Large-scale neural dynamics: Simple and complex

Coombes, Stephen

doi:10.1016/j.neuroimage.2010.01.045

Cited by 152 publications

(133 citation statements)

References 99 publications

Supporting

Mentioning

130

Contrasting

Order By: Relevance

“…In many modern uses of the Wilson-Cowan equations the refractory terms are often dropped. For exponential or Gaussian choices of the connectivity function the Wilson-Cowan model is known to support a wide variety of solutions, including spatially and temporally periodic patterns (beyond a Turing instability), localised regions of activity (bumps and multi-bumps) and travelling waves (fronts, pulses, target waves and spirals), as reviewed in [19,20,32] and in Chaps. 4, 5, 7 or 8.…”

Section: Introductionmentioning

confidence: 99%

Tutorial on Neural Field Theory

2014

View full text Add to dashboard Cite

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this tutorial chapter we describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integrodifferential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of spatiotemporal patterns, based around natural extensions of those used for local differential equation models. We present an overview of these techniques, covering Turing instability analysis, amplitude equations, and travelling waves. Finally we address inverse problems for neural fields to train synaptic weight kernels from prescribed field dynamics.

show abstract

Section: Introductionmentioning

confidence: 99%

Tutorial on Neural Field Theory

2014

View full text Add to dashboard Cite

show abstract

“…For example, experimentally there is signal distortion between different fMRI voxels (Jezzard and Clare 1999;Weiskopf et al 2006), compromising the idea of a clean separation into signal regions. Or on the theoretical side, the NPM might be based upon a continuum approximation (Coombes 2010;Liley et al 2012), in which case the predicted signal could derive from an average over the designated source region, with the underlying field values possibly being quite inhomogeneous across this region. Nevertheless, it remains useful to connect the spatial resolution of a neuroimaging modality to a conceptual "population size" of the NPM if one uses the NPM as model for the recorded signals.…”

Section: Spatial Resolution Of Neuroimaging and Coherent Activitymentioning

confidence: 99%

Neuroimaging, Neural Population Models for

Bojak¹,

Breakspear²

2014

Encyclopedia of Computational Neuroscience

View full text Add to dashboard Cite

SynonymsEEG, neural population models of; fMRI BOLD, neural population models of; Multimodal neural population models DefinitionNeuroimaging denotes measurements of the brain with sufficient spatial resolution to construct maps of anatomy (structural neuroimaging) and activity (functional neuroimaging), respectively. Where a functional neuroimaging modality can capture spatial snapshots at sufficient speed, its data can be used to infer spatiotemporal brain dynamics. The spatial resolution of noninvasive functional neuroimaging in humans is limited to about one millimeter and requires the coherent activity of a large number of neurons to generate a signal that exceeds the noise floor. This is an ideal match for neural population models (NPMs), which are designed to capture the mass activity of neural groupings at mesoscopic scales and above. However, in order to compare NPM predictions to neuroimaging data, one also has to include signal expression -a measurement function -that maps the NPM-generated activity onto the sensor recordings. For most popular neuroimaging modalities, including multimodal approaches, such forward modelling "pipelines" are now available and have been used to predict and analyze data.

show abstract

“…Indeed now that this field has moved on from its early beginnings in the biophysical modelling of single cells it is a challenge to pick from the many possible topics that researchers could contribute on, such as bursting patterns [5], coupled oscillator networks [6], largescale neural dynamics [7,8], waves and patterns [9], delay effects in brain dynamics [10], stochastic methods in neuroscience [11], or indeed novel techniques for analysis, including Evans functions [12], heteroclinic cycling [13], geometric singular perturbation theory [14], amplitude equations [15] and information geometry [16]. To provide a focus for this special issue we have therefore chosen to cover some of the topics recently discussed at and addressed the current state of research in mathematical approaches to neuroscience, covering developmental neuroscience, synaptic integration, synaptic depression, stochastic point process models of spiking activity, canards, microcircuit modelling and meanfield analysis, synchrony in cerebellar networks, population coding, spatial correlations in strongly coupled networks, cell assemblies, electrorhythmogenesis, thalamocortical networks, models of sleep/wake cycles, dimension reduction of network models and largescale models of the ultra-slow resting brain state.…”

mentioning

confidence: 99%