Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations

“…fluctuation analysis has been developed for quantifying correlation properties in nonstationary signals, e.g., in physiological time series, because long-range correlations—revealed by an ACF analysis—can arise also as an artifact of the “patchiness” of nonstationary data (Peng et al., 1994, 1995).”

“Unlike deterministic approaches aimed at finding low-dimensional chaos, the SOC framework allows for a highdimensional character of the dynamics and for the presence of stochastic effects.”

“and Marchesi, 1999), heartbeats (Peng et al., 1995), and human”

“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”

“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”

“Often, Hurst exponents of H >0:5 were interpreted as a sign of long-range correlations in EEG time series and microstate sequences (Linkenkaer-Hansen et al., 2001; Van de Ville et al., 2010; Gschwind et al., 2015).”

“…Ethernet traffic [14], finance and economy [15–17], written language [18, 19], as well as physiological records [9, 20, 21], Human brain activity [22–24] and human motor activity [25] also comprise long-term correlations as well as city growth [26–29], biological networks [30] and the spreading…”

“dynamics of brain activities [24,25]; our IMF1 corresponded to slow-3 waves defined by Buzsaki et al.”

“This unassuming detail, however, poses a challenge if one wants to explore this class of models to reproduce the above mentioned long-range time correlations which were observed experimentally [17, 25].”

“In spite of different studies’ designs, our results are in agreement with previous reports (Watters, 1998a,b, 2000; Linkenkaer-Hansen et al., 2001, 2005; Shen et al., 2003; Hwa and Ferree, 2004; Lee et al., 2004; Parish et al., 2004; Nikulin and Brismar, 2005), showing that a persistent process…”

“Correlated amplitude fluctuations reveal information about the temporal structure of the EEG (Linkenkaer-Hansen et al., 2001).”

“After 1 week of recovery, rats were acclimated to attachment of the electrode cable in the operant box for four 30-min sessions and retrained to criterion performance at the 300 ms stimulus duration.”

“Hence, multiple avalancheindependent options were proposed as alternative assessments of criticality in the brain: 1) detrended fluctuation analysis [60] allows to capture the scale-free behavior in long-range temporal correlations of EEG/MEG data, 2) critical slowing down [194] suggests a closeness to a bifurcation p…”

“Techniques such as postmortem diffusion tractography (Haber 1988; Miller et al. 2012), retrograde tracing (Markov et al. 2014; Oh et al. 2014; Zingg et al. 2014), diffusion tensor imaging (DTI; O’Donnell and Westin 2011), electroencephalography (EEG; Nunez and Srinivasan 2006), magnetoencephalography (MEG; Baillet 201…”

“( f ) The long-time scale differences in beta oscillations are reflected in the grand average DFA showing larger scaling exponents for peak scopolamine ( red ) than for the baseline recording ( blue ).”

“…suggested that critical-state dynamics of spontaneous oscillations, even when performance of a particular cognitive task is not required, render neural networks capable of quick reorganization in order to meet future processing demands (Linkenkaer-Hansen et al., 2001; Kitzbichler et al., 2009).”

“Recent studies have shown that sudden transitions in the amplitude of the human electroencephalogram (EEG) are represented by power laws and scale invariance and long-range temporal correlations [Freeman, 2003; Linkenkaer-Hansen et al., 2001; Nikulin and Brismar, 2005; Parish et al., 2004].”

“(8) A final possibility to be considered is that the brain as a system might function in a state of self-organized criticality (Schroeder, 1991; Bak, 1997; Jensen, 1998; Linkenkaer-Hansen et al., 2001; Freeman, 2005).”

“Other research, however, has demonstrated that spontaneous cortical activity in vitro [4–6] and in vivo [1, 7, 8] at the population level manifests as precisely organized spatiotemporal cascades of activity termed neuronal avalanches.”

“First, in the timescales of seconds to tens of minutes, powerlaw long-range temporal correlations (LRTCs) characterize the amplitude envelopes of neuronal oscillations in human MEG and EEG (Linkenkaer-Hansen et al., 2001) as well as in intracranial recordings (Monto et al.”

“The power spectral densities in both time and space of ECoGs from surface arrays conform to power-law distributions [13, 14, 35, 36, 37], which suggests that the activity patterns generated by neocortical neuropil might be scale-free [38, 39] with self-similarity in ECoGs patterns over distances ranging from hypercolu…”

“It should be pointed out that, since the organizational dynamics of individual proteins, cells, organs, organisms, and economies display longrange correlations in time [24-29], the structure and dynamics of any living system - be it a protein, a cell, an organism, an organization, or an economy - carry within them the…”

“Additionally, it has been shown that local beta range activity of distant cortical networks is temporally correlated during resting-state EEG [16].”

“Although this method is commonly viewed as the gold standard for anatomical connectivity estimation, it is important to note that tractography always yields merely an estimate of the actual anatomical connectivity between brain regions, and is subject to several methodological pitfalls (Maier-Hein et al., 2017), such…”

“We applied this method to the amplitude envelope of each oscillation frequency band the way it was introduced by Linkenkaer-Hansen et al. (2001) and it has been explained in detail with reference to open-access Matlab scripts elsewhere (Hardstone et al., 2012).”

“and scale-free temporal patterns (Kello et al., 2010), mean-”

“LRTC have been suggested to reflect the degree to which the brain remains capable of quick reorganization (Deco et al., 2013; Linkenkaer-Hansen et al., 2001; Singer, 2013; Tognoli & Kelso, 2014) and, thus, is responsive to different processing demands.”

“…matrix, as well as decoding without boosting as per preregistration). at the high probability location ( t (12)= 6.751, p < 0.001, d Z = 1.9, 95% CI [25.27, 52.76]) suggesting that our observed results were not solely driven by a subset of aware participants (see Supplementary Fig.”

“…and temporal correlations have been very well documented by analyzing brain activity from several different perspectives, including the temporal fluctuations of power of brain oscillations [39,40], the distribution of size of neural avalanches [41], and the intervals of synchronized activity [42].”

“We used detrended fluctuation analysis (DFA) to assess the scaling exponents of the longrange temporal correlations (LRTCs; Linkenkaer-Hansen et al., 2001; J. M. Palva et al., 2013; Peng, Havlin, Stanley, & Goldberger, 1995).”

“…measurements such as temporal patterns of heartbeats (Goldberger et al., 2002) have been interpreted as a consequence of an underlying fractal physical structure (Di Ieva et al., 2014; Werner, 2010) and are a signature of correlations on many temporal scales (Linkenkaer-Hansen et al., 2001).”

“In neurophysiology, similar long-range correlation effects have been identified from microscopic to macroscopic domains, ranging from the spike patterns of maintained discharges of retinal ganglion cells, lateral geniculate nucleus (Teich et al., 1997) and medullary sympathetic neurons (Lewis et al., 2001 )t o global…”

“This neural mechanism depends on robust maintenance by cortex approximating scale-free dynamics at criticality (Linkenkaer-Hansen et al, 2001; Freeman, 2007a ), where all frequencies and wavelengths of activity may simultaneously be expressed, as revealed in the power-law distributions of spectra…”

“Previous electrophysiological studies have measured verylow-frequency fluctuations in power within the traditional frequency bands from EEG recordings, reporting large power variations with 1/f-like power spectra (Linkenkaer-Hansen et al., 2001).”

“Future studies are needed to resolve the role of these mechanisms in ISFs in vivo as well as the contributions that the slow amplitude dynamics of fast >1 Hz neuronal activities (Deco et al., 2011; Linkenkaer-Hansen et al., 2001) have in shaping the ISFs and ICN fluctuations.”

“At the neural level, there is coordination across multiple time scales of the neural firing patterns ranging from relatively slow alpha rhythms to very high frequency theta oscillations (Linkenkaer-Hansen et al., 2001; cf. Buzsaki, 2006).”

“A view shared by many is that scale-free fluctuations are the result of an underlying self-organized critical state of the brain that gives rise for its ability to perform large-scale reorganizations quickly in response to external/internal stimuli (Linkenkaer-Hansen et al., 2001; Bullmore et al., 2009; Chialvo, 2010;…”

“Importantly, LRTCs indicate the presence of a scale-free structure of neuronal activation on multiple time scales that is important for optimal neuronal processing in the human brain (Linkenkaer-Hansen et al., 2001; Hardstone et al., 2012; Palva et al., 2013).”

“We used Detrended Fluctuation Analysis (DFA) to estimate mono-fractal scaling exponents of neuronal LRTCs that typically vary between 0.5 and 1 30,52,55,64 .”

“The observation of long network timescales during wake is in agreement with this criticality hypothesis (Linkenkaer-Hansen et al., 2001) and indicates that the ability to maintain memory of past activity is preserved in neural systems across different spatial scales (Meisel et al., 2015).”

“A line of research into diverse directions found them ubiquitous in nature [2–17].”

“Fractal geometry has been applied to the study of temporal dynamics, such as human brain dynamics in health (Lutzenberger et al., 1995; Pereda et al., 1998; Eke et al., 2000, 2002; Linkenkaer-Hansen et al., 2001; Bullmore et al., 2003, 2009; Gong et al., 2003; Acharya et al., 2005; Bassett et al., 2006, 2010; Hsu et a…”

“The brain generates fluctuations with complex scaling properties (Novikov et al., 1997; Linkenkaer-Hansen et al., 2001; Gong et al., 2002, 2007; Freeman et al., 2003; Bianco et al., 2007; Suckling et al., 2009; Freyer et al., 2009), even in the absence of exogenous perturbations or changes in…”

“…∼ exp [−(t/τ)α] at microscopic scales (t < τ), and asymptotical convergence to an inverse power law ∼ [−(t/τ)α] for t τ, 0 < α < 1 (Novikov et al., 1997; Linkenkaer-Hansen et al., 2001; Gong et al., 2002; Freeman et al., 2003; Stam and de Bruin, 2004; Buiatti et al., 2007; van de Ville et…”

“org/journal/rsfs Inrface Fcus 13:(2)0220079 2 methods have looked at temporal activity and used detrended fluctuation analysis [11,12], the Hurst exponent [13,14], or the power spectrum [15] to provide further evidence for criticality in neural recordings.”

“…studies have demonstrated that LRTC in cortical alpha and beta oscillations were not very sensitive to whether eyes were open or closed (known to represent different levels of arousal: Niedermeyer & Lopes da Silva, 2004) in healthy subjects (Linkenkaer-Hansen et al., 2001; Nikulin & Brismar, 2005).”

“Given that specifically the slow APF values have yielded predictive power (for overview see Arns and Olbrich, 2013) and LRCTs indicate power laws in which slow frequencies dominate the signal (Babloyantz, 1991; Linkenkaer-Hansen et al., 2005; Linkenkaer-Hansen et al., 2001), we used the above frequency band.”

“The open-source toolbox is freely available and is well tested (Linkenkaer-Hansen et al. 2001; Moy et al. 2002; Holdsworth et al. 2012).”

“The DFA was introduced as a method to quantify correlations in complex data with less strict assumptions about the stationarity of the signal than the classical autocorrelation function or power spectral density (Peng et al., 1995; Linkenkaer-Hansen et al., 2001; Hardstone et al., 2012).”

“These findings are consistent with prior reports of intermittent non-linear structure within (Stam et al., 1999) and between (Breakspear and Terry, 2002) surface EEG channels.”

“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].”

“frequency ranges, suggesting the distinct significance of neuronal oscillations in human behaviour (Linkenkaer-Hansen et al., 2001; Nikouline et al., 2001).”

“Such passive states would therefore exhibit a characteristic 1/f spectrum (Freeman, 2004; He, 2014; Linkenkaer-Hansen et al., 2001).”

“…1/f brain activity during aging (Bak et al., 1987; Voytek et al., 2015), of slope-modulations during sleep versus awake states (Gilden et al., 1995; Linkenkaer-Hansen et al., 2001; He et al., 2010; Van de Ville et al., 2010; Zempel et al., 2012), of slope-modulations during task activation in…”