Propagation and stability of waves of electrical activity in the cerebral cortex

Robinson, P. A.; Rennie, Christopher J.; Wright, J. J.

doi:10.1103/physreve.56.826

Cited by 442 publications

(709 citation statements)

References 11 publications

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“…We base this work upon the well-documented mean-field theory of Robinson and co-workers [40,39,7,37]. Rather than modeling individual neurons, we consider averaging properties over local groups of neurons.…”

Section: Methodsmentioning

confidence: 99%

“…Here the subscripts a and b can be assigned either 'e' to denote excitatory cells, or 'i' to denote inhibitory cells. Changes in firing rate are modelled as a linear response to the incoming input from other cells [39,40,21]. We therefore concern ourselves with changes in firing rate and spike rate from their equilibrium values.…”

Section: Methodsmentioning

confidence: 99%

“…The transfer functions L ab (ω) and Γ ab (ω) can be written in Fourier space as follows. The synaptic and soma response is typically described by a bi-exponential function [39,40,21,7]. For the case of excitatory synapses (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…The axonal transfer function can be modelled with a damped wave equation [19,40,26,7]; we use the form of Robinson et al [40], leading to:…”

Section: Methodsmentioning

confidence: 99%

“…Neural behaviour is modelled in terms of average firing rates and axonal flux rates of populations of neurons, rather than in terms of the behaviours of individual neurons [51,30,9,19,40,4,46,7,37,52]. This approach is particularly suited to the modelling of large-scale measures of brain activity, such as the electroencephalogram (EEG), which involve the sampling of many neurons.…”

Section: Introductionmentioning

confidence: 99%

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Numerical modelling of plasticity induced by transcranial magnetic stimulation

et al. 2013

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We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short (<∼ 10 ms) and long (>∼ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual's electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…The axonal transfer function can be modelled with a damped wave equation [19,40,26,7]; we use the form of Robinson et al [40], leading to:…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical modelling of plasticity induced by transcranial magnetic stimulation

et al. 2013

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Linear Analysis of the Corticothalamic Model with Time Delay

Yamaguchi

Ogawa

Nakao

et al. 2014

Elect Comm in Japan

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SUMMARYThe corticothalamic Compact Model with time delay proposed by Kim and Robinson is analyzed focusing on the resting EEG, which can be described by the linear version of the model with white-noise input, under the assumption of spatial homogeneity and temporal steadiness. After discussing the availability and restriction of the model by comparing to the original Pre-Compact Model, a data analysis method for the resting EEG using the model is presented. The experimental results analyzed by the method suggest that the eye-closed state compared to the eye-open state would be characterized by enhanced corticothalamic feedback and depressed cortical excitation. The validity of the Reduced Equations derived in our previous paper is also investigated for the resting EEG, concluding that the Reduced Equations would be available with some restriction for the resting EEG, although the center manifold theory on which the Reduced Equations are based is justified at the edge of linear stability in principle. C⃝ 2014 Wiley Periodicals, Inc. Electron Comm Jpn, 97(8): 32-44, 2014; Published online in Wiley Online Library (wileyonlinelibrary.com).

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Spatial‐temporal structures of human alpha rhythms: Theory, microcurrent sources, multiscale measurements, and global binding of local networks

Nunez¹,

Wingeier²,

Silberstein³

2001

Human Brain Mapping

470

356

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A theoretical framework supporting experimental measures of dynamic properties of human EEG is proposed with emphasis on distinct alpha rhythms. Robust relationships between measured dynamics and cognitive or behavioral conditions are reviewed, and proposed physiological bases for EEG at cellular levels are considered. Classical EEG data are interpreted in the context of a conceptual framework that distinguishes between locally and globally dominated dynamic processes, as estimated with coherence or other measures of phase synchronization. Macroscopic (scalp) potentials generated by cortical current sources are described at three spatial scales, taking advantage of the columnar structure of neocortex. New EEG data demonstrate that both globally coherent and locally dominated behavior can occur within the alpha band, depending on narrow band frequency, spatial measurement scale, and brain state. Quasi-stable alpha phase structures consistent with global standing waves are observed. At the same time, alpha and theta phase locking between cortical regions during mental calculations is demonstrated, consistent with neural network formation. The brain-binding problem is considered in the context of EEG dynamic behavior that generally exhibits both of these local and global aspects. But specific experimental designs and data analysis methods may severely bias physiological interpretations in either local or global directions.

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Propagation and stability of waves of electrical activity in the cerebral cortex

Cited by 442 publications

References 11 publications

Numerical modelling of plasticity induced by transcranial magnetic stimulation

Numerical modelling of plasticity induced by transcranial magnetic stimulation

Linear Analysis of the Corticothalamic Model with Time Delay

Spatial‐temporal structures of human alpha rhythms: Theory, microcurrent sources, multiscale measurements, and global binding of local networks

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