Elsevier

Neurocomputing

Volume 57, March 2004, Pages 411-433
Neurocomputing

A continuum-field model of visual cortex stimulus-driven behaviour: emergent oscillations and coherence fields

https://doi.org/10.1016/j.neucom.2003.10.016Get rights and content

Abstract

The problem of the genesis of oscillatory phenomena in a continuous distribution of excitatory and inhibitory neurons is addressed by introducing a neural field model of the reaction-diffusion type. The presence of the diffusive term, combined with the non-linear point interactions, allows the system to exhibit cooperative activation properties in both space and time. A detailed analysis of the resulting oscillatory behaviour of the model evidences its capability of generating stimulus-induced spatio-temporal coherence fields, similar to the ones experimentally observed in the mammalian visual cortex. The perceptual role of the related association fields, as flexible media to establish feature association in the visual space, is discussed.

Introduction

Over the past few years, a large amount of data have been accumulated which demonstrate that coherent perceptual states are associated with collective activities of large ensembles of neurons in cortical areas [2], [30], [36], [46], [51], [62]. Specifically, it has been observed that visual stimulations drive synchronous oscillatory behaviours over a range of spatial scales, from single unit responses to visually evoked potentials [94], [78], [88]. These stimulus-dependent neuronal oscillations occur mainly in the γ-frequency band (20–70Hz), and can synchronize across separate cortical locations with a precision in the ms range and with near-zero phase-lag, depending on the configuration of the visual stimulus [19], [22], [32], [38], [39], [40], [53]. From this perspective, phase relationships of neuronal oscillations may be used to define cortical assemblies, i.e., clusters of spatially distributed neuronal groups that represent segments of a visual scene. On the basis of this body of evidence, synchronous oscillatory cortical responses have been indicated as the physiological substrate for a mechanism of feature binding [19], [21], [23], [33], [76], [85], [90].

Several models have been proposed to study the emergence of synchronous oscillations in networks of reciprocally coupled neural oscillators [1], [5], [14], [20], [41], [52], [54], [55], [75], [81], [91], [94]. (for a review, see [25], [83]). In all these models, synchronization/desynchronization behaviours are achieved by couplings among oscillating units considered as interacting discretely with one another.

In this paper, our aim is to investigate the joint spatio-temporal properties of the sensory-evoked activity in cortical networks. Toward this end, coupling weights among oscillators are modelled as a diffusion process: any cell activates, through a spreading-out process, nearby cells in proportion to its own level of activation. The neural field model associated with this choice of the coupling weights allows us to investigate spatial distributions of coherence and synchrony as continuum properties of large fields of interconnected cells. Desynchronization behaviour in our model is introduced by an appropriate long-range inhibitory coupling. In this way, we can analyse the role of horizontal interactions in the establishment of ordered oscillatory behaviours and in the control of the spatio-temporal distribution of coherence. We show that the resulting system exhibits a stimulus-dependent assembly formation of oscillatory responses, similar to those found in the physiological experiments on slow-wave field potentials [14], [18].

Section snippets

Cortical model

Visual cortex is a densely packed volume of neurons in which intracortical connections greatly exceed afferent projections [9]. This implies that the collective behaviour of neural assemblies depends on complex synaptic and dendritic processes of large cortical networks; therefore, to determine the degree of relevant detail is a hard problem. Given the huge number of cells involved in such networks, macroscopic approaches are frequently adopted to offer simpler insights into the basic physical

Results

The spatio-temporal dynamics of a 1-D neural field driven by finite stochastic point sources is studied by numerical simulations. The system parameters used in the following were chosen to produce desirables slow-wave forms resembling LFPs recorded extracellularly in the visual cortices of the cat and the monkey. Our standard set of parameters is: αe=αi=1.0, τ0=5ms, wie=wei=4.4, τieei=1.5ms, D=0.06λ20, b=0.045, d=0.5λ0, A=4, σ=6.0, θ=1.0.

Discussion

In this paper, we have aimed to model the joint spatio-temporal oscillatory dynamics observed in the visual cortices [18], [74], [78], [88], through the behaviour of a field oscillatory system. Toward this end, we have introduced a second-order delayed partial differential equation characterized by a non-linear point interaction similar to König and Schillen's basic oscillatory element [52] and by a recurrent linear coupling, modelled by an excitatory diffusion term and lateral inhibition. The

Acknowledgements

We wish to thank G.M. Bisio and L. Raffo for their contributions to the accomplishment of this work. The work was partially supported by the University of Genoa within the framework of the Project “Operatori spazio-temporali per l'analisi binoculare del moto in profondità”.

Silvio P. Sabatini graduated in Electronic Engineering at the University of Genoa, Italy (1992); PhD in Electronic Engineering and Computer Science at the Department of Biophysical and Electronic Engineering (DIBE) of Genoa (1996). Since 1999 Assistant Professor in Computer Science at the University of Genoa. In 1995 he promoted the creation of the “Physical Structure of Perception and Computation” (PSPC) Research Group at DIBE (http://pspc.dibe.unige.it/) to develop models that capture the

References (101)

  • M.N. Shadlen et al.

    Noise, neural codes and cortical organization

    Curr. Opin. Neurobiol.

    (1994)
  • C. Tallon-Baudry et al.

    Oscillatory gamma activity in humans and its role in object representation

    Trends Cognitive Sci.

    (1999)
  • D. Terman et al.

    Global competition and local cooperation in a network of neural oscillators

    Physica D

    (1995)
  • J.J. Tyson et al.

    Singular perturbation theory of traveling waves in excitable mediaa review

    Physica D

    (1988)
  • A. van Rotterdam et al.

    A model of the spatial-temporal characteristics of the alpha rhythms

    Bull. Math. Biol.

    (1982)
  • L.F. Abbott

    A network of oscillators

    J. Phys. A: Math.

    (1990)
  • M. Ahissar et al.

    Encoding of sound-source location and movementactivity of single neurons and interactions between adjacent neurons in the monkey auditory cortex

    J. Neurophysiol.

    (1992)
  • S. Amari

    Dynamics of pattern formation in lateral-inhibition type neural fields

    Biol. Cybernet.

    (1977)
  • S. Amari

    Mathematical foundations of neurocomputing

    Proc. IEEE

    (1990)
  • P. Baldi et al.

    Computing with arrays of coupled oscillators: an application to preattentive texture discrimination

    Neural. Comput.

    (1990)
  • G.G. Blasdel

    Orientation selectivity, preference, and continuity in monkey striate cortex

    J. Neurosci.

    (1992)
  • R.M. Borisyuk et al.

    Bifurcation analysis of a neural network model

    Biol. Cybernet.

    (1992)
  • W.H. Bosking et al.

    Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex

    J. Neurosci.

    (1997)
  • V. Braitenberg et al.

    Cortex: Statistics and Geometry of Neuronal Connectivity

    (1998)
  • S.R. Campbell et al.

    Synchronization and desynchronization in a network of locally coupled Wilson–Cowan oscillators

    IEEE Trans. Neural Networks

    (1996)
  • E. Cesmeli et al.

    An oscillatory correlation model of visual motion analysis

    Percept. Psychophys.

    (2002)
  • Y. Choe, Perceptual grouping in a self-organizing map of spiking neurons, Ph.D. Thesis, Department of Computer...
  • A. Destexhe

    Oscillations, complex spatiotemporal behavior and information transport in networks of excitatory and inhibitory neurons

    Phys. Rev. E

    (1994)
  • A. Destexhe et al.

    Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states

    J. Neurosci.

    (1999)
  • R. Dilao et al.

    Validation and calibration of models for reaction-diffusion systems

    Int. J. Bifurc. Chaos

    (1998)
  • R.J. Douglas et al.

    A canonical microcircuit for neocortex

    Neural Comput.

    (1989)
  • R. Eckhorn, Oscillatory and non-oscillatory synchronizations in the visual cortex and their possible roles in...
  • R. Eckhorn et al.

    Coherent oscillationsa mechanism of feature linking in the visual cortex?

    Biol. Cybernet.

    (1988)
  • R. Eckhorn et al.

    Feature linking via synchronization among distribuited assembliessimulations of results from cat visual cortex

    Neural Comput.

    (1990)
  • A.K. Engel et al.

    Direct physiological evidence for scene segmentation by temporal coding

    Proc. Natl. Acad. Sci.

    (1991)
  • A.K. Engel et al.

    Role of the temporal domain for response selection and perceptual binding

    Cereb. Cortex

    (1997)
  • G.B. Ermentrout

    Stripes or spots? Nonlinear effects in bifurcation of reaction-diffusion equations on the square

    Proc. Roy. Soc. London A

    (1992)
  • B. Ermentrout

    Neural networks as spatio-temporal pattern-forming systems

    Rep. Prog. Phys.

    (1998)
  • P.C. Fife

    Mathematical Aspects of Reacting and Diffusing Systems

    (1979)
  • W.J. Freeman

    Mass Action in the Nervous System

    (1974)
  • W.J. Freeman

    Simulation of chaotic EEG patterns with a dymanic model of olfactory system

    Biol. Cybernet.

    (1987)
  • W.J. Freeman

    The physiology of perception

    Sci. Am.

    (1991)
  • A. Frien et al.

    Functional coupling shows stronger stimulus dependency for fast oscillations than for low-frequency components in striate cortex of awake monkey

    Eur. J. Neurosci.

    (2000)
  • A. Frien et al.

    Fast oscillations display sharper orientation tuning than slower components of the same recordings in stiate cortex of the awake monkey

    Eur. J. Neurosci.

    (2000)
  • P. Fries et al.

    Oscillatory neural synchronisation in primary visual cortex as a correlate of stimulus selection

    J. Neurosci.

    (2002)
  • W. Gerstner et al.

    What matters in neuronal locking?

    Neural Comput.

    (1996)
  • P.M. Gochin et al.

    Neural ensemble coding in inferior temporal cortex

    J. Neurophysiol.

    (1994)
  • R.E. Grannan et al.

    Stimulus dependent synchronization of neuronal assemblies

    Neural Comput.

    (1993)
  • C.M. Gray et al.

    Stimulus-dependent neuronal oscillations and local synchronization in striate cortex of the alert cat

    J. Neurosci.

    (1997)
  • C.M. Gray et al.

    Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex

    Proc. Natl. Acad. Sci.

    (1989)
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    Silvio P. Sabatini graduated in Electronic Engineering at the University of Genoa, Italy (1992); PhD in Electronic Engineering and Computer Science at the Department of Biophysical and Electronic Engineering (DIBE) of Genoa (1996). Since 1999 Assistant Professor in Computer Science at the University of Genoa. In 1995 he promoted the creation of the “Physical Structure of Perception and Computation” (PSPC) Research Group at DIBE (http://pspc.dibe.unige.it/) to develop models that capture the ”pysicalist” nature of the information processing that takes place in the visual cortex, to understand the signal processing strategies adopted by the brain and build novel algorithms and hardware devices for artificial perception machines. His current research interests include biocybernetics of vision, theoretical neuroscience, neuromorphic engineering, and artificial vision. He is author of more than 50 international papers in peer-reviewed journals and conferences.

    Fabio Solari received the Laurea degree in Electronic Engineering from the University of Genoa, Italy, in 1995. In 1999 he obtained his Ph.D. in Electronic Engineering and Computer Science from the same University. He is currently a postdoctoral fellow at the Department of Biophysical and Electronic Engineering (DIBE), University of Genoa. His research activity concerns the study of the physical processes of biological vision to inspire the design of artificial perceptual machines based on neuromorphic computational paradigms. In particular, he is interested in cortical modelling, dynamic stereopsis, visual motion analysis, and probabilistic modelling.

    Luca Secchi received the Laurea degree in Electronic Engineering from the University of Cagliari, Italy, in 1999. Since 1999 he is a IT Specialist working for IBM Global Services in Italy. His areas of expertise include security and network management.

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