Aperiodic phase re‐setting in scalp EEG of beta–gamma oscillations by state transitions at alpha–theta rates

“When plotted in logarithmic coordinates, these power spectra appeared as a straight line with positive deviations (i.e., peaks) at particular frequencies, consistent with previous findings that iEEG power has a 1/f a distribution (Freeman et al., 2003; Miller et al., 2007).”

“Likewise, Freeman has observed, in both awake cats and humans, sharp transitions in the phase of local potentials that occur simultaneously at distant sites across the scalp and delimit metastable periods of 100–300 ms duration [95].”

“Llinas and Pare (1991) have emphasized the integration of specific and non-specific thalamocortical signaling, and Freeman et al. (2003) have developed a conception of hemisphere-wide signaling and phase changes.”

“The standard padding was adopted (Freeman et al., 2003).”

“Finally, several authors have suggested that the complex dynamics of synchronization and desynchronization processes in the brain might be due to so called “self-organized criticality” [Bak et al., 1987; Freeman et al., 2003; Le van Quyen, 2003].”

“Freeman WJ, Burke BC, Holmes MD. 2003 Aperiodic phase re-setting in scalp EEG of beta – gamma oscillations by state transitions at alpha – theta rates.”

“Likewise the EEG gives records that appear chaotic, with temporal and spatial spectra that are 1/f α, where the exponent α has been estimated 1 < α < 3 (Pereda et al., 1998; Freeman et al., 2003).”

“During EEG recording the sulci were avoided by making the 8x8 square array small enough (1x1 cm) to fit onto a single gyrus [Freeman et al., 2000; Freeman et al. 2005].”

“Synchronization of neural electical activity while completing cognitive tasks is studied in various animals, e.g., in cats, rabbits, gerbils, macaque monkeys (Barrie et al, 1996; Ohl, et al, 2001, 2003, Freeman et al, 2003a; Bressler, 2003).”

“A method to distinguish zero phase lag due to volume conduction versus zero phase lag due to network connectivity is by phase reset measures that precisely define the onset and offset of phase shift in single pairs of electrodes which is by definition independent of volume conduction ( Freeman & Rogers, 2002 ; Freeman…”

“Changes in brain state—for example, from synchronous to asynchronous, or substantial changes between oscillatory phases, may result from GABAmediated thalamocortical circuit inhibitory bursts [148, 149].”

“A new cospectral peak appeared in the theta range at 4.6 Hz, reflecting the change in recurrence rate of the spatially aligned jumps in |AP| differences.”

“Nonetheless, both findings seem closely related because they each describe stimulus-specific patterns of gamma-amplitude modulation that occur during periods of elevated overall gamma activity and that are linked to theta oscillations (Freeman et al., 2003).”

“The power spectral densities (PSD) of the EEGs had power-law distributions (1/f) in log–log displays; the maximal energy of carrier waves was in spectral peaks in the beta (12–30 Hz) or gamma (30–80 Hz) ranges, while the repetition of frames gave peaks in the theta and alpha ranges (Freeman et al., 2003).”

“Both the analytic signal approach (Freeman et al., 2003; Le Van Quyen et al., 2001; Rosenblum et al., 2001; Tass et al., 1998) and the wavelet transform (Lachaux et al.”

“More rarely, spatial correlation in terms of spatial power spectral density (Freeman et al., 2003) and of synchronisation (Astolfi et al.”

“Several authors have attempted to utilize the properties of the Hilbert transform in order to demonstrate it in neurophysiological data (Breakspear, 2002; Freeman et al., 2002, 2003; Breakspear et al., 2003d).”

“In order to quantify the intra- and inter-limb phase coordination, a phase analysis using the Hilbert transform [32] was applied to the left and right limbs.”

“The differences in amplitude and phase among channels demonstrated that the shared waveform was intrinsic to the dynamics and could not be ascribed solely to activity at the reference electrode or to volume conduction [Freeman et al., 2003].”

“…fall in log power with increasing log frequency imposed by the impedance of the skull and scalp, and partly due to a spatial spectral peak in the middle spatial frequency range that corresponded to the spatial frequency of the gyri and sulci of the human cerebral hemisphere [Freeman et al., 2003].”

“The most valuable tool is the spatial power spectral density (PSDX), which has been calculated for the scalp EEG (Freeman et al., 2003), intracranial human electrocorticogram (ECoG, Freeman et al., 2000) and fMRI (Worsely, 2005) but surprisingly not for MEG.”

“In several studies, Freeman and colleagues demonstrated that human EEG obeys a 1/f property (Freeman et al. 2000, 2003).”

“Such properties were attributed by some researchers to a universal phenomenon displayed by global synchronization dynamics, known as ‘self-organized criticality’ (SOC; Freeman et al., 2003; Kitzbichler et al., 2009; Le van Quyen, 2003).”

“Phase shift duration is a period of high uncertainty and instability, whereas, phase locking is a period of stability and low uncertainty (Freeman et al., 2003; Thatcher et al., in press).”

“…significant background synchrony has also been reported by Freeman and colleagues, both in ECoG measurements from a grid of electrodes implanted on the surface of rabbit sensory cortex (Freeman and Rogers, 2002; Freeman, 2004a,b) and in EEG measurements from human scalp (Freeman et al., 2003a,b).”

“Pass bands for individuals varied from the normative values after classifier-directed optimization of the filter settings with tuning curves [Freeman et al., 2003a].”

“…are consistent with physiological models of EEG PR and have added to earlier studies by Varela (1995), Breakspear (2002, 2004), Freeman (2003), and Freeman et al. (2003) by measuring discontinuities of electrical potentials and current sources of the two main physiological processes that underlie…”

“The concept of chaotic itinerancy offers a theoretical basis for the transient character of brain dynamics, which has been observed in many studies besides the present one [Stam et al., 2003; Freeman et al., 2003; Breakspear et al., 2004; Schack, 2004] and raised as a property essential for effective and integrated br…”

“Studies by Freeman and Rogers (2002) and Freeman et al. (2003) show that the spontaneous EEG is made up of a mixture of synchronous processes that involve rapid phase shifts (approx.”

“…of the binomial probability of the classification rate of the features es (C3, C2 and C1) and 6 post-stimulus test frames (T1, T2, T3, T4, T5 and T6) for tom: mean classification rate for same frames, vertical bars represent the standard theta range (Freeman et al., 2003a; Freeman, 2006, 2009).”

“37 implying a global state transition of cortical activity occuring with a phase velocity of over 40 m/s (Freeman et al., 2003).”

“A similar transitivity behavior of brain dynamics has been observed in many previous studies (Breakspear et al. 2004; Freeman et al. 2003; Schack 2004; Stam et al. 2003) and appears as an essential property of the dynamics of the intact brain (Friston 2000a, b, c; Freeman 2004a, b, 2005, 2006; Kaplan et al.”

“proximity by synaptic connections enables rapid changes in states of neuron populations over large areas of cortex [21, 67], the diameters of which exceed the mean length of”

“The present work is based on recent progress on phase transitions in brains using advanced, highresolution spatio-temporal EEG measurements (Freeman et al., 2003; Freeman, 2007).”

“Examples are EEG recordings aimed at evaluating synchronization between cortical states on the scalp (Freeman et al., 2003), andmagnetoencephalography (MEG) studies on patients affected by Parkinson's disease (Tass et al.”

“Phase locking is a telltale sign of synchronization, and this is why Freeman and colleagues (Freeman et al., 2003; Freeman & Rogers, 2002) and Breakspear and Williams (2004) and others (Lachaux et al., 2000; Lachaux, Rodriguez, Martinerie, & Varela, 1999; LeVan Quyen et al., 2001; Varela, Lachaux,…”

“…animals we proposed that the behavioral transition from waking rest to engagement with the environment is based in arousal that supports the likelihood of repetitive phase transitions recurring at rates in the theta range [Skarda and Freeman, 1987; Freeman, Burke and Holmes, 2003; Freeman, 2005].”

“Hilbert transform has the potential to avoid these difficulties , and it has been applied successfully to EEG analysis in the past few years (Lachaux et al., 1999; Le Van Quyen et al., 2001; Freeman and Rogers, 2002, 2003; Quiroga et al., 2002).”

“This phase and amplitude coupling has been observed in different cortical regions (Freeman et al., 2003; Palva et al., 2005; Canolty et al., 2006; Isler et al., 2008; Sauseng et al., 2008), across the conventional EEG spectra (0.5 ≥ f ≤ 100 Hz); Lakatos et al., 2005), and extending into…”

“Synchronization of neural electical activity while completing cognitive tasks is studied in various animals, e.g., in cats, rabbits, gerbils, macaque monkeys (Barrie et al, 1996; Ohl, et al, 2001, 2003, Freeman et al, 2003a; Bressler, 2003).”

“4 For other major methodologies of EEG analysis which explicitly utilize EEG nonstationarity see the work of Lehman and coworkers (60, 61, 67, 80, 138, 147, 149, 150, 165), Freeman and coworkers (62, 64, 65, 85, 87, 89, 90, 112, 123, 158, 166), and Breakspear and Stam with coworkers (75, 134, 145, 167-169).”

“Definitive exploration of hubs may be optimized by recording EEG/MEG from a dense array of channels overlying a large percentage of the surface each hemisphere, and with sampling at 1 cm intervals corresponding to the width of gyri so as to capture adequately the texture of AM patterns of spatially coherent activity […”

“The result is seen in the fluctuations of the gamma band activity in the ECoG; the amplitude histogram is close to Gaussian; the envelope of the activity conforms to the Rayleigh distribution [14], p. 148, Fig. 3.13c; and the power spectral density in log-log coordinates has a slope near ‐2. The spikes in SDX (t) recu…”

“…phase lag due to volume conduction vs zero phase lag due to network connectivity is by phase reset measures that precisely define the onset and offset of phase shift which is by definition independent of volume conduction [Buzsaki, 2006; Freeman et al., 2003, 2006; Thatcher et al., 2008c, 2009].”

“…brain activity (Stam 2005, Chialvo 2010, Werner 2010), considering it as a plausible mechanism underlying scale-free structuring in neural dynamics (Freeman et al 2003, de Arcangelis et al 2006), in neural avalanches (Beggs and Plenz 2003) and in EEG synchronization (Stam and de Bruin 2004, Stam…”

“By recording and analyzing electroencephalography data from the scalp of healthy subjects, Freeman discovered that chaotic firing also exists in the human brain and suggested that this brain chaos is called stochastic chaos (Freeman 1990, 2000; Freeman et al. 2003).”

“Scalp EEG technology is the clinical gold standard for studying the human brain (Müller-Putz, 2020) and EEG recordings can be classified into specific frequency bands: alpha, beta, delta, gamma, and theta (Cho et al., 2014; Freeman et al., 2003; Pedregosa et al., 2011; Zhao et al., 2018).”

“…authors ’ knowledge, despite the rich literature on EEG phase, only some general guidelines have been proposed for the phase extraction procedure (Freeman et al 2003, Freeman 2007), and researchers have been basically using arbitrary and un-unified narrow-band filtering and phase extraction…”

“These episodes emerge, hold, and dissipate on different temporal scales and in different brain structures (Friston 2000; Freeman et al. 2003; Gong et al. 2003; Stam et al. 2003; Ito et al. 2005).”

“Phase transitions between chaotic states constitute the dynamics that explains how brains perform such remarkable feats as abstraction of the essentials of figures from complex, unknown and unpredictable backgrounds, generalization over examples of recurring objects, reliable assignment to classes that lead to appropr…”

“…& Malach, 2015; Voytek, Kramer, Case, Lepage, Tempesta, Knight & Gazzaley, 2015), whereby power decreases exponentially as a function of frequency (f) (Donoghue, Haller, Peterson, Varma, Sebastian, Gao, Noto, Lara, Wallis, Knight, Shestyuk & Voytek, 2020; Freeman, Burke & Holmes, 2003; He, 2014).”

“, 2007) and to cognitive studies of areal interactions (Freeman et al., 2003; Jensen and Colgin, 2007).”

“We have also discovered their traces in electrical fields at the surface of the human scalp (Freeman et al., 2003), but we cannot yet read them, because we do not yet know how to encode their patterns in terms of information and symbols adequately to correlate them with behavioral measurements that…”

“While most of these studies describe synchrony only between activity recorded at widely separated but discrete sites, Freeman et al. (2003a), using a high density curvilinear array of electrodes, actually find synchrony in the human brain that is continuous over a distance of 189 mm, a significant…”

“Incidentally, discontinuous behavior of brain activity during no-task conditions has also been observed with very different analysis approaches (Breakspear et al., 2004; Freeman et al., 2003; Kitzbichler et al. 2009).”

“According to Freeman, the cortical code consists of repetitive spatial frames of metastable amplitude modulation (AM) patterns (Freeman 2000a, b, 2003, 2004a, b, 2005, 2006b; Freeman et al. 2000, 2003a, b; Freeman and Rogers 2002).”

“The Hilbert transform can be used to extract “instantaneous”measures of phase and amplitude of a signal and is considered to be a useful method for tracking changes in phase with high temporal resolution (Freeman et al., 2003; Le Van Quyen and Bragin, 2007).”