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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 references 79

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          An MRI time course of 512 echo-planar images (EPI) in resting human brain obtained every 250 ms reveals fluctuations in signal intensity in each pixel that have a physiologic origin. Regions of the sensorimotor cortex that were activated secondary to hand movement were identified using functional MRI methodology (FMRI). Time courses of low frequency (< 0.1 Hz) fluctuations in resting brain were observed to have a high degree of temporal correlation (P < 10(-3)) within these regions and also with time courses in several other regions that can be associated with motor function. It is concluded that correlation of low frequency fluctuations, which may arise from fluctuations in blood oxygenation or flow, is a manifestation of functional connectivity of the brain.
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              The brainweb: phase synchronization and large-scale integration.

              The emergence of a unified cognitive moment relies on the coordination of scattered mosaics of functionally specialized brain regions. Here we review the mechanisms of large-scale integration that counterbalance the distributed anatomical and functional organization of brain activity to enable the emergence of coherent behaviour and cognition. Although the mechanisms involved in large-scale integration are still largely unknown, we argue that the most plausible candidate is the formation of dynamic links mediated by synchrony over multiple frequency bands.

                Author and article information

                1simpleSchool of Psychiatry, University of New South Wales Sydney, NSW, Australia
                2simpleThe Black Dog Institute, Prince of Wales Hospital Sydney, NSW, Australia
                3simpleQueensland Institute of Medical Research Brisbane, QLD, Australia
                4simpleRoyal Brisbane and Women's Hospital, Brisbane QLD, Australia
                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@
                Front Hum Neurosci
                Front. Hum. Neurosci.
                Frontiers in Human Neuroscience
                Frontiers Research Foundation
                11 November 2010
                : 4
                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.

                Figures: 6, Tables: 0, Equations: 27, References: 86, Pages: 14, Words: 10919
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