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      Detrended Fluctuation Analysis: A Scale-Free View on Neuronal Oscillations

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          Abstract

          Recent years of research have shown that the complex temporal structure of ongoing oscillations is scale-free and characterized by long-range temporal correlations. Detrended fluctuation analysis (DFA) has proven particularly useful, revealing that genetic variation, normal development, or disease can lead to differences in the scale-free amplitude modulation of oscillations. Furthermore, amplitude dynamics is remarkably independent of the time-averaged oscillation power, indicating that the DFA provides unique insights into the functional organization of neuronal systems. To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the DFA algorithm and its underlying theory. Practical advice on applying DFA to oscillations is supported by MATLAB scripts from the Neurophysiological Biomarker Toolbox (NBT) and links to the NBT tutorial website http://www.nbtwiki.net/. Finally, we provide a brief overview of insights derived from the application of DFA to ongoing oscillations in health and disease, and discuss the putative relevance of criticality for understanding the mechanism underlying scale-free modulation of oscillations.

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          Rhythms of the Brain

          György Buzsáki (2006)
          Book 0 comments Cited 490 times – based on 0 reviews
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            The temporal structures and functional significance of scale-free brain activity.

            Biyu J. He, John M. Zempel, Abraham Snyder … (2010)
            Scale-free dynamics, with a power spectrum following P proportional to f(-beta), are an intrinsic feature of many complex processes in nature. In neural systems, scale-free activity is often neglected in electrophysiological research. Here, we investigate scale-free dynamics in human brain and show that it contains extensive nested frequencies, with the phase of lower frequencies modulating the amplitude of higher frequencies in an upward progression across the frequency spectrum. The functional significance of scale-free brain activity is indicated by task performance modulation and regional variation, with beta being larger in default network and visual cortex and smaller in hippocampus and cerebellum. The precise patterns of nested frequencies in the brain differ from other scale-free dynamics in nature, such as earth seismic waves and stock market fluctuations, suggesting system-specific generative mechanisms. Our findings reveal robust temporal structures and behavioral significance of scale-free brain activity and should motivate future study on its physiological mechanisms and cognitive implications. Copyright 2010 Elsevier Inc. All rights reserved.
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              Nonlinear dynamical analysis of EEG and MEG: review of an emerging field.

              C. Stam (2005)
              Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called 'chaos theory', has now progressed to a stage, where it becomes possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of EEG or MEG, an attractor of the underlying dynamical system, and characterizing it in terms of its dimension (an estimate of the degrees of freedom of the system), or its Lyapunov exponents and entropy (reflecting unpredictability of the dynamics due to the sensitive dependence on initial conditions). More recently developed nonlinear measures characterize other features of local brain dynamics (forecasting, time asymmetry, determinism) or the nonlinear synchronization between recordings from different brain regions. Nonlinear time series has been applied to EEG and MEG of healthy subjects during no-task resting states, perceptual processing, performance of cognitive tasks and different sleep stages. Many pathologic states have been examined as well, ranging from toxic states, seizures, and psychiatric disorders to Alzheimer's, Parkinson's and Cre1utzfeldt-Jakob's disease. Interpretation of these results in terms of 'functional sources' and 'functional networks' allows the identification of three basic patterns of brain dynamics: (i) normal, ongoing dynamics during a no-task, resting state in healthy subjects; this state is characterized by a high dimensional complexity and a relatively low and fluctuating level of synchronization of the neuronal networks; (ii) hypersynchronous, highly nonlinear dynamics of epileptic seizures; (iii) dynamics of degenerative encephalopathies with an abnormally low level of between area synchronization. Only intermediate levels of rapidly fluctuating synchronization, possibly due to critical dynamics near a phase transition, are associated with normal information processing, whereas both hyper-as well as hyposynchronous states result in impaired information processing and disturbed consciousness.
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                Author and article information

                Journal
                Journal ID (nlm-ta): Front Physiol
                Journal ID (iso-abbrev): Front Physiol
                Journal ID (publisher-id): Front. Physio.
                Title: Frontiers in Physiology
                Publisher: Frontiers Media S.A.
                ISSN (Electronic): 1664-042X
                Publication date (Electronic): 30 November 2012
                Publication date Collection: 2012
                Volume: 3
                Electronic Location Identifier: 450
                Affiliations
                [1] 1Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, Neuroscience Campus Amsterdam, VU University Amsterdam Amsterdam, Netherlands
                [2] 2Department of Psychiatry, VU University Medical Center, Neuroscience Campus Amsterdam Amsterdam, Netherlands
                [3] 3Neurophysics Group, Department of Neurology, Charité – Universitätsmedizin Berlin, Germany
                Author notes

                Edited by: Biyu J. He, NIH, NINDS, USA

                Reviewed by: Andras Eke, Semmelweis University, Hungary; Simon Farmer, National Hospital for Neurology & Neurosurgery and Institute of Neurology, UK

                *Correspondence: Klaus Linkenkaer-Hansen, Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, Neuroscience Campus Amsterdam, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, Netherlands. e-mail: klaus.linkenkaer@ 123456cncr.vu.nl

                This article was submitted to Frontiers in Fractal Physiology, a specialty of Frontiers in Physiology.

                Article
                DOI: 10.3389/fphys.2012.00450
                PMC ID: 3510427
                PubMed ID: 23226132
                SO-VID: b1df5e17-b783-4d8f-b679-6f8738e053d2
                Copyright © Copyright © 2012 Hardstone, Poil, Schiavone, Jansen, Nikulin, Mansvelder and Linkenkaer-Hansen.
                License:

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and subject to any copyright notices concerning any third-party graphics etc.

                History
                Date received : 30 January 2012
                Date accepted : 10 November 2012
                Page count
                Figures: 8, Tables: 0, Equations: 10, References: 55, Pages: 13, Words: 9800
                Categories
                Subject: Physiology
                Subject: Methods Article

                ScienceOpen disciplines: Anatomy & Physiology
                Keywords: detrended fluctuation analysis,ongoing oscillations,scale-free dynamics,long-range temporal correlations,criticality
                Data availability:
                ScienceOpen disciplines: Anatomy & Physiology
                Keywords: detrended fluctuation analysis, ongoing oscillations, scale-free dynamics, long-range temporal correlations, criticality

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