A continuum-field model of visual cortex stimulus-driven behaviour: emergent oscillations and coherence fields
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–), 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, , wie=wei=4.4, , 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
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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.