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      Generative Models of Cortical Oscillations: Neurobiological Implications of the Kuramoto Model


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          Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, and which has elucidated the core mechanisms of a range of biological and physical phenomena. In this paper, we provide a brief introduction to the Kuramoto model in its original, rather abstract, form and then focus on modifications that increase its neurobiological plausibility by incorporating topological properties of local cortical connectivity. The extended model elicits elaborate spatial patterns of synchronous oscillations that exhibit persistent dynamical instabilities reminiscent of cortical activity. We review how the Kuramoto model may be recast from an ordinary differential equation to a population level description using the nonlinear Fokker–Planck equation. We argue that such formulations are able to provide a mechanistic and unifying explanation of oscillatory phenomena in the human cortex, such as fluctuating beta oscillations, and their relationship to basic computational processes including multistability, criticality, and information capacity.

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          Most cited references67

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          Noise in the nervous system.

          Noise--random disturbances of signals--poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.
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            From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

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              Phase lag index: assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources.

              To address the problem of volume conduction and active reference electrodes in the assessment of functional connectivity, we propose a novel measure to quantify phase synchronization, the phase lag index (PLI), and compare its performance to the well-known phase coherence (PC), and to the imaginary component of coherency (IC). The PLI is a measure of the asymmetry of the distribution of phase differences between two signals. The performance of PLI, PC, and IC was examined in (i) a model of 64 globally coupled oscillators, (ii) an EEG with an absence seizure, (iii) an EEG data set of 15 Alzheimer patients and 13 control subjects, and (iv) two MEG data sets. PLI and PC were more sensitive than IC to increasing levels of true synchronization in the model. PC and IC were influenced stronger than PLI by spurious correlations because of common sources. All measures detected changes in synchronization during the absence seizure. In contrast to PC, PLI and IC were barely changed by the choice of different montages. PLI and IC were superior to PC in detecting changes in beta band connectivity in AD patients. Finally, PLI and IC revealed a different spatial pattern of functional connectivity in MEG data than PC. The PLI performed at least as well as the PC in detecting true changes in synchronization in model and real data but, at the same token and like-wise the IC, it was much less affected by the influence of common sources and active reference electrodes. Copyright 2007 Wiley-Liss, Inc.

                Author and article information

                Front Hum Neurosci
                Front. Hum. Neurosci.
                Frontiers in Human Neuroscience
                Frontiers Research Foundation
                11 November 2010
                : 4
                : 190
                [1] 1simpleSchool of Psychiatry, University of New South Wales Sydney, NSW, Australia
                [2] 2simpleThe Black Dog Institute, Prince of Wales Hospital Sydney, NSW, Australia
                [3] 3simpleQueensland Institute of Medical Research Brisbane, QLD, Australia
                [4] 4simpleRoyal Brisbane and Women's Hospital, Brisbane QLD, Australia
                [5] 5simpleResearch Institute MOVE, VU University Amsterdam Amsterdam, Netherlands
                Author notes

                Edited by: Kai J. Miller, University of Washington, USA

                Reviewed by: Carson Chow, University of Pittsburgh, USA; National Institutes of Health, USA; Ole Paulsen, University of Cambridge, UK; University of Oxford, UK

                *Correspondence: Michael Breakspear, 300 Herston Rd, Herston, QLD, 4009, Australia.; e-mail: mbreak@ 123456unsw.edu.au
                Copyright © 2010 Breakspear, Heitmann and Daffertshofer.

                This is an open-access article subject to an exclusive license agreement between the authors and the Frontiers Research Foundation, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are credited.

                : 05 June 2010
                : 22 September 2010
                Page count
                Figures: 6, Tables: 0, Equations: 27, References: 86, Pages: 14, Words: 10919
                Review Article

                fokker–planck equation,kuramoto model,cortical oscillations,neural synchrony
                fokker–planck equation, kuramoto model, cortical oscillations, neural synchrony


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