Distinct Excitatory and Inhibitory Bump Wandering in a Stochastic Neural Field

Localized persistent cortical neural activity is a validated neural substrate of parametric working memory. Such activity "bumps" represent the continuous location of a cue over several seconds. Pyramidal (excitatory (E )) and interneuronal (inhibitory (I )) subpopulations exhibit tuned bumps of activity, linking neural dynamics to behavioral inaccuracies observed in memory recall. However, many bump attractor models collapse these subpopulations into a single joint E /I (lateral inhibitory) population and do not consider the role of interpopulation neural architecture and noise correlations. Both factors have a high potential to impinge upon the stochastic dynamics of these bumps, ultimately shaping behavioral response variance. In our study, we consider a neural field model with separate E /I populations and leverage asymptotic analysis to derive a nonlinear Langevin system describing E /I bump interactions. While the E bump attracts the I bump, the I bump stabilizes but can also repel the E bump, which can result in prolonged relaxation dynamics when both bumps are perturbed. Furthermore, the structure of noise correlations within and between subpopulations strongly shapes the variance in bump position. Surprisingly, higher interpopulation correlations reduce variance.

Intersubject variability and induced gamma in the visual cortex: DCM with empirical Bayes and neural fields

This article describes the first application of a generic (empirical) Bayesian analysis of between‐subject effects in the dynamic causal modeling (DCM) of electrophysiological (MEG) data. It shows that (i) non‐invasive (MEG) data can be used to characterize subject‐specific differences in cortical microcircuitry and (ii) presents a validation of DCM with neural fields that exploits intersubject variability in gamma oscillations. We find that intersubject variability in visually induced gamma responses reflects changes in the excitation‐inhibition balance in a canonical cortical circuit. Crucially, this variability can be explained by subject‐specific differences in intrinsic connections to and from inhibitory interneurons that form a pyramidal‐interneuron gamma network. Our approach uses Bayesian model reduction to evaluate the evidence for (large sets of) nested models—and optimize the corresponding connectivity estimates at the within and between‐subject level. We also consider Bayesian cross‐validation to obtain predictive estimates for gamma‐response phenotypes, using a leave‐one‐out procedure. Hum Brain Mapp 37:4597–4614, 2016. © The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Metastable dynamics in heterogeneous neural fields

We present numerical simulations of metastable states in heterogeneous neural fields that are connected along heteroclinic orbits. Such trajectories are possible representations of transient neural activity as observed, for example, in the electroencephalogram. Based on previous theoretical findings on learning algorithms for neural fields, we directly construct synaptic weight kernels from Lotka-Volterra neural population dynamics without supervised training approaches. We deliver a MATLAB neural field toolbox validated by two examples of one- and two-dimensional neural fields. We demonstrate trial-to-trial variability and distributed representations in our simulations which might therefore be regarded as a proof-of-concept for more advanced neural field models of metastable dynamics in neurophysiological data.

Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration

Perceptual multistability is a phenomenon in which alternate interpretations of a fixed stimulus are perceived intermittently. Although correlates between activity in specific cortical areas and perception have been found, the complex patterns of activity and the underlying mechanisms that gate multistable perception are little understood. Here, we present a neural field competition model in which competing states are represented in a continuous feature space. Bifurcation analysis is used to describe the different types of complex spatio-temporal dynamics produced by the model in terms of several parameters and for different inputs. The dynamics of the model was then compared to human perception investigated psychophysically during long presentations of an ambiguous, multistable motion pattern known as the barberpole illusion. In order to do this, the model is operated in a parameter range where known physiological response properties are reproduced whilst also working close to bifurcation. The model accounts for characteristic behaviour from the psychophysical experiments in terms of the type of switching observed and changes in the rate of switching with respect to contrast. In this way, the modelling study sheds light on the underlying mechanisms that drive perceptual switching in different contrast regimes. The general approach presented is applicable to a broad range of perceptual competition problems in which spatial interactions play a role.

The anesthetic propofol shifts the frequency of maximum spectral power in EEG during general anesthesia: analytical insights from a linear model

The work introduces a linear neural population model that allows to derive analytically the power spectrum subjected to the concentration of the anesthetic propofol. The analytical study of the power spectrum of the systems activity gives conditions on how the frequency of maximum power in experimental electroencephalographic (EEG) changes dependent on the propofol concentration. In this context, we explain the anesthetic-induced power increase in neural activity by an oscillatory instability and derive conditions under which the power peak shifts to larger frequencies as observed experimentally in EEG. Moreover the work predicts that the power increase only occurs while the frequency of maximum power increases. Numerically simulations of the systems activity complement the analytical results.

From invasion to extinction in heterogeneous neural fields

In this paper, we analyze the invasion and extinction of activity in heterogeneous neural fields. We first consider the effects of spatial heterogeneities on the propagation of an invasive activity front. In contrast to previous studies of front propagation in neural media, we assume that the front propagates into an unstable rather than a metastable zero-activity state. For sufficiently localized initial conditions, the asymptotic velocity of the resulting pulled front is given by the linear spreading velocity, which is determined by linearizing about the unstable state within the leading edge of the front. One of the characteristic features of these so-called pulled fronts is their sensitivity to perturbations inside the leading edge. This means that standard perturbation methods for studying the effects of spatial heterogeneities or external noise fluctuations break down. We show how to extend a partial differential equation method for analyzing pulled fronts in slowly modulated environments to the case of neural fields with slowly modulated synaptic weights. The basic idea is to rescale space and time so that the front becomes a sharp interface whose location can be determined by solving a corresponding local Hamilton-Jacobi equation. We use steepest descents to derive the Hamilton-Jacobi equation from the original nonlocal neural field equation. In the case of weak synaptic heterogenities, we then use perturbation theory to solve the corresponding Hamilton equations and thus determine the time-dependent wave speed. In the second part of the paper, we investigate how time-dependent heterogenities in the form of extrinsic multiplicative noise can induce rare noise-driven transitions to the zero-activity state, which now acts as an absorbing state signaling the extinction of all activity. In this case, the most probable path to extinction can be obtained by solving the classical equations of motion that dominate a path integral representation of the stochastic neural field in the weak noise limit. These equations take the form of nonlocal Hamilton equations in an infinite-dimensional phase space.

Short-Term Facilitation may Stabilize Parametric Working Memory Trace

Networks with continuous set of attractors are considered to be a paradigmatic model for parametric working memory (WM), but require fine tuning of connections and are thus structurally unstable. Here we analyzed the network with ring attractor, where connections are not perfectly tuned and the activity state therefore drifts in the absence of the stabilizing stimulus. We derive an analytical expression for the drift dynamics and conclude that the network cannot function as WM for a period of several seconds, a typical delay time in monkey memory experiments. We propose that short-term synaptic facilitation in recurrent connections significantly improves the robustness of the model by slowing down the drift of activity bump. Extending the calculation of the drift velocity to network with synaptic facilitation, we conclude that facilitation can slow down the drift by a large factor, rendering the network suitable as a model of WM.

Analysis of a hyperbolic geometric model for visual texture perception

We study the neural field equations introduced by Chossat and Faugeras to model the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, the structure tensor, intrinsically lives in a non-Euclidean, in effect hyperbolic, space. Its spatio-temporal behaviour is governed by nonlinear integro-differential equations defined on the Poincaré disc model of the two-dimensional hyperbolic space. Using methods from the theory of functional analysis we show the existence and uniqueness of a solution of these equations. In the case of stationary, that is, time independent, solutions we perform a stability analysis which yields important results on their behavior. We also present an original study, based on non-Euclidean, hyperbolic, analysis, of a spatially localised bump solution in a limiting case. We illustrate our theoretical results with numerical simulations.Mathematics Subject Classification: 30F45, 33C05, 34A12, 34D20, 34D23, 34G20, 37M05, 43A85, 44A35, 45G10, 51M10, 92B20, 92C20.

Integrating verbal and nonverbal communication in a dynamic neural field architecture for human-robot interaction

How do humans coordinate their intentions, goals and motor behaviors when performing joint action tasks? Recent experimental evidence suggests that resonance processes in the observer's motor system are crucially involved in our ability to understand actions of others’, to infer their goals and even to comprehend their action-related language. In this paper, we present a control architecture for human–robot collaboration that exploits this close perception-action linkage as a means to achieve more natural and efficient communication grounded in sensorimotor experiences. The architecture is formalized by a coupled system of dynamic neural fields representing a distributed network of neural populations that encode in their activation patterns goals, actions and shared task knowledge. We validate the verbal and nonverbal communication skills of the robot in a joint assembly task in which the human–robot team has to construct toy objects from their components. The experiments focus on the robot's capacity to anticipate the user's needs and to detect and communicate unexpected events that may occur during joint task execution.

Effects of the anesthetic agent propofol on neural populations

The neuronal mechanisms of general anesthesia are still poorly understood. Besides several characteristic features of anesthesia observed in experiments, a prominent effect is the bi-phasic change of power in the observed electroencephalogram (EEG), i.e. the initial increase and subsequent decrease of the EEG-power in several frequency bands while increasing the concentration of the anaesthetic agent. The present work aims to derive analytical conditions for this bi-phasic spectral behavior by the study of a neural population model. This model describes mathematically the effective membrane potential and involves excitatory and inhibitory synapses, excitatory and inhibitory cells, nonlocal spatial interactions and a finite axonal conduction speed. The work derives conditions for synaptic time constants based on experimental results and gives conditions on the resting state stability. Further the power spectrum of Local Field Potentials and EEG generated by the neural activity is derived analytically and allow for the detailed study of bi-spectral power changes. We find bi-phasic power changes both in monostable and bistable system regime, affirming the omnipresence of bi-spectral power changes in anesthesia. Further the work gives conditions for the strong increase of power in the δ-frequency band for large propofol concentrations as observed in experiments.