Research Contributions in 2008

2002 / 2003 / 2004 / 2005 / 2006 / 2007

Assemblies of neuron models and simulation

On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses

Keywords:
Dynamical systems, spiking neurons, conductance based synapses, spike coding
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $\delta$, where $\delta$ can be \textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the ``edge of chaos'', a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely ``in the spikes'' in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.

Bumps in simple two-dimensional neural field models

Participants:
François Grimbert
Keywords:
neural fields, neural masses, bumps, prefrontal cortex, linear stability analysis
Neural field models first appeared in the 50's, but the theory really took off in the 70's with the works of Wilson and Cowan {wilson-cowan:72,wilson-cowan:73} and Amari {amari:75,amari:77}. Neural fields are continuous networks of interacting neural masses, describing the dynamics of the cortical tissue at the population level. In this report, we study homogeneous stationary solutions (i.e independent of the spatial variable) and bump stationary solutions (i.e. localized areas of high activity) in two kinds of infinite two-dimensional neural field models composed of two neuronal layers (excitatory and inhibitory neurons). We particularly focus on bump patterns, which have been observed in the prefrontal cortex and are involved in working memory tasks {goldman-rakic:95}. We first show how to derive neural field equations from the spatialization of mesoscopic cortical column models. Then, we introduce classical techniques borrowed from Coombes {coombes:05} and Folias and Bressloff {folias-bressloff:04} to express bump solutions in a closed form and make their stability analysis. Finally we instantiate these techniques to construct stable two-dimensional bump solutions.

Neural Field Model of VSD Optical Imaging Signals

Participants:
François Grimbert
Participants:
Frédéric Chavane
Keywords:
neural field, cortical area, biophysical model, optical imaging, voltage-sensitive dye, direct problem, connectivity, visual cortex, barrel cortex
We propose a solution to the direct problem of VSD optical imaging based on a neural field model of a cortical area and reproduce optical signals observed in various mammals cortices. We first present a biophysical approach to neural fields and show that these easily integrate the biological knowledge on cortical structure, especially horizontal and vertical connectivity patterns. After having introduced the reader to VSD optical imaging, we propose a biophysical formula expressing the optical imaging signal in terms of the activity of the field. Then, we simulate optical signals that have been observed by experimentalists. We have chosen two experimental sets: the line-motion illusion in the visual cortex of mammals (jancke, chavane, et al. 2004} and the spread of activity in the rat barrel cortex (petersen, grinvald, et al. 2003). We begin with a structural description of both areas, with a focus on horizontal connectivity. Finally we simulate the corresponding neural field equations and extract the optical signal using the direct problem formula developed in the preceding sections. We have been able to reproduce the main experimental results with these models.

Single neuron models

No contributions available for this research topic

Brain anatomical imaging using Diffusion MRI

No contributions available for this research topic

Brain functional imaging using MEG/EEG

Comparison of BEM and FEM Methods for the E/MEG Problem

Participants:
Théo Papadopoulo
Participants:
Maureen Clerc
Keywords:
MEEG forward problem, Integral Formulation, Boundary Element Method, Finite Element Method
The direct electro/magnetoencephalographic (E/MEG) problem consists of simulating the electromagnetic field produced by neuronal sources on the cortex. We compare two different methods for the resolution of this problem, from the point of view of computational complexity and accuracy. First, the finite element method (FEM), based on the discretization of the PDE in the entire head volume. Second, the boundary element method (BEM), discretizing the equivalent integral equations on the surfaces separating volumes with different electrical parameters. We also study the behaviour of BEM and FEM for the sources approaching the discontinuity in conductivity. We conclude that at the current state of investigation, for equivalent meshes, the FEM is significantly faster than BEM and provides similar or better accuracy.

Cortical Mapping

Contribution Image:
Participants:
Maureen Clerc
Keywords:
Electroencephalography; EEG; Boundary Element Method; BEM; Cortical Mapping
The Laplace-Cauchy problem of propagating Dirichlet and Neumann data from a portion to the rest of the boundary is an ill-posed inverse problem. Many regularizing algorithms have been recently proposed, in order to stabilize the solution with respect to noisy or incomplete data. Our main application is in electro-encephalography (EEG) where potential measurements available at part of the scalp are used to reconstruct the potential and the current on the inner skull surface. This problem, known as cortical mapping, and other applications --- in fields such as nondestructive testing, or biomedical engineering --- require to solve the problem in realistic, three-dimensional geometry. We propose a new boundary element based method for solving the Laplace-Cauchy problem in three dimensions, in a multilayer geometry. We validate the method experimentally on simulated data.

Biological and computational vision

Virtual Retina: A biological retina model and simulation software

Participants:
Adrien Wohrer
Keywords:
retina, contrast gain control, spiking simulator
Virtual Retina is a simulation software developped in the Odyssée research team (INRIA Sophia Antipolis - Méditerannée) by Adrien Wohrer (PhD, supervised by Pierre Kornprobst and Thierry Viéville). Virtual Retina allows large-scale simulations of biologically-plausible retinas, with customizable parameters, and different possible biological features: 1. Spatio-temporal linear filter implementing the basic Center/Surround organization of retinal filtering. 2. Non-linear contrast gain control mechanism providing instantaneous adaptation to the local level of contrast. This stage is modelled through dynamical adaptation conductances in the membranes of bipolar cells; the resulting model reproduces contrast-dependent amplitude and phase non-linearities, as measured in real mammalian retinas by Shapley & Victor 78. 3. Spike generation by one or several layers of ganglion cells paving the visual field. Magnocellular and Parvocellular pathways can be modelled in the same framework according to the parameters chosen. Large-scale simulations can be pursued on up to 100,000 spiking cells. 4. Possibility of a global radial inhomogeneity modeling the foveated organization of mammalian retinas. In this case, the spatial scales of filtering, and the density of spiking cells, both depend on the eccentricity from the center of the retina. 5. Possibility to include a basic microsaccades generator at the input of the retina, to account for fixational eye movements. Virtual Retina is under INRIA CeCill C open-source licence (IDDN number IDDN.FR.001.210034.000.S.P.2007.000.31235), so that you can download it, install it and run it on your own sequences. Virtual Retina also offers you a web service, so that you may test directly the main software on your own data, without any installation. This webservice was developed in collaboration with Nicolas Debeissat. Virtual Retina is the result of a research contribution, and you will also find the associated research publications if you want to learn more.

Motion integration modulated by form information

Keywords:
Motion integration, feedbacks, motion perception, extrinsic junctions, MT
We develop a model of motion integration modulated by form information, inspired by neurobiological data. Our dynamical system models several key features of the motion processing stream in primate visual cortex. Thanks to a multi-layer architecture incorporating both feedforward and feedback and inhibitive lateral connections, our model is able to solve local motion ambiguities. One important feature of our model is to propose an anisotropic integration of motion based on the form information. Our model can be implemented efficiently on GPU and we show its properties on classical psychophysical examples. First, a simple read-out allows us to reproduce the dynamics of ocular following for a moving bar stimulus. Second, we show how our models able to discriminate between extrinsic and intrinsic junctions present in the chopstick illusion. We also obtain some promising results on real videos.

Action Recognition with a Bio-Inspired Feedforward Motion Processing Model

Keywords:
action recognition, V1, MT, center-surround interactions, feedforward neural model, motion processing
We propose a bio-inspired feedforward model for motion processing based on the neurophysiology literature, and we show how the estimated motion representation can be successfully used to recognize actions in real videos. As a major difference with the model proposed by Jhuang et al. (2007), we do really focus on proposing a model of motion processing which reproduces some key elements of the visual system in terms of dynamics and connectivity between the V1 and MT layers. In particular, we model the richness of center surround interactions in MT, arising from the integration of motion from the V1 cells. As it is observed in neurophysiology, the cells in our MT model not only behave like simple velocity detectors, but also respond to several kinds of motion contrasts. Interestingly, we show that this diversity of motion representation at the MT level is a major advantage for an action recognition task. We compare our results for action recognition on the Weizmann database, and show the performance of our approach with respect to approaches based on simply classical motion detectors.

A Simple Mechanims to Reproduce te Neural Solution of the Aperture Problem in Monkey Area MT

Keywords:
Aperture problem, surround inhibition, MT, barberpole
We propose a simple mechanism to reproduce the neural solution of the aperture problem in monkey area MT. More precisely, our goal is to propose a model able to reproduce the dynamical change of the preferred direction (PD) of a MT cell depending on the motion information contained in the input stimulus. The PD of a MT cell measured through drifting gratings differs of the one measured using a barberpole, which is highly related with its aspect ratio. For a barberpole, the PD evolves from the perpendicular direction of the drifting grating to a PD shifted according to the aspect ratio of the barberpole. The mechanisms underlying this dynamic are unknown (lateral connections, surround suppression, feed-backs from higher layers). Here, we show that a simple mechanism such as surround-inhibition in V1 neurons can produce a significant shift in the PD of MT neurons as observed with barberpoles of different aspect ratios.