A model for feature linking via collective oscillations in the primary visual cortex

Chawanya, Tsuyoshi; Aoyagi, Toshio; Nishikawa, Ikuko; Okuda, Koji; Kuramoto, Yoshio

doi:10.1007/bf00200807

Cited by 46 publications

(17 citation statements)

References 16 publications

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“…While the modularity of brain regions motivates simplification via spatial coarse-graining, irregular temporal fluctuations in the neuronal membrane potentials and the synaptic inputs [50,46,3,45] suggest time-scales for temporal coarse-graining. Various theoretical approaches, based on spatial and temporal coarse-graining assumptions, have led to the development of dimensional-reduced descriptions of the network dynamics through examining a probabilistic representation of the network dynamics and deriving an evolution equation governing a probability 1 density function (pdf) [26,55,1,52,18,5,39,7,20,38,37,35,36,22,19]. In this work, we propose an efficient numerical scheme for the simulation of a nonlinear Fokker-Planck equation representation for neuronal network dynamics.…”

Section: Introductionmentioning

confidence: 99%

A numerical solver for a nonlinear Fokker–Planck equation representation of neuronal network dynamics

Cáceres¹,

Carrillo²,

Tao³

2011

Journal of Computational Physics

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Abstract. To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13,12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

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Section: Introductionmentioning

confidence: 99%

A numerical solver for a nonlinear Fokker–Planck equation representation of neuronal network dynamics

Cáceres¹,

Carrillo²,

Tao³

2011

Journal of Computational Physics

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“…(For earlier probabilistic representations, see, e.g., refs. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].) This powerful approach allows for both computational scale-up and structural insight into the mechanisms of the cortical network.…”

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confidence: 99%

An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex

Cai

Tao

Shelley

et al. 2004

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

121

160

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A coarse-grained representation of neuronal network dynamics is developed in terms of kinetic equations, which are derived by a moment closure, directly from the original large-scale integrate-andfire (I&F) network. This powerful kinetic theory captures the full dynamic range of neuronal networks, from the mean-driven limit (a limit such as the number of neurons N 3 ؕ, in which the fluctuations vanish) to the fluctuation-dominated limit (such as in small N networks). Comparison with full numerical simulations of the original I&F network establishes that the reduced dynamics is very accurate and numerically efficient over all dynamic ranges. Both analytical insights and scale-up of numerical representation can be achieved by this kinetic approach. Here, the theory is illustrated by a study of the dynamical properties of networks of various architectures, including excitatory and inhibitory neurons of both simple and complex type, which exhibit rich dynamic phenomena, such as, transitions to bistability and hysteresis, even in the presence of large fluctuations. The implication for possible connections between the structure of the bifurcations and the behavior of complex cells is discussed. Finally, I&F networks and kinetic theory are used to discuss orientation selectivity of complex cells for ''ring-model'' architectures that characterize changes in the response of neurons located from near ''orientation pinwheel centers'' to far from them. N euronal networks, whether real cortical networks (1, 2) or computer models (3, 4), frequently operate in a regime in which spiking is caused by irregular temporal fluctuations of the membrane potential. At this ''cortical operating point,'' the mean membrane potential (e.g., obtained by averaging over many voltage traces under the same stimulus condition or by averaging locally in time), does not reach firing threshold. Thus, the spiking process is fluctuation-driven.A theoretical challenge is to construct efficient and effective representations of such fluctuation-driven networks, which are needed both to ''scale-up'' computational models to large enough regions of the cortex to capture interesting cortical processing (such as optical illusions related to ''contour completion''), and to gain qualitative understanding of the cortical mechanisms underlying this level of cortical processing. In this article, we develop such a construction: Starting with large-scale model networks of integrateand-fire (I&F) neurons, which are sufficiently detailed for modeling neuronal computation of large systems but are difficult to scale-up, we tile the cortex with coarse-grained (CG) patches. Each CG patch is sufficiently small that the cortical architecture does not change systematically across it, yet it is sufficiently large to contain many (hundreds) of neurons. We then derive an effective dynamics to capture the statistical behavior of the many neurons within each CG patch in their interaction with other CG patches. This representation is achieved by a kinetic theory, accomplished by ...

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“…The above problem has been discussed in the prevailing theories of selective attention that are based on synchronized oscillations (18)(19)(20)(21)(22). The main emphasis in the latter has been an attempt to explain the binding problem, i.e., how the features of very different kinds, while being detected in different places, can be combined into a unified perceived item.…”

Section: Discussionmentioning

confidence: 99%

Modeling of automatic capture and focusing of visual attention

Kohonen¹

2002

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

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An explanation, based on simple analysis of the spatiotemporal variations of the visual environment, is given to the automatic capture and focusing of visual attention. It is assumed that the transmittance for the sensory signals is modulated by separate control circuits that sample input from the same area of the visual field but at a lower resolution. When these circuits detect significant spatial and͞or temporal variations, they ''open gates'' for the more accurate information arising from the same area. If the variations are related to the spatial resolution, which varies within wide limits over the retina, the visual field is ''opened'' up to a radius where it captures the most salient structures of the image. If the temporal variations of the signals are further emphasized, the high spatial frequencies begin to dominate. If then the gaze is moved by a small amount, the transmittance of the foveal signal paths is activated strongest.

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A model for feature linking via collective oscillations in the primary visual cortex

Cited by 46 publications

References 16 publications

A numerical solver for a nonlinear Fokker–Planck equation representation of neuronal network dynamics

A numerical solver for a nonlinear Fokker–Planck equation representation of neuronal network dynamics

An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex

Modeling of automatic capture and focusing of visual attention

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