Neural population modes capture biologically realistic large scale network dynamics

A Non-spiking Neuron Model With Dynamic Leak to Avoid Instability in Recurrent Networks

Recurrent circuitry components are distributed widely within the brain, including both excitatory and inhibitory synaptic connections. Recurrent neuronal networks have potential stability problems, perhaps a predisposition to epilepsy. More generally, instability risks making internal representations of information unreliable. To assess the inherent stability properties of such recurrent networks, we tested a linear summation, non-spiking neuron model with and without a “dynamic leak”, corresponding to the low-pass filtering of synaptic input current by the RC circuit of the biological membrane. We first show that the output of this neuron model, in either of its two forms, follows its input at a higher fidelity than a wide range of spiking neuron models across a range of input frequencies. Then we constructed fully connected recurrent networks with equal numbers of excitatory and inhibitory neurons and randomly distributed weights across all synapses. When the networks were driven by pseudorandom sensory inputs with varying frequency, the recurrent network activity tended to induce high frequency self-amplifying components, sometimes evident as distinct transients, which were not present in the input data. The addition of a dynamic leak based on known membrane properties consistently removed such spurious high frequency noise across all networks. Furthermore, we found that the neuron model with dynamic leak imparts a network stability that seamlessly scales with the size of the network, conduction delays, the input density of the sensory signal and a wide range of synaptic weight distributions. Our findings suggest that neuronal dynamic leak serves the beneficial function of protecting recurrent neuronal circuitry from the self-induction of spurious high frequency signals, thereby permitting the brain to utilize this architectural circuitry component regardless of network size or recurrency.

The pacemaker role of thalamic reticular nucleus in controlling spike-wave discharges and spindles

Absence epilepsy, characterized by 2-4 Hz spike-wave discharges (SWDs), can be caused by pathological interactions within the thalamocortical system. Cortical spindling oscillations are also demonstrated to involve the oscillatory thalamocortical rhythms generated by the synaptic circuitry of the thalamus and cortex. This implies that SWDs and spindling oscillations can share the common thalamocortical mechanism. Additionally, the thalamic reticular nucleus (RE) is hypothesized to regulate the onsets and propagations of both the epileptic SWDs and sleep spindles. Based on the proposed single-compartment thalamocortical neural field model, we firstly investigate the stimulation effect of RE on the initiations, terminations, and transitions of SWDs. It is shown that the activations and deactivations of RE triggered by single-pulse stimuli can drive the cortical subsystem to behave as the experimentally observed onsets and self-abatements of SWDs, as well as the transitions from 2-spike and wave discharges (2-SWDs) to SWDs. In particular, with increasing inhibition from RE to the specific relay nucleus (TC), rich transition behaviors in cortex can be obtained through the upstream projection path, RE→TC→Cortex. Although some of the complex dynamical patterns can be expected from the earlier single compartment thalamocortical model, the effect of brain network topology on the emergence of SWDs and spindles, as well as the transitions between them, has not been fully investigated. We thereby develop a spatially extended 3-compartment coupled network model with open-/closed-end connective configurations, to investigate the spatiotemporal effect of RE on the SWDs and spindles. Results show that the degrees of activations of RE₁ can induce the rich spatiotemporal evolution properties including the propagations from SWDs to spindles within different compartments and the transitions between them, through the RE₁→TC₁→Cortex₁ and Cortex₁→Cortex₂→Cortex₃ projecting paths, respectively. Overall, those results imply that RE possesses the pacemaker function in controlling SWDs and spindling oscillations, which computationally provide causal support for the involvement of RE in absence seizures and sleep spindles.

Functional Mechanisms of Recovery after Chronic Stroke: Modeling with the Virtual Brain

We have seen important strides in our understanding of mechanisms underlying stroke recovery, yet effective translational links between basic and applied sciences, as well as from big data to individualized therapies, are needed to truly develop a cure for stroke. We present such an approach using The Virtual Brain (TVB), a neuroinformatics platform that uses empirical neuroimaging data to create dynamic models of an individual’s human brain; specifically, we simulate fMRI signals by modeling parameters associated with brain dynamics after stroke.

In 20 individuals with stroke and 11 controls, we obtained rest fMRI, T1w, and diffusion tensor imaging (DTI) data. Motor performance was assessed pre-therapy, post-therapy, and 6–12 months post-therapy. Based on individual structural connectomes derived from DTI, the following steps were performed in the TVB platform: (1) optimization of local and global parameters (conduction velocity, global coupling); (2) simulation of BOLD signal using optimized parameter values; (3) validation of simulated time series by comparing frequency, amplitude, and phase of the simulated signal with empirical time series; and (4) multivariate linear regression of model parameters with clinical phenotype. Compared with controls, individuals with stroke demonstrated a consistent reduction in conduction velocity, increased local dynamics, and reduced local inhibitory coupling. A negative relationship between local excitation and motor recovery, and a positive correlation between local dynamics and motor recovery were seen.

TVB reveals a disrupted post-stroke system favoring excitation-over-inhibition and local-over-global dynamics, consistent with existing mammal literature on stroke mechanisms. Our results point to the potential of TVB to determine individualized biomarkers of stroke recovery.

Network-scale effect on synchronizability of fully coupled network with connection delay

Network-scale effect on synchronizability of fully coupled network with connection delay is investigated in this paper. The master stability function, which governs the stability of synchronization manifold, is first obtained by separating the synchronization manifold direction from other transverse directions. Then, by introducing a new time variable in the master stability function, it is shown the effect of connection delay can be weakened with the increase of network scale, and thus, in contrast to the situation without connection delay, large network scale is more positive to the synchronizability of fully coupled network with connection delay. Those findings are confirmed by the studies on two specific networks with nodes of typical nonlinear dynamical systems.

Multivariate dynamical systems-based estimation of causal brain interactions in fMRI: Group-level validation using benchmark data, neurophysiological models and human connectome project data

BACKGROUND

Causal estimation methods are increasingly being used to investigate functional brain networks in fMRI, but there are continuing concerns about the validity of these methods.

NEW METHOD

Multivariate dynamical systems (MDS) is a state-space method for estimating dynamic causal interactions in fMRI data. Here we validate MDS using benchmark simulations as well as simulations from a more realistic stochastic neurophysiological model. Finally, we applied MDS to investigate dynamic casual interactions in a fronto-cingulate-parietal control network using human connectome project (HCP) data acquired during performance of a working memory task. Crucially, since the ground truth in experimental data is unknown, we conducted novel stability analysis to determine robust causal interactions within this network.

RESULTS

MDS accurately recovered dynamic causal interactions with an area under receiver operating characteristic (AUC) above 0.7 for benchmark datasets and AUC above 0.9 for datasets generated using the neurophysiological model. In experimental fMRI data, bootstrap procedures revealed a stable pattern of causal influences from the anterior insula to other nodes of the fronto-cingulate-parietal network.

COMPARISON WITH EXISTING METHODS

MDS is effective in estimating dynamic causal interactions in both the benchmark and neurophysiological model based datasets in terms of AUC, sensitivity and false positive rates.

CONCLUSIONS

Our findings demonstrate that MDS can accurately estimate causal interactions in fMRI data. Neurophysiological models and stability analysis provide a general framework for validating computational methods designed to estimate causal interactions in fMRI. The right anterior insula functions as a causal hub during working memory.

Multistability in Large Scale Models of Brain Activity

Noise driven exploration of a brain network’s dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network’s capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain’s dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system’s attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i) a uniform activation threshold or (ii) a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the “resting state” condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.

Recent developments in non-invasive brain imaging allow reconstructing axonal tracts in the human brain and building realistic network models of the human brain. These models resemble brain systems in their network character and allow deciphering how different regions share signals and process information. Inspired by the metastable dynamics of the spin glass model in statistical physics, we systematically explore the brain network’s capacity to process information and investigate novel avenues how to enhance it. In particular, we study how the brain activates and switches between different functional networks across time. Such non-stationary behavior has been observed in human brain imaging data and hypothesized to be linked to information processsing. To shed light on the conditions under which large-scale brain network models exhibit such dynamics, we characterize the principal network patterns and confront them with modular structures observed both in graph theoretical analysis and resting-state functional Magnetic Resonance Imaging (rs-fMRI).

On the origins of the 'global signal' determined by functional magnetic resonance imaging in the resting state

OBJECTIVE

Functional magnetic resonance imaging blood oxygen level dependent (BOLD) determinations of correlations between 'resting-state' neuronal activity in different regions of cortex have generated much interest. Determination of these correlations requires regressing out signals that are correlated in all parts of the cortex and are taken to be artefactual, such as those due to movement, respiration and cardiovascular activity. However when these are removed there still remains a 'global signal' (GS), which is taken to be of unknown physiological origin, and is regressed out by some researchers but not by others.

APPROACH

We have investigated the origin of this GS using cortical models consisting of coupled networks of modules representing regions of interest.

MAIN RESULTS

We show that the GS has an amplitude that is linearly related to the average correlation between the modules/voxels in the network over a large range of such correlations. The GS arises as a consequence of feedback between the modules/voxels leading to correlations in their BOLD signals. Given the relationship between the GS and the average correlations it might be anticipated that regressing out the GS during preprocessing will significantly modify the correlations subsequently determined. This is shown to be the case when comparing the connections of individual modules with that predicted by the correlations.

SIGNIFICANCE

The present model shows that such correlations can arise as a consequence of the intermodular feedback connectivity without recourse to imposing a GS independent of the connectivity. Our model indicates that the GS reflects the extent of feedback pathways provided by the intermodular/inter-regional connections and hence the average correlation between modules or regions of cortex. However the model has not been used to elucidate the possible contributions of a GS independent of the connectivity, which might indeed contribute to the GS of the cortex.

An automated pipeline for constructing personalized virtual brains from multimodal neuroimaging data

Large amounts of multimodal neuroimaging data are acquired every year worldwide. In order to extract high-dimensional information for computational neuroscience applications standardized data fusion and efficient reduction into integrative data structures are required. Such self-consistent multimodal data sets can be used for computational brain modeling to constrain models with individual measurable features of the brain, such as done with The Virtual Brain (TVB). TVB is a simulation platform that uses empirical structural and functional data to build full brain models of individual humans. For convenient model construction, we developed a processing pipeline for structural, functional and diffusion-weighted magnetic resonance imaging (MRI) and optionally electroencephalography (EEG) data. The pipeline combines several state-of-the-art neuroinformatics tools to generate subject-specific cortical and subcortical parcellations, surface-tessellations, structural and functional connectomes, lead field matrices, electrical source activity estimates and region-wise aggregated blood oxygen level dependent (BOLD) functional MRI (fMRI) time-series. The output files of the pipeline can be directly uploaded to TVB to create and simulate individualized large-scale network models that incorporate intra- and intercortical interaction on the basis of cortical surface triangulations and white matter tractograpy. We detail the pitfalls of the individual processing streams and discuss ways of validation. With the pipeline we also introduce novel ways of estimating the transmission strengths of fiber tracts in whole-brain structural connectivity (SC) networks and compare the outcomes of different tractography or parcellation approaches. We tested the functionality of the pipeline on 50 multimodal data sets. In order to quantify the robustness of the connectome extraction part of the pipeline we computed several metrics that quantify its rescan reliability and compared them to other tractography approaches. Together with the pipeline we present several principles to guide future efforts to standardize brain model construction. The code of the pipeline and the fully processed data sets are made available to the public via The Virtual Brain website (thevirtualbrain.org) and via github (https://github.com/BrainModes/TVB-empirical-data-pipeline). Furthermore, the pipeline can be directly used with High Performance Computing (HPC) resources on the Neuroscience Gateway Portal (http://www.nsgportal.org) through a convenient web-interface.

Cortical network models of impulse firing in the resting and active states predict cortical energetics

Measurements of the cortical metabolic rate of glucose oxidation [CMR(glc(ox))] have provided a number of interesting and, in some cases, surprising observations. One is the decline in CMR(glc(ox)) during anesthesia and non-rapid eye movement (NREM) sleep, and another, the inverse relationship between the resting-state CMR(glc(ox)) and the transient following input from the thalamus. The recent establishment of a quantitative relationship between synaptic and action potential activity on the one hand and CMR(glc(ox)) on the other allows neural network models of such activity to probe for possible mechanistic explanations of these phenomena. We have carried out such investigations using cortical models consisting of networks of modules with excitatory and inhibitory neurons, each receiving excitatory inputs from outside the network in addition to intermodular connections. Modules may be taken as regions of cortical interest, the inputs from outside the network as arising from the thalamus, and the intermodular connections as long associational fibers. The model shows that the impulse frequency of different modules can differ from each other by less than 10%, consistent with the relatively uniform CMR(glc(ox)) observed across different regions of cortex. The model also shows that, if correlations of the average impulse rate between different modules decreases, there is a concomitant decrease in the average impulse rate in the modules, consistent with the observed drop in CMR(glc(ox)) in NREM sleep and under anesthesia. The model also explains why a transient thalamic input to sensory cortex gives rise to responses with amplitudes inversely dependent on the resting-state frequency, and therefore resting-state CMR(glc(ox)).

Large-scale modeling of epileptic seizures: scaling properties of two parallel neuronal network simulation algorithms

Our limited understanding of the relationship between the behavior of individual neurons and large neuronal networks is an important limitation in current epilepsy research and may be one of the main causes of our inadequate ability to treat it. Addressing this problem directly via experiments is impossibly complex; thus, we have been developing and studying medium-large-scale simulations of detailed neuronal networks to guide us. Flexibility in the connection schemas and a complete description of the cortical tissue seem necessary for this purpose. In this paper we examine some of the basic issues encountered in these multiscale simulations. We have determined the detailed behavior of two such simulators on parallel computer systems. The observed memory and computation-time scaling behavior for a distributed memory implementation were very good over the range studied, both in terms of network sizes (2,000 to 400,000 neurons) and processor pool sizes (1 to 256 processors). Our simulations required between a few megabytes and about 150 gigabytes of RAM and lasted between a few minutes and about a week, well within the capability of most multinode clusters. Therefore, simulations of epileptic seizures on networks with millions of cells should be feasible on current supercomputers.

Cross-frequency coupling in real and virtual brain networks

Information processing in the brain is thought to rely on the convergence and divergence of oscillatory behaviors of widely distributed brain areas. This information flow is captured in its simplest form via the concepts of synchronization and desynchronization and related metrics. More complex forms of information flow are transient synchronizations and multi-frequency behaviors with metrics related to cross-frequency coupling (CFC). It is supposed that CFC plays a crucial role in the organization of large-scale networks and functional integration across large distances. In this study, we describe different CFC measures and test their applicability in simulated and real electroencephalographic (EEG) data obtained during resting state. For these purposes, we derive generic oscillator equations from full brain network models. We systematically model and simulate the various scenarios of CFC under the influence of noise to obtain biologically realistic oscillator dynamics. We find that (i) specific CFC-measures detect correctly in most cases the nature of CFC under noise conditions, (ii) bispectrum (BIS) and bicoherence (BIC) correctly detect the CFCs in simulated data, (iii) empirical resting state EEG show a prominent delta-alpha CFC as identified by specific CFC measures and the more classic BIS and BIC. This coupling was mostly asymmetric (directed) and generally higher in the eyes closed (EC) than in the eyes open (EO) condition. In conjunction, these two sets of measures provide a powerful toolbox to reveal the nature of couplings from experimental data and as such allow inference on the brain state dependent information processing. Methodological advantages of using CFC measures and theoretical significance of delta and alpha interactions during resting and other brain states are discussed.

The Virtual Brain: a simulator of primate brain network dynamics

We present The Virtual Brain (TVB), a neuroinformatics platform for full brain network simulations using biologically realistic connectivity. This simulation environment enables the model-based inference of neurophysiological mechanisms across different brain scales that underlie the generation of macroscopic neuroimaging signals including functional MRI (fMRI), EEG and MEG. Researchers from different backgrounds can benefit from an integrative software platform including a supporting framework for data management (generation, organization, storage, integration and sharing) and a simulation core written in Python. TVB allows the reproduction and evaluation of personalized configurations of the brain by using individual subject data. This personalization facilitates an exploration of the consequences of pathological changes in the system, permitting to investigate potential ways to counteract such unfavorable processes. The architecture of TVB supports interaction with MATLAB packages, for example, the well known Brain Connectivity Toolbox. TVB can be used in a client-server configuration, such that it can be remotely accessed through the Internet thanks to its web-based HTML5, JS, and WebGL graphical user interface. TVB is also accessible as a standalone cross-platform Python library and application, and users can interact with the scientific core through the scripting interface IDLE, enabling easy modeling, development and debugging of the scientific kernel. This second interface makes TVB extensible by combining it with other libraries and modules developed by the Python scientific community. In this article, we describe the theoretical background and foundations that led to the development of TVB, the architecture and features of its major software components as well as potential neuroscience applications.

Inferring network properties of cortical neurons with synaptic coupling and parameter dispersion

Computational models at different space-time scales allow us to understand the fundamental mechanisms that govern neural processes and relate uniquely these processes to neuroscience data. In this work, we propose a novel neurocomputational unit (a mesoscopic model which tell us about the interaction between local cortical nodes in a large scale neural mass model) of bursters that qualitatively captures the complex dynamics exhibited by a full network of parabolic bursting neurons. We observe that the temporal dynamics and fluctuation of mean synaptic action term exhibits a high degree of correlation with the spike/burst activity of our population. With heterogeneity in the applied drive and mean synaptic coupling derived from fast excitatory synapse approximations we observe long term behavior in our population dynamics such as partial oscillations, incoherence, and synchrony. In order to understand the origin of multistability at the population level as a function of mean synaptic coupling and heterogeneity in the firing rate threshold we employ a simple generative model for parabolic bursting recently proposed by Ghosh et al. (2009). Further, we use here a mean coupling formulated for fast spiking neurons for our analysis of generic model. Stability analysis of this mean field network allow us to identify all the relevant network states found in the detailed biophysical model. We derive here analytically several boundary solutions, a result which holds for any number of spikes per burst. These findings illustrate the role of oscillations occurring at slow time scales (bursts) on the global behavior of the network.

Synchrony of two brain regions predicts the blood oxygen level dependent activity of a third

Spontaneously emerging coherent fluctuations have been long observed in electrophysiological and functional magnetic resonance imaging studies. These dynamics have been identified in multiple brain areas in the 1-100 and < 0.1 Hz frequency ranges spanning neurophysiological oscillations and blood oxygen level dependent (BOLD) signals, respectively. In this article, we demonstrate that transient neural synchronization between two sites may lead to the emergence of ultra-slow frequency fluctuations in the BOLD signal at another (third) site. Starting with a network model comprised of three neural oscillators, we illustrate the critical role of time delay and coupling strength in generating these slow coherent fluctuations as a function of intermittently occurring neural coherence. When extending the network toward biologically realistic primate connectivity, we find that the BOLD activation patterns arise from neurophysiological coherence, especially among medial cortical areas. This finding demonstrates a network-level mechanism whereby the BOLD activity at a given region is critically influenced by the neuroelectric synchronization patterns of other regions in the network.

The virtual brain integrates computational modeling and multimodal neuroimaging

Brain function is thought to emerge from the interactions among neuronal populations. Apart from traditional efforts to reproduce brain dynamics from the micro- to macroscopic scales, complementary approaches develop phenomenological models of lower complexity. Such macroscopic models typically generate only a few selected-ideally functionally relevant-aspects of the brain dynamics. Importantly, they often allow an understanding of the underlying mechanisms beyond computational reproduction. Adding detail to these models will widen their ability to reproduce a broader range of dynamic features of the brain. For instance, such models allow for the exploration of consequences of focal and distributed pathological changes in the system, enabling us to identify and develop approaches to counteract those unfavorable processes. Toward this end, The Virtual Brain (TVB) ( www.thevirtualbrain.org ), a neuroinformatics platform with a brain simulator that incorporates a range of neuronal models and dynamics at its core, has been developed. This integrated framework allows the model-based simulation, analysis, and inference of neurophysiological mechanisms over several brain scales that underlie the generation of macroscopic neuroimaging signals. In this article, we describe how TVB works, and we present the first proof of concept.

Complementarity of spike- and rate-based dynamics of neural systems

Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other.

Ongoing cortical activity at rest: criticality, multistability, and ghost attractors

The ongoing activity of the brain at rest, i.e., under no stimulation and in absence of any task, is astonishingly highly structured into spatiotemporal patterns. These spatiotemporal patterns, called resting state networks, display low-frequency characteristics (<0.1 Hz) observed typically in the BOLD-fMRI signal of human subjects. We aim here to understand the origins of resting state activity through modeling via a global spiking attractor network of the brain. This approach offers a realistic mechanistic model at the level of each single brain area based on spiking neurons and realistic AMPA, NMDA, and GABA synapses. Integrating the biologically realistic diffusion tensor imaging/diffusion spectrum imaging-based neuroanatomical connectivity into the brain model, the resultant emerging resting state functional connectivity of the brain network fits quantitatively best the experimentally observed functional connectivity in humans when the brain network operates at the edge of instability. Under these conditions, the slow fluctuating (<0.1 Hz) resting state networks emerge as structured noise fluctuations around a stable low firing activity equilibrium state in the presence of latent "ghost" multistable attractors. The multistable attractor landscape defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity.