG channels into 4 clusters using all measures together.<\/td>\n<\/tr>\n
Cluster #<\/td>\nSleep stage<\/td>\n<\/tr>\n
NREM4<\/td>\nNREM2<\/td>\nREM<\/td>\n<\/tr>\n
1<\/td>\nFp1, Fp2, F3, F4, Fz<\/td>\nFp1, Fp2, F7, F8<\/td>\nFp1, Fp2, F7, F8<\/td>\n<\/tr>\n
2<\/td>\nC3, C4, Cz<\/td>\nF3, F4, Fz, C3, C4, Cz<\/td>\nF3, F4, Fz, C3, C4, Cz<\/td>\n<\/tr>\n
3<\/td>\nF7, F8, T3, T4<\/td>\nP3, P4<\/td>\nT3, T4, T5, T6<\/td>\n<\/tr>\n
4<\/td>\nT5, T6, P3, P4, O1, O2<\/td>\nT3, T4, T5, T6, O1, O2<\/td>\nP3, P4, O1, O2<\/td>\n<\/tr>\n
Hierarchical cluster trees were generated using the cosine similarity metric and the unweighted average linkage method. The cophenet correlation coefficient values were as follows: 0.749 (NREM4), 0.843 (NREM2) and 0.826 (REM).<\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

When combining the fractal measures only (Table 5) or the relative\u00a0band powers only (Table 6) less symmetrical and slightly\u00a0different topographic grouping of channels was obtained, e.g. the\u00a0separate cluster that was formed for the parietal channels during\u00a0NREM2 using all measures together (Table 4) was not found using\u00a0the fractal measures only.
\nIn the next step we hierarchically clustered the computed EEG\u00a0measures based on the 18 EEG channels (Fig. 6). In all sleep stages\u00a0H was closest to relative band powers of slow activities (SO and \u03b4\u00a0bands). Measure \u0394D was clustered with P\u03b2r<\/sub> and P\u03b3r<\/sub> during NREM4\u00a0and NREM2, while it formed a common cluster with P\u03b1r<\/sub> and P\u03c3r <\/sub>during REM. As expected from Eq. (14), with sleep deepening fse <\/sub>was clustered with decreasing frequency bands, i.e. during REM fse <\/sub>was clustered with P\u03b3r<\/sub>, during NREM2 with P\u03b1r <\/sub>and during NREM4\u00a0with P\u03b8r<\/sub>.<\/p>\n\n\n\n\n\n\n\n\n\n\n
Table 5<\/strong>
\nClustering of EEG channels into 4 clusters using the fractal measures only.<\/td>\n<\/tr>\n
Cluster #<\/td>\nSleep stage<\/td>\n<\/tr>\n
NREM4<\/td>\nNREM2<\/td>\nREM<\/td>\n<\/tr>\n
1<\/td>\nFp1, Fp2, F3, F4, Fz<\/td>\nFp1, Fp2, F7, F8<\/td>\nFp1, Fp2, F7, F8<\/td>\n<\/tr>\n
2<\/td>\nC3, C4, Cz, P3<\/td>\nF3, F4, Fz<\/td>\nF3, F4, Fz<\/td>\n<\/tr>\n
3<\/td>\nF7, F8, T3, T4, P4<\/td>\nC3, C4, Cz, P3, P4<\/td>\nC3, C4, Cz, P3, P4<\/td>\n<\/tr>\n
4<\/td>\nT5, T6, O1, O2<\/td>\nT3, T4, T5, T6, O1, O2<\/td>\nT3, T4, T5, T6, O1, O2<\/td>\n<\/tr>\n
Hierarchical cluster trees were generated using the cosine similarity metric and the unweighted average linkage method. The cophenet correlation coefficient values were as follows: 0.739 (NREM4), 0.776 (NREM2) and 0.926 (REM).<\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n\n
Table 6<\/strong>
\nClustering of EEG channels into 4 clusters using the relative band power measures only.<\/td>\n<\/tr>\n
Cluster #<\/td>\nSleep stage<\/td>\n<\/tr>\n
NREM4<\/td>\nNREM2<\/td>\nREM<\/td>\n<\/tr>\n
1<\/td>\nFp1, Fp2, F7, F8<\/td>\nFp1, Fp2, F7, F8 F3, F4, Fz<\/td>\nFp1, Fp2, F7, F8<\/td>\n<\/tr>\n
2<\/td>\nF3, F4, Fz, C3, C4, Cz<\/td>\nC3, C4, Cz<\/td>\nF3, F4, Fz, C3, C4, Cz<\/td>\n<\/tr>\n
3<\/td>\nT3, T4, P4<\/td>\nP3, P4<\/td>\nT3, T4, T6<\/td>\n<\/tr>\n
4<\/td>\nT5, T6, P3, O1, O2<\/td>\nT3, T4, T5, T6, O1, O2<\/td>\nT5, P3, P4, O1, O2<\/td>\n<\/tr>\n
Hierarchical cluster trees were generated using the cosine similarity metric and the unweighted average linkage method. The cophenet correlation coefficient values were as follows: 0.733 (NREM4), 0.876 (NREM2) and 0.842 (REM).<\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/p>\n

Fig. 6. <\/strong>Clustergrams generated for sleep stages NREM4, NREM2 and REM using\u00a0group level medians of all measures in all channels. Heat maps and hereby the\u00a0dendrograms were generated after z-standardization of the measures across the\u00a0channels. Hierarchical channel cluster trees were generated using the cosine similarity\u00a0metric and the unweighted average linkage method. The corresponding cophenet\u00a0correlation coefficients (CCCs) were as follows: 0.749 (NREM4), 0.843 (NREM2) and\u00a00.826 (REM). Measure dendrograms were constructed applying the Euclidean distance\u00a0as a similarity measure and the unweighted average method for linkage (CCC:\u00a00.959 (NREM4), 0974 (NREM2) and 0.886 (REM)). Relative band powers are denoted\u00a0by the labels of the corresponding frequency bands.<\/p>\n

3.4. Classification of sleep stages<\/p>\n

Wecarried out a sleep stage classification using LDA both at individual\u00a0and group levels. Maximal \u02c6K values across subjects (Fig. 7A)\u00a0yielded best classifications for \u0394D, fse<\/sub> and P\u03b2r<\/sub> features. There were\u00a09 channels with highest \u02c6K values for \u0394D and 8 channels for fse<\/sub>.\u00a0Kappa analysis did not reveal significant differences between the\u00a0performances of these two measures at either channel (Table 7,\u00a0imax<\/em> test). Taking the average of \u02c6K values across subjects, \u0394D provided\u00a0the best performance in all channels (Fig. 7B). At the group\u00a0level (Fig. 7C) highest \u02c6K values were also found for \u0394D for most\u00a0of the channels (except for T5, P3, P4, O1 and O2 channels) followed\u00a0by measures fse<\/sub> and P\u03b2r<\/sub>. Comparing these three measures\u00a0there were 8 channels (with a predominance of circumferential\u00a0electrodes) where \u0394D achieved significantly better performance\u00a0compared to measures fse<\/sub> and P\u03b2r<\/sub> (Table 7, g test). Considering\u00a0the individual level conditional \u02c6K values averaged across subjects\u00a0\u0394D showed best performance for NREM4 (Fig. 7D) as well as for\u00a0NREM2 (Fig. 7E) in all channels while during REM \u0394D, P\u03b2r<\/sub>, P\u03b3r<\/sub> and\u00a0fse<\/sub> revealed similar performance (Fig. 7F). Group level conditional\u00a0\u02c6K\u00a0values were presented in the last three columns of Fig. 7 (G, H, I).\u00a0For NREM4 (Fig. 7G), \u0394D showed the best classification results in\u00a0all channels except for the occipital electrodes (Table 7, gcN4<\/em> test).\u00a0During NREM2 best performance was also achieved for \u0394D in most\u00a0channels (13 channels) (Fig. 7H). Performance of \u0394D significantly\u00a0exceeded those of fse<\/sub> and P\u03b2r<\/sub> in 9 channels (Table 7, gcN2<\/em> test). By\u00a0contrast, during REM fse<\/sub> and P\u03b2r<\/sub> significantly outperformed \u0394D in\u00a0all channels (Table 7, gcR test). Best classifications were obtained\u00a0for measure P\u03b2r<\/sub> in all channels. For all columns presented in Fig. 7\u00a0maximal \u02c6K values of \u0394D were found in the circumferential channels\u00a0(Table 8) with the best performance in T4 channel in 4 cases\u00a0including mean \u02c6K values for the individual level (row B), \u02c6K values\u00a0at the group level (row C) as well as conditional \u02c6K values in rows\u00a0D and H. As can be seen in Table 8, best classification performance\u00a0across EEG measures was found for \u0394D considering all rows with\u00a0the exception of rows (F, I) that is the conditional values for REM.<\/p>\n

In (rows A\u2013C) best classifications of \u0394D exceeded 80% (peaking in\u00a097.78% at individual level for subject #3) considering the overall\u00a0accuracy measure.
\nCompared with other measures, H generally performed below\u00a0the average with central peaks in \u02c6K values. In contrast to its general\u00a0low level of performance it quite efficiently classified NREM4.\u00a0When regarding results obtained for relative band powers (Fig. 7),\u00a0higher overall performance was found for faster brain activities. In\u00a0general, better classification results were found for NREM4 as compered with NREM2 and REM. Worst and non-significant (comparing\u00a0against a random classifier) classification results were obtained at\u00a0group level for sleep stage NREM2 using measures PSOr<\/sub> (channel\u00a0Fp2) and P\u03b4r<\/sub> (channels F3, Fz, F4, F7, C4).<\/p>\n

<\/p>\n

Fig. 7.<\/strong> Sleep stage classification results using linear discriminant analysis both at individual and group levels. (A) Maximal \u02c6K values taken across subjects. (B) Averaged\u00a0individual \u02c6K values. (C) Group level \u02c6K values. (D) Individual conditional \u02c6K values averaged across subjects for sleep stage NREM4. (E) Individual conditional \u02c6K values averaged\u00a0across subjects for sleep stage NREM2. (F) Individual conditional \u02c6K values averaged across subjects for REM sleep. (G) Group level conditional \u02c6K for NREM4 sleep. (H) Group\u00a0level conditional \u02c6K for sleep stage NREM2. (I) Group level conditional \u02c6K for REM sleep. Relative band powers are denoted by the labels of the corresponding frequency bands.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Table 7<\/strong>
\nKappa analysis of sleep stage classifications performed by linear discriminant analysis.<\/td>\n<\/tr>\n
Test<\/td>\nMeasures<\/td>\nChannel<\/td>\n<\/tr>\n
Fp2<\/td>\nF8<\/td>\nT4<\/td>\nT6<\/td>\nO2<\/td>\nFp1<\/td>\nF7<\/td>\nT3<\/td>\nT5<\/td>\nO1<\/td>\nF4<\/td>\nC4<\/td>\nP4<\/td>\nF3<\/td>\nC3<\/td>\nP3<\/td>\nFz<\/td>\nCz<\/td>\n<\/tr>\n
imax(A)<\/td>\n\u0394D vs.\u00a0\u03b2<\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n><\/td>\n><\/td>\n>*<\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n<\/tr>\n
\u0394\u00a0D vs. fse<\/td>\n<<\/td>\n<<\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n<<\/td>\n<<\/td>\n<<\/td>\n><\/td>\n<<\/td>\n<<\/td>\n><\/td>\n<<\/td>\n><\/td>\n><\/td>\n=<\/td>\n><\/td>\n<\/tr>\n
fse vs. \u00a0\u03b2<\/td>\n><\/td>\n>*<\/td>\n><\/td>\n><\/td>\n><\/td>\n>*<\/td>\n><\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n<\/tr>\n
g(C)<\/td>\n\u0394\u00a0D vs. \u00a0\u03b2<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n<*<\/td>\n><\/td>\n><\/td>\n<<\/td>\n>*<\/td>\n>*<\/td>\n<<\/td>\n><\/td>\n><\/td>\n<\/tr>\n
\u0394\u00a0D vs. fse<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<<\/td>\n<*<\/td>\n><\/td>\n><\/td>\n<<\/td>\n><\/td>\n>*<\/td>\n<<\/td>\n>*<\/td>\n><\/td>\n<\/tr>\n
fse vs. \u00a0\u03b2<\/td>\n>*<\/td>\n><\/td>\n>*<\/td>\n<<\/td>\n><\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<<\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n><\/td>\n<*<\/td>\n<<\/td>\n<\/tr>\n
gcN4(G)<\/td>\n\u0394\u00a0D vs. \u00a0\u03b2<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<\/tr>\n
\u0394\u00a0D vs. fse<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<\/tr>\n
fse vs. \u00a0\u03b2<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<\/tr>\n
gcN2(H)<\/td>\n\u0394\u00a0D vs. \u00a0\u03b2<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n<*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n<*<\/td>\n><\/td>\n><\/td>\n<<\/td>\n>*<\/td>\n>*<\/td>\n<<\/td>\n>*<\/td>\n><\/td>\n<\/tr>\n
\u0394\u00a0D vs. fse<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<*<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n<<\/td>\n<*<\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n>*<\/td>\n><\/td>\n<\/tr>\n
fse vs. \u00a0\u03b2<\/td>\n><\/td>\n><\/td>\n><\/td>\n<*<\/td>\n<<\/td>\n>*<\/td>\n>*<\/td>\n>*<\/td>\n><\/td>\n>*<\/td>\n<<\/td>\n<<\/td>\n<*<\/td>\n><\/td>\n<<\/td>\n<<\/td>\n<*<\/td>\n<<\/td>\n<\/tr>\n
gcR(I)<\/td>\n\u0394\u00a0D vs. \u00a0\u03b2<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<\/tr>\n
\u0394\u00a0D vs. fse<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<\/tr>\n
fse vs. \u00a0\u03b2<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<*<\/td>\n<<\/td>\n<*<\/td>\n<*<\/td>\n<<\/td>\n<*<\/td>\n<*<\/td>\n<<\/td>\n<*<\/td>\n<<\/td>\n<\/tr>\n
imax: maximal \u02c6K values taken across subjects; g: group level \u02c6K values; gcN4: group level conditional \u02c6K values for NREM4; gcN2: group level conditional \u02c6K values for NREM2; gcR: group level conditional \u02c6K values for REM. Letters in brackets indicate the appropriate columns in Fig. 7. The > (<) sign denotes grater (smaller) \u02c6K values of front measures. Significance of differences was determined using a 95% confidence level, i.e., Z\u03b1\/2<\/sub> = 1.96 and denoted by an asterisk.\u00a0 \u00a0\u03b2 \u00a0denotes the relative power of the beta frequency band.<\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Table 8<\/strong>
\nMaximal \u02c6K values, corresponding overall accuracy values and EEG derivations of D, Pr and fse measures for all columns in Fig. 7.<\/td>\n<\/tr>\n
\u00a0<\/td>\nMeasure<\/td>\n<\/tr>\n
\u0394\u00a0D<\/td>\n\u03b2<\/td>\nfse<\/td>\n<\/tr>\n
(A)<\/td>\n0.9667, (97.78); T6, O2 (3)<\/td>\n0.9167, (94.44); T6 (3)<\/td>\n0.9611, (97.41); T3, T5 (3)<\/td>\n<\/tr>\n
(B)<\/td>\n0.8432, (89.55); T4<\/td>\n0.7585, (83. 90); F3<\/td>\n0.7657, (84.38); P4<\/td>\n<\/tr>\n
(C)<\/td>\n0.7210, (81.40); T4<\/td>\n0.6695, (77.97); P4<\/td>\n0.6877, (79.19); T3<\/td>\n<\/tr>\n
(D)<\/td>\n0.9810, T4<\/td>\n0.8215, O2<\/td>\n0.9193, O2<\/td>\n<\/tr>\n
(E)<\/td>\n0.7927, T3<\/td>\n0.6753, F4<\/td>\n0.6327, T6<\/td>\n<\/tr>\n
(F)<\/td>\n0.7652, T6<\/td>\n0.9047, Fz<\/td>\n0.8270, F3<\/td>\n<\/tr>\n
(G)<\/td>\n0.9440, Fp1<\/td>\n0.7361, O2<\/td>\n0.8649, O2<\/td>\n<\/tr>\n
(H)<\/td>\n0.6053, T4<\/td>\n0.5153, P4<\/td>\n0.5305, T3<\/td>\n<\/tr>\n
(I)<\/td>\n0.6616, T3<\/td>\n0.9083, F3<\/td>\n0.8599, F3<\/td>\n<\/tr>\n
First column denote column labels in Fig. 7. (A) Maximal \u02c6K values taken across subjects. (B) Averaged individual \u02c6K values. (C) Group level \u02c6K values. (D) Individual conditional \u02c6K values averaged across subjects for sleep stage NREM4. (E) Individual conditional \u02c6K values averaged across subjects for sleep stage NREM2. (F) Individual conditional \u02c6K values averaged across subjects for REM sleep. (G) Group level conditional \u02c6K for NREM4 sleep. (H) Group level conditional \u02c6K for sleep stage NREM2. (I) Group level conditional \u02c6K for REM sleep. Overall accuracy is provided in brackets only where applicable (the first three rows only). In the first row the subject id is also provided in brackets after the channel labels to denote for which subject was the maximal \u02c6K value found. Relative power of the beta frequency band is denoted by\u00a0 \u03b2.<\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

4. Discussion<\/strong><\/p>\n

To our knowledge this is the first study providing a detailed\u00a0comparison of fractal and power spectral features of the human\u00a0EEG considering the effects of topography and sleep stages. Fractality\u00a0of EEG signals was assessed using both monofractal and multifractal measures. Power spectral properties were described\u00a0by relative band powers and in amore compact way by estimating\u00a0the spectral edge frequency. Sleep was analyzed considering sleep\u00a0stages NREM4, NREM2 and REM separately as well as together.\u00a0Topography was assessed with regard to functional connectivity\u00a0by analyzing interhemispheric differences and regional clustering\u00a0of EEG derivations.<\/p>\n

Our data indicate that despite of correlations between fractal\u00a0and power spectral measures, fractal features carry additional\u00a0information about EEG signals. Moreover, brain electrical activities\u00a0are more complex than they could be fully described by a single\u00a0monofractal exponent and therefore a multifractal approach may\u00a0be more appropriate for modeling the fractal properties of brain\u00a0dynamics.<\/p>\n

A main and novel finding of the study is that the overall sleep\u00a0stage discrimination capability of the multifractal measure is superior\u00a0compared to the relative band powers, the compact power\u00a0spectral measure fse<\/sub> as well as the monofractal exponentH. Regarding\u00a0overall accuracy \u0394D exceeded 80% at the group level and\u00a0achieved even 97.78% at the individual level. This finding speaks\u00a0in favor of the individual level classification. Our results, in addition,\u00a0indicate highest accuracy for the temporal channels which\u00a0might surprise given that previous studies typically used central\u00a0EEG channels for sleep stage classification.<\/p>\n

4.1. Topographic and sleep stage-wise distribution of measures<\/em><\/p>\n

Topographic distribution of the analyzed measures (Fig. 1) was\u00a0in general agreement with expectations. Results obtained for the\u00a0fractal measures were completely in agreement with those findings\u00a0published in [95]. Higher H values occurred for deeper sleep\u00a0stages, while \u0394D showed an opposite trend indicating that brain\u00a0electrical activities tend to be less multifractal and to posses longer\u00a0memory properties during deeper sleep stages. The decrease of\u00a0\u0394D with the deepening of sleep was opposite to the behavior of\u00a0another multifractal measure, the range of singularity strength\u00a0in a previous study [63] where the multifractality of EEG signals\u00a0was assessed analyzing the distribution of zero-crossings. This discrepancy\u00a0indicates a need for a systematic comparison of different\u00a0estimation methods for multifractal analysis of EEG signals. The\u00a0HNREM4<\/sub> >HNREM2<\/sub> >HREM<\/sub> trend was in agreement with results of previous\u00a0studies that assessed the DFA \u03bb exponent [53\u201355,86], the\u00a0fractal exponent \u039a [74] or the fractal dimension Df [73]. Namely,\u00a0DFA exponent \u03bb and \u03ba increased with the deepening of sleep, while\u00a0Df <\/sub>exhibited the opposite trend. This suggests that the Hurst exponent\u00a0estimated based on R\/S statistics might be able to reflect\u00a0the self-similarity properties of the sleep EEG, although the aforementioned\u00a0trend could not be observed for H in [1]. Nevertheless,\u00a0searching for the direct relationship between exact values of fractal\u00a0measures and physiological processes has less sense, because\u00a0of the already mentioned doubts related to estimation of fractal\u00a0measures from time series of finite length. Even classification of\u00a0actual brain dynamics into one of two types of fractional time series\u00a0(fGn and fBm) is questionable. According to one part of the studies,\u00a0fGn behavior of the sleep EEG could be conjectured based on DFA\u00a0\u03bb exponent values below 1 [54,55] or estimated Hurst exponents\u00a0below 1 using the R\/S statistics approach such as in the present\u00a0study and in [1,95]. Other studies, on the contrary, indicated fBm\u00a0nature of the human sleep EEG by revealing DFA \u03ba exponent values\u00a0above 1 [53,86] or fractal exponent values in the range 1 <\u03ba\u00a0<3[74].\u00a0These discrepancies might be due to different estimation settings\u00a0and indicate a need for a comprehensive comparison of different\u00a0approaches used for the assessment of fractal properties, including\u00a0classification of EEG signals into one of two classes of fractional\u00a0time series (fGn or fBm) as it was proposed in [24\u201326]. Moreover,\u00a0we should keep in mind that sleep EEG signals exhibit multifractal\u00a0properties and thus monofractal analysis can only give a measure\u00a0of the largest of their fractal dimensions. The 1\/f noise-like power\u00a0spectrum ofEEGsignals can be distorted during different conditions\u00a0by characteristic peak frequencies (e.g. due to the alpha rhythm or\u00a0intensive sleep spindles) that could destroy the self-similar nature\u00a0of EEG. Possible analyses for such cases were proposed in [29,57].\u00a0Finally, we should also note that recent investigations revealed\u00a0effects of gender and age [68] as well as genetic contributions to\u00a0long-range temporal correlations [60] in wake EEG signals. Therefore,\u00a0effects of these factors should be investigated during different\u00a0sleep stages as well.\u00a0
\nOur data on the topography of relative band powers only\u00a0partially agreed with those published earlier. Slow activities\u00a0characterizing NREM4 occurred in anterior channels, while\u00a0faster activities during REM dominated posteriorly. This anteroposterior\u00a0tendency is in general agreement with previous studies\u00a0[21,22,45,96,97]. During NREM sleep stages, the fronto-central\u00a0maximum of slow activities as well as the posterior maximum of\u00a0theta activity and the parietal maximum of the sigma band are also\u00a0in agreement with results presented in [31,92]. Nevertheless, the\u00a0frontal maximum of alpha and beta band activities [31,92] was\u00a0not supported by our results. Also, instead of the frontal sigma\u00a0and beta peaks during REM in the study of Tinguely et al. [92] we\u00a0found posterior and temporal peaks in these activities. We could\u00a0neither confirm the frontal peak of NREM4 slow oscillation activity\u00a0described by Happe et al. [40]. We assume that discrepancies\u00a0might be due to methodological differences. Firstly, previous studies\u00a0mostly used absolute power values while we used relative band\u00a0powers. Secondly, several previous studies [31,45,92,96,97] evaluated\u00a0NREM sleep stages together, while we examined NREM4 and\u00a0NREM2 stages separately. Nevertheless, we were able to confirm\u00a0the known topographic spectral features of characteristic sleep EEG\u00a0patterns. The revealed fronto-central peak in delta activity during\u00a0NREM4 and NREM2 likely reflects delta waves and K-complexes\u00a0[39,40]. The parietal peak of sigma activity during NREM2 may\u00a0stand for fast sleep spindles [20,98,100]. At the same time no salient\u00a0topographic feature could be related to frontal slow spindle activity.\u00a0Vertex peaks in delta and theta bands during REM sleep likely\u00a0reflects saw tooth waves, characteristic EEG patterns during REM\u00a0with a know central maximum [99].<\/p>\n

4.2. <\/em>Cross-correlations between measures<\/em><\/p>\n

In our previous study [95] we found a tendency for an overall\u00a0negative cross-correlation between H and \u0394D. In that study we\u00a0also revealed a specific topography of this relationship. Here we\u00a0extend the characterization of the cross-correlation between H and\u00a0\u0394D by assessing sleep stages separately. Combining all sleep stages\u00a0we found a strong negative correlation between H and \u0394D with a\u00a0nadir in the posterior channels (Fig. 3). As revealed by the sleep\u00a0stage-wise analysis NREM2 and NREM4 contributed most to this\u00a0occipital nadir. As compared to NREM4 weaker and less significant\u00a0correlations emerged during NREM2. During REM there was a further\u00a0weakening of correlations with a non-significant positive peak\u00a0in the F3, Fz, F4 channels.
\nTo reveal how spectral properties are reflected in fractal measures, we performed cross-correlation analysis between these measures (Fig. 4). Measure H exhibited positive correlation with relative powers of slow activities (especially PSOr)<\/sub>, while it mostly showed negative correlation with faster activities. More significant values tended to occur for slower activities (except P\u03b4r<\/sub>) and for deeper sleep stages. All these findings support the theory that H is linearly related to the spectral exponent \u03ba (see Section 2.2.2.1). Parameter \u03ba\u00a0can be estimated by plotting the power spectrum on the log-log scale and by fitting a straight line to this plot. The slope of this line is equal to -\u03ba. This indicates that higher amount of slow activities and lower amount of faster activities result in higher\u00a0\u03ba and H values and vice versa. The log\u2013log plot of the power spectrum produces several points at higher frequencies and only few points at lower frequencies. Hence, the fitting of a straight line is much more affected by lower frequencies which might be the cause of more significant correlations of H with slower brain activities. Thus the correlation withHdepends not only on the position, width and power amount of a given frequency band but it is also affected by properties of other bands. This provides an explanation why P\u03b4r<\/sub> exhibited weaker and less significant correlations with H as it could have been expected. As it could be conjectured from the overall negative cross-correlation between the fractal measures, \u0394D generally revealed opposite correlations with power spectral measures compared to those of H. That is,\u0394D was negatively correlated with slow activities and positively correlated with RBPs of higher frequency bands. Additionally, faster activities (> 4 Hz) showed more significant correlations with \u0394D as compared to slower activities and for deeper sleep stages. All this suggests that slower EEG patterns tend to make the amplitude distribution more even, while the opposite is true for faster EEG patterns. Characteristic topography of cross-correlations between H and \u0394D were also reflected in crosscorrelations between the fractal measures and RBPs, e.g. one of the most striking topographic features of cross-correlations between fractal measures and relative band powers could be observed for REM sleep in the fronto-central region where weakest correlations occurred. This might explain weak and non-significant positive cross-correlation between the two fractal measures during REM. Multiple linear regressions supported results of cross-correlation analysis between fractal and RBP measures by revealing contribution of individual RBPs to the compact EEG measures. We found a positive contribution of slow (SO and \u0394 bands) activities to H. Out of the faster activities P\u03b1r<\/sub> and P\u03b3r<\/sub> contributed positively while P\u03b8r<\/sub>, P\u03c3r<\/sub> and P\u03b2r<\/sub> contributed negatively to the same measure. The positive contribution of P\u03b1r<\/sub> and P\u03b3r<\/sub> might be explained by the observed weak positive cross-correlation between these measures and H\u00a0during REM sleep in the central zone (see Fig. 4). Highest coefficients\u00a0were revealed for PSOr<\/sub> and P\u03b8r<\/sub>. Considering \u0394D, negative\u00a0and non-significant contribution of slow activities was obtained.\u00a0Positive coefficients were found for faster activities (above 4 Hz)\u00a0reaching the significance level only for P\u03b8r<\/sub>. In addition, expected\u00a0results were also found considering fse<\/sub> as a predicted variable.\u00a0Highest positive and significant coefficients were found for two\u00a0fastest activities (P\u03b2r<\/sub> and P\u03b3r<\/sub>). Fraction of variation that could be\u00a0explained by the relative band powers was highest in case of fse<\/sub> (adjusted R2<\/sup> = 0.97), while the worst regression result was found for\u00a0\u0394D (adjusted R2<\/sup> = 0.89). This finding could have been anticipated\u00a0since fse<\/sub> is directly computed from power spectra and H may be\u00a0related to the power spectrum, while \u0394D reflects the amplitude\u00a0distribution of time series. Distance of compact EEG features and\u00a0RBPs was also analyzed by hierarchical clustering of the measures\u00a0using group level medians in all channels (Fig. 6). These results\u00a0were in agreement with those obtained by cross-correlation analyses\u00a0and MLR. Namely, H was clustered with relative powers of slow\u00a0brain activities (SO and \u03b4 frequency bands) in all sleep stages, while\u00a0\u0394D tended to cluster with faster activities (\u03b2 and \u03b3 bands during\u00a0NREM4 and NREM2; and bands during REM sleep).\u00a0
\nA direct comparison of our correlation results (between H and\u00a0spectral measures) with those of previous investigators is not possible\u00a0since previous investigators used different measures and only\u00a0few EEG channels. Nevertheless, our results regarding the correlation\u00a0between H and power spectral measures could be related\u00a0to those results by Pereda et al. [73] who revealed a similar trend\u00a0of measures D2<\/sub> and Df<\/sub> across sleep stages and a negative crosscorrelation\u00a0between D2<\/sub> and powers of slower frequency bands\u00a0[74]. Another study revealing negative cross-correlation between\u00a0D2<\/sub> and DFA exponent \u03bb and negative cross-correlation between\u00a0D2<\/sub> and slower activities [86] also seem to be in accordance with\u00a0our data. On the contrary, the weak positive cross-correlation\u00a0between D2<\/sub> and \u039a during NREM4 and NREM3 found in [74] would\u00a0suggest negative correlation between H and slow activities. As\u00a0far as we know there are no studies in the literature examining\u00a0the relationship between multifractality and spectral measures of\u00a0sleep EEG.<\/p>\n

4.3. Interhemispheric differences and inter-site correlations<\/em><\/p>\n

In the present study we also compared inter-site correlations\u00a0(Fig. 2) and interhemispheric differences of fractal and power spectral\u00a0measures (Table 2). Surprisingly interhemispheric differences\u00a0of specific measures varied with sleep stages and locations more\u00a0than expected. In addition, it is difficult to relate these results\u00a0to previous data where sleep stages were combined and\/or EEG\u00a0recordingwaslimited to a few channels. Nevertheless,wewere able\u00a0to reveal some coherent tendencies regarding the interhemispheric\u00a0differences of spectral powers, e.g.weobserved a right-hemisphere\u00a0predominance of SO duringNREM4which might be related to those\u00a0results by Sekimoto et al. [84] finding predominance of 0.5\u20132 Hz\u00a0activity over the right hemisphere during all night sleep. At the\u00a0same time delta activity on the left side tended to predominate\u00a0in each sleep stage. During NREM4 and NREM2 we found higher\u00a0theta activity on the right side, while during REM theta predominated\u00a0on the left side corroborating the findings of Roth et al.\u00a0[82]. The majority of interhemispheric comparisons of H and \u0394D\u00a0were not significant. Previous investigators revealed interhemispheric\u00a0asymmetries for measures D2<\/sub>, L1<\/sub> and Df <\/sub>considering C3\u2013C4\u00a0channels [73] and interhemishperic differences for D2 in C3\u2013C4,\u00a0T3\u2013T4 and O1\u2013O2 locations [50]. Differences between earlier and\u00a0the present data might be due to several methodological differences.\u00a0Inter-site correlations of RBPs (Fig. 2) partially agreed with\u00a0those results of coherence analyses revealed in [2,30,46]. Specifically,\u00a0we found stronger interhemispheric P\u03b3r<\/sub> correlations during\u00a0REM compared to NREM4 and NREM2, a finding similar to obtained\u00a0by Achermann and Borb\u00e9ly [2]. However, this result should be\u00a0regarded with caution since disconnection of the hemispheres during\u00a0NREM4 and NREM2 sleep regarding P\u03b3r<\/sub> might also occur due to\u00a0the application of two separate references [27,36,43].
\nAs expected, less significant differences were found for the symmetrical\u00a0channel pairs as compared with the non-symmetrical\u00a0channel pair Fz\u2013Cz. These results indicate stronger functional connectivity\u00a0between the homologous hemispheric regions that could\u00a0be mediated to a large part by the corpus callosum and other\u00a0commissural pathways [93,94]. During NREM4 most significant\u00a0interhemispheric differences were found for occipital and parietal\u00a0symmetrical channel pairs (Table 2). Results in the interhemisperic\u00a0analysis were confirmed by the inter-site correlation analysis\u00a0(Fig. 2) revealing strongest correlations between the anterior channels\u00a0during NREM4. During NREM2 and REM strongest correlations\u00a0were located more posteriorly. The 9-cluster analysis (Table S2,\u00a0Table 3) also confirmed this trend by revealing a tendency of clustering\u00a0together the frontal symmetrical channels during NREM4\u00a0and the posterior homologous channels during REM sleep. These\u00a0findings suggest stronger interhemispheric functional connectivity\u00a0anteriorly during NREM4 and posteriorly during REM sleep. Topography\u00a0of inter-site correlations of compact EEG features (including\u00a0fractal measures and fse<\/sub>) reflect those of RBPs to some extent\u00a0but due to the compression of information several properties are\u00a0lost, e.g. the disconnection of the hemispheres during NREM4 and\u00a0NREM2 regarding the gamma band activity cannot be revealed\u00a0from compact features. The 4-cluster analysis revealed similar\u00a0channel clusters (anterior, posterior, central and temporal) for the\u00a0combined fractal measures (Table 5) and for the combined RBPs\u00a0(Table 6). Nevertheless, there were some differences between these\u00a0two latter clusterings which could be related to the aforementione d\u00a0information loss. For example, the separate cluster that was formed\u00a0for the parietal channels using the RBP measures was modified by\u00a0clustering the parietal channels together with central derivations\u00a0based on combination of fractal measures. Combination of fractal\u00a0features and PSMs (Fig. 6 and Table 4) provided more symmetrical\u00a0topographic clusters than those obtained for the combined fractal measures or the combined RBP measures (as well as combined\u00a0PSMs: data not presented) alone. Nevertheless, all these results\u00a0indicate a re-organization of functional connectivity between brain\u00a0regions across sleep stages.<\/p>\n


\n4.4. Discriminability of sleep stages<\/em><\/p>\n

Sleep stage discrimination capabilities of EEG features were\u00a0tested in each channel both at individual and group levels (see Fig. 7\u00a0and Tables 7 and 8). Results indicate best overall classifications for\u00a0\u0394D followed by fse <\/sub>and P\u03b2r<\/sub>. This could have been assumed from\u00a0Table S1 since these three measures tended to reveal most significant\u00a0differences for all sleep stage pairs. Superior performance of\u00a0\u0394D and fse<\/sub> is in agreement with results obtained previously for the\u00a0entropy of amplitudes and spectral edge frequency measures [28].\u00a0In the present study best classifications for \u0394D were revealed for\u00a0the temporal channels. Measure H performed below the average\u00a0considering all measures. This result is in contrast with a previous\u00a0study [91] finding a superior performance of two other monofractal\u00a0measures (the fractal exponent and the fractal dimension) when\u00a0compared to spectral measures. To our surprise, worst classification\u00a0performance was obtained for the relative band power of slow\u00a0activities. This might be explained by confining the \u03b4 band to the 1-\u00a04Hz range and considering slow oscillations (0.5\u20131 Hz) separately.\u00a0The outstanding performance of \u0394D, fse<\/sub> and P\u03b2r<\/sub> indicate that it is\u00a0the faster rather than the slow activities that might be of superior\u00a0performance in the classification of sleep stages. As expected, better\u00a0classifications were achieved at the individual level as compared to\u00a0the group level, a finding that could be related to the considerable\u00a0individual variability of sleep EEG features [23,32].
\nExamination of conditional \u0088K^ values revealed that high overall\u00a0performance of \u0394D was achieved due to significantly better classification\u00a0of the NREM4 sleep stage. Comparatively, measure \u0394D was\u00a0found to be less efficient in classifying NREM2 and REM. Nevertheless,\u00a0these latter stages could be classified better based on specific\u00a0EEG measures at specific locations, e.g. best classification of NREM2\u00a0was revealed using P\u03c3r<\/sub> centrally (Fig. 7H) and best classification\u00a0of REM was found using P\u03b2r<\/sub> in frontal channels (Fig. 7I). Thus we\u00a0assume that overall sleep stage classification performance could be\u00a0improved by combining different measures at different locations. In\u00a0addition application of more sophisticated classification paradigms\u00a0and their combinations could be also beneficial. Polygraphic information\u00a0(EMG, EOG, ECG) might obviously improve the sleep stage\u00a0classification performance. Nevertheless, developing sleep stage\u00a0classifications not relying on polygraphic information might be useful\u00a0for invasive intracranial EEG recordings where polygraphy is\u00a0typically not available.
\nIn this study we assessed the relatively well-distinguishable\u00a0sleep stages NREM4, NREM2 and REM. It remains to be tested\u00a0whether other sleep stages (NREM1 and NREM3), waking states\u00a0or the wake-sleep transition can be classified and detected with a\u00a0same performance using fractal measures alone or combined with\u00a0other features.<\/p>\n

Conflict of interest<\/strong><\/p>\n

The authors declare that they have no competing financial interests.<\/p>\n

Acknowledgment
\n<\/strong>This research was supported by the Faculty of Information Technology\u00a0and the Jedlik Laboratories of the P\u00e1zm\u00e1ny P\u00e9ter Catholic\u00a0University, Budapest, Hungary.<\/p>\n

Appendix A. Supplementary data
\n<\/strong>Supplementary data associated with this article can be found, in\u00a0the online version, at doi:10.1016\/j.brainresbull.2010.12.005.<\/p>\n

References<\/strong><\/p>\n

[1] R. Acharya, O. Faust, N. Kannathal, T. Chua, S. Laxminarayan, Non-linear analysis\u00a0of EEG signals at various sleep stages, Comput. Methods Progr. Biomed.\u00a080 (1) (2005) 37\u201345.<\/p>\n

[2] P. Achermann, A. Borb\u00e9ly, Coherence analysis of the human sleep electroencephalogram,\u00a0Neuroscience 85 (4) (1998) 1195\u20131208.<\/p>\n

[3] P. Achermann, A. Borb\u00e9ly, Low-frequency (<1 Hz) oscillations in the human\u00a0sleep electroencephalogram, Neuroscience 81 (1) (1997) 213\u2013222.<\/p>\n

[4] P. Bak, How Nature Works: The Science of Self-organized Criticality, Oxford\u00a0University Press, Oxford, 1997.<\/p>\n

[5] P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality: an explanation of the\u00a01\/f noise, Phys. Rev. Lett. 59 (4) (1987) 381\u2013384.<\/p>\n

[6] P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality, Phys Rev A 38 (1)\u00a0(1988) 364\u2013374.<\/p>\n

[7] A.L. Barab\u00e1si, H.E. Stanley, Fractal Concepts in Surface Growth, Cambridge\u00a0University Press, Cambridge, 1994.<\/p>\n

[8] J.B. Bassingthwaighte, L.S. Liebovitch, B.J. West, Fractal Physiology, Oxford\u00a0University Press, New York, 1994.<\/p>\n

[9] C. B\u00e9dard, H. Kr\u00f6ger, A. Destexhe, Does the 1\/f frequency scaling of brain\u00a0signals reflect self-organized critical states? Phys. Rev. Lett. 97 (11) (2006)\u00a0118102.<\/p>\n

[10] J. Beggs, D. Plenz, Neuronal avalanches in neocortical circuits, J. Neurosci. 23\u00a0(35) (2003) 11167\u201311177.<\/p>\n

[11] O. Benoit, A. Daurat, J. Prado, Slow (0.7\u20132 Hz) and fast (2\u20134 Hz) delta components\u00a0are differently correlated to theta, alpha and beta frequency bands\u00a0during NREM sleep, Clin. Neurophysiol. 111 (12) (2000) 2103\u20132106.<\/p>\n

[12] J. Beran, Statistics for Long-Memory Processes, 1st ed., Chapman & Hall\/CRC,\u00a0New York, 1994.<\/p>\n

[13] T. Boji\u00b4 c, A. Vuckovic, A. Kalauzi, Modeling EEG fractal dimension changes in\u00a0wake and drowsy states in humans\u2014a preliminary study, J. Theor. Biol. 262\u00a0(2) (2010) 214\u2013222.<\/p>\n

[14] R. Cerf, A. Daoudi, M. Ould H\u00e9noune, E. el Ouasdad, Episodes of\u00a0low-dimensional self-organized dynamics from electroencephalographic\u00a0alpha-signals, Biol. Cybern. 77 (4) (1997) 235\u2013245.<\/p>\n

[15] Z. Chen, K. Hu, P. Carpena, P. Bernaola-Galvan, H. Stanley, P. Ivanov, Effect of\u00a0nonlinear filters on detrended fluctuation analysis, Phys. Rev. E Stat. Nonlin.\u00a0Soft Matter Phys. 71 (1 Pt 1) (2005) 011104.<\/p>\n

[16] Z. Chen, P. Ivanov, K. Hu, H. Stanley, Effect of nonstationarities on detrended\u00a0fluctuation analysis, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65 (4 Pt 1)\u00a0(2002) 041107.<\/p>\n

[17] D. Chialvo, P. Bak, Learning from mistakes, Neuroscience 90 (4) (1999)\u00a01137\u20131148.<\/p>\n

[18] R.G. Congalton, K. Green, Assessing the Accuracy of Remotely Sensed Data:\u00a0Principles and Practices, 2nd ed., CRC Press, Boca Raton, 2008.<\/p>\n

[19] P. Couto, Assessing the accuracy of spatial simulation models, Ecol. Modell.\u00a0167 (1\u20132) (2003) 181\u2013198.<\/p>\n

[20] L. De Gennaro, M. Ferrara, Sleep spindles: an overview, Sleep Med. Rev. 7 (5)\u00a0(2003) 423\u2013440.<\/p>\n

[21] L. De Gennaro, M. Ferrara, G. Curcio, R. Cristiani, M. Bertini, Cortical EEG topography\u00a0of REM onset: the posterior dominance of middle and high frequencies,\u00a0Clin. Neurophysiol. 113 (4) (2002) 561\u2013570.<\/p>\n

[22] L. De Gennaro, M. Ferrara, G. Curcio, R. Cristiani, Antero-posterior EEG changes\u00a0during the wakefulness-sleep transition, Clin. Neurophysiol. 112 (10) (2001)\u00a01901\u20131911.<\/p>\n

[23] L. De Gennaro, M. Ferrara, F. Vecchio, G. Curcio, M. Bertini, An electroencephalographic\u00a0fingerprint of human sleep, Neuroimage 26 (1) (2005)\u00a0114\u2013122.<\/p>\n

[24] D. Delignieres, S. Ramdani, L. Lemoine, K. Torre, M. Fortes, G. Ninot, Fractal\u00a0analyses for \u2018short\u2019 time series: a re-assessment of classical methods, J. Math.\u00a0Psychol. 50 (6) (2006) 525\u2013544.<\/p>\n

[25] A. Eke, P. Herman, L. Kocsis, L. Kozak, Fractal characterization of complexity\u00a0in temporal physiological signals, Physiol. Meas. 23 (1) (2002) R1\u201338.<\/p>\n

[26] A. Eke, P. Herm\u00e1n, J. Bassingthwaighte, G. Raymond, D. Percival, M. Cannon, I.\u00a0Balla, C. Ikr\u00e9nyi, Physiological time series: distinguishing fractal noises from\u00a0motions, Pflugers Arch. 439 (4) (2000) 403\u2013415.<\/p>\n

[27] M. Essl, P. Rappelsberger, EEG coherence and reference signals: experimental\u00a0results and mathematical explanations, Med. Biol. Eng. Comput. 36 (4) (1998)\u00a0399\u2013406.<\/p>\n

[28] J. Fell, J. R\u00f6schke, K. Mann, C. Sch\u00e4ffner, Discrimination of sleep stages: a comparison\u00a0between spectral and nonlinear EEG measures, Electroencephalogr.\u00a0Clin. Neurophysiol. 98 (5) (1996) 401\u2013410.<\/p>\n

[29] T.C. Ferree, R.C. Hwa, Power-law scaling in human EEG: relation to Fourier\u00a0power spectrum, Neurocomputing 52\u201354 (2003) 755\u2013761.<\/p>\n

[30] R. Ferri, F. Rundo, O. Bruni, M. Terzano, C. Stam, Regional scalp EEG slowwave\u00a0synchronization during sleep cyclic alternating pattern A1 subtypes,\u00a0Neurosci. Lett. 404 (3) (2006) 352\u2013357.<\/p>\n

[31] L. Finelli, A. Borb\u00e9ly, P. Achermann, Functional topography of the human\u00a0nonREM sleep electroencephalogram, Eur. J. Neurosci. 13 (12) (2001)\u00a02282\u20132290.<\/p>\n

[32] L. Finelli, P. Achermann, A. Borb\u00e9ly, Individual, \u2018fingerprints\u2019 in human sleep\u00a0EEG topography, Neuropsychopharmacology 25 (5 Suppl.) (2001) S57\u2013S62.<\/p>\n

[33] W. Freeman, L. Rogers, M. Holmes, D. Silbergeld, Spatial spectral analysis of\u00a0human electrocorticograms including the alpha and gamma bands, J. Neurosci.\u00a0Methods 95 (2) (2000) 111\u2013121.<\/p>\n

[34] W. Freeman, M. Holmes, B. Burke, S. Vanhatalo, Spatial spectra of scalp EEG\u00a0O. Jenni, E. van Reen, M. Carskadon, Regional differences of the sleep electroencephalogram\u00a0and EMG from awake humans, Clin. Neurophysiol. 114 (6) (2003) 1053\u20131068.<\/p>\n

[35] J. Gonz\u00e1lez, A. Gamundi, R. Rial, M. Nicolau, L. de Vera, E. Pereda, Nonlinear,\u00a0fractal, and spectral analysis of the EEG of lizard, Gallotia galloti, Am. J. Physiol.\u00a0277 (1 Pt 2) (1999) R86\u2013R93.<\/p>\n

[36] S. Gudmundsson, T. Runarsson, S. Sigurdsson, G. Eiriksdottir, K. Johnsen,\u00a0Reliability of quantitative EEG features, Clin. Neurophysiol. 118 (10) (2007)\u00a02162\u20132171.<\/p>\n

[37] G. Gurman, Assessment of depth of general anesthesia. Observations on processed\u00a0EEG and spectral edge frequency, Int. J. Clin. Monit. Comput. 11 (3)\u00a0(1994) 185\u2013189.<\/p>\n

[38] G. Gurman, S. Fajer, A. Porat, M. Schily, A. Pearlman, Use of EEG spectral edge\u00a0as index of equipotency in a comparison of propofol and isoflurane for maintenance\u00a0of general anaesthesia, Eur. J. Anaesthesiol. 11 (6) (1994) 443\u2013448.<\/p>\n

[39] P. Halasz, K-complex, a reactive EEG graphoelement of NREM sleep: an old\u00a0chap in a new garment, Sleep Med. Rev. 9 (5) (2005) 391\u2013412.<\/p>\n

[40] S. Happe, P. Anderer, G. Gruber, G. Kl\u00f6sch, B. Saletu, J. Zeitlhofer, Scalp topography\u00a0of the spontaneous K-complex and of delta-waves in human sleep, Brain\u00a0Topogr. 15 (1) (2002) 43\u201349.<\/p>\n

[41] T. Higuchi, Relationship between the fractal dimension and the power law\u00a0index for a time series: a numerical investigation, Physica D: Nonlin. Phenomena\u00a046 (2) (1990) 254\u2013264.<\/p>\n

[42] K. Hu, P. Ivanov, Z. Chen, P. Carpena, H. Stanley, Effect of trends on detrended\u00a0fluctuation analysis, Phys. Rev. E: Stat. Nonlin. Soft Matter Phys. 64 (1 Pt 1)\u00a0(2001) 011114.<\/p>\n

[43] S. Hu, M. Stead, Q. Dai, G. Worrell, On the recording reference contribution\u00a0to EEG correlation, phase synchorony, and coherence, IEEE Trans. Syst. Man.\u00a0Cybern. B Cybern. (2010).<\/p>\n

[44] H.E. Hurst, Long term storage capacity of reservoirs, Trans. Am. Soc. Civil Eng.\u00a0116 (1951) 770\u2013799.<\/p>\n

[45] O. Jenni, E. van Reen, M. Carskadon, Regional differences of the sleep electroencephalogram\u00a0in adolescents, J. Sleep Res. 14 (2) (2005) 141\u2013147.<\/p>\n

[46] M. Kamin\u00b4 ski, K. Blinowska, W. Szclenberger, Topographic analysis of coherence\u00a0and propagation of EEG activity during sleep and wakefulness,\u00a0Electroencephalogr. Clin. Neurophysiol. 102 (3) (1997) 216\u2013227.<\/p>\n

[47] H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, 2nd ed., Cambridge\u00a0University Press, Cambridge, New York and Melbourne, 2003.<\/p>\n

[48] S. Katsev, I. L\u2019Heureux, Are Hurst exponents estimated from short or irregular\u00a0time series meaningful? Comput. Geosci. (2003) 1085\u20131089.<\/p>\n

[49] V.G. Kiselev, K.R. Hahn, D.P. Auer, Is the brain cortex a fractal? Neuroimage\u00a020 (3) (2003) 1765\u20131774.<\/p>\n

[50] T. Kobayashi, S. Madokoro, K. Misaki, J. Murayama, H. Nakagawa, Y. Wada,\u00a0Interhemispheric differences of the correlation dimension in a human\u00a0sleep electroencephalogram, Psychiatry Clin. Neurosci. 56 (3) (2002) 265\u2013266.<\/p>\n

[51] V. Kulish, A. Sourin, O. Sourina, Human electroencephalograms seen as fractal\u00a0time series: mathematical analysis and visualization, Comput. Biol. Med. 36\u00a0(3) (2006) 291\u2013302.<\/p>\n

[52] J. Landis, G. Koch, The measurement of observer agreement for categorical\u00a0data, Biometrics 33 (1) (1977) 159\u2013174.<\/p>\n

[53] J.M. Lee, D.J. Kim, I.Y. Kim, K.S. Park, S.I. Kim, Nonlinear-analysis of human\u00a0sleep EEG using detrended fluctuation analysis, Med. Eng. Phys. 26 (9) (2004)\u00a0773\u2013776.<\/p>\n

[54] S. Leistedt, M. Dumont, N. Coumans, J. Lanquart, F. Jurysta, P. Linkowski, The\u00a0modifications of the long-range temporal correlations of the sleep EEG due\u00a0to major depressive episode disappear with the status of remission, Neuroscience\u00a0148 (3) (2007) 782\u2013793.<\/p>\n

[55] S. Leistedt, M. Dumont, J.P. Lanquart, F. Jurysta, P. Linkowski, Characterization\u00a0of the sleep EEG in acutely depressed men using detrended fluctuation\u00a0analysis, Clin. Neurophysiol. 118 (4) (2007) 940\u2013950.<\/p>\n

[56] C.D. Lewis, G.L. Gebber, P.D. Larsen, S.M. Barman, Long-term correlations in\u00a0the spike trains of medullary sympathetic neurons, J. Neurophysiol. 85 (4)\u00a0(2001) 1614\u20131622.<\/p>\n

[57] D. Lin, A. Sharif, H. Kwan, Scaling and organization of electroencephalographic\u00a0background activity and alpha rhythm in healthy young adults, Biol. Cybern.\u00a095 (5) (2006) 401\u2013411.<\/p>\n

[58] K. Linkenkaer-Hansen, V. Nikouline, J. Palva, R. Ilmoniemi, Long-range temporal\u00a0correlations and scaling behavior in human brain oscillations, J. Neurosci.\u00a021 (4) (2001) 1370\u20131377.<\/p>\n

[59] K. Linkenkaer-Hansen, V. Nikulin, J. Palva, K. Kaila, R. Ilmoniemi, Stimulusinduced\u00a0change in long-range temporal correlations and scaling behaviour of\u00a0sensorimotor oscillations, Eur. J. Neurosci. 19 (1) (2004) 203\u2013211.<\/p>\n

[60] K. Linkenkaer-Hansen, D. Smit, A. Barkil, T. van Beijsterveldt, A. Brussaard,\u00a0D. Boomsma, A. van Ooyen, E. de Geus, Genetic contributions to long-range\u00a0temporal correlations in ongoing oscillations, J. Neurosci. 27 (50) (2007)\u00a013882\u201313889.<\/p>\n

[61] C. Long, N. Shah, C. Loughlin, J. Spydell, R. Bedford, A comparison of EEG determinants\u00a0of near-awakening from isoflurane and fentanyl anesthesia. Spectral\u00a0edge, median power frequency, and delta ratio, Anesth. Analg. 69 (2) (1989)\u00a0169\u2013173.<\/p>\n

[62] S.B. Lowen, L.S. Liebovitch, J.A. White, Fractal ion-channel behavior generates\u00a0fractal firing patterns in neuronal models, Phys. Rev. E Stat. Phys. Plasmas\u00a0Fluids Relat. Interdiscip. Top. 59 (5 Pt B) (1999) 5970\u20135980.<\/p>\n

[63] Q.L. Ma, X.B. Ning, J. Wang, C.H. Bian, A new measure to characterize multifractality\u00a0of sleep electroencephalogram, Chin. Sci. Bull. 51 (24) (2006)\u00a03059\u20133064.<\/p>\n

[64] B.B. Mandelbrot, M.S. Taqqu, Robust R\/S analysis of long-run serial correlation,\u00a0in: Proceedings of the 42nd Session of the International Statistical Institute,\u00a048, Book 2, Manila, 1979, pp. 69\u2013104.<\/p>\n

[65] B.B. Mandelbrot, The Fractal Geometry of Nature, 1st ed., W.H. Freeman and\u00a0Company, New York, 1982.<\/p>\n

[66] M. Massimini, R. Huber, F. Ferrarelli, S. Hill, G. Tononi, The sleep slow oscillation\u00a0as a traveling wave, J. Neurosci. 24 (31) (2004) 6862\u20136870.<\/p>\n

[67] V. Nikulin, T. Brismar, Long-range temporal correlations in alpha and beta\u00a0osc illations: effect of arousal level and test-retest reliability, Clin. Neurophysiol.\u00a0115 (8) (2004) 1896\u20131908.<\/p>\n

[68] V. Nikulin, T. Brismar, Long-range temporal correlations in electroencephalographic\u00a0oscillations: Relation to topography, frequency band, age and gender,\u00a0Neuroscience 130 (2) (2005) 549\u2013558.<\/p>\n

[69] M. Palus, Nonlinearity in normal human EEG: cycles, temporal asymmetry,\u00a0nonstationarity and randomness, not chaos, Biol. Cybern. 75 (5) (1996)\u00a0389\u2013396.<\/p>\n

[70] A. Pellionisz, Neural geometry: towards a fractal model of neurons, in: R.M.J.\u00a0Cotterill (Ed.), Models of Brain Function, Cambridge University Press, Cambridge,\u00a0New York and Melbourne, 1989, pp. 453\u2013464.<\/p>\n

[71] C. Peng, S. Havlin, H. Stanley, A. Goldberger, Quantification of scaling exponents\u00a0and crossover phenomena in nonstationary heartbeat time series,\u00a0Chaos 5 (1) (1995) 82\u201387.<\/p>\n

[72] C.K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger,\u00a0Mosaic organization of DNA nucleotides, Phys. Rev. E 49 (2) (1994)\u00a01685.<\/p>\n

[73] E. Pereda, A. Gamundi, M. Nicolau, R. Rial, J. Gonz\u00e1lez, Interhemispheric differences\u00a0in awake and sleep human EEG: a comparison between non-linear\u00a0and spectral measures, Neurosci. Lett. 263 (1) (1999) 37\u201340.<\/p>\n

[74] E. Pereda, A. Gamundi, R. Rial, J. Gonz\u00e1lez, Non-linear behaviour of human\u00a0EEG: fractal exponent versus correlation dimension in awake and sleep stages,\u00a0Neurosci. Lett. 250 (2) (1998) 91\u201394.<\/p>\n

[75] L. Poupard, R. Sart\u010dne, J. Wallet, Scaling behavior in beta-wave amplitude\u00a0modulation and its relationship to alertness, Biol. Cybern. 85 (1) (2001) 19\u201326.<\/p>\n

[76] G. Rangarajan, M. Ding, Integrated approach to the assessment of long range\u00a0correlation in time series data, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat.\u00a0Interdiscip. Top. 61 (5A) (2000) 4991\u20135001.<\/p>\n

[77] P. Rapp, A. Albano, T. Schmah, L. Farwell, Filtered noise can mimic lowdimensional\u00a0chaotic attractors, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat.\u00a0Interdiscip. Top. 47 (4) (1993) 2289\u20132297.<\/p>\n

[78] A. Rechtschaffen, A. Kales, Amanual of standardized terminology, techniques\u00a0and scoring system for sleep stages of human subjects, Bethesda, MD, U.S.\u00a0National Institute of Neurological Diseases and Blindness, Neurol. Inform.\u00a0Netw. (1968).<\/p>\n

[79] A. R\u00e9nyi, Probability Theory, North Holland, Amsterdam, 1971.<\/p>\n

[80] P.A. Robinson, C.J. Rennie, J.J. Wright, H. Bahramali, E. Gordon, D.L. Rowe,\u00a0Prediction of electroencephalographic spectra from neurophysiology, Phys.\u00a0Rev. E 63 (2) (2001) 021903.<\/p>\n

[81] P.A. Robinson, C.J. Rennie, D.L. Rowe, Dynamics of large-scale brain activity\u00a0in normal arousal states and epileptic seizures, Phys. Rev. E 65 (4) (2002)\u00a0041924.<\/p>\n

[82] C. Roth, P. Achermann, A. Borb\u00e9ly, Frequency and state specific hemispheric\u00a0asymmetries in the human sleep EEG, Neurosci. Lett. 271 (3) (1999) 139\u2013142.<\/p>\n

[83] T. Schreiber, A. Schmitz, Surrogate time series, Physica D: Nonlin. Phenom.\u00a0142 (3\u20134) (2000) 346\u2013382.<\/p>\n

[84] M. Sekimoto, M. Kato, N. Kajimura, T. Watanabe, K. Takahashi, T. Okuma,\u00a0Asymmetric interhemispheric delta waves during all-night sleep in humans,\u00a0Clin. Neurophysiol. 111 (5) (2000) 924\u2013928.<\/p>\n

[85] M. Shadlen, W. Newsome, The variable discharge of cortical neurons: implications\u00a0for connectivity, computation, and information coding, J. Neurosci. 18\u00a0(10) (1998) 3870\u20133896.<\/p>\n

[86] Y. Shen, E. Olbrich, P. Achermann, P.F. Meier, Dimensional complexity and\u00a0spectral properties of the human sleep EEG, Clin. Neurophysiol. 114 (2) (2003)\u00a0199\u2013209.<\/p>\n

[87] Y. Shu, A. Hasenstaub, D. McCormick, Turning on and off recurrent balanced\u00a0cortical activity, Nature 423 (6937) (2003) 288\u2013293.<\/p>\n

[88] S. Spasic, A. Kalauzi, G. Grbic, L. Martac, M. Culic, Fractal analysis of rat brain\u00a0activity after injury, Med. Biol. Eng. Comput. 43 (3) (2005) 345\u2013348.<\/p>\n

[89] C. Stam, J. Pijn, P. Suffczynski, F. Lopes da Silva, Dynamics of the human\u00a0alpha rhythm: evidence for non-linearity? Clin. Neurophysiol. 110 (10) (1999)\u00a01801\u20131813.<\/p>\n

[90] C. Stam, Nonlinear dynamical analysis of EEG and MEG: review of an emerging\u00a0field, Clin. Neurophysiol. 116 (10) (2005) 2266\u20132301.<\/p>\n

[91] K. Susm\u00e1kov\u00e1, A. Krakovsk\u00e1, Discrimination ability of individual measures\u00a0used in sleep stages classification, Artif. Intell. Med. 44 (3) (2008) 261\u2013277.<\/p>\n

[92] G. Tinguely, L.A. Finelli, H.P. Landolt, A.A. Borbely, P. Achermann, Functional\u00a0EEGtopography in sleep and waking: state-dependent and state-independent\u00a0features, Neuroimage 32 (1) (2006) 283\u2013292.<\/p>\n

[93] V. Vyazovskiy, P. Achermann, A. Borb\u00e9ly, I. Tobler, Interhemispheric coherence\u00a0of the sleep electroencephalogram in mice with congenital callosal\u00a0dysgenesis, Neuroscience 124 (2) (2004) 481\u2013488.<\/p>\n

[94] V. Vyazovskiy, I. Tobler, Regional differences in NREM sleep slow-wave activity\u00a0in mice with congenital callosal dysgenesis, J. Sleep Res. 14 (3) (2005)\u00a0299\u2013304.<\/p>\n

[95] B. Weiss, Z. Clemens, R. B\u00f3dizs, Z. V\u00e1g\u00f3, P. Hal\u00e1sz, Spatio-temporal analysis of\u00a0monofractal and multifractal properties of the human sleep EEG, J. Neurosci.\u00a0Methods 185 (1) (2009) 116\u2013124.<\/p>\n

[96] E. Werth, P. Achermann, A. Borb\u00e9ly, Brain topography of thehumansleep EEG:\u00a0antero-posterior shifts of spectral power, Neuroreport 8 (1) (1996) 123\u2013127.<\/p>\n

[97] E. Werth, P. Achermann, A. Borb\u00e9ly, Fronto-occipital EEG power gradients in\u00a0human sleep, J. Sleep Res. 6 (2) (1997) 102\u2013112.<\/p>\n

[98] E. Werth, P. Achermann, D. Dijk, A. Borb\u00e9ly, Spindle frequency activity in\u00a0the sleep EEG: individual differences and topographic distribution, Electroencephalogr.\u00a0Clin. Neurophysiol. 103 (5) (1997) 535\u2013542.<\/p>\n

[99] A. Yasoshima, H. Hayashi, S. Iijima, Y. Sugita, Y. Teshima, T. Shimizu, Y.\u00a0Hishikawa, Potential distribution of vertex sharp wave and saw-toothed wave\u00a0on the scalp, Electroencephalogr. Clin. Neurophysiol. 58 (1) (1984) 73\u201376.<\/p>\n

[100] J. Zeitlhofer, G. Gruber, P. Anderer, S. Asenbaum, P. Schimicek, B. Saletu, Topographic\u00a0distribution of sleep\u00a0spindles in young healthy subjects, J. Sleep Res.6 (3) (1997) 149\u2013155.<\/p>\n

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