71 research outputs found
Conditions for wave trains in spiking neural networks
Spatiotemporal patterns such as traveling waves are frequently observed in
recordings of neural activity. The mechanisms underlying the generation of such
patterns are largely unknown. Previous studies have investigated the existence
and uniqueness of different types of waves or bumps of activity using
neural-field models, phenomenological coarse-grained descriptions of
neural-network dynamics. But it remains unclear how these insights can be
transferred to more biologically realistic networks of spiking neurons, where
individual neurons fire irregularly. Here, we employ mean-field theory to
reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with
distance-dependent connectivity to an effective neural-field model. In contrast
to existing phenomenological descriptions, the dynamics in this neural-field
model depends on the mean and the variance in the synaptic input, both
determining the amplitude and the temporal structure of the resulting effective
coupling kernel. For the neural-field model we employ liner stability analysis
to derive conditions for the existence of spatial and temporal oscillations and
wave trains, that is, temporally and spatially periodic traveling waves. We
first prove that wave trains cannot occur in a single homogeneous population of
neurons, irrespective of the form of distance dependence of the connection
probability. Compatible with the architecture of cortical neural networks, wave
trains emerge in two-population networks of excitatory and inhibitory neurons
as a combination of delay-induced temporal oscillations and spatial
oscillations due to distance-dependent connectivity profiles. Finally, we
demonstrate quantitative agreement between predictions of the analytically
tractable neural-field model and numerical simulations of both networks of
nonlinear rate-based units and networks of LIF neurons.Comment: 36 pages, 8 figures, 4 table
Bifurcation Analysis of Large Networks of Neurons
The human brain contains on the order of a hundred billion neurons, each with several
thousand synaptic connections. Computational neuroscience has successfully modeled
both the individual neurons as various types of oscillators, in addition to the synaptic coupling
between the neurons. However, employing the individual neuronal models as a large
coupled network on the scale of the human brain would require massive computational and
financial resources, and yet is the current undertaking of several research groups. Even if
one were to successfully model such a complicated system of coupled differential equations,
aside from brute force numerical simulations, little insight may be gained into how the
human brain solves problems or performs tasks.
Here, we introduce a tool that reduces large networks of coupled neurons to a much
smaller set of differential equations that governs key statistics for the network as a whole,
as opposed to tracking the individual dynamics of neurons and their connections. This
approach is typically referred to as a mean-field system. As the mean-field system is derived
from the original network of neurons, it is predictive for the behavior of the network as
a whole and the parameters or distributions of parameters that appear in the mean-field
system are identical to those of the original network. As such, bifurcation analysis is
predictive for the behavior of the original network and predicts where in the parameter
space the network transitions from one behavior to another.
Additionally, here we show how networks of neurons can be constructed with a mean-field
or macroscopic behavior that is prescribed. This occurs through an analytic extension
of the Neural Engineering Framework (NEF). This can be thought of as an inverse mean-field
approach, where the networks are constructed to obey prescribed dynamics as opposed
to deriving the macroscopic dynamics from an underlying network. Thus, the work done
here analyzes neuronal networks through both top-down and bottom-up approaches
How Structure Determines Correlations in Neuronal Networks
Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
Classes de dynamiques neuronales et correlations structurées par l'experience dans le cortex visuel.
Neuronal activity is often considered in cognitive neuroscience by the evoked response but most the energy used by the brain is devoted to the sustaining of ongoing dynamics in cortical networks. A combination of classification algorithms (K means, Hierarchical tree, SOM) is used on intracellular recordings of the primary visual cortex of the cat to define classes of neuronal dynamics and to compare it with the activity evoked by a visual stimulus. Those dynamics can be studied with simplified models (FitzHugh Nagumo, hybrid dynamical systems, Wilson Cowan) for which an analysis is presented. Finally, with simulations of networks composed of columns of spiking neurons, we study the ongoing dynamics in a model of the primary visual cortex and their effect on the response evoked by a stimulus. After a learning period during which visual stimuli are presented, waves of depolarization propagate through the network. The study of correlations in this network shows that the ongoing dynamics reflect the functional properties acquired during the learning period.L'activité neuronale est souvent considérée en neuroscience cognitive par la réponse évoquée mais l'essentiel de l'énergie consommée par le cerveau permet d'entretenir les dynamiques spontanées des réseaux corticaux. L'utilisation combinée d'algorithmes de classification (K means, arbre hirarchique, SOM) sur des enregistrements intracellulaires du cortex visuel primaire du chat nous permet de définir des classes de dynamiques neuronales et de les comparer l'activité évoquée par un stimulus visuel. Ces dynamiques peuvent être étudiées sur des systèmes simplifiés (FitzHugh-Nagumo, systèmes dynamiques hybrides, Wilson-Cowan) dont nous présentons l'analyse. Enfin, par des simulations de réseaux composés de colonnes de neurones, un modèle du cortex visuel primaire nous permet d'étudier les dynamiques spontanées et leur effet sur la réponse à un stimulus. Après une période d'apprentissage pendant laquelle des stimuli visuels sont presentés, des vagues de dépolarisation se propagent dans le réseau. L'étude des correlations dans ce réseau montre que les dynamiques spontanées reflètent les propriétés fonctionnelles acquises au cours de l'apprentissage
Spatial and temporal correlations in human cortex are inherently linked and predicted by functional hierarchy, vigilance state as well as antiepileptic drug load
The ability of neural circuits to integrate information over time and across different cortical areas is believed an essential ingredient for information processing in the brain. Temporal and spatial correlations in cortex dynamics have independently been shown to capture these integration properties in task-dependent ways. A fundamental question remains if temporal and spatial integration properties are linked and what internal and external factors shape these correlations. Previous research on spatio-temporal correlations has been limited in duration and coverage, thus providing only an incomplete picture of their interdependence and variability. Here, we use long-term invasive EEG data to comprehensively map temporal and spatial correlations according to cortical topography, vigilance state and drug dependence over extended periods of time. We show that temporal and spatial correlations in cortical networks are intimately linked, decline under antiepileptic drug action, and break down during slow-wave sleep. Further, we report temporal correlations in human electrophysiology signals to increase with the functional hierarchy in cortex. Systematic investigation of a neural network model suggests that these dynamical features may arise when dynamics are poised near a critical point. Our results provide mechanistic and functional links between specific measurable changes in the network dynamics relevant for characterizing the brain's changing information processing capabilities.Author summary
A growing body of research suggests spatial and temporal correlations, which capture the propagation of information in space and time, to be useful characterizations of information processing in the human brain. The criticality hypothesis, the hypothesis that networks in the brain reside in the vicinity of a phase transition, posits that spatial and temporal correlations are intimately linked and maximized near the critical point. Previous research has predominantly focused on spatial and temporal correlations independently and was often restricted in duration, thus limiting our knowledge whether spatial and temporal correlations indeed co-vary and what other factors influence these information integration properties in general. Here, we use long-term invasive EEG data to comprehensively map temporal and spatial correlations according to cortical topography, vigilance state, and drug dependence over extended periods of time. We show that temporal and spatial correlations in cortical networks are strongly linked, decline under antiepileptic drug action, and completely break down during slow-wave sleep. We provide direct electrophysical evidence that temporal correlations follow a gradient which aligns with the functional hierarchy. Systematic investigation alongside a companion neural network model suggests that these findings may arise due to dynamics being poised near a critical point. The ability of neural circuits to integrate information over time and across different cortical areas is believed an essential ingredient for information processing in the brain. Temporal and spatial correlations in cortex dynamics have independently been shown to capture these integration properties in task-dependent ways. A fundamental question remains if temporal and spatial integration properties are linked and what internal and external factors shape these correlations. Previous research on spatio-temporal correlations has been limited in duration and coverage, thus providing only an incomplete picture of their interdependence and variability. Here, we use long-term invasive EEG data to comprehensively map temporal and spatial correlations according to cortical topography, vigilance state and drug dependence over extended periods of time. We show that temporal and spatial correlations in cortical networks are intimately linked, decline under antiepileptic drug action, and break down during slow-wave sleep. Further, we report temporal correlations in human electrophysiology signals to increase with the functional hierarchy in cortex. Systematic investigation of a neural network model suggests that these dynamical features may arise when dynamics are poised near a critical point. Our results provide mechanistic and functional links between specific measurable changes in the network dynamics relevant for characterizing the brain's changing information processing capabilities
Whole Brain Network Dynamics of Epileptic Seizures at Single Cell Resolution
Epileptic seizures are characterised by abnormal brain dynamics at multiple
scales, engaging single neurons, neuronal ensembles and coarse brain regions.
Key to understanding the cause of such emergent population dynamics, is
capturing the collective behaviour of neuronal activity at multiple brain
scales. In this thesis I make use of the larval zebrafish to capture single
cell neuronal activity across the whole brain during epileptic seizures.
Firstly, I make use of statistical physics methods to quantify the collective
behaviour of single neuron dynamics during epileptic seizures. Here, I
demonstrate a population mechanism through which single neuron dynamics
organise into seizures: brain dynamics deviate from a phase transition.
Secondly, I make use of single neuron network models to identify the synaptic
mechanisms that actually cause this shift to occur. Here, I show that the
density of neuronal connections in the network is key for driving generalised
seizure dynamics. Interestingly, such changes also disrupt network response
properties and flexible dynamics in brain networks, thus linking microscale
neuronal changes with emergent brain dysfunction during seizures. Thirdly, I
make use of non-linear causal inference methods to study the nature of the
underlying neuronal interactions that enable seizures to occur. Here I show
that seizures are driven by high synchrony but also by highly non-linear
interactions between neurons. Interestingly, these non-linear signatures are
filtered out at the macroscale, and therefore may represent a neuronal
signature that could be used for microscale interventional strategies. This
thesis demonstrates the utility of studying multi-scale dynamics in the larval
zebrafish, to link neuronal activity at the microscale with emergent properties
during seizures
Dynamic Communications Between GABAA Switch, Local Connectivity, and Synapses During Cortical Development: A Computational Study
Several factors regulate cortical development, such as changes in local connectivity and the influences of dynamical synapses. In this study, we simulated various factors affecting the regulation of neural network activity during cortical development. Previous studies have shown that during early cortical development, the reversal potential of GABAA shifts from depolarizing to hyperpolarizing. Here we provide the first integrative computational model to simulate the combined effects of these factors in a unified framework (building on our prior work: Khalil et al., 2017a,b). In the current study, we extend our model to monitor firing activity in response to the excitatory action of GABAA. Precisely, we created a Spiking Neural Network model that included certain biophysical parameters for lateral connectivity (distance between adjacent neurons) and nearby local connectivity (complex connections involving those between neuronal groups). We simulated different network scenarios (for immature and mature conditions) based on these biophysical parameters. Then, we implemented two forms of Short-term synaptic plasticity (depression and facilitation). Each form has two distinct kinds according to its synaptic time constant value. Finally, in both sets of networks, we compared firing rate activity responses before and after simulating dynamical synapses. Based on simulation results, we found that the modulation effect of dynamical synapses for evaluating and shaping the firing activity of the neural network is strongly dependent on the physiological state of GABAA. Moreover, the STP mechanism acts differently in every network scenario, mirroring the crucial modulating roles of these critical parameters during cortical development. Clinical implications for pathological alterations of GABAergic signaling in neurological and psychiatric disorders are discussed
VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output
Neuronal network models and corresponding computer simulations are invaluable
tools to aid the interpretation of the relationship between neuron properties,
connectivity and measured activity in cortical tissue. Spatiotemporal patterns
of activity propagating across the cortical surface as observed experimentally
can for example be described by neuronal network models with layered geometry
and distance-dependent connectivity. The interpretation of the resulting stream
of multi-modal and multi-dimensional simulation data calls for integrating
interactive visualization steps into existing simulation-analysis workflows.
Here, we present a set of interactive visualization concepts called views for
the visual analysis of activity data in topological network models, and a
corresponding reference implementation VIOLA (VIsualization Of Layer Activity).
The software is a lightweight, open-source, web-based and platform-independent
application combining and adapting modern interactive visualization paradigms,
such as coordinated multiple views, for massively parallel neurophysiological
data. For a use-case demonstration we consider spiking activity data of a
two-population, layered point-neuron network model subject to a spatially
confined excitation originating from an external population. With the multiple
coordinated views, an explorative and qualitative assessment of the
spatiotemporal features of neuronal activity can be performed upfront of a
detailed quantitative data analysis of specific aspects of the data.
Furthermore, ongoing efforts including the European Human Brain Project aim at
providing online user portals for integrated model development, simulation,
analysis and provenance tracking, wherein interactive visual analysis tools are
one component. Browser-compatible, web-technology based solutions are therefore
required. Within this scope, with VIOLA we provide a first prototype.Comment: 38 pages, 10 figures, 3 table
- …