The Virtual Mouse Brain: A Computational Neuroinformatics Platform to Study Whole Mouse Brain Dynamics

Spatially integrated cortico-subcortical tracing data for analyses of rodent brain topographical organization

The cerebral cortex extends axonal projections to several subcortical brain regions, including the striatum, thalamus, superior colliculus, and pontine nuclei. Experimental tract-tracing studies have shown that these subcortical projections are topographically organized, reflecting the spatial organization of sensory surfaces and body parts. Several public collections of mouse- and rat- brain tract-tracing data are available, with the Allen mouse brain connectivity atlas being most prominent. There, a large body of image data can be inspected, but it is difficult to combine data from different experiments and compare spatial distribution patterns. To enable co-visualization and comparison of topographical organization in mouse brain cortico-subcortical projections across experiments, we represent axonal labelling data as point data in a common 3D brain atlas space. We here present a collection of point-cloud data representing spatial distribution of corticostriatal, corticothalamic, corticotectal, and corticopontine projections in mice and exemplify how these spatially integrated point data can be used as references for experimental investigations of topographic organization in transgenic mice, and for cross-species comparison with corticopontine projections in rats.

A Whole-Brain Model of the Aging Brain During Slow Wave Sleep

Age-related brain changes affect sleep and are reflected in properties of sleep slow-waves, however, the precise mechanisms behind these changes are still not completely understood. Here, we adapt a previously established whole-brain model relating structural connectivity changes to resting state dynamics, and extend it to a slow-wave sleep brain state. In particular, starting from a representative connectome at the beginning of the aging trajectory, we have gradually reduced the inter-hemispheric connections, and simulated sleep-like slow-wave activity. We show that the main empirically observed trends, namely a decrease in duration and increase in variability of the slow waves are captured by the model. Furthermore, comparing the simulated EEG activity to the source signals, we suggest that the empirically observed decrease in amplitude of the slow waves is caused by the decrease in synchrony between brain regions.

Impact of the day/night cycle on functional connectome in ageing male and female mice

To elucidate how time of day, sex, and age affect functional connectivity (FC) in mice, we aimed to examine whether the mouse functional connectome varied with the day/night cycle and whether it depended on sex and age. We explored C57Bl6/J mice (6♀ and 6♂) at mature age (5 ± 1 months) and middle-age (14 ± 1 months). Each mouse underwent Blood Oxygen-Level-Dependent (BOLD) resting-state functional MRI (rs-fMRI) on a 7T scanner at four different times of the day, two under the light condition and two under the dark condition. Data processing consisted of group independent component analysis (ICA) and region-level analysis using resting-state networks (RSNs) derived from literature. Linear mixed-effect models (LMEM) were used to assess the effects of sex, lighting condition and their interactions for each RSN obtained with group-ICA (RSNs-GICA) and six bilateral RSNs adapted from literature (RSNs-LIT). Our study highlighted new RSNs in mice related to day/night alternation in addition to other networks already reported in the literature. In mature mice, we found sex-related differences in brain activation only in one RSNs-GICA comprising the cortical, hippocampal, midbrain and cerebellar regions of the right hemisphere. In males, brain activity was significantly higher in the left hippocampus, the retrosplenial cortex, the superior colliculus, and the cerebellum regardless of lighting condition; consistent with the role of these structures in memory formation and integration, sleep, and sex-differences in memory processing. Experimental constraints limited the analysis to the impact of light/dark cycle on the RSNs for middle-aged females. We detected significant activation in the pineal gland during the dark condition, a finding in line with the nocturnal activity of this gland. For the analysis of RSNs-LIT, new variables "sexage" (sex and age combined) and "edges" (pairs of RSNs) were introduced. FC was calculated as the Pearson correlation between two RSNs. LMEM revealed no effect of sexage or lighting condition. The FC depended on the edges, but there were no interaction effects between sexage, lighting condition and edges. Interaction effects were detected between i) sex and lighting condition, with higher FC in males under the dark condition, ii) sexage and edges with higher FC in male brain regions related to vision, memory, and motor action. We conclude that time of day and sex should be taken into account when designing, analyzing, and interpreting functional imaging studies in rodents.

Multiscale co-simulation design pattern for neuroscience applications

Integration of information across heterogeneous sources creates added scientific value. Interoperability of data, tools and models is, however, difficult to accomplish across spatial and temporal scales. Here we introduce the toolbox Parallel Co-Simulation, which enables the interoperation of simulators operating at different scales. We provide a software science co-design pattern and illustrate its functioning along a neuroscience example, in which individual regions of interest are simulated on the cellular level allowing us to study detailed mechanisms, while the remaining network is efficiently simulated on the population level. A workflow is illustrated for the use case of The Virtual Brain and NEST, in which the CA1 region of the cellular-level hippocampus of the mouse is embedded into a full brain network involving micro and macro electrode recordings. This new tool allows integrating knowledge across scales in the same simulation framework and validating them against multiscale experiments, thereby largely widening the explanatory power of computational models.

Network models to enhance the translational impact of cross-species studies

Neuroscience studies are often carried out in animal models for the purpose of understanding specific aspects of the human condition. However, the translation of findings across species remains a substantial challenge. Network science approaches can enhance the translational impact of cross-species studies by providing a means of mapping small-scale cellular processes identified in animal model studies to larger-scale inter-regional circuits observed in humans. In this Review, we highlight the contributions of network science approaches to the development of cross-species translational research in neuroscience. We lay the foundation for our discussion by exploring the objectives of cross-species translational models. We then discuss how the development of new tools that enable the acquisition of whole-brain data in animal models with cellular resolution provides unprecedented opportunity for cross-species applications of network science approaches for understanding large-scale brain networks. We describe how these tools may support the translation of findings across species and imaging modalities and highlight future opportunities. Our overarching goal is to illustrate how the application of network science tools across human and animal model studies could deepen insight into the neurobiology that underlies phenomena observed with non-invasive neuroimaging methods and could simultaneously further our ability to translate findings across species.

Learning how network structure shapes decision-making for bio-inspired computing

To better understand how network structure shapes intelligent behavior, we developed a learning algorithm that we used to build personalized brain network models for 650 Human Connectome Project participants. We found that participants with higher intelligence scores took more time to solve difficult problems, and that slower solvers had higher average functional connectivity. With simulations we identified a mechanistic link between functional connectivity, intelligence, processing speed and brain synchrony for trading accuracy with speed in dependence of excitation-inhibition balance. Reduced synchrony led decision-making circuits to quickly jump to conclusions, while higher synchrony allowed for better integration of evidence and more robust working memory. Strict tests were applied to ensure reproducibility and generality of the obtained results. Here, we identify links between brain structure and function that enable to learn connectome topology from noninvasive recordings and map it to inter-individual differences in behavior, suggesting broad utility for research and clinical applications.

Mean-field based framework for forward modeling of LFP and MEG signals

The use of mean-field models to describe the activity of large neuronal populations has become a very powerful tool for large-scale or whole brain simulations. However, the calculation of brain signals from mean-field models, such as the electric and magnetic fields, is still under development. Thus, the emergence of new methods for an accurate and efficient calculation of such brain signals is currently of great relevance. In this paper we propose a novel method to calculate the local field potentials (LFP) and magnetic fields from mean-field models. The calculation of LFP is done via a kernel method based on unitary LFP's (the LFP generated by a single axon) that was recently introduced for spiking-networks simulations and that we adapt here for mean-field models. The calculation of the magnetic field is based on current-dipole and volume-conductor models, where the secondary currents (due to the conducting extracellular medium) are estimated using the LFP calculated via the kernel method and the effects of medium-inhomogeneities are incorporated. We provide an example of the application of our method for the calculation of LFP and MEG under slow-waves of neuronal activity generated by a mean-field model of a network of Adaptive-Exponential Integrate-and-Fire (AdEx) neurons. We validate our method via comparison with results obtained from the corresponding spiking neuronal networks. Finally we provide an example of our method for whole brain simulations performed with The Virtual Brain (TVB), a recently developed tool for large scale simulations of the brain. Our method provides an efficient way of calculating electric and magnetic fields from mean-field models. This method exhibits a great potential for its application in large-scale or whole-brain simulations, where calculations via detailed biological models are not feasible.

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.

Normalizing the brain connectome for communication through synchronization

Networks in neuroscience determine how brain function unfolds, and their perturbations lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual, particle-wave, perspective, integrate time delays due to finite transmission speeds, and derive a normalization of the connectome. When applied to the database of the Human Connectome Project, it explains the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects (N = 100) and are a fundamental network property within the wave picture. The normalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms. These two perspectives are orthogonal, but not incommensurable, when understood within the novel, here-proposed, generalized framework of structural connectivity.

Extracting Dynamical Understanding From Neural-Mass Models of Mouse Cortex

New brain atlases with high spatial resolution and whole-brain coverage have rapidly advanced our knowledge of the brain's neural architecture, including the systematic variation of excitatory and inhibitory cell densities across the mammalian cortex. But understanding how the brain's microscale physiology shapes brain dynamics at the macroscale has remained a challenge. While physiologically based mathematical models of brain dynamics are well placed to bridge this explanatory gap, their complexity can form a barrier to providing clear mechanistic interpretation of the dynamics they generate. In this work, we develop a neural-mass model of the mouse cortex and show how bifurcation diagrams, which capture local dynamical responses to inputs and their variation across brain regions, can be used to understand the resulting whole-brain dynamics. We show that strong fits to resting-state functional magnetic resonance imaging (fMRI) data can be found in surprisingly simple dynamical regimes-including where all brain regions are confined to a stable fixed point-in which regions are able to respond strongly to variations in their inputs, consistent with direct structural connections providing a strong constraint on functional connectivity in the anesthetized mouse. We also use bifurcation diagrams to show how perturbations to local excitatory and inhibitory coupling strengths across the cortex, constrained by cell-density data, provide spatially dependent constraints on resulting cortical activity, and support a greater diversity of coincident dynamical regimes. Our work illustrates methods for visualizing and interpreting model performance in terms of underlying dynamical mechanisms, an approach that is crucial for building explanatory and physiologically grounded models of the dynamical principles that underpin large-scale brain activity.

Vector Auto-Regressive Deep Neural Network: A Data-Driven Deep Learning-Based Directed Functional Connectivity Estimation Toolbox

An important goal in neuroscience is to elucidate the causal relationships between the brain's different regions. This can help reveal the brain's functional circuitry and diagnose lesions. Currently there are a lack of approaches to functional connectome estimation that leverage the state-of-the-art in deep learning architectures and training methodologies. Therefore, we propose a new framework based on a vector auto-regressive deep neural network (VARDNN) architecture. Our approach consists of a set of nodes, each with a deep neural network structure. These nodes can be mapped to any spatial sub-division based on the data to be analyzed, such as anatomical brain regions from which representative neural signals can be obtained. VARDNN learns to reproduce experimental time series data using modern deep learning training techniques. Based on this, we developed two novel directed functional connectivity (dFC) measures, namely VARDNN-DI and VARDNN-GC. We evaluated our measures against a number of existing functional connectome estimation measures, such as partial correlation and multivariate Granger causality combined with large dimensionality counter-measure techniques. Our measures outperformed them across various types of ground truth data, especially as the number of nodes increased. We applied VARDNN to fMRI data to compare the dFC between 41 healthy control vs. 32 Alzheimer's disease subjects. Our VARDNN-DI measure detected lesioned regions consistent with previous studies and separated the two groups well in a subject-wise evaluation framework. Summarily, the VARDNN framework has powerful capabilities for whole brain dFC estimation. We have implemented VARDNN as an open-source toolbox that can be freely downloaded for researchers who wish to carry out functional connectome analysis on their own data.

Neuronal Cascades Shape Whole-Brain Functional Dynamics at Rest

At rest, mammalian brains display remarkable spatiotemporal complexity, evolving through recurrent functional connectivity (FC) states on a slow timescale of the order of tens of seconds. While the phenomenology of the resting state dynamics is valuable in distinguishing healthy and pathologic brains, little is known about its underlying mechanisms. Here, we identify neuronal cascades as a potential mechanism. Using full-brain network modeling, we show that neuronal populations, coupled via a detailed structural connectome, give rise to large-scale cascades of firing rate fluctuations evolving at the same time scale of resting-state networks (RSNs). The ignition and subsequent propagation of cascades depend on the brain state and connectivity of each region. The largest cascades produce bursts of blood oxygen level-dependent (BOLD) co-fluctuations at pairs of regions across the brain, which shape the simulated RSN dynamics. We experimentally confirm these theoretical predictions. We demonstrate the existence and stability of intermittent epochs of FC comprising BOLD co-activation (CA) bursts in mice and human functional magnetic resonance imaging (fMRI). We then provide evidence for the existence and leading role of the neuronal cascades in humans with simultaneous EEG/fMRI recordings. These results show that neuronal cascades are a major determinant of spontaneous fluctuations in brain dynamics at rest.

Modeling seizures: From single neurons to networks

Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.

Progress towards a cellularly resolved mouse mesoconnectome is empowered by data fusion and new neuroanatomy techniques

Over the past decade there has been a rapid improvement in techniques for obtaining large-scale cellular level data related to the mouse brain connectome. However, a detailed mapping of cell-type-specific projection patterns is lacking, which would, for instance, allow us to study the role of circuit motifs in cognitive processes. In this work, we review advanced neuroanatomical and data fusion techniques within the context of a proposed Multimodal Connectomic Integration Framework for augmenting the cellularly resolved mouse mesoconnectome. First, we emphasize the importance of registering data modalities to a common reference atlas. We then review a number of novel experimental techniques that can provide data for characterizing cell-types in the mouse brain. Furthermore, we examine a number of data integration strategies, which involve fine-grained cell-type classification, spatial inference of cell densities, latent variable models for the mesoconnectome and multi-modal factorisation. Finally, we discuss a number of use cases which depend on connectome augmentation techniques, such as model simulations of functional connectivity and generating mechanistic hypotheses for animal disease models.

Brain States and Transitions: Insights from Computational Neuroscience

Within the field of computational neuroscience there are great expectations of finding new ways to rebalance the complex dynamic system of the human brain through controlled pharmacological or electromagnetic perturbation. Yet many obstacles remain between the ability to accurately predict how and where best to perturb to force a transition from one brain state to another. The foremost challenge is a commonly agreed definition of a given brain state. Recent progress in computational neuroscience has made it possible to robustly define brain states and force transitions between them. Here, we review the state of the art and propose a framework for determining the functional hierarchical organization describing any given brain state. We describe the latest advances in creating sophisticated whole-brain computational models with interacting neuronal and neurotransmitter systems that can be studied fully in silico to predict and design novel pharmacological and electromagnetic interventions to rebalance them in disease.

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.

Accelerating with FlyBrainLab the discovery of the functional logic of the Drosophila brain in the connectomic and synaptomic era

In recent years, a wealth of Drosophila neuroscience data have become available including cell type and connectome/synaptome datasets for both the larva and adult fly. To facilitate integration across data modalities and to accelerate the understanding of the functional logic of the fruit fly brain, we have developed FlyBrainLab, a unique open-source computing platform that integrates 3D exploration and visualization of diverse datasets with interactive exploration of the functional logic of modeled executable brain circuits. FlyBrainLab's User Interface, Utilities Libraries and Circuit Libraries bring together neuroanatomical, neurogenetic and electrophysiological datasets with computational models of different researchers for validation and comparison within the same platform. Seeking to transcend the limitations of the connectome/synaptome, FlyBrainLab also provides libraries for molecular transduction arising in sensory coding in vision/olfaction. Together with sensory neuron activity data, these libraries serve as entry points for the exploration, analysis, comparison, and evaluation of circuit functions of the fruit fly brain.

Highlights from the Era of Open Source Web-Based Tools

High digital connectivity and a focus on reproducibility are contributing to an open science revolution in neuroscience. Repositories and platforms have emerged across the whole spectrum of subdisciplines, paving the way for a paradigm shift in the way we share, analyze, and reuse vast amounts of data collected across many laboratories. Here, we describe how open access web-based tools are changing the landscape and culture of neuroscience, highlighting six free resources that span subdisciplines from behavior to whole-brain mapping, circuits, neurons, and gene variants.

Asymmetric high-order anatomical brain connectivity sculpts effective connectivity

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

Individual structural features constrain the mouse functional connectome

Whole brain dynamics intuitively depend upon the internal wiring of the brain; but to which extent the individual structural connectome constrains the corresponding functional connectome is unknown, even though its importance is uncontested. After acquiring structural data from individual mice, we virtualized their brain networks and simulated in silico functional MRI data. Theoretical results were validated against empirical awake functional MRI data obtained from the same mice. We demonstrate that individual structural connectomes predict the functional organization of individual brains. Using a virtual mouse brain derived from the Allen Mouse Brain Connectivity Atlas, we further show that the dominant predictors of individual structure-function relations are the asymmetry and the weights of the structural links. Model predictions were validated experimentally using tracer injections, identifying which missing connections (not measurable with diffusion MRI) are important for whole brain dynamics in the mouse. Individual variations thus define a specific structural fingerprint with direct impact upon the functional organization of individual brains, a key feature for personalized medicine.

A Neuromorphic Prosthesis to Restore Communication in Neuronal Networks

Recent advances in bioelectronics and neural engineering allowed the development of brain machine interfaces and neuroprostheses, capable of facilitating or recovering functionality in people with neurological disability. To realize energy-efficient and real-time capable devices, neuromorphic computing systems are envisaged as the core of next-generation systems for brain repair. We demonstrate here a real-time hardware neuromorphic prosthesis to restore bidirectional interactions between two neuronal populations, even when one is damaged or missing. We used in vitro modular cell cultures to mimic the mutual interaction between neuronal assemblies and created a focal lesion to functionally disconnect the two populations. Then, we employed our neuromorphic prosthesis for bidirectional bridging to artificially reconnect two disconnected neuronal modules and for hybrid bidirectional bridging to replace the activity of one module with a real-time hardware neuromorphic Spiking Neural Network. Our neuroprosthetic system opens avenues for the exploitation of neuromorphic-based devices in bioelectrical therapeutics for health care.

Background EEG Connectivity Captures the Time-Course of Epileptogenesis in a Mouse Model of Epilepsy

Large-scale brain networks are increasingly recognized as important for the generation of seizures in epilepsy. However, how a network evolves from a healthy state through the process of epileptogenesis remains unclear. To address this question, here, we study longitudinal epicranial background EEG recordings (30 electrodes, EEG free from epileptiform activity) of a mouse model of mesial temporal lobe epilepsy. We analyze functional connectivity networks and observe that over the time course of epileptogenesis the networks become increasingly asymmetric. Furthermore, computational modelling reveals that a set of nodes, located outside of the region of initial insult, emerges as particularly important for the network dynamics. These findings are consistent with experimental observations, thus demonstrating that ictogenic mechanisms can be revealed on the EEG, that computational models can be used to monitor unfolding epileptogenesis and that both the primary focus and epileptic network play a role in epileptogenesis.

A macaque connectome for large-scale network simulations in TheVirtualBrain

Models of large-scale brain networks that are informed by the underlying anatomical connectivity contribute to our understanding of the mapping between the structure of the brain and its dynamical function. Connectome-based modelling is a promising approach to a more comprehensive understanding of brain function across spatial and temporal scales, but it must be constrained by multi-scale empirical data from animal models. Here we describe the construction of a macaque (Macaca mulatta and Macaca fascicularis) connectome for whole-cortex simulations in TheVirtualBrain, an open-source simulation platform. We take advantage of available axonal tract-tracing datasets and enhance the existing connectome data using diffusion-based tractography in macaques. We illustrate the utility of the connectome as an extension of TheVirtualBrain by simulating resting-state BOLD-fMRI data and fitting it to empirical resting-state data.

Synchronization dependent on spatial structures of a mesoscopic whole-brain network

Complex structural connectivity of the mammalian brain is believed to underlie the versatility of neural computations. Many previous studies have investigated properties of small subsystems or coarse connectivity among large brain regions that are often binarized and lack spatial information. Yet little is known about spatial embedding of the detailed whole-brain connectivity and its functional implications. We focus on closing this gap by analyzing how spatially-constrained neural connectivity shapes synchronization of the brain dynamics based on a system of coupled phase oscillators on a mammalian whole-brain network at the mesoscopic level. This was made possible by the recent development of the Allen Mouse Brain Connectivity Atlas constructed from viral tracing experiments together with a new mapping algorithm. We investigated whether the network can be compactly represented based on the spatial dependence of the network topology. We found that the connectivity has a significant spatial dependence, with spatially close brain regions strongly connected and distal regions weakly connected, following a power law. However, there are a number of residuals above the power-law fit, indicating connections between brain regions that are stronger than predicted by the power-law relationship. By measuring the sensitivity of the network order parameter, we show how these strong connections dispersed across multiple spatial scales of the network promote rapid transitions between partial synchronization and more global synchronization as the global coupling coefficient changes. We further demonstrate the significance of the locations of the residual connections, suggesting a possible link between the network complexity and the brain’s exceptional ability to swiftly switch computational states depending on stimulus and behavioral context.

In a previous study, a data-driven large-scale model of mouse brain connectivity was constructed. This mouse brain connectivity model is estimated by a simplified model which only takes in account anatomy and distance dependence of connection strength which is best fit by a power law. The distance dependence model captures the connection strengths of the mouse whole-brain network well. But can it capture the dynamics? In this study, we show that a small number of connections which are missed by the simple spatial model lead to significant differences in dynamics. The presence of a small number of strong connections over longer distances increases sensitivity of synchronization to perturbations. Unlike the data-driven network, the network without these long-range connections, as well as the network in which these long range connections are shuffled, lose global synchronization while maintaining localized synchrony, underlining the significance of the exact topology of these distal connections in the data-driven brain network.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.

Minimal model of interictal and ictal discharges "Epileptor-2"

Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures.

In pathological conditions of epilepsy, the functioning of the neural network crucially depends on the ionic concentrations inside and outside neurons. A number of factors that affect neuronal activity is large. That is why the development of a minimal model that reproduces typical seizures could structure further experimental and analytical studies of the pathological mechanisms. Here, on a base of known biophysical models, we present a simple population-type model that includes only four principal variables, the extracellular potassium concentration, the intracellular sodium concentration, the membrane potential and the synaptic resource diminishing due to short-term synaptic depression. A simple modeled neuron is used as an observer of the population activity. We validate the model assumptions with in vitro experiments. Our model reproduces ictal and interictal events, where the latter result in bursts of spikes in single neurons, and the former represent the cluster of spike bursts. Mathematical analysis reveals that the bursts are spontaneous large-amplitude oscillations, which may cluster after a saddle-node on invariant circle bifurcation in the pro-epileptic conditions. Our consideration has significant bearing in understanding pathological neuronal network dynamics.

Personalized brain network models for assessing structure-function relationships

Many recent efforts in computational modeling of macro-scale brain dynamics have begun to take a data-driven approach by incorporating structural and/or functional information derived from subject data. Here, we discuss recent work using personalized brain network models to study structure-function relationships in human brains. We describe the steps necessary to build such models and show how this computational approach can provide previously unobtainable information through the ability to perform virtual experiments. Finally, we present examples of how personalized brain network models can be used to gain insight into the effects of local stimulation and improve surgical outcomes in epilepsy.