Model of brain rhythmic activity

Silva, F. H. Lopes da; Hoeks, Arnold P.G.; Smits, H.; Zetterberg, Lena

doi:10.1007/bf00270757

Cited by 656 publications

(372 citation statements)

References 7 publications

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“…Rather than representing the electrical activity of an individual neuron, mean-field or "lumped" models represent the aggregate activity of neural populations and are therefore particularly suitable for representing neural fields-such as the EEG, ECoG, and LFP of primary interest here-which are thought to represent the coordinated synaptic and intrinsic currents of neural populations (23)(24)(25). Mean-field models have a long history in computational neuroscience (e.g., [26][27][28][29], including many important applications for seizure modeling. These include, for example, mean-field models of absence seizures (30)(31)(32), of depth and surface electrode recordings from patients with temporal lobe epilepsy (33,34), seizure generalization (35), and anesthetic-induced seizures (36).…”

Section: Signatures Of a Critical Transition In A Mean-field Model Ofmentioning

confidence: 99%

Human seizures self-terminate across spatial scales via a critical transition

Kramer

Truccolo

Eden

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

190

147

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Why seizures spontaneously terminate remains an unanswered fundamental question of epileptology. Here we present evidence that seizures self-terminate via a discontinuous critical transition or bifurcation. We show that human brain electrical activity at various spatial scales exhibits common dynamical signatures of an impending critical transition-slowing, increased correlation, and flickering-in the approach to seizure termination. In contrast, prolonged seizures (status epilepticus) repeatedly approach, but do not cross, the critical transition. To support these results, we implement a computational model that demonstrates that alternative stable attractors, representing the ictal and postictal states, emulate the observed dynamics. These results suggest that self-terminating seizures end through a common dynamical mechanism. This description constrains the specific biophysical mechanisms underlying seizure termination, suggests a dynamical understanding of status epilepticus, and demonstrates an accessible system for studying critical transitions in nature.critical slowing down | epilepsy | electrocorticogram | local field potential A lthough extensive observations and research have elucidated some mechanism of seizure initiation and maintenance, how seizures spontaneously terminate remains one of the most important, but still unanswered, questions in epileptology (1). Some of the potential mechanisms of seizure termination (2) include glutamate depletion (3), dynamic changes in ion concentrations (4-6), persistent activation of a hyperpolarization-activated cation conductance (7), changing synaptic effectiveness (5, 8), modulatory effects from subcortical structures and the cerebellum (9), and reduced pH (10). Together, these studies suggest distinct pathways to seizure termination through specific biophysical mechanisms.We propose here a dynamical understanding of seizure termination that encompasses and constrains these and other hypothesized biophysical mechanisms. Specifically, we propose that focal seizures with secondary generalization terminate in a manner consistent with crossing a critical transition or bifurcation in which the system traverses a critical threshold and shifts suddenly to an alternative, attracting dynamical regime (11). Such regime shifts between alternative stable states have been described in many real-world systems (12-14) and exhibit a repertoire of early warning indicators (15-17). The seizing brain provides a unique living system for studying the signatures of an impending critical transition as well as one in which interventions can have profound practical import.We characterize the features of seizure termination in both multiscale in vivo data from patients with epilepsy and a computational model of cortical field activity. We show that population electrical activity-observed at macroscopic spatial scales-exhibits numerous signatures of an impending critical transition, whereas spatially localized recordings of neural spiking activity possess different dynamics. These insi...

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Section: Signatures Of a Critical Transition In A Mean-field Model Ofmentioning

confidence: 99%

Human seizures self-terminate across spatial scales via a critical transition

Kramer

Truccolo

Eden

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

190

147

View full text Add to dashboard Cite

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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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“…This is consistent with experimental observation of a phase reversal at cortical layer V by Lopes da Silva and Storm Van Leeuwen (1977). Lopes da Silva et al (1997) and Lopes da Silva et al (1974) suggest that rather than self-sustained oscillations, scalp alpha rhythm may reflect noise filtered by frequency selective neural populations locally in both cortex and thalamus. Of course mechanisms at different scales are not mutually exclusive and if coexistent could interact between scales to reinforce or entrain each other.…”

Section: Physiological Origin Of Macroscopic Neural Oscillationssupporting

confidence: 77%

“…Contemporaneously Wilson and Cowan (1972) developed two-dimensional dynamical models of interacting excitation and inhibition at this scale and other early contributors to the field include Nunez (1974) and Lopes da Silva et al (1974). In the literature models of this type are sometimes called mean field models by reference to mean field methods in physics.…”

Section: Neural Mass Modelsmentioning

confidence: 99%

“…Most commonly, neural mass models model a small area of neocortex, sometimes called a cortical column because it includes neural populations representing all layers of a cross-section of the folded neocortical sheet. 2 However neural mass modeling has also been applied to allocortical and subcortical brain regions including hippocampus (Wendling et al, 2002), thalamus (Lopes da Silva et al, 1974) and basal ganglia (van Albada and Robinson, 2009;Holgado et al, 2010).…”

Section: Neural Mass Modelsmentioning

confidence: 99%

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Critical fluctuations and coupling of stochastic neural mass models

Aburn¹

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Neuroimaging and implanted medical devices give a view onto large scale oscillations in the brain that rapidly change in both power and synchrony at different frequencies. These measured time series reveal a projection to just one dimension for each location, a moving shadow of the complex underlying activity. For this reason mathematical models of the activity are essential to make full use of the time series. The flexible onset and cessation of oscillations may have an important role in allowing the brain rapidly to rearrange its effective network structure. The onset of pathological oscillations is also central to neurological disorders such as epilepsy and Parkinson's disease. It is in the regime close to linear instability that transitions to and from oscillation can readily occur, by mechanisms of bifurcation and multistability. Empirical evidence of critical fluctuations and critical slowing down in neural dynamics also suggest proximity to linear instability. This thesis develops novel methods to analyze stochastic dynamical models near the point of transitionwhere oscillations start and stop, allowing to relate transitions in the models to changes in time series statistics that are accessible in clinical and experimental recordings.Taking as an example a widely used biophysical model of collective neural dynamics (the Jansen-Rit model) we show that near the point of oscillation onset at a supercritical Hopf bifurcation there can be a dramatic increase in autocorrelation length as well as power law scaling over four orders of magnitude in fluctuation size and duration, but that these time series indicators will depend sensitively on the direction in state space of input fluctuations and hence on which neuronal subpopulation is stochastically perturbed.In general near a supercritical Hopf bifurcation non-circular oscillations emerge on an arbitrarily curved two-dimensional surface embedded within the N -dimensional state space. This makes it difficult to determine exactly how noise will affect oscillation phase and amplitude. By applying Poincaré normal form transformations to find a parameter-dependent coordinate system in which the unperturbed oscillations are simple circles in a flat plane, then using Stratonovich stochastic calculus to transform noise perturbations to the same coordinate system, this makes explicit the effect of noise on phase and amplitude. We give a criterion for this reduced model to be a good approximation, balancing noise intensity and center manifold stability. Abstract iiOptionally averaging the diffusion process in Fokker-Planck form gives a still simpler weak approximation of the oscillations in a symmetrical standard form that retains the leading order stochastic effects on phase and amplitude dynamics. We demonstrate by large scale numerical simulation of the stochastic differential equations that the oscillation time series statistics of interest are preserved by transformation to this symmetrical weak approximation.Close to instability, dynamic synchrony of networ...

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Model of brain rhythmic activity

Cited by 656 publications

References 7 publications

Human seizures self-terminate across spatial scales via a critical transition

Human seizures self-terminate across spatial scales via a critical transition

Neural field dynamics with local and global connectivity and time delay

Critical fluctuations and coupling of stochastic neural mass models

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