A coupled ordinary differential equation lattice model for the simulation of epileptic seizures

Larter, Raima; Speelman, Brent; Worth, Robert M.

doi:10.1063/1.166453

Cited by 86 publications

(96 citation statements)

References 33 publications

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“…To emulate neuronal dynamics within the macaque neocortex we implemented a neural mass model adopted from a conductance-based model of neuronal dynamics (30) for local population activity (31). Units of the model describe local populations of densely interconnected inhibitory and excitatory neurons whose behaviors are determined by voltage-and ligand-gated membrane channels.…”

Section: Resultsmentioning

confidence: 99%

Network structure of cerebral cortex shapes functional connectivity on multiple time scales

Honey

Kötter

Breakspear

et al. 2007

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

1,631

1,356

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Neuronal dynamics unfolding within the cerebral cortex exhibit complex spatial and temporal patterns even in the absence of external input. Here we use a computational approach in an attempt to relate these features of spontaneous cortical dynamics to the underlying anatomical connectivity. Simulating nonlinear neuronal dynamics on a network that captures the large-scale interregional connections of macaque neocortex, and applying information theoretic measures to identify functional networks, we find structure-function relations at multiple temporal scales. Functional networks recovered from long windows of neural activity (minutes) largely overlap with the underlying structural network. As a result, hubs in these long-run functional networks correspond to structural hubs. In contrast, significant fluctuations in functional topology are observed across the sequence of networks recovered from consecutive shorter (seconds) time windows. The functional centrality of individual nodes varies across time as interregional couplings shift. Furthermore, the transient couplings between brain regions are coordinated in a manner that reveals the existence of two anticorrelated clusters. These clusters are linked by prefrontal and parietal regions that are hub nodes in the underlying structural network. At an even faster time scale (hundreds of milliseconds) we detect individual episodes of interregional phase-locking and find that slow variations in the statistics of these transient episodes, contingent on the underlying anatomical structure, produce the transfer entropy functional connectivity and simulated blood oxygenation level-dependent correlation patterns observed on slower time scales.functional MRI ͉ graph theory ͉ neuroanatomy ͉ synchrony T he anatomical connections between regions of the cerebral cortex form a structural network upon which neural activity unfolds. Cortical regions dynamically couple to one another forming functional networks associated with perception, cognition, and action (1-4), as well as during spontaneous activity in the default or resting state (5-12). Functional networks extracted from higher-frequency dynamics (Ϸ10 Hz) undergo rapid reconfiguration, e.g., in perceptual binding (13) or sensorimotor coordination (14). Functional networks extracted from lowerfrequency (Ͻ0.1 Hz) spontaneous cortical dynamics are organized into anticorrelated clusters (8, 10), and the transient activation of these clusters has been linked to attentional processes (10, 12). Recent analyses suggest that structural and functional brain networks share ''small-world'' topologies and hub nodes (15)(16)(17)(18)(19)(20) and that structural and functional clusters may closely correspond (21, 22). Nevertheless, it remains unclear how functional networks at different time scales relate to one another and to their common structural substrate.Here we studied mappings between structural and functional networks using a computational approach. A structural network of segregated regions and interregional pathways was obtained...

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Section: Resultsmentioning

confidence: 99%

Network structure of cerebral cortex shapes functional connectivity on multiple time scales

Honey

Kötter

Breakspear

et al. 2007

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

1,631

1,356

View full text Add to dashboard Cite

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“…Parameter ranges are constrained and informed by biophysical priors (Breakspear et al, 2003;Larter et al, 1999;Scherg and Berg, 1991;Sotero and Trujillo-Barreto, 2008). Dictionaries are created that associate specific parameter settings with resulting model dynamics.…”

Section: Identification Of Spatiotemporal Motifsmentioning

confidence: 99%

The Virtual Brain Integrates Computational Modeling and Multimodal Neuroimaging

et al. 2013

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Brain function is thought to emerge from the interactions among neuronal populations. Apart from traditional efforts to reproduce brain dynamics from the micro-to macroscopic scales, complementary approaches develop phenomenological models of lower complexity. Such macroscopic models typically generate only a few selected-ideally functionally relevant-aspects of the brain dynamics. Importantly, they often allow an understanding of the underlying mechanisms beyond computational reproduction. Adding detail to these models will widen their ability to reproduce a broader range of dynamic features of the brain. For instance, such models allow for the exploration of consequences of focal and distributed pathological changes in the system, enabling us to identify and develop approaches to counteract those unfavorable processes. Toward this end, The Virtual Brain (TVB) (www.thevirtualbrain.org), a neuroinformatics platform with a brain simulator that incorporates a range of neuronal models and dynamics at its core, has been developed. This integrated framework allows the modelbased simulation, analysis, and inference of neurophysiological mechanisms over several brain scales that underlie the generation of macroscopic neuroimaging signals. In this article, we describe how TVB works, and we present the first proof of concept.

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“…The dynamical variables studied are the mean membrane potential of pyramidal cells, V , and inhibitory interneurons, Z, and the average number of 'open' potassium ion channels, W . The evolution equations are adapted from a study of epileptic seizures in hippocampal slices [6] consisting of coupled di erential equations, which in turn are derived from the model of Morris and Lecar [8]. The mean cell membrane potential of the pyramidal cells is governed by the conductance of sodium, potassium and calcium ion through voltage-and ligand-gated membrane channels,…”

Section: Evolution Equationsmentioning

confidence: 99%

“…C =1 corresponds to maximum coupling, with excitatory input from outside each column surpassing excitatory input from within each column. All physiologically measurable parameters (conductances, threshold potentials and Nernst potentials) are set to their accepted values [6], These are given in Table 1. …”

Section: Evolution Equationsmentioning

confidence: 99%

Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a nonlinear model of neuronal dynamics

2003

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We study dynamical synchronization in a model of a neural system constituted by local networks of densely interconnected excitatory and inhibitory neurons. Neural dynamics are determined by voltage-and ligand-gated ion channels. Coupling between the local networks is introduced via sparse excitatory connectivity. With modulation of this long-range synaptic coupling the system undergoes a transition from independent oscillations to chaotic synchronization. Between these states exists a 'weakly' stable state with epochs of synchronization and complex intermittent desynchronization. This may facilitate adaptive brain function by engendering a diverse repertoire of dynamics and contribute to the genesis of complexity in the EEG.

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A coupled ordinary differential equation lattice model for the simulation of epileptic seizures

Cited by 86 publications

References 33 publications

Network structure of cerebral cortex shapes functional connectivity on multiple time scales

Network structure of cerebral cortex shapes functional connectivity on multiple time scales

The Virtual Brain Integrates Computational Modeling and Multimodal Neuroimaging

Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a nonlinear model of neuronal dynamics

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