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Journal ArticleDOI

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

TL;DR: It is argued that critical-state dynamics of spontaneous oscillations may lend neural networks capable of quick reorganization during processing demands, and the demonstrated scaling laws pose novel quantitative constraints on computational models of network oscillations.
Abstract: The human brain spontaneously generates neural oscillations with a large variability in frequency, amplitude, duration, and recurrence. Little, however, is known about the long-term spatiotemporal structure of the complex patterns of ongoing activity. A central unresolved issue is whether fluctuations in oscillatory activity reflect a memory of the dynamics of the system for more than a few seconds. We investigated the temporal correlations of network oscillations in the normal human brain at time scales ranging from a few seconds to several minutes. Ongoing activity during eyes-open and eyes-closed conditions was recorded with simultaneous magnetoencephalography and electroencephalography. Here we show that amplitude fluctuations of 10 and 20 Hz oscillations are correlated over thousands of oscillation cycles. Our analyses also indicated that these amplitude fluctuations obey power-law scaling behavior. The scaling exponents were highly invariant across subjects. We propose that the large variability, the long-range correlations, and the power-law scaling behavior of spontaneous oscillations find a unifying explanation within the theory of self-organized criticality, which offers a general mechanism for the emergence of correlations and complex dynamics in stochastic multiunit systems. The demonstrated scaling laws pose novel quantitative constraints on computational models of network oscillations. We argue that critical-state dynamics of spontaneous oscillations may lend neural networks capable of quick reorganization during processing demands.
Citations
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Journal ArticleDOI
TL;DR: This article reviews studies investigating complex brain networks in diverse experimental modalities and provides an accessible introduction to the basic principles of graph theory and highlights the technical challenges and key questions to be addressed by future developments in this rapidly moving field.
Abstract: Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

9,700 citations


Cites background from "Long-Range Temporal Correlations an..."

  • ...This timescale invariance of wavelet correlations and the brain functional network parameters derived from them is a theoretically predictable corollary of the long-range autocorrelations of neurophysiological time serie...

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Journal ArticleDOI
TL;DR: Recent studies examining spontaneous fluctuations in the blood oxygen level dependent (BOLD) signal of functional magnetic resonance imaging as a potentially important and revealing manifestation of spontaneous neuronal activity are reviewed.
Abstract: The majority of functional neuroscience studies have focused on the brain's response to a task or stimulus. However, the brain is very active even in the absence of explicit input or output. In this Article we review recent studies examining spontaneous fluctuations in the blood oxygen level dependent (BOLD) signal of functional magnetic resonance imaging as a potentially important and revealing manifestation of spontaneous neuronal activity. Although several challenges remain, these studies have provided insight into the intrinsic functional architecture of the brain, variability in behaviour and potential physiological correlates of neurological and psychiatric disease.

6,135 citations


Cites background from "Long-Range Temporal Correlations an..."

  • ...This 1/f distribution has also been observed in studies of spontaneous electroencephalography (EEG...

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Book
01 Jan 2006
TL;DR: The brain's default state: self-organized oscillations in rest and sleep, and perturbation of the default patterns by experience.
Abstract: Prelude. Cycle 1. Introduction. Cycle 2. Structure defines function. Cycle 3. Diversity of cortical functions is provided by inhibition. Cycle 4. Windows on the brain. Cycle 5. A system of rhythms: from simple to complex dynamics. Cycle 6. Synchronization by oscillation. Cycle 7. The brain's default state: self-organized oscillations in rest and sleep. Cycle 8. Perturbation of the default patterns by experience. Cycle 9. The gamma buzz: gluing by oscillations in the waking brain. Cycle 10. Perceptions and actions are brain state-dependent. Cycle 11. Oscillations in the "other cortex:" navigation in real and memory space. Cycle 12. Coupling of systems by oscillations. Cycle 13. The tough problem. References.

4,266 citations


Cites background from "Long-Range Temporal Correlations an..."

  • ...(2002), Aks and Sprott (2003), for EEG measures, Linkenkaer-Hansen et al. (2001), Freeman et al. (2003), Leopold et al. (2003), Stam and de Bruin (2004). 49. Izhikevich et al. (2004). The embodiment of recent history is the temporal correlation represented by the 1/f memory of scale-free systems....

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  • ...(2002), Aks and Sprott (2003), for EEG measures, Linkenkaer-Hansen et al. (2001), Freeman et al....

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  • ...The exponent of the 1/fα relationship is somewhat different for gamma and theta power fluctuation (Linkenkaer-Hansen et al., 2001; Stam and de Bruin, 2004)....

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  • ...The exponent of the 1/fα relationship is somewhat different for gamma and theta power fluctuation (Linkenkaer-Hansen et al., 2001; Stam and de Bruin, 2004). In agreement with these findings, Başar (1990) was among the first to suggest that EEG activity is best described as quasi-deterministic activity....

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  • ...eyes closed) but is highly invariant across subjects (Linkenkaer-Hansen et al., 2001)....

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Journal ArticleDOI
TL;DR: The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses.
Abstract: Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.

2,822 citations

Journal ArticleDOI
TL;DR: It is concluded that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex, and could provide a physiological substrate for segregated and distributed information processing.
Abstract: Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequency-dependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03–0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.

2,345 citations


Cites background from "Long-Range Temporal Correlations an..."

  • ...Moreover, long period or very low-frequency coherent oscillations have been described recently in both monkey and human electrophysiological data (Linkenkaer-Hansen et al., 2001; Leopold et al., 2003)....

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References
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Journal ArticleDOI
TL;DR: In this article, a step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino-Southern Oscillation (ENSO).
Abstract: A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change...

12,803 citations


"Long-Range Temporal Correlations an..." refers methods in this paper

  • ...The signals were filtered with a Morlet wavelet; the modulus of the complex-valued outcome, W(t,f) , represents the amplitude of the signal at a time range centered at t and in a frequency band centered at f (Torrence and Compo, 1998)....

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Journal ArticleDOI
TL;DR: It is shown that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point, and flicker noise, or 1/f noise, can be identified with the dynamics of the critical state.
Abstract: We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state. This picture also yields insight into the origin of fractal objects.

6,486 citations


"Long-Range Temporal Correlations an..." refers background in this paper

  • ...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....

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  • ...Neural networks host the common features of SOC systems, such as a large number of units (neurons), local and nonlinear interactions between neurons, externally imposed perturbations, a certain amount of stochastic variation of internal parameters, and ability to store information in spatial patterns....

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  • ...After this stage, the dynamics of the system exhibit power-law scaling behavior, and the underlying process operates in a critical state, a phenomenon often termed self-organized criticality (SOC) (Bak et al., 1987, 1988)....

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  • ...Since the first reports on self-organized criticality (Bak et al., 1987, 1988), ample evidence has indicated that several complex systems self-organize through local interactions to a critical state with long-range spatiotemporal correlations (Bak et al., 1989; Mantegna and Stanley, 1995; Boettcher…...

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  • ...Based on the analogy with other SOC systems, one prediction is power-law statistics for the probability that a number of neurons, n, is recruited into an oscillatory event....

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Journal ArticleDOI
TL;DR: This work analyzes two classes of controls consisting of patchy nucleotide sequences generated by different algorithms--one without and one with long-range power-law correlations, finding that both types of sequences are quantitatively distinguishable by an alternative fluctuation analysis method.
Abstract: Long-range power-law correlations have been reported recently for DNA sequences containing noncoding regions We address the question of whether such correlations may be a trivial consequence of the known mosaic structure ("patchiness") of DNA We analyze two classes of controls consisting of patchy nucleotide sequences generated by different algorithms--one without and one with long-range power-law correlations Although both types of sequences are highly heterogenous, they are quantitatively distinguishable by an alternative fluctuation analysis method that differentiates local patchiness from long-range correlations Application of this analysis to selected DNA sequences demonstrates that patchiness is not sufficient to account for long-range correlation properties

4,365 citations


"Long-Range Temporal Correlations an..." refers background in this paper

  • ...…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)....

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Book
01 Jan 1995
TL;DR: The first chapter of this important new text is available on the Cambridge Worldwide Web server: http://www.cup.cam.ac.uk/onlinepubs/Textbooks/textbookstop.html as discussed by the authors.
Abstract: This book brings together two of the most exciting and widely studied subjects in modern physics: namely fractals and surfaces. To the community interested in the study of surfaces and interfaces, it brings the concept of fractals. To the community interested in the exciting field of fractals and their application, it demonstrates how these concepts may be used in the study of surfaces. The authors cover, in simple terms, the various methods and theories developed over the past ten years to study surface growth. They describe how one can use fractal concepts successfully to describe and predict the morphology resulting from various growth processes. Consequently, this book will appeal to physicists working in condensed matter physics and statistical mechanics, with an interest in fractals and their application. The first chapter of this important new text is available on the Cambridge Worldwide Web server: http://www.cup.cam.ac.uk/onlinepubs/Textbooks/textbookstop.html

3,891 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time or length scales, and the temporal fingerprint of the self-organized critical state is the presence of flicker noise or 1/f noise; its spatial signature is the emergence of scale-invariant (fractal) structure.
Abstract: We show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time or length scales. The temporal ``fingerprint'' of the self-organized critical state is the presence of flicker noise or 1/f noise; its spatial signature is the emergence of scale-invariant (fractal) structure.

3,828 citations