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Wave speed in excitable random networks with spatially constrained connections.

Vladimirov N, Traub RD, Tu Y - PLoS ONE (2011)

Bottom Line: We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length.When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments <k2>/<k> rather than on mean degree <k>, which is explained by general network theory.Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.

View Article: PubMed Central - PubMed

Affiliation: IBM T. J. Watson Research Center, Yorktown Heights, New York, United States of America. nikita.vladimirov@gmail.com

ABSTRACT
Very fast oscillations (VFO) in neocortex are widely observed before epileptic seizures, and there is growing evidence that they are caused by networks of pyramidal neurons connected by gap junctions between their axons. We are motivated by the spatio-temporal waves of activity recorded using electrocorticography (ECoG), and study the speed of activity propagation through a network of neurons axonally coupled by gap junctions. We simulate wave propagation by excitable cellular automata (CA) on random (Erdös-Rényi) networks of special type, with spatially constrained connections. From the cellular automaton model, we derive a mean field theory to predict wave propagation. The governing equation resolved by the Fisher-Kolmogorov PDE fails to describe wave speed. A new (hyperbolic) PDE is suggested, which provides adequate wave speed v() that saturates with network degree , in agreement with intuitive expectations and CA simulations. We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length. When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments / rather than on mean degree , which is explained by general network theory. The wave speeds are strikingly similar in a diverse set of networks, including regular, Poisson, exponential and power law distributions, supporting our theory for various network topologies. Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.

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Neural network activity in experiments and in the cellular automaton model.A. A snapshot of electrocorticographic (ECoG) data of brain activity, measured by 8×6 subdural array of electrodes. Data is interpolated between nodes, white areas correspond to high activity. B. A snapshot of activity from a cellular automaton model in an 400×400 network. The network is subject to noisy input from spontaneously activating cells (rate ). Active cells are white, refractory and excitable are black (simplified color code). C. Snapshot of activity in a 10×10 sub-network with detailed color code: red for active, blue for refractory, black for excitable nodes. Lines show links between nodes. D. Rules of the CA model: excitable node (black) may become active (red), if activated by a neighbor. After being activated, the node becomes refractory (blue) for a period of time , after which it becomes excitable again. Data in A is a courtesy of Miles Whittington, recorded in Patient B of [29].
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pone-0020536-g001: Neural network activity in experiments and in the cellular automaton model.A. A snapshot of electrocorticographic (ECoG) data of brain activity, measured by 8×6 subdural array of electrodes. Data is interpolated between nodes, white areas correspond to high activity. B. A snapshot of activity from a cellular automaton model in an 400×400 network. The network is subject to noisy input from spontaneously activating cells (rate ). Active cells are white, refractory and excitable are black (simplified color code). C. Snapshot of activity in a 10×10 sub-network with detailed color code: red for active, blue for refractory, black for excitable nodes. Lines show links between nodes. D. Rules of the CA model: excitable node (black) may become active (red), if activated by a neighbor. After being activated, the node becomes refractory (blue) for a period of time , after which it becomes excitable again. Data in A is a courtesy of Miles Whittington, recorded in Patient B of [29].

Mentions: A case study in our work is the emergence of spatiotemporal patterns with very fast oscillations (VFO, 80 Hz) measured by electrocorticography [9], recorded in neocortex of patients prior to epileptic seizures (Figure 1A). There is growing experimental and theoretical evidence that VFO are caused by electrically coupled pyramidal neurons which are connected by gap junctions, thus providing direct excitation from one to another, which does not require synaptic transmission [9], [12], [13].


Wave speed in excitable random networks with spatially constrained connections.

Vladimirov N, Traub RD, Tu Y - PLoS ONE (2011)

Neural network activity in experiments and in the cellular automaton model.A. A snapshot of electrocorticographic (ECoG) data of brain activity, measured by 8×6 subdural array of electrodes. Data is interpolated between nodes, white areas correspond to high activity. B. A snapshot of activity from a cellular automaton model in an 400×400 network. The network is subject to noisy input from spontaneously activating cells (rate ). Active cells are white, refractory and excitable are black (simplified color code). C. Snapshot of activity in a 10×10 sub-network with detailed color code: red for active, blue for refractory, black for excitable nodes. Lines show links between nodes. D. Rules of the CA model: excitable node (black) may become active (red), if activated by a neighbor. After being activated, the node becomes refractory (blue) for a period of time , after which it becomes excitable again. Data in A is a courtesy of Miles Whittington, recorded in Patient B of [29].
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3108581&req=5

pone-0020536-g001: Neural network activity in experiments and in the cellular automaton model.A. A snapshot of electrocorticographic (ECoG) data of brain activity, measured by 8×6 subdural array of electrodes. Data is interpolated between nodes, white areas correspond to high activity. B. A snapshot of activity from a cellular automaton model in an 400×400 network. The network is subject to noisy input from spontaneously activating cells (rate ). Active cells are white, refractory and excitable are black (simplified color code). C. Snapshot of activity in a 10×10 sub-network with detailed color code: red for active, blue for refractory, black for excitable nodes. Lines show links between nodes. D. Rules of the CA model: excitable node (black) may become active (red), if activated by a neighbor. After being activated, the node becomes refractory (blue) for a period of time , after which it becomes excitable again. Data in A is a courtesy of Miles Whittington, recorded in Patient B of [29].
Mentions: A case study in our work is the emergence of spatiotemporal patterns with very fast oscillations (VFO, 80 Hz) measured by electrocorticography [9], recorded in neocortex of patients prior to epileptic seizures (Figure 1A). There is growing experimental and theoretical evidence that VFO are caused by electrically coupled pyramidal neurons which are connected by gap junctions, thus providing direct excitation from one to another, which does not require synaptic transmission [9], [12], [13].

Bottom Line: We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length.When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments <k2>/<k> rather than on mean degree <k>, which is explained by general network theory.Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.

View Article: PubMed Central - PubMed

Affiliation: IBM T. J. Watson Research Center, Yorktown Heights, New York, United States of America. nikita.vladimirov@gmail.com

ABSTRACT
Very fast oscillations (VFO) in neocortex are widely observed before epileptic seizures, and there is growing evidence that they are caused by networks of pyramidal neurons connected by gap junctions between their axons. We are motivated by the spatio-temporal waves of activity recorded using electrocorticography (ECoG), and study the speed of activity propagation through a network of neurons axonally coupled by gap junctions. We simulate wave propagation by excitable cellular automata (CA) on random (Erdös-Rényi) networks of special type, with spatially constrained connections. From the cellular automaton model, we derive a mean field theory to predict wave propagation. The governing equation resolved by the Fisher-Kolmogorov PDE fails to describe wave speed. A new (hyperbolic) PDE is suggested, which provides adequate wave speed v() that saturates with network degree , in agreement with intuitive expectations and CA simulations. We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length. When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments / rather than on mean degree , which is explained by general network theory. The wave speeds are strikingly similar in a diverse set of networks, including regular, Poisson, exponential and power law distributions, supporting our theory for various network topologies. Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.

Show MeSH
Related in: MedlinePlus