A mean-field model of gamma-frequency oscillations in networks of excitatory and inhibitory neurons.

Gamma oscillations are widely seen in the cerebral cortex in different states of the wake-sleep cycle and are thought to play a role in sensory processing and cognition. Here, we study the emergence of gamma oscillations at two levels, in networks of spiking neurons, and a mean-field model. At the network level, we consider two different mechanisms to generate gamma oscillations and show that they are best seen if one takes into account the synaptic delay between neurons. At the mean-field level, we show that, by introducing delays, the mean-field can also produce gamma oscillations. The mean-field matches the mean activity of excitatory and inhibitory populations of the spiking network, as well as their oscillation frequencies, for both mechanisms. This mean-field model of gamma oscillations should be a useful tool to investigate large-scale interactions through gamma oscillations in the brain.

Local orchestration of distributed functional patterns supporting loss and restoration of consciousness in the primate brain.

A central challenge of neuroscience is to elucidate how brain function supports consciousness. Here, we combine the specificity of focal deep brain stimulation with fMRI coverage of the entire cortex, in awake and anaesthetised non-human primates. During propofol, sevoflurane, or ketamine anaesthesia, and subsequent restoration of responsiveness by electrical stimulation of the central thalamus, we investigate how loss of consciousness impacts distributed patterns of structure-function organisation across scales. We report that distributed brain activity under anaesthesia is increasingly constrained by brain structure across scales, coinciding with anaesthetic-induced collapse of multiple dimensions of hierarchical cortical organisation. These distributed signatures are observed across different anaesthetics, and they are reversed by electrical stimulation of the central thalamus, coinciding with recovery of behavioural markers of arousal. No such effects were observed upon stimulating the ventral lateral thalamus, demonstrating specificity. Overall, we identify consistent distributed signatures of consciousness that are orchestrated by specific thalamic nuclei.

High-Density Exploration of Activity States in a Multi-Area Brain Model.

To simulate whole brain dynamics with only a few equations, biophysical, mesoscopic models of local neuron populations can be connected using empirical tractography data. The development of mesoscopic mean-field models of neural populations, in particular, the Adaptive Exponential (AdEx mean-field model), has successfully summarized neuron-scale phenomena leading to the emergence of global brain dynamics associated with conscious (asynchronous and rapid dynamics) and unconscious (synchronized slow-waves, with Up-and-Down state dynamics) brain states, based on biophysical mechanisms operating at cellular scales (e.g. neuromodulatory regulation of spike-frequency adaptation during sleep-wake cycles or anesthetics). Using the Virtual Brain (TVB) environment to connect mean-field AdEx models, we have previously simulated the general properties of brain states, playing on spike-frequency adaptation, but have not yet performed detailed analyses of other parameters possibly also regulating transitions in brain-scale dynamics between different brain states. We performed a dense grid parameter exploration of the TVB-AdEx model, making use of High Performance Computing. We report a remarkable robustness of the effect of adaptation to induce synchronized slow-wave activity. Moreover, the occurrence of slow waves is often paralleled with a closer relation between functional and structural connectivity. We find that hyperpolarization can also generate unconscious-like synchronized Up and Down states, which may be a mechanism underlying the action of anesthetics. We conclude that the TVB-AdEx model reveals large-scale properties identified experimentally in sleep and anesthesia.

A Network Model of the Modulation of γ Oscillations by NMDA Receptors in Cerebral Cortex.

Psychotic drugs such as ketamine induce symptoms close to schizophrenia and stimulate the production of γ oscillations, as also seen in patients, but the underlying mechanisms are still unclear. Here, we have used computational models of cortical networks generating γ oscillations, and have integrated the action of drugs such as ketamine to partially block NMDA receptors (NMDARs). The model can reproduce the paradoxical increase of γ oscillations by NMDA receptor antagonists, assuming that antagonists affect NMDA receptors with higher affinity on inhibitory interneurons. We next used the model to compare the responsiveness of the network to external stimuli, and found that when NMDA channels are blocked, an increase of γ power is observed altogether with an increase of network responsiveness. However, this responsiveness increase applies not only to γ states, but also to asynchronous states with no apparent γ. We conclude that NMDA antagonists induce an increased excitability state, which may or may not produce γ oscillations, but the response to external inputs is exacerbated, which may explain phenomena such as altered perception or hallucinations.

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics.

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

Modeling the relationship between neuronal activity and the BOLD signal: contributions from astrocyte calcium dynamics.

Functional magnetic resonance imaging relies on the coupling between neuronal and vascular activity, but the mechanisms behind this coupling are still under discussion. Recent experimental evidence suggests that calcium signaling may play a significant role in neurovascular coupling. However, it is still controversial where this calcium signal is located (in neurons or elsewhere), how it operates and how relevant is its role. In this paper we introduce a biologically plausible model of the neurovascular coupling and we show that calcium signaling in astrocytes can explain main aspects of the dynamics of the coupling. We find that calcium signaling can explain so-far unrelated features such as the linear and non-linear regimes, the negative vascular response (undershoot) and the emergence of a (calcium-driven) Hemodynamic Response Function. These features are reproduced here for the first time by a single model of the detailed neuronal-astrocyte-vascular pathway. Furthermore, we analyze how information is coded and transmitted from the neuronal to the vascular system and we predict that frequency modulation of astrocytic calcium dynamics plays a key role in this process. Finally, our work provides a framework to link neuronal activity to the BOLD signal, and vice-versa, where neuronal activity can be inferred from the BOLD signal. This opens new ways to link known alterations of astrocytic calcium signaling in neurodegenerative diseases (e.g. Alzheimer's and Parkinson's diseases) with detectable changes in the neurovascular coupling.

Assessing brain state and anesthesia level with two-photon calcium signals.

Brain states, such as wake, sleep, or different depths of anesthesia are usually assessed using electrophysiological techniques, such as the local field potential (LFP) or the electroencephalogram (EEG), which are ideal signals for detecting activity patterns such as asynchronous or oscillatory activities. However, it is technically challenging to have these types of measures during calcium imaging recordings such as two-photon or wide-field techniques. Here, using simultaneous two-photon and LFP measurements, we demonstrate that despite the slower dynamics of the calcium signal, there is a high correlation between the LFP and two-photon signals taken from the neuropil outside neuronal somata. Moreover, we find the calcium signal to be systematically delayed from the LFP signal, and we use a model to show that the delay between the two signals is due to the physical distance between the recording sites. These results suggest that calcium signals alone can be used to detect activity patterns such as slow oscillations and ultimately assess the brain state and level of anesthesia.

Noise Enhancement of Neural Information Processing.

Cortical neurons in vivo function in highly fluctuating and seemingly noisy conditions, and the understanding of how information is processed in such complex states is still incomplete. In this perspective article, we first overview that an intense "synaptic noise" was measured first in single neurons, and computational models were built based on such measurements. Recent progress in recording techniques has enabled the measurement of highly complex activity in large numbers of neurons in animals and human subjects, and models were also built to account for these complex dynamics. Here, we attempt to link these two cellular and population aspects, where the complexity of network dynamics in awake cortex seems to link to the synaptic noise seen in single cells. We show that noise in single cells, in networks, or structural noise, all participate to enhance responsiveness and boost the propagation of information. We propose that such noisy states are fundamental to providing favorable conditions for information processing at large-scale levels in the brain, and may be involved in sensory perception.

A Model for the Propagation of Seizure Activity in Normal Brain Tissue.

Epilepsies are characterized by paroxysmal electrophysiological events and seizures, which can propagate across the brain. One of the main unsolved questions in epilepsy is how epileptic activity can invade normal tissue and thus propagate across the brain. To investigate this question, we consider three computational models at the neural network scale to study the underlying dynamics of seizure propagation, understand which specific features play a role, and relate them to clinical or experimental observations. We consider both the internal connectivity structure between neurons and the input properties in our characterization. We show that a paroxysmal input is sometimes controlled by the network while in other instances, it can lead the network activity to itself produce paroxysmal activity, and thus will further propagate to efferent networks. We further show how the details of the network architecture are essential to determine this switch to a seizure-like regime. We investigated the nature of the instability involved and in particular found a central role for the inhibitory connectivity. We propose a probabilistic approach to the propagative/non-propagative scenarios, which may serve as a guide to control the seizure by using appropriate stimuli.

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.

Awake perception is associated with dedicated neuronal assemblies in the cerebral cortex.

Neural activity in the sensory cortex combines stimulus responses and ongoing activity, but it remains unclear whether these reflect the same underlying dynamics or separate processes. In the present study, we show in mice that, during wakefulness, the neuronal assemblies evoked by sounds in the auditory cortex and thalamus are specific to the stimulus and distinct from the assemblies observed in ongoing activity. By contrast, under three different anesthetics, evoked assemblies are indistinguishable from ongoing assemblies in the cortex. However, they remain distinct in the thalamus. A strong remapping of sensory responses accompanies this dynamic state change produced by anesthesia. Together, these results show that the awake cortex engages dedicated neuronal assemblies in response to sensory inputs, which we suggest is a network correlate of sensory perception.

A method to convert neural signals into sound sequences.

We present a method to convert neural signals into sound sequences, with the constraint that the sound sequences precisely reflect the sequences of events in the neural signal. The method consists in quantifying the wave motifs in the signal and using these parameters to generate sound envelopes. We illustrate the procedure for sleep delta waves in the human electro-encephalogram (EEG), which are converted into sound sequences that encode the time structure of the original EEG waves. This procedure can be applied to synthesize personalized sound sequences specific to the EEG of a given subject.

Properties and Computational Consequences of Fast Dendritic Spikes during Natural Behavior.

The dendritic membrane potential was recently measured for the first time in drug-free, naturally behaving rats over several days. These showed that neuronal dendrites generate a lot of sodium spikes, up to ten times as many as the somatic spikes. These key experimental findings are reviewed here, along with a discussion of computational models, and computational consequences of such intense spike traffic in dendrites. We overview the experimental techniques that enabled these measurements as well as a variety of models, ranging from conceptual models to detailed biophysical models. The biophysical models suggest that the intense dendritic spiking activity can arise from the biophysical properties of the dendritic voltage-dependent and synaptic ion channels, and delineate some computational consequences of fast dendritic spike activity. One remarkable aspect is that in the model, with fast dendritic spikes, the efficacy of synaptic strength in terms of driving the somatic activity is much less dependent on the position of the synapse in dendrites. This property suggests that fast dendritic spikes is a way to confer to neurons the possibility to grow complex dendritic trees with little computational loss for the distal most synapses, and thus form very complex networks with high density of connections, such as typically in the human brain. Another important consequence is that dendritically localized spikes can allow simultaneous but different computations on different dendritic branches, thereby greatly increasing the computational capacity and complexity of neuronal networks.

Extracellular and intracellular components of the impedance of neural tissue.

Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depends on the electric structure and properties of extracellular media, but the measurements of these electric properties are still debated. Some measurements point to a model in which the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements (in the 1-10 kHz frequency range) using the same setup in various preparations, from primary cell cultures to acute brain slices, and a comparison with similar measurements performed in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean-field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated with Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity that should be taken into account to correctly interpret extracellular potentials generated by neurons.

Linking Brain Structure, Activity, and Cognitive Function through Computation.

Understanding the human brain is a "Grand Challenge" for 21st century research. Computational approaches enable large and complex datasets to be addressed efficiently, supported by artificial neural networks, modeling and simulation. Dynamic generative multiscale models, which enable the investigation of causation across scales and are guided by principles and theories of brain function, are instrumental for linking brain structure and function. An example of a resource enabling such an integrated approach to neuroscientific discovery is the BigBrain, which spatially anchors tissue models and data across different scales and ensures that multiscale models are supported by the data, making the bridge to both basic neuroscience and medicine. Research at the intersection of neuroscience, computing and robotics has the potential to advance neuro-inspired technologies by taking advantage of a growing body of insights into perception, plasticity and learning. To render data, tools and methods, theories, basic principles and concepts interoperable, the Human Brain Project (HBP) has launched EBRAINS, a digital neuroscience research infrastructure, which brings together a transdisciplinary community of researchers united by the quest to understand the brain, with fascinating insights and perspectives for societal benefits.

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.

Optimal responsiveness and information flow in networks of heterogeneous neurons.

Cerebral cortex is characterized by a strong neuron-to-neuron heterogeneity, but it is unclear what consequences this may have for cortical computations, while most computational models consider networks of identical units. Here, we study network models of spiking neurons endowed with heterogeneity, that we treat independently for excitatory and inhibitory neurons. We find that heterogeneous networks are generally more responsive, with an optimal responsiveness occurring for levels of heterogeneity found experimentally in different published datasets, for both excitatory and inhibitory neurons. To investigate the underlying mechanisms, we introduce a mean-field model of heterogeneous networks. This mean-field model captures optimal responsiveness and suggests that it is related to the stability of the spontaneous asynchronous state. The mean-field model also predicts that new dynamical states can emerge from heterogeneity, a prediction which is confirmed by network simulations. Finally we show that heterogeneous networks maximise the information flow in large-scale networks, through recurrent connections. We conclude that neuronal heterogeneity confers different responsiveness to neural networks, which should be taken into account to investigate their information processing capabilities.

Integration, coincidence detection and resonance in networks of spiking neurons expressing Gamma oscillations and asynchronous states.

Gamma oscillations are widely seen in the awake and sleeping cerebral cortex, but the exact role of these oscillations is still debated. Here, we used biophysical models to examine how Gamma oscillations may participate to the processing of afferent stimuli. We constructed conductance-based network models of Gamma oscillations, based on different cell types found in cerebral cortex. The models were adjusted to extracellular unit recordings in humans, where Gamma oscillations always coexist with the asynchronous firing mode. We considered three different mechanisms to generate Gamma, first a mechanism based on the interaction between pyramidal neurons and interneurons (PING), second a mechanism in which Gamma is generated by interneuron networks (ING) and third, a mechanism which relies on Gamma oscillations generated by pacemaker chattering neurons (CHING). We find that all three mechanisms generate features consistent with human recordings, but that the ING mechanism is most consistent with the firing rate change inside Gamma bursts seen in the human data. We next evaluated the responsiveness and resonant properties of these networks, contrasting Gamma oscillations with the asynchronous mode. We find that for both slowly-varying stimuli and precisely-timed stimuli, the responsiveness is generally lower during Gamma compared to asynchronous states, while resonant properties are similar around the Gamma band. We could not find conditions where Gamma oscillations were more responsive. We therefore predict that asynchronous states provide the highest responsiveness to external stimuli, while Gamma oscillations tend to overall diminish responsiveness.

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.