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).”

“Later studies using non-invasive EEG and magnetoencephalography (MEG) (Linkenkaer-Hansen et al., 2001, 2005), and invasive electrocorticography (ECoG) (Ko et al., 2011; Monto et al., 2007), have shown that the amplitude fluctuations of human cortical oscillations in theta- (4–8 Hz), alpha-, and beta(14–30 Hz) frequenc…”

“This is because slow frequencies dominate the EEG spectrum (1/f spectrum, Robinson et al., 2001; Linkenkaer-Hansen et al., 2001) and strongly vary with sleep depth.”

“…release (Lowen et al. 1997), neuronal spike trains (Lowen et al. 2001), network firing rates (Garcia-perez et al. 2007), field potentials (Linkenkaer-Hansen et al. 2001; Manning et al. 2009; Miller et al. 2009; He et al. 2010; Palva et al. 2013), to fMRI signals (He et al. 2010; He 2011).”

“Power laws have also been witnessed within the brain in electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings while studying a wide variety of brain function [5,6,7].”

“This finding is in agreement with previous studies (Linkenkaer-Hansen et al., 2001; Nikulin and Brismar, 2004; Parish et al., 2004; Monto et al., 2007), albeit that the duration of the EEG recordings in the present study only allowed an investigation of LRTC on time scales up to 20 s ( 1/10 of the data length).”

“In conclusion, the observation of LRTC in human electrophysiology further supports the hypothesis that criticality is a robust property of cortical activity and a relevant biomarker of E/I balance.”

“Long-term temporal correlations have been soundly established at the population level, such as the EEG (Linkenkaer-Hansen et al., 2001) and ECoG (He et al.”

“Other findings include the observation of 1/f power spectra from simultaneously recorded magnetoencephalography and electroencephalography signals [22], fMRI signals [23–25] as well as from cognitive responses [26], all indicative of long range correlations in brain dynamics processes.”

“Our results build upon previous studies to provide direct evidence that successful retrieval involves the reinstatement of a temporal context, and that such reinstatement occurs with precise spatiotemporal dynamics. memory | intracranial EEG | oscillations | reinstatement Reinstatement of neural activity is hypothesiz…”

“These neurons interact in a mainly local and non-linear way and generate activity, which exhibits two seemingly contradictory properties: First, activity levels fluctuate over many orders of magnitude in time and space [1-8] even when external conditions are held as constant as possible [9-11].”

“In living animals, power-law distributions were found in LFPs of macaques [38], rhesus monkeys [39, 40], and cats [41, 42], in two-photon microscopy in mice [43, 44], in light-sheet microscopy of whole-brain GCaMP activity in zebrafish larvae [45], in LFPs from intracranial depth electrodes in humans [46], in MEG and…”

“The statistical properties described above characterize a system that can maintain itself in a state of selforganized criticality (Bak et al. 1987; Barrie et al. 1996; Linkenkaer-Hansen et al. 2001; Freeman et al. 2000; Hwa and Ferree 2002).”

“For fairly constant amplitudes of the sources, scalp amplitudes simultaneously reach a minimum when incident relative phase crosses p rad and a maximum when crossing 0 rad (Fig. 7). Remarkably, amplitude fluctuation is a pervasive feature of electroencephalographic data both in the temporal (e.g., Linkenkaer-Hansen et…”

“…stronger power than faster ones, the latter are temporally nested within the former—there is thus “temporal nestedness” that indexes a fractal organization between the different frequencies in the brain’s spontaneous activity (He, 2011; He, 2014; Linkenkaer-Hansen et al., 2001; Palva et al., 2013).”

“There is already a large body of evidence for critical brain dynamics in neurophysiological processes including spike frequency, endogenous EEG and fMRI oscillations (Maxim et al., 2005; Bullmore et al., 1994; Linkenkaer-Hansen et al., 2001), which all display characteristic power law scaling in anatomically localized…”

“Although there have been recent papers arguing for criticality and power law effects in large-scale cortical activity (e.g. Kitzbichler et al., 2009; Linkenkaer-Hansen et al., 2001; Stam and de Bruin, 2004; Freyer et al., 2009) there is also work that argues otherwise; at least at higher…”

“It is consistent with temporal scaling properties manifested in EEG [57, 59, 66, 75], such that spatially coherent cortical activity patterns may coexist for epochs ranging in duration from ms to s, and with spatial scaling properties in EEG [40], as manifested in patterns ranging in diameter from under a mm through h…”

“First, in contrast to prior studies (such as Novikov et al. 1997; Linkenkaer-Hansen et al. 2001), we calculated the frequency scaling of all the sensors and did not confine our analysis to a specific region.”

“Examples are computer communication in an Ethernet [Beran, 1994] or neural oscillations in the human brain [Linkenkaer-Hansen et al., 2001].”

“…highlighted the adaptive nature of self-organizing neural networks: A network that is in a state of criticality is able to quickly reorganize and swiftly adapt to new situations (Alstrøm & Stassinopoulos, 1995; cf. Linkenkaer-Hansen, 2002; Linkenkaer- Hansen, Nikouline, Palva, & Ilmoniemi, 2001).”

“In addition to dominant brain waves, physiological states are characterized by specific signatures in the temporal modulation of brain waves (Linkenkaer-Hansen et al., 2001; Poil et al., 2008) and their synchronization across different locations (White et al., 1998; Kopell et al., 2000).”

“LRTCs can persist over several seconds and obey a power-law function.(121) There is evidence that LRTCs are indicative of neuronal networks operating in a critical state(122) and are controlled by E/I-balance parameters.”

“Recent studies showed an existence of longrange temporal correlations (LRTC) in the amplitude dynamics of alpha and beta oscillations (Linkenkaer-Hansen et al., 2001, 2004; Nikulin and Brismar, 2004, 2005).”

“Recent findings have demonstrated that spontaneous neuronal activity in the human brain demonstrates longrange temporal (auto-) correlations (Linkenkaer-Hansen et al., 2001; Shen et al., 2003; Watters, 1998).”

“The mechanisms giving rise to this statistical hallmark are poorly understood, but it has been suggested to reflect self-organized activity in critical networks [Linkenkaer-Hansen et al., 2001].”

“I T is well known in the neuroimaging community that both fMRI and EEG time series exhibit temporal autocorrelations both in the short and long range regardless of experimental stimuli [9], [10].”

“Similar power-law scaling behavior was observed in spontaneous neural oscillations generated in the human brain 21 .”

“4, A and B, in Linkenkaer-Hansen et al. 2001).”

“Thus, analyzing scale-invariance in temporal dynamics may provide novel insights into brain mechanisms underlying cognition and behavior (Linkenkaer-Hansen et al., 2001; Shimizu et al., 2004; Stam and de Bruin, 2004; He et al., 2008; He et al., 2010; He, 2011; Ciuciu et al., 2012; Suckling et al., 2008; Maxim et al.,…”

“The significant information storage in the heart and brain systems indicates the presence of structured dynamics that, at the time scales explored in this study, are probably reflecting the long-range correlations observable when looking at the temporal evolution of the heartbeat intervals [41] and of the brain waves…”

“organized criticality in physical systems [111] and in the brain [24,57,188-192].”

“…field potential, and spike trains recorded from network-embedded neurons in vivo and in vitro (Teich, 1989; Teich et al., 1997; Lowen et al., 1997; Linkenkaer-Hansen et al., 2001, 2005; Buzsaki, 2006; Nir et al., 2007, 2008; Monto et al., 2008; Wink et al., 2008; Esposti et al., 2009; Freyer et…”

“…synchronization rate, single neuron spike counts and synaptic release in vivo and in vitro (Teich, 1989; Teich et al., 1997; Lowen et al., 1997; Linkenkaer-Hansen et al., 2001; Segev et al., 2002; Beggs and Plenz, 2003, 2004; Linkenkaer-Hansen et al., 2005; Wagenaar et al., 2006; Nir et al.,…”

“• Neurosciences (Linkenkaer-Hansen et al. 2001; Bédard et al. 2006).”

“Since it has been argued that neuronal oscillatory dynamics, as well as fluctuations in connectivity, can be characterized by scale-freeness (Stam and De Bruin, 2004; Linkenkaer-Hansen et al., 2001), there is a need to move beyond conventional fixed sliding window analyses.”

“Although there have been recent papers arguing for criticality and power law effects in large-scale cortical activity (e.g. Kitzbichler et al., 2009; Linkenkaer-Hansen et al., 2001; Stam and de Bruin, 2004; Freyer et al., 2009), there is also work that argues otherwise; at least at higher…”

“In neuroscience; long-term persistence has been identified in resting-state and task fluctuations of electrophysiological and imaging signals (Linkenkaer-Hansen et al., 2001; Van de Ville et al., 2010; He, 2014) and found to correlate with behavior (Palva et al.”

“…we used the DFA method as in most recent papers investigating the autocorrelation structure of amplitude fluctuations in ongoing oscillations (e.g., Linkenkaer-Hansen et al., 2001; Parish et al., 2004; Nikulin and Brismar, 2005; Monto et al., 2007; Poil et al., 2008; Berthouze et al., 2010).”

“5 to 1, which, in line with previous reports, is indicative of long-range temporal correlations in the EEG signals [26].”

“…(Himberger et al., 2018; Honey et al., 2012; Murray et al., 2014) and PLE (Chialvo, 2010; Eke et al., 2000, 2002; He, 2011, 2014; He et al., 2010; Linkenkaer-Hansen et al., 2001) are analogous measures of temporal integration on the neuronal level; they assess the same property (the fractal…”

“(Methodological), 289-300. Benwell CSY, Tagliabue CF, Veniero D, Cecere R, Sav azzi S, Thut G (2017) Prestimulus EEG power predicts conscious awareness but not objectiv e visual performance.”

“Brain electrical data may provide more direct evidence into time scales of the global brain dynamics: decay times of EEG auto-correlation functions are reported in the range ≈100 s (Linkenkaer-Hansen et al., 2001).”

“Several types of network have been proposed to model (Friston 2000; Linkenkaer–Hansen et al. 2001; Stam et al. 2003; Kozma et al. 2005) the long-distance synchronization that is readily observed in scalp EEG (Rodriguez et al.”

“For example, long-range temporal correlations (LRTCs) of narrowband amplitudes provide an alternative window on the irregularity of temporal dynamics [107–109].”

“This spontaneous 1/f aperiodic brain dynamics almost always pervasively co-exists in EEG/magnetoencephalography (MEG)/LFP signals (Lyne et al., 1992; Linkenkaer-Hansen et al., 2001; Beggs and Plenz, 2003; Bédard et al., 2006; Voytek et al., 2015) and critically influence oscillatory signatures in…”

“…dynamics are often studied without any reference to the external events, i. e., during resting state, where the interest is to understand dynamics of oscillations unfolding without perturbations (Linkenkaer-Hansen et al., 2001; Nikouline et al., 2001; Nikulin and Brismar, 2005; Hipp et al., 2012).”

“For its task-free procedure and confirmed inter-subject stability, rs-fMRI is used not only for cognitive neuroscience investigations (Linkenkaer-Hansen et al., 2001; Weissman-Fogel et al., 2010), but also for its great potential to study functional brain changes (plasticity) under a number of…”

“For example, the spectra of the amplitude modulation of neuronal oscillations in different frequency bands show power-law frequency spectra over a large frequency range (Linkenkaer-Hansen et al., 2001; Berthouze et al., 2010).”

“These envelopes typically exhibit long-range temporal correlations and power-law scaling , which indicate that the ongoing neural activity fluctuates over a wide range of timescales 112,114 .”

“However it was later shown that this topological pattern is superimposable dIscussIon The experimental discovery of 1/f noise in the brain (e.g., Novikov et al., 1997; Linkenkaer-Hansen et al., 2001; Buiatti et al., 2007) has normally been interpreted as an indication of self-organization.”