Systematic approximations of neural fields through networks of neural masses in the virtual brain

Altered synaptic plasticity at hippocampal CA1-CA3 synapses in Alzheimer's disease: integration of amyloid precursor protein intracellular domain and amyloid beta effects into computational models

Alzheimer's disease (AD) is a progressive memory loss and cognitive dysfunction brain disorder brought on by the dysfunctional amyloid precursor protein (APP) processing and clearance of APP peptides. Increased APP levels lead to the production of AD-related peptides including the amyloid APP intracellular domain (AICD) and amyloid beta (Aβ), and consequently modify the intrinsic excitability of the hippocampal CA1 pyramidal neurons, synaptic protein activity, and impair synaptic plasticity at hippocampal CA1-CA3 synapses. The goal of the present study is to build computational models that incorporate the effect of AD-related peptides on CA1 pyramidal neuron and hippocampal synaptic plasticity under the AD conditions and investigate the potential pharmacological treatments that could normalize hippocampal synaptic plasticity and learning in AD. We employ a phenomenological N-methyl-D-aspartate (NMDA) receptor-based voltage-dependent synaptic plasticity model that includes the separate receptor contributions on long-term potentiation (LTP) and long-term depression (LTD) and embed it into the a detailed compartmental model of CA1 pyramidal neuron. Modeling results show that partial blockade of Glu2NB-NMDAR-gated channel restores intrinsic excitability of a CA1 pyramidal neuron and rescues LTP in AICD and Aβ conditions. The model provides insight into the complex interactions in AD pathophysiology and suggests the conditions under which the synchronous activation of a cluster of synaptic inputs targeting the dendritic tree of CA1 pyramidal neuron leads to restored synaptic plasticity.

Bayesian inference of a spectral graph model for brain oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which cannot be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Geometric constraints on human brain function

The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. The classical and dominant paradigm in neuroscience is that neuronal dynamics are driven by interactions between discrete, functionally specialized cell populations connected by a complex array of axonal fibres1-3. However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity4-6, suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity7,8. Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. Specifically, we show that cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain's geometry (that is, its shape) rather than from modes of complex interregional connectivity, as classically assumed. We then use these geometric modes to show that task-evoked activations across over 10,000 brain maps are not confined to focal areas, as widely believed, but instead excite brain-wide modes with wavelengths spanning over 60 mm. Finally, we confirm predictions that the close link between geometry and function is explained by a dominant role for wave-like activity, showing that wave dynamics can reproduce numerous canonical spatiotemporal properties of spontaneous and evoked recordings. Our findings challenge prevailing views and identify a previously underappreciated role of geometry in shaping function, as predicted by a unifying and physically principled model of brain-wide dynamics.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass model, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen-Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

Bayesian Inference of a Spectral Graph Model for Brain Oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which can not be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

A comprehensive neural simulation of slow-wave sleep and highly responsive wakefulness dynamics

Hallmarks of neural dynamics during healthy human brain states span spatial scales from neuromodulators acting on microscopic ion channels to macroscopic changes in communication between brain regions. Developing a scale-integrated understanding of neural dynamics has therefore remained challenging. Here, we perform the integration across scales using mean-field modeling of Adaptive Exponential (AdEx) neurons, explicitly incorporating intrinsic properties of excitatory and inhibitory neurons. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. We report that when AdEx mean-field neural populations are connected via structural tracts defined by the human connectome, macroscopic dynamics resembling human brain activity emerge. Importantly, the model can qualitatively and quantitatively account for properties of empirically observed spontaneous and stimulus-evoked dynamics in space, time, phase, and frequency domains. Large-scale properties of cortical dynamics are shown to emerge from both microscopic-scale adaptation that control transitions between wake-like to sleep-like activity, and the organization of the human structural connectome; together, they shape the spatial extent of synchrony and phase coherence across brain regions consistent with the propagation of sleep-like spontaneous traveling waves at intermediate scales. Remarkably, the model also reproduces brain-wide, enhanced responsiveness and capacity to encode information particularly during wake-like states, as quantified using the perturbational complexity index. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. This approach not only provides a scale-integrated understanding of brain states and their underlying mechanisms, but also open access tools to investigate brain responsiveness, toward producing a more unified, formal understanding of experimental data from conscious and unconscious states, as well as their associated pathologies.

The quest for multiscale brain modeling

Addressing the multiscale organization of the brain, which is fundamental to the dynamic repertoire of the organ, remains challenging. In principle, it should be possible to model neurons and synapses in detail and then connect them into large neuronal assemblies to explain the relationship between microscopic phenomena, large-scale brain functions, and behavior. It is more difficult to infer neuronal functions from ensemble measurements such as those currently obtained with brain activity recordings. In this article we consider theories and strategies for combining bottom-up models, generated from principles of neuronal biophysics, with top-down models based on ensemble representations of network activity and on functional principles. These integrative approaches are hoped to provide effective multiscale simulations in virtual brains and neurorobots, and pave the way to future applications in medicine and information technologies.

Predicting Functional Connectivity From Observed and Latent Structural Connectivity via Eigenvalue Mapping

Understanding how complex dynamic activity propagates over a static structural network is an overarching question in the field of neuroscience. Previous work has demonstrated that linear graph-theoretic models perform as well as non-linear neural simulations in predicting functional connectivity with the added benefits of low dimensionality and a closed-form solution which make them far less computationally expensive. Here we show a simple model relating the eigenvalues of the structural connectivity and functional networks using the Gamma function, producing a reliable prediction of functional connectivity with a single model parameter. We also investigate the impact of local activity diffusion and long-range interhemispheric connectivity on the structure-function model and show an improvement in functional connectivity prediction when accounting for such latent variables which are often excluded from traditional diffusion tensor imaging (DTI) methods.

Emergence of canonical functional networks from the structural connectome

How do functional brain networks emerge from the underlying wiring of the brain? We examine how resting-state functional activation patterns emerge from the underlying connectivity and length of white matter fibers that constitute its “structural connectome”. By introducing realistic signal transmission delays along fiber projections, we obtain a complex-valued graph Laplacian matrix that depends on two parameters: coupling strength and oscillation frequency. This complex Laplacian admits a complex-valued eigen-basis in the frequency domain that is highly tunable and capable of reproducing the spatial patterns of canonical functional networks without requiring any detailed neural activity modeling. Specific canonical functional networks can be predicted using linear superposition of small subsets of complex eigenmodes. Using a novel parameter inference procedure we show that the complex Laplacian outperforms the real-valued Laplacian in predicting functional networks. The complex Laplacian eigenmodes therefore constitute a tunable yet parsimonious substrate on which a rich repertoire of realistic functional patterns can emerge. Although brain activity is governed by highly complex nonlinear processes and dense connections, our work suggests that simple extensions of linear models to the complex domain effectively approximate rich macroscopic spatial patterns observable on BOLD fMRI.

Bridging Scales in Alzheimer's Disease: Biological Framework for Brain Simulation With The Virtual Brain

Despite the acceleration of knowledge and data accumulation in neuroscience over the last years, the highly prevalent neurodegenerative disease of AD remains a growing problem. Alzheimer's Disease (AD) is the most common cause of dementia and represents the most prevalent neurodegenerative disease. For AD, disease-modifying treatments are presently lacking, and the understanding of disease mechanisms continues to be incomplete. In the present review, we discuss candidate contributing factors leading to AD, and evaluate novel computational brain simulation methods to further disentangle their potential roles. We first present an overview of existing computational models for AD that aim to provide a mechanistic understanding of the disease. Next, we outline the potential to link molecular aspects of neurodegeneration in AD with large-scale brain network modeling using The Virtual Brain (www.thevirtualbrain.org), an open-source, multiscale, whole-brain simulation neuroinformatics platform. Finally, we discuss how this methodological approach may contribute to the understanding, improved diagnostics, and treatment optimization of AD.

In silico exploration of mouse brain dynamics by focal stimulation reflects the organization of functional networks and sensory processing

Resting-state functional networks such as the default mode network (DMN) dominate spontaneous brain dynamics. To date, the mechanisms linking brain structure and brain dynamics and functions in cognition, perception, and action remain unknown, mainly due to the uncontrolled and erratic nature of the resting state. Here we used a stimulation paradigm to probe the brain’s resting behavior, providing insights on state-space stability and multiplicity of network trajectories after stimulation. We performed explorations on a mouse model to map spatiotemporal brain dynamics as a function of the stimulation site. We demonstrated the emergence of known functional networks in brain responses. Several responses heavily relied on the DMN and were suggestive of the DMN playing a mechanistic role between functional networks. We probed the simulated brain responses to the stimulation of regions along the information processing chains of sensory systems from periphery up to primary sensory cortices. Moreover, we compared simulated dynamics against in vivo brain responses to optogenetic stimulation. Our results underwrite the importance of anatomical connectivity in the functional organization of brain networks and demonstrate how functionally differentiated information processing chains arise from the same system.

We demonstrate how functionally differentiated information processing chains arise from the same anatomical network. The main result of the in-silico mouse brain simulations is the emergence of specific functional networks based on structural data from the mouse brain. When the brain is stimulated, for example, by sensory inputs or direct electrical stimulation, the brain initially responds with activities in specific regions. The brain’s anatomical connectivity constrains the subsequent pattern formation. We built a high-resolution mouse brain network model. The model structure originated from experimental data. We systematically explored the mouse model and investigated the simulated brain dynamics after stimulation. Known functional networks emerged in the simulated brain responses. The default mode network occurred in almost all characteristic response patterns. Simulated brain response dynamics and in-vivo response dynamics of the mouse brain to optogenetic stimulation showed similarities even without parameter tuning. Anatomical connectivity and dynamics shape the functional organization of brain networks.

Whole-brain modelling of resting state fMRI differentiates ADHD subtypes and facilitates stratified neuro-stimulation therapy

Recent advances in non-linear computational and dynamical modelling have opened up the possibility to parametrize dynamic neural mechanisms that drive complex behavior. Importantly, building models of neuronal processes is of key importance to fully understand disorders of the brain as it may provide a quantitative platform that is capable of binding multiple neurophysiological processes to phenotype profiles. In this study, we apply a newly developed adaptive frequency-based model of whole-brain oscillations to resting-state fMRI data acquired from healthy controls and a cohort of attention deficit hyperactivity disorder (ADHD) subjects. As expected, we found that healthy control subjects differed from ADHD in terms of attractor dynamics. However, we also found a marked dichotomy in neural dynamics within the ADHD cohort. Next, we classified the ADHD group according to the level of distance of each individual's empirical network from the two model-based simulated networks. Critically, the model was mirrored in the empirical behavior data with the two ADHD subgroups displaying distinct behavioral phenotypes related to emotional instability (i.e., depression and hypomanic personality traits). Finally, we investigated the applicability and feasibility of our whole-brain model in a therapeutic setting by conducting in silico excitatory stimulations to parsimoniously mimic clinical neuro-stimulation paradigms in ADHD. We tested the effect of stimulating any individual brain region on the key network measures derived from the simulated brain network and its contribution in rectifying the brain dynamics to that of the healthy brain, separately for each ADHD subgroup. This showed that this was indeed possible for both subgroups. However, the current effect sizes were small suggesting that the stimulation protocol needs to be tailored at the individual level. These findings demonstrate the potential of this new modelling framework to unveil hidden neurophysiological profiles and establish tailored clinical interventions.

Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes

Recently, it has been proposed that the harmonic patterns emerging from the brain's structural connectivity underlie the resting state networks of the human brain. These harmonic patterns, termed connectome harmonics, are estimated as the Laplace eigenfunctions of the combined gray and white matters connectivity matrices and yield a connectome-specific extension of the well-known Fourier basis. However, it remains unclear how topological properties of the combined connectomes constrain the precise shape of the connectome harmonics and their relationships to the resting state networks. Here, we systematically study how alterations of the local and long-range connectivity matrices affect the spatial patterns of connectome harmonics. Specifically, the proportion of local gray matter homogeneous connectivity versus long-range white-matter heterogeneous connectivity is varied by means of weight-based matrix thresholding, distance-based matrix trimming, and several types of matrix randomizations. We demonstrate that the proportion of local gray matter connections plays a crucial role for the emergence of wide-spread, functionally meaningful, and originally published connectome harmonic patterns. This finding is robust for several different cortical surface templates, mesh resolutions, or widths of the local diffusion kernel. Finally, using the connectome harmonic framework, we also provide a proof-of-concept for how targeted structural changes such as the atrophy of inter-hemispheric callosal fibers and gray matter alterations may predict functional deficits associated with neurodegenerative conditions.

Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed "connectome harmonics", have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.

Algebraic relationship between the structural network's Laplacian and functional network's adjacency matrix is preserved in temporal lobe epilepsy subjects

The relationship between anatomic and resting state functional connectivity of large-scale brain networks is a major focus of current research. In previous work, we introduced a model based on eigen decomposition of the Laplacian which predicts the functional network from the structural network in healthy brains. In this work, we apply the eigen decomposition model to two types of epilepsy; temporal lobe epilepsy associated with mesial temporal sclerosis, and MRI-normal temporal lobe epilepsy. Our findings show that the eigen relationship between function and structure holds for patients with temporal lobe epilepsy as well as normal individuals. These results suggest that the brain under TLE conditions reconfigures and rewires the fine-scale connectivity (a process which the model parameters are putatively sensitive to), in order to achieve the necessary structure-function relationship.

Spectral graph theory of brain oscillations

The relationship between the brain's structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structure-function problem, specified by the graph spectrum of the structural connectome's Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. The resulting parsimonious and analytical solution stands in contrast to complex numerical simulations of high dimensional coupled nonlinear neural field models. This spectral graph model accurately predicts spatial and spectral features of neural oscillatory activity across the brain and was successful in simultaneously reproducing empirically observed spatial and spectral patterns of alpha-band (8-12 Hz) and beta-band (15-30 Hz) activity estimated from source localized magnetoencephalography (MEG). This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics. .

Non-invasive inference of information flow using diffusion MRI, functional MRI, and MEG

OBJECTIVE

To infer information flow in the white matter of the brain and recover cortical activity using functional MRI, diffusion MRI, and MEG without a manual selection of the white matter connections of interest.

APPROACH

A Bayesian network which encodes the priors knowledge of possible brain states is built from imaging data. Diffusion MRI is used to enumerate all possible connections between cortical regions. Functional MRI is used to prune connections without manual intervention and increase the likelihood of specific regions being active. MEG data is used as evidence into this network to obtain a posterior distribution on cortical regions and connections.

MAIN RESULTS

We show that our proposed method is able to identify connections associated with the a sensory-motor task. This allows us to build the Bayesian network with no manual selection of connections of interest. Using sensory-motor MEG evoked response as evidence into this network, our method identified areas known to be involved in a visuomotor task. In addition, information flow along white matter fiber bundles connecting those regions was also recovered.

SIGNIFICANCE

Current methods to estimate white matter information flow are extremely invasive, therefore limiting our understanding of the interaction between cortical regions. The proposed method makes use of functional MRI, diffusion MRI, and M/EEG to infer communication between cortical regions, therefore opening the door to the non-invasive exploration of information flow in the white matter.

Linking Molecular Pathways and Large-Scale Computational Modeling to Assess Candidate Disease Mechanisms and Pharmacodynamics in Alzheimer's Disease

Introduction: While the prevalence of neurodegenerative diseases associated with dementia such as Alzheimer's disease (AD) increases, our knowledge on the underlying mechanisms, outcome predictors, or therapeutic targets is limited. In this work, we demonstrate how computational multi-scale brain modeling links phenomena of different scales and therefore identifies potential disease mechanisms leading the way to improved diagnostics and treatment. Methods: The Virtual Brain (TVB; thevirtualbrain.org) neuroinformatics platform allows standardized large-scale structural connectivity-based simulations of whole brain dynamics. We provide proof of concept for a novel approach that quantitatively links the effects of altered molecular pathways onto neuronal population dynamics. As a novelty, we connect chemical compounds measured with positron emission tomography (PET) with neural function in TVB addressing the phenomenon of hyperexcitability in AD related to the protein amyloid beta (Abeta). We construct personalized virtual brains based on an averaged healthy connectome and individual PET derived distributions of Abeta in patients with mild cognitive impairment (MCI, N = 8) and Alzheimer's Disease (AD, N = 10) and in age-matched healthy controls (HC, N = 15) using data from ADNI-3 data base (http://adni.loni.usc.edu). In the personalized virtual brains, individual Abeta burden modulates regional Excitation-Inhibition balance, leading to local hyperexcitation with high Abeta loads. We analyze simulated regional neural activity and electroencephalograms (EEG). Results: Known empirical alterations of EEG in patients with AD compared to HCs were reproduced by simulations. The virtual AD group showed slower frequencies in simulated local field potentials and EEG compared to MCI and HC groups. The heterogeneity of the Abeta load is crucial for the virtual EEG slowing which is absent for control models with homogeneous Abeta distributions. Slowing phenomena primarily affect the network hubs, independent of the spatial distribution of Abeta. Modeling the N-methyl-D-aspartate (NMDA) receptor antagonism of memantine in local population models, reveals potential functional reversibility of the observed large-scale alterations (reflected by EEG slowing) in virtual AD brains. Discussion: We demonstrate how TVB enables the simulation of systems effects caused by pathogenetic molecular candidate mechanisms in human virtual brains.

White matter information flow mapping from diffusion MRI and EEG

The human brain can be described as a network of specialized and spatially distributed regions. The activity of individual regions can be estimated using electroencephalography and the structure of the network can be measured using diffusion magnetic resonance imaging. However, the communication between the different cortical regions occurring through the white matter, coined information flow, cannot be observed by either modalities independently. Here, we present a new method to infer information flow in the white matter of the brain from joint diffusion MRI and EEG measurements. This is made possible by the millisecond resolution of EEG which makes the transfer of information from one region to another observable. A subject specific Bayesian network is built which captures the possible interactions between brain regions at different times. This network encodes the connections between brain regions detected using diffusion MRI tractography derived white matter bundles and their associated delays. By injecting the EEG measurements as evidence into this model, we are able to estimate the directed dynamical functional connectivity whose delays are supported by the diffusion MRI derived structural connectivity. We present our results in the form of information flow diagrams that trace transient communication between cortical regions over a functional data window. The performance of our algorithm under different noise levels is assessed using receiver operating characteristic curves on simulated data. In addition, using the well-characterized visual motor network as grounds to test our model, we present the information flow obtained during a reaching task following left or right visual stimuli. These promising results present the transfer of information from the eyes to the primary motor cortex. The information flow obtained using our technique can also be projected back to the anatomy and animated to produce videos of the information path through the white matter, opening a new window into multi-modal dynamic brain connectivity.

Physical brain connectomics

Brain connectivity and structure-function relationships are analyzed from a physical perspective in place of common graph-theoretic and statistical approaches that overwhelmingly ignore the brain's physical structure and geometry. Field theory is used to define connectivity tensors in terms of bare and dressed propagators, and discretized representations are implemented that respect the physical nature and dimensionality of the quantities involved, retain the correct continuum limit, and enable diagrammatic analysis. Eigenfunction analysis is used to simultaneously characterize and probe patterns of brain connectivity and activity, in place of statistical or phenomenological patterns. Physically based measures that characterize the connectivity are then developed in coordinate and spectral domains; some of which generalize or rectify graph-theoretic measures to implement correct dimensionality and continuum limits, and some replace graph-theoretic quantities. Traditional graph-based measures are shown to be highly prone to artifacts introduced by discretization and threshold, often because essential physical constraints have not been imposed, dimensionality has not been included, and/or distinctions between scalar, vector, and tensor quantities have not been considered. The results can replace them in ways that converge correctly and measure properties of brain structure, rather than of its discretization, and thus potentially enable physical interpretation of the many phenomenological results in the literature. Geometric effects are shown to dominate in determining many brain properties and care must be taken not to interpret geometric differences as differences in intrinsic neural connectivity. The results demonstrate the need to use systematic physical methods to analyze the brain and the potential of such methods to obtain new insights from data, make new predictions for experimental test, and go beyond phenomenological classification to dynamics and mechanisms.

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

A user ready, portable, documented software package, NFTsim, is presented to facilitate numerical simulations of a wide range of brain systems using continuum neural field modeling. NFTsim enables users to simulate key aspects of brain activity at multiple scales. At the microscopic scale, it incorporates characteristics of local interactions between cells, neurotransmitter effects, synaptodendritic delays and feedbacks. At the mesoscopic scale, it incorporates information about medium to large scale axonal ranges of fibers, which are essential to model dissipative wave transmission and to produce synchronous oscillations and associated cross-correlation patterns as observed in local field potential recordings of active tissue. At the scale of the whole brain, NFTsim allows for the inclusion of long range pathways, such as thalamocortical projections, when generating macroscopic activity fields. The multiscale nature of the neural activity produced by NFTsim has the potential to enable the modeling of resulting quantities measurable via various neuroimaging techniques. In this work, we give a comprehensive description of the design and implementation of the software. Due to its modularity and flexibility, NFTsim enables the systematic study of an unlimited number of neural systems with multiple neural populations under a unified framework and allows for direct comparison with analytic and experimental predictions. The code is written in C++ and bundled with Matlab routines for a rapid quantitative analysis and visualization of the outputs. The output of NFTsim is stored in plain text file enabling users to select from a broad range of tools for offline analysis. This software enables a wide and convenient use of powerful physiologically-based neural field approaches to brain modeling. NFTsim is distributed under the Apache 2.0 license.

Multistability in the corticothalamic system

Neural field theory of the corticothalamic system is used to analyze the properties of its steady-state solutions, including their linear stability, in the parameter space of synaptic couplings for physiological parameter ranges representing normal arousal waking states in adult humans. The independent connections of the corticothalamic model define an eight-dimensional parameter space, while specific combinations of these connections parameterize intracortical, corticothalamic, and intrathalamic loops. Multistable regions are systematically identified and the existence of up to five steady-state solutions is confirmed, up to three of which are linearly stable. A key determinant for the existence of five steady states is found to be the number of nonzero connections. This finding had not been previously proposed as the determining factor of high multiplicities of multistability in mesoscopic models of the brain. In the corticothalamic model presented here, multistability occurs when the intrathalamic loop is present (i.e., the reticular nucleus inhibits the relay nuclei), and when the net synaptic effect of the intracortical loop is inhibitory. The signature of these additional waking states is an overall increased level of thalamic activity. It is argued that the additional steady states found may represent hyperarousal states which occur when the corticothalamic projections do not attenuate the activity of the cortex.

Selective Activation of Resting-State Networks following Focal Stimulation in a Connectome-Based Network Model of the Human Brain

When the brain is stimulated, for example, by sensory inputs or goal-oriented tasks, the brain initially responds with activities in specific areas. The subsequent pattern formation of functional networks is constrained by the structural connectivity (SC) of the brain. The extent to which information is processed over short- or long-range SC is unclear. Whole-brain models based on long-range axonal connections, for example, can partly describe measured functional connectivity dynamics at rest. Here, we study the effect of SC on the network response to stimulation. We use a human whole-brain network model comprising long- and short-range connections. We systematically activate each cortical or thalamic area, and investigate the network response as a function of its short- and long-range SC. We show that when the brain is operating at the edge of criticality, stimulation causes a cascade of network recruitments, collapsing onto a smaller space that is partly constrained by SC. We found both short- and long-range SC essential to reproduce experimental results. In particular, the stimulation of specific areas results in the activation of one or more resting-state networks. We suggest that the stimulus-induced brain activity, which may indicate information and cognitive processing, follows specific routes imposed by structural networks explaining the emergence of functional networks. We provide a lookup table linking stimulation targets and functional network activations, which potentially can be useful in diagnostics and treatments with brain stimulation.

How do parcellation size and short-range connectivity affect dynamics in large-scale brain network models?

Recent efforts to model human brain activity on the scale of the whole brain rest on connectivity estimates of large-scale networks derived from diffusion magnetic resonance imaging (dMRI). This type of connectivity describes white matter fiber tracts. The number of short-range cortico-cortical white-matter connections is, however, underrepresented in such large-scale brain models. It is still unclear on the one hand, which scale of representation of white matter fibers is optimal to describe brain activity on a large-scale such as recorded with magneto- or electroencephalography (M/EEG) or functional magnetic resonance imaging (fMRI), and on the other hand, to which extent short-range connections that are typically local should be taken into account. In this article we quantified the effect of connectivity upon large-scale brain network dynamics by (i) systematically varying the number of brain regions before computing the connectivity matrix, and by (ii) adding generic short-range connections. We used dMRI data from the Human Connectome Project. We developed a suite of preprocessing modules called SCRIPTS to prepare these imaging data for The Virtual Brain, a neuroinformatics platform for large-scale brain modeling and simulations. We performed simulations under different connectivity conditions and quantified the spatiotemporal dynamics in terms of Shannon Entropy, dwell time and Principal Component Analysis. For the reconstructed connectivity, our results show that the major white matter fiber bundles play an important role in shaping slow dynamics in large-scale brain networks (e.g. in fMRI). Faster dynamics such as gamma oscillations (around 40 Hz) are sensitive to the short-range connectivity if transmission delays are considered.

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).

TVB-EduPack-An Interactive Learning and Scripting Platform for The Virtual Brain

The Virtual Brain (TVB; thevirtualbrain.org) is a neuroinformatics platform for full brain network simulation based on individual anatomical connectivity data. The framework addresses clinical and neuroscientific questions by simulating multi-scale neural dynamics that range from local population activity to large-scale brain function and related macroscopic signals like electroencephalography and functional magnetic resonance imaging. TVB is equipped with a graphical and a command-line interface to create models that capture the characteristic biological variability to predict the brain activity of individual subjects. To enable researchers from various backgrounds a quick start into TVB and brain network modeling in general, we developed an educational module: TVB-EduPack. EduPack offers two educational functionalities that seamlessly integrate into TVB's graphical user interface (GUI): (i) interactive tutorials introduce GUI elements, guide through the basic mechanics of software usage and develop complex use-case scenarios; animations, videos and textual descriptions transport essential principles of computational neuroscience and brain modeling; (ii) an automatic script generator records model parameters and produces input files for TVB's Python programming interface; thereby, simulation configurations can be exported as scripts that allow flexible customization of the modeling process and self-defined batch- and post-processing applications while benefitting from the full power of the Python language and its toolboxes. This article covers the implementation of TVB-EduPack and its integration into TVB architecture. Like TVB, EduPack is an open source community project that lives from the participation and contribution of its users. TVB-EduPack can be obtained as part of TVB from thevirtualbrain.org.

Integrating neuroinformatics tools in TheVirtualBrain

TheVirtualBrain (TVB) is a neuroinformatics Python package representing the convergence of clinical, systems, and theoretical neuroscience in the analysis, visualization and modeling of neural and neuroimaging dynamics. TVB is composed of a flexible simulator for neural dynamics measured across scales from local populations to large-scale dynamics measured by electroencephalography (EEG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI), and core analytic and visualization functions, all accessible through a web browser user interface. A datatype system modeling neuroscientific data ties together these pieces with persistent data storage, based on a combination of SQL and HDF5. These datatypes combine with adapters allowing TVB to integrate other algorithms or computational systems. TVB provides infrastructure for multiple projects and multiple users, possibly participating under multiple roles. For example, a clinician might import patient data to identify several potential lesion points in the patient's connectome. A modeler, working on the same project, tests these points for viability through whole brain simulation, based on the patient's connectome, and subsequent analysis of dynamical features. TVB also drives research forward: the simulator itself represents the culmination of several simulation frameworks in the modeling literature. The availability of the numerical methods, set of neural mass models and forward solutions allows for the construction of a wide range of brain-scale simulation scenarios. This paper briefly outlines the history and motivation for TVB, describing the framework and simulator, giving usage examples in the web UI and Python scripting.

How delays matter in an oscillatory whole-brain spiking-neuron network model for MEG alpha-rhythms at rest

In recent years the study of the intrinsic brain dynamics in a relaxed awake state in the absence of any specific task has gained increasing attention, as spontaneous neural activity has been found to be highly structured at a large scale. This so called resting-state activity has been found to be comprised by nonrandom spatiotemporal patterns and fluctuations, and several Resting-State Networks (RSN) have been found in BOLD-fMRI as well as in MEG signal power envelope correlations. The underlying anatomical connectivity structure between areas of the brain has been identified as being a key to the observed functional network connectivity, but the mechanisms behind this are still underdetermined. Theoretical large-scale brain models for fMRI data have corroborated the importance of the connectome in shaping network dynamics, while the importance of delays and noise differ between studies and depend on the models' specific dynamics. In the current study, we present a spiking neuron network model that is able to produce noisy, distributed alpha-oscillations, matching the power peak in the spectrum of group resting-state MEG recordings. We studied how well the model captured the inter-node correlation structure of the alpha-band power envelopes for different delays between brain areas, and found that the model performs best for propagation delays inside the physiological range (5-10 m/s). Delays also shift the transition from noisy to bursting oscillations to higher global coupling values in the model. Thus, in contrast to the asynchronous fMRI state, delays are important to consider in the presence of oscillation.