A model of the spatial-temporal characteristics of the alpha rhythm

Rotterdam, A. van; Silva, F. H. Lopes da; Ende, Jan van den; Viergever, Max A.; Hermans, A. J.

doi:10.1007/bf02463252

Cited by 189 publications

(54 citation statements)

References 6 publications

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“…However, we will assume that the mean field approximation is sufficient for our purposes. The majority of neural mass models of MEG/EEG have been designed to generate alpha rhythms (Jansen and Rit, 1995;Lopes da Silva et al, 1974;Stam et al, 1999;Van Rotterdam et al, 1982). Recent studies have shown that it is possible to reproduce the whole spectrum of MEG/EEG oscillations, using appropriate values of model parameters (David and Friston, 2003;Robinson et al, 2001).…”

Section: Neural Mass Modelsmentioning

confidence: 99%

“…This means that MEG/EEG observation models rely upon simplifying assumptions and empirical priors (David and Friston, 2003;Freeman, 1978;Lopes da Silva et al, 1974;Robinson et al, 2001;Stam et al, 1999;Valdes et al, 1999;Van Rotterdam et al, 1982;Wendling et al, 2000). The primary aim of this paper is to describe a candidate forward model and establish its face validity.…”

Section: Neural Mass Modelsmentioning

confidence: 99%

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Modelling event-related responses in the brain

2005

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The aim of this work was to investigate the mechanisms that shape evoked electroencephalographic (EEG) and magneto-encephalographic (MEG) responses. We used a neuronally plausible model to characterise the dependency of response components on the models parameters. This generative model was a neural mass model of hierarchically arranged areas using three kinds of inter-area connections (forward, backward and lateral). We investigated how responses, at each level of a cortical hierarchy, depended on the strength of connections or coupling. Our strategy was to systematically add connections and examine the responses of each successive architecture. We did this in the context of deterministic responses and then with stochastic spontaneous activity. Our aim was to show, in a simple way, how event-related dynamics depend on extrinsic connectivity. To emphasise the importance of nonlinear interactions, we tried to disambiguate the components of event-related potentials (ERPs) or event-related fields (ERFs) that can be explained by a linear superposition of trial-specific responses and those engendered nonlinearly (e.g., by phase-resetting). Our key conclusions were; (i) when forward connections, mediating bottom-up or extrinsic inputs, are sufficiently strong, nonlinear mechanisms cause a saturation of excitatory interneuron responses. This endows the system with an inherent stability that precludes nondissipative population dynamics. (ii) The duration of evoked transients increases with the hierarchical depth or level of processing. (iii) When backward connections are added, evoked transients become more protracted, exhibiting damped oscillations. These are formally identical to late or endogenous components seen empirically. This suggests that late components are mediated by reentrant dynamics within cortical hierarchies. (iv) Bilateral connections produce similar effects to backward connections but can also mediate zero-lag phase-locking among areas. (v) Finally, with spontaneous activity, ERPs/ERFs can arise from two distinct mechanisms: For low levels of (stimulus related and ongoing) activity, the systems response conforms to a quasi-linear superposition of separable responses to the fixed and stochastic inputs. This is consistent with classical assumptions that motivate trial averaging to suppress spontaneous activity and disclose the ERP/ ERF. However, when activity is sufficiently high, there are nonlinear interactions between the fixed and stochastic inputs. This interaction is expressed as a phase-resetting and represents a qualitatively different explanation for the ERP/ERF. D 2004 Elsevier Inc. All rights reserved.Keywords: Electroencephalography; Magnetoencephalography; Neural networks; Nonlinear dynamics; Causal modelling IntroductionClassical event-related potentials (ERPs) and event-related fields (ERFs) have been used for decades as putative electrophysiological correlates of perceptual and cognitive operations. However, the exact neurobiological mechanisms underlying their generation are largely unk...

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Section: Neural Mass Modelsmentioning

confidence: 99%

Section: Neural Mass Modelsmentioning

confidence: 99%

Modelling event-related responses in the brain

2005

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“…global, connectivity of the network components, as well as their local connectivity and dynamics (Sporns & Tononi 2002Sporns 2003;Jirsa 2004;Beggs et al 2007). So far, theoretical efforts have focused almost exclusively on the study of networks with discretely connected nodes and complicated connectivity, but simple local dynamics, in which all neural activity is lumped into a single neural mass (Lopes da Silva et al 1974;Freeman 1975;van Rotterdam et al 1982;Tagamets & Horwitz 1998;David & Friston 2003;Jirsa & Ding 2004;Campbell et al 2006;see Ermentrout (1998) and Jirsa (2004) for reviews).…”

Section: Introductionmentioning

confidence: 99%

Neural field dynamics with local and global connectivity and time delay

Jirsa¹

2009

Phil. Trans. R. Soc. A.

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Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in particular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, we investigate the stability of the rest-state activity of a neural field as a function of its connectivity. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix, as well as by variation of connectivity strength and a finite transmission speed. The latter results in a time delay of communication among individual brain areas. We demonstrate that the local connectivity generates the well-known power-law behaviour of the electroencephalographic power spectrum with an exponent close to K2, whereas the global connections generate a more characteristic line spectrum. These spectral characteristics are routinely observed in large-scale topographies of the human brain.

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“…2, showing the second-order (finite rise time) and first-order (instantaneous response) kernels. The second-order synaptic kernel reproduces experimental excitatory and inhibitory post-synaptic potentials (EPSPs and IPSPs) features (Van Rotterdam et al, 1982). Similarly, both the connectivity kernel and the activity function (firing rate) can take various forms.…”

Section: Ide Neural Field Modelmentioning

confidence: 67%

“…The second-order postsynaptic kernel proposed in Van Rotterdam et al (1982) leads to dynamics that are more reminiscent to real postsynaptic potentials (see Spiegler et al (2010Spiegler et al ( , 2011 for example). Another extension of this framework is the inclusion of finite distant-dependent action potential propagation velocity into the parametric neural field equations.…”

Section: Extensions To the Frameworkmentioning

confidence: 99%

Spatiotemporal multi-resolution approximation of the Amari type neural field model

Aram

Freestone

Dewar³

et al. 2013

NeuroImage

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Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way, a flexible framework is created, whereby both macroscopic and microscopic behavior of the system can be represented simultaneously. State and parameter estimation is performed using the expectation maximization (EM) algorithm. A synthetic example is provided to demonstrate the framework.

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A model of the spatial-temporal characteristics of the alpha rhythm

Cited by 189 publications

References 6 publications

Modelling event-related responses in the brain

Modelling event-related responses in the brain

Neural field dynamics with local and global connectivity and time delay

Spatiotemporal multi-resolution approximation of the Amari type neural field model

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