Neural field dynamics with local and global connectivity and time delay

Jirsa, Viktor K.

doi:10.1098/rsta.2008.0260

Cited by 78 publications

(79 citation statements)

References 46 publications

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“…Spatial networks of spiking elements can exhibit a variety of dynamical behaviors [23][24][25][26][27]. We here reported on a novel phenomenon, namely recurrent events of synchrony, emerging robustly from networks of identical, deterministic oscillators.…”

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confidence: 96%

Recurrent events of synchrony in complex networks of pulse-coupled oscillators

Rothkegel

Lehnertz

2011

EPL

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-We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may be separated by periods of asynchrony with varying duration. The phenomenon is specific to spatial networks with both short-and longranged connections and requires delayed interactions and refractoriness of oscillators.Nature possesses various examples of systems composed of many oscillatory elements in which, through mutual interactions, collective dynamics emerges [1][2][3]. In many biological networks (like the heart or the brain) interactions are short-lasting and may be modeled as pulses, which are fired at a given oscillator phase [4,5]. Such pulse-coupled oscillators show, for large arrangements, a variety of collective dynamics with a convergence of global observables after transients. Examples range from stable synchronous [5,6] and asynchronous states [7], phase-locking [8], partial synchrony [9][10][11], to transitions from asynchronous to synchronous states [12]. The human brain with its 100 billion neurons, however, may show recurrent changes in global synchrony (as seen, e.g., on the electroencephalogram) associated with physiologic or pathophysiologic functioning [13,14].In this Letter, we present a spatial network model of pulse-coupled oscillators (PCOs), which shows collective dynamics with no convergence to either synchrony, partial synchrony, or asynchrony. Instead, the network generates -even without noise influences or a change of parameters -recurrent events that are comprised of an increase and decline in synchrony. Events may occur at random looking times and be separated by prolonged periods of asynchrony. Events may also be initiated immediately after completion of the preceding event leading to an oscillatory behavior. The oscillators thus generate a rhythm, which is not directly linked to their intrinsic time-scales (the delay of interactions and the duration of the refractory period) but is an emerging property of the network.We study networks of oscillators n ∈ N with phases φ n (t) ∈ [0, 1], dφn dt = 1. If for some t f and some oscillator n the phase reaches 1 (φ n (t f ) = 1), it is reset to 0 (φ n (t + f ) = 0) and we introduce a phase jump in all oscillators n which are adjacent to n according to some directed graph:∆ denotes the phase response curve. A refractory period of length ϑ can easily be incorporated into ∆ by setting ∆(φ) = 0 for φ < ϑ. Consider identical time delays τ < ϑ on all outgoing connections of oscillator n, such that all its excitations are received when φ n = τ . In this case, n can be replaced equivalently with an undelayed oscillator with periodically shifted phase and phase response curve. We can thus incorporate both refractoriness and delay into an arbitrary phase response curve ∆ (yielding an formally undelayed phase response curve ∆) by setting:Here denotes some coupling strength. Our choice for ∆ (φ) is...

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confidence: 96%

Recurrent events of synchrony in complex networks of pulse-coupled oscillators

Rothkegel

Lehnertz

2011

EPL

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“…The advantage of neglecting the oscillatory physiological signals lies in the fact that we can neglect the time delays via signal transmission between brain areas. This is justified in this particular case, because time delays do not alter the stationary attractor states of a network, however, they may alter the stability boundaries of the oscillatory network states (for review, see Jirsa, 2004;Jirsa and Ding, 2004;Jirsa, 2009). As a consequence, the resulting dynamic repertoire will be mostly determined by the properties of the neuroanatomical connectivity matrix.…”

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confidence: 99%

Ongoing Cortical Activity at Rest: Criticality, Multistability, and Ghost Attractors

Deco

Jirsa²

2012

J. Neurosci.

667

662

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The ongoing activity of the brain at rest, i.e., under no stimulation and in absence of any task, is astonishingly highly structured into spatiotemporal patterns. These spatiotemporal patterns, called resting state networks, display low-frequency characteristics (Ͻ0.1 Hz) observed typically in the BOLD-fMRI signal of human subjects. We aim here to understand the origins of resting state activity through modeling via a global spiking attractor network of the brain. This approach offers a realistic mechanistic model at the level of each single brain area based on spiking neurons and realistic AMPA, NMDA, and GABA synapses. Integrating the biologically realistic diffusion tensor imaging/diffusion spectrum imaging-based neuroanatomical connectivity into the brain model, the resultant emerging resting state functional connectivity of the brain network fits quantitatively best the experimentally observed functional connectivity in humans when the brain network operates at the edge of instability. Under these conditions, the slow fluctuating (Ͻ0.1 Hz) resting state networks emerge as structured noise fluctuations around a stable low firing activity equilibrium state in the presence of latent "ghost" multistable attractors. The multistable attractor landscape defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity.

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“…Our initial application of the novel hybrid model aimed to study the effect of input injection while minimizing the degrees of freedom of the simulation and the set of parameters to be varied. Further studies are required to determine the effect of coupling delays, as previous studies demonstrated their important role for emerging large-scale dynamics (Deco et al, 2011;Jirsa, 2008Jirsa, , 2009. We observed that the prediction quality of resting-state network activation time courses fluctuates over time and is highest during epochs of highest variance of the respective temporal mode.…”

Section: Discussionmentioning

confidence: 76%

Inferring multi-scale neural mechanisms with brain network modelling

Schirner

McIntosh

Jirsa

et al. 2017

Preprint

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The neurophysiological processes underlying non-invasive brain activity measurements are incompletely understood. Here, we developed a connectome-based brain network model that integrates individual structural and functional data with neural population dynamics to support multi-scale neurophysiological inference. Simulated populations were linked by structural connectivity and, as a novelty, driven by electroencephalography (EEG) source activity. Simulations not only predicted subjects' individual resting-state functional magnetic resonance imaging (fMRI) time series and spatial network topologies over 20 minutes of activity, but more importantly, they also revealed precise neurophysiological mechanisms that underlie and link six empirical observations from different scales and modalities: (1) resting-state fMRI oscillations, (2) functional connectivity networks, (3) excitation-inhibition balance, (4, 5) inverse relationships between arhythms, spike-firing and fMRI on short and long time scales, and (6) fMRI power-law scaling. These findings underscore the potential of this new modelling framework for general inference and integration of neurophysiological knowledge to complement empirical studies.

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Neural field dynamics with local and global connectivity and time delay

Cited by 78 publications

References 46 publications

Recurrent events of synchrony in complex networks of pulse-coupled oscillators

Recurrent events of synchrony in complex networks of pulse-coupled oscillators

Ongoing Cortical Activity at Rest: Criticality, Multistability, and Ghost Attractors

Inferring multi-scale neural mechanisms with brain network modelling

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