Dynamics of large-scale brain activity in normal arousal states and epileptic seizures

Computational modeling of frequency-dependent neocortical response to thalamic neurostimulation in epilepsy

The therapeutic application of centromedian nucleus stimulation (CMS) has been limited by uncertainties regarding its mechanism of action. In this study, we used stereoelectro-encephalography (SEEG) signals recorded from a patient with refractory epilepsy, caused by focal cortical dysplasia, which is a malformation of cortical development. SEEG recordings revealed that neocortical interictal discharges could be suppressed by CMS. These effects were found to be frequency-dependent: while 50 Hz CMS induced no change in neocortical epileptiform activity, CMS at 70 Hz, 100 Hz and 150 Hz led to periods of suppression of neocortical epileptiform activity. These periods were shown to have different durations depending on the stimulation protocol. We developed a neurophysiologically-plausible thalamocortical model to explain these observations. This model included glutamatergic subpopulations and GABAergic subpopulations in the neocortical and the thalamic compartments. Synaptic inhibition and short-term plasticity mechanisms were integrated into the latter compartment. We hypothesized that the enhanced activation of thalamic inhibitory subpopulations during high frequency CMS (>70Hz) would result in GABA spillover which activated synaptic GABAergic receptors on the thalamocortical relay cells. This decreased the thalamic driving-input to the neocortex, hence suppressing interictal discharges in the dysplastic neocortical tissue. While inhibition of thalamocortical relay cells was maximal for CMS at 70 Hz and 100 Hz, this was not the case for 150 Hz CMS, suggesting that presynaptic GABAergic receptors were activated and that the rate of GABA reuptake was increased. Thus, our model suggests that the transient suppression of the neocortical epileptic activity with CMS may be primarily due to extra-synaptic tonic inhibition in the thalamocortical relay cells. These findings contribute to a deeper understanding of high-frequency CMS in epilepsy and pave the way for further research and optimization of this therapeutic approach.

Distributed Synaptic Connection Strength Changes Dynamics in a Population Firing Rate Model in Response to Continuous External Stimuli

Neural network complexity allows for diverse neuronal population dynamics and realizes higherorder brain functions such as cognition and memory. Complexity is enhanced through chemical synapses with exponentially decaying conductance and greater variation in the neuronal connection strength due to synaptic plasticity. However, in the macroscopic neuronal population model, synaptic connections are often described by spike connections, and connection strengths within the population are assumed to be uniform. Thus, the effects of synaptic connections variation on network synchronization remain unclear. Based on recent advances in mean field theory for the quadratic integrate-and-fire neuronal network model, we introduce synaptic conductance and variation of connection strength into the excitatory and inhibitory neuronal population model and derive the macroscopic firing rate equations for faithful modeling. We then introduce a heuristic switching rule of the dynamic system with respect to the mean membrane potentials to avoid divergences in the computation caused by variations in the neuronal connection strength. We show that the switching rule agrees with the numerical computation of the microscopic level model. In the derived model, variations in synaptic conductance and connection strength strongly alter the stability of the solutions to the equations, which is related to the mechanism of synchronous firing. When we apply physiologically plausible values from layer 4 of the mammalian primary visual cortex to the derived model, we observe event-related desynchronization at the alpha and beta frequencies and event-related synchronization at the gamma frequency over a wide range of balanced external currents. Our results show that the introduction of complex synaptic connections and physiologically valid numerical values into the low-dimensional mean field equations reproduces dynamic changes such as eventrelated (de)synchronization, and provides a unique mathematical insight into the relationship between synaptic strength variation and oscillatory mechanism.

A comprehensive investigation of intracortical and corticothalamic models of the alpha rhythm

The electroencephalographic alpha rhythm is one of the most robustly observed and widely studied empirical phenomena in all of neuroscience. However, despite its extensive implication in a wide range of cognitive processes and clinical pathologies, the mechanisms underlying alpha generation in neural circuits remain poorly understood. In this paper we offer a renewed foundation for research on this question, by undertaking a systematic comparison and synthesis of the most prominent theoretical models of alpha rhythmogenesis in the published literature. We focus on four models, each studied intensively by multiple authors over the past three decades: (i) Jansen-Rit, (ii) Moran-David-Friston, (iii) Robinson-Rennie-Wright, and (iv) Liley-Wright. Several common elements are identified, such as the use of second-order differential equations and sigmoidal potential-to-rate operators to represent population-level neural activity. Major differences are seen in other features such as wiring topologies and conduction delays. Through a series of mathematical analyses and numerical simulations, we nevertheless demonstrate that the selected models can be meaningfully compared, by associating parameters and circuit motifs of analogous biological significance. With this established, we conduct explorations of rate constant and synaptic connectivity parameter spaces, with the aim of identifying common patterns in key behaviours, such as the role of excitatory-inhibitory interactions in the generation of oscillations. Finally, using linear stability analysis we identify two qualitatively different alpha-generating dynamical regimes across the models: (i) noise-driven fluctuations and (ii) self-sustained limit-cycle oscillations, emerging due to an Andronov-Hopf bifurcation. The comprehensive survey and synthesis developed here can, we suggest, be used to help guide future theoretical and experimental work aimed at disambiguating these and other candidate theories of alpha rhythmogenesis.

Possible regulatory mechanisms of typical and atypical absence seizures through an equivalent projection from the subthalamic nucleus to the cortex: Evidence in a computational model

The subthalamic nucleus (STN) is an important structure that regulates basal ganglia output and has been involved in the pathophysiology of epilepsy disease. In this paper, we propose an equivalent inhibitory pathway directly projecting from the STN to the cortex and systematically study its regulatory effect on absence seizures. Interestingly, we find that this equivalent inhibitory projection is a key factor for assisting in the development of atypical absence seizures. Through computational simulation and model analysis, we find that the enhancement of coupling strength on this equivalent STN-cortex projection can effectively suppress typical and atypical spike and wave discharges (TSWDs and ASWDs) during absence seizures. Furthermore, altering the activation level of STN through external stimuli can also control seizures, and the presence of equivalent STN-cortex projection makes the control effect more easier to achieve. Several direct and indirect pathways related to the STN can achieve inhibition of SWDs by regulating the activation level of STN, and relevant control strategies have high biological plausibility. Therefore, the STN may be an effective target for the deep brain stimulation (DBS) to control absence seizures. Importantly, we observe that the control effect of DBS-STN on SWDs is significantly superior to other basal ganglia targets in this model. Moreover, we find that the parameter range and value with high biological plausibility for the coupling weight in this equivalent STN-cortex projection can be effectively estimated in this model. Our results imply that the inhibitory effect from the STN to the cortex plays a crucial role in regulating both typical and atypical SWDs, and the STN might be a potential and reasonable DBS target for the treatment of absence epilepsy.

Functional connectotomy of a whole-brain model reveals tumor-induced alterations to neuronal dynamics in glioma patients

Brain tumors can induce pathological changes in neuronal dynamics that are reflected in functional connectivity measures. Here, we use a whole-brain modeling approach to investigate pathological alterations to neuronal activity in glioma patients. By fitting a Hopf whole-brain model to empirical functional connectivity, we investigate glioma-induced changes in optimal model parameters. We observe considerable differences in neuronal dynamics between glioma patients and healthy controls, both on an individual and population-based level. In particular, model parameter estimation suggests that local tumor pathology causes changes in brain dynamics by increasing the influence of interregional interactions on global neuronal activity. Our approach demonstrates that whole-brain models provide valuable insights for understanding glioma-associated alterations in functional connectivity.

Analyzing the brain's dynamic response to targeted stimulation using generative modeling

Generative models of brain activity have been instrumental in testing hypothesized mechanisms underlying brain dynamics against experimental datasets. Beyond capturing the key mechanisms underlying spontaneous brain dynamics, these models hold an exciting potential for understanding the mechanisms underlying the dynamics evoked by targeted brain stimulation techniques. This paper delves into this emerging application, using concepts from dynamical systems theory to argue that the stimulus-evoked dynamics in such experiments may be shaped by new types of mechanisms distinct from those that dominate spontaneous dynamics. We review and discuss (a) the targeted experimental techniques across spatial scales that can both perturb the brain to novel states and resolve its relaxation trajectory back to spontaneous dynamics and (b) how we can understand these dynamics in terms of mechanisms using physiological, phenomenological, and data-driven models. A tight integration of targeted stimulation experiments with generative quantitative modeling provides an important opportunity to uncover novel mechanisms of brain dynamics that are difficult to detect in spontaneous settings.

Sleep and circadian rhythms modeling: From hypothalamic regulatory networks to cortical dynamics and behavior

Sleep and circadian rhythms are regulated by dynamic physiologic processes that operate across multiple spatial and temporal scales. These include, but are not limited to, genetic oscillators, clearance of waste products from the brain, dynamic interplay among brain regions, and propagation of local dynamics across the cortex. The combination of these processes, modulated by environmental cues, such as light-dark cycles and work schedules, represents a complex multiscale system that regulates sleep-wake cycles and brain dynamics. Physiology-based mathematical models have successfully explained the mechanisms underpinning dynamics at specific scales and are a useful tool to investigate interactions across multiple scales. They can help answer questions such as how do electroencephalographic (EEG) features relate to subthalamic neuron activity? Or how are local cortical dynamics regulated by the homeostatic and circadian mechanisms? In this chapter, we review two types of models that are well-positioned to consider such interactions. Part I of the chapter focuses on the subthalamic sleep regulatory networks and a model of arousal dynamics capable of predicting sleep, circadian rhythms, and cognitive outputs. Part II presents a model of corticothalamic circuits, capable of predicting spatial and temporal EEG features. We then discuss existing approaches and unsolved challenges in developing unified multiscale models.

Near-critical corticothalamic eigenmodes: Effects of nonuniform connectivity on modes, activity, and communication channels

The effects of nonuniformities in axonal connectivity on natural modes of brain activity are explored to determine their contributions to modal eigenvalues, structure, and communication and to clarify the limits of validity of widely used uniform-connectivity approximations. Preferred channels of communication are demonstrated that are supported by natural modes of mean connectivity and resulting activity. The effects of axonal tracts on these modes are calculated using perturbation methods, and it is found that modes and their spectra are only moderately perturbed by even the largest white matter tracts. However, perturbations of activity are greatly magnified when modes are near-critical and realistic connectivity and gain perturbations can then enable rapid responses to stimuli on the observed timescales of evoked responses. It is thus argued that dynamic mode-mode communication channels complement ones based on white matter tracts and that both rely on near-criticality to have their observed effects.

From brain connectivity to cognitive function: Dissecting the salience network in pediatric BECTS-ESES

BACKGROUND

Benign childhood epilepsy with centrotemporal spikes (BECTS), a common pediatric epilepsy, may lead to cognitive decline when compounded by Electrical Status Epilepticus during Sleep (ESES). Emerging evidence suggests that disruptions in the Salience Network (SN) contribute significantly to the cognitive deficits observed in BECTS-ESES. Our study rigorously investigates the dynamic functional connectivity (dFC) within the SN and its correlation with cognitive impairments in BECTS-ESES, employing advanced neuroimaging and neuropsychological assessments.

METHODS

In this research, 45 patients diagnosed with BECTS-ESES and 55 age-matched healthy controls (HCs) participated. We utilized resting-state functional magnetic resonance imaging (fMRI) and Independent Component Analysis (ICA) to identify three fundamental SN nodes: the right Anterior Insula (rAI), left Anterior Insula (lAI), and the Anterior Cingulate Cortex (ACC). A two-sample t-test facilitated the comparison of dFC between these pivotal regions and other brain areas.

RESULTS

Significantly, the BECTS-ESES group demonstrated increased dFC, particularly between the ACC and the right Middle Occipital Gyrus, and from the rAI to the right Superior Parietal Gyrus and Cerebellum, and from the lAI to the left Postcentral Gyrus. Such dFC augmentations provide neural insights potentially explaining the neuropsychological deficits in BECTS-ESES children. Employing comprehensive neuropsychological evaluations, we mapped these dFC disruptions to specific cognitive impairments encompassing memory, executive functioning, language, and attention. Through multiple regression analysis and path analysis, a preliminary but compelling association was discovered linking dFC disturbances directly to cognitive impairments. These findings underscore the critical role of SN disruptions in BECTS-ESES cognitive dysfunctions.

LIMITATION

Our cross-sectional design and analytic methods preclude definitive mediation models and causal inferences, leaving the precise nature of dFC's mediating role and its direct impact by BECTS-ESES partially unresolved. Future longitudinal and confirmatory studies are needed to comprehensively delineate these associations.

CONCLUSION

Our study heralds dFC within the SN as a vital biomarker for cognitive impairment in pediatric epilepsy, advocating for targeted cognitive-specific interventions in managing BECTS-ESES. The preliminary nature of our findings invites further studies to substantiate these associations, offering profound implications for the prognosis and therapeutic strategies in BECTS-ESES, thereby underlining the importance of this research in the field of pediatric neurology and epilepsy management.

Propagation effect of the thalamic feed-forward and feed-back inhibition in multi-type coupling models

Seizure waves of epilepsy can propagate in a coupled thalamocortical model, which typically occurs in malfunctioning neuronal networks. However, it remains unclear whether thalamic feed-forward inhibition (FFI) and feed-back inhibition (FBI), the two most important microcircuits in this network, have propagation effects. In this study, we first investigated the importance of the pyramidal neuronal population-thalamic reticular nucleus and specific relay nucleus-thalamic reticular nucleus pathways in the Taylor model for seizure control as FFI and FBI, respectively. Subsequently, using the FBI as a crucial parameter, we constructed 2- and 3-compartment coupling models and evaluated their impact on seizure propagation in other chambers by varying the degree of coupling strength. Finally, we replicated the above study in a 10-compartment model to ensure the robustness of the findings. We confirmed that FBI is more effective by analyzing the combined effect of FFI and FBI, and the pathology state does advance as the coupling strength is increased. These findings elucidate the roles that these two pathways play in the propagation of epileptic seizures and may offer fresh perspectives on the clinical management of epilepsy.

Homeodynamic feedback inhibition control in whole-brain simulations

Simulations of large-scale brain dynamics are often impacted by overexcitation resulting from heavy-tailed structural network distributions, leading to biologically implausible simulation results. We implement a homeodynamic plasticity mechanism, known from other modeling work, in the widely used Jansen-Rit neural mass model for The Virtual Brain (TVB) simulation framework. We aim at heterogeneously adjusting the inhibitory coupling weights to reach desired dynamic regimes in each brain region. We show that, by using this dynamic approach, we can control the target activity level to obtain biologically plausible brain simulations, including post-synaptic potentials and blood-oxygen-level-dependent functional magnetic resonance imaging (fMRI) activity. We demonstrate that the derived dynamic Feedback Inhibitory Control (dFIC) can be used to enable increased variability of model dynamics. We derive the conditions under which the simulated brain activity converges to a predefined target level analytically and via simulations. We highlight the benefits of dFIC in the context of fitting the TVB model to static and dynamic measures of fMRI empirical data, accounting for global synchronization across the whole brain. The proposed novel method helps computational neuroscientists, especially TVB users, to easily "tune" brain models to desired dynamical regimes depending on the specific requirements of each study. The presented method is a steppingstone towards increased biological realism in brain network models and a valuable tool to better understand their underlying behavior.

Striatum is the potential target for treating absence epilepsy: a theoretical evidence

The output of the basal ganglia to the corticothalamic system plays an important role in regulating absence seizures. Inspired by experiments, we systematically study the crucial roles of two newly identified direct inhibitory striatal-cortical projections that project from the striatal D1 nucleus (SD1) and striatal D2 nucleus (SD2) to the cerebral cortex, in controlling absence seizures. Through computational simulation, we observe that typical 2-4 Hz spike and wave discharges (SWDs) can be induced through the pathological mechanism of cortical circuits, and both enhancing the inhibitory coupling weight on the striatal-cortical projections and improving the discharge activation level of striatal populations can effectively control typical SWDs. Furthermore, typical SWDs can be suppressed by appropriately adjusting several input projections directly related to the striatum, through regulating the activation level of striatal populations. Interestingly, several indirect striatum-related basal ganglia projections also have significant effects on the inhibition of typical SWDs, through the direct inhibitory striatal-cortical projections. Both the unidirectional control mode and bidirectional control mode for typical SWDs exist in our modified model. Importantly, the enhancement of coupling strengths on inhibitory striatal-cortical projections is beneficial for suppressing SWDs and may play a decisive regulatory role in the formation of control modes. Therefore, our study suggests that striatum may be potential effective targets for the treatment of absence seizures, through two newly identified direct inhibitory striatal-cortical projections. Interestingly, we find that external stimuli simultaneously targeting the striatum and another basal ganglia nucleus have a better control effect on SWDs than targeting a single basal ganglia nucleus, and the obtained results provide testable hypotheses for future experiments.

Secondary thalamic dysfunction underlies abnormal large-scale neural dynamics in chronic stroke

Stroke causes pronounced and widespread slowing of neural activity. Despite decades of work exploring these abnormal neural dynamics and their associated functional impairments, their causes remain largely unclear. To close this gap in understanding, we applied a neurophysiological corticothalamic circuit model to simulate magnetoencephalography (MEG) power spectra recorded from chronic stroke patients. Comparing model-estimated physiological parameters to those of controls, patients demonstrated significantly lower intrathalamic inhibition in the lesioned hemisphere, despite the absence of direct damage to the thalamus itself. We hypothesized that this disinhibition could instead be related to secondary degeneration of the thalamus, for which growing evidence exists in the literature. Further analyses confirmed that spectral slowing correlated significantly with overall secondary degeneration of the ipsilesional thalamus, encompassing decreased thalamic volume, altered tissue microstructure, and decreased blood flow. Crucially, this relationship was mediated by model-estimated thalamic disinhibition, suggesting a causal link between secondary thalamic degeneration and abnormal brain dynamics via thalamic disinhibition. Finally, thalamic degeneration was correlated significantly with poorer cognitive and language outcomes, but not lesion volume, reinforcing that thalamus damage may account for additional individual variability in poststroke disability. Overall, our findings indicate that the frequently observed poststroke slowing reflects a disruption of corticothalamic circuit dynamics due to secondary thalamic dysfunction, and highlights the thalamus as an important target for understanding and potentially treating poststroke brain dysfunction.

Unified theory of alpha, mu, and tau rhythms via eigenmodes of brain activity

A compact description of the frequency structure and topography of human alpha-band rhythms is obtained by use of the first four brain activity eigenmodes previously derived from corticothalamic neural field theory. Just two eigenmodes that overlap in frequency are found to reproduce the observed topography of the classical alpha rhythm for subjects with a single, occipitally concentrated alpha peak in their electroencephalograms. Alpha frequency splitting and relative amplitudes of double alpha peaks are explored analytically and numerically within this four-mode framework using eigenfunction expansion and perturbation methods. These effects are found to result primarily from the different eigenvalues and corticothalamic gains corresponding to the eigenmodes. Three modes with two non-overlapping frequencies suffice to reproduce the observed topography for subjects with a double alpha peak, where the appearance of a distinct second alpha peak requires an increase of the corticothalamic gain of higher eigenmodes relative to the first. Conversely, alpha blocking is inferred to be linked to a relatively small attention-dependent reduction of the gain of the relevant eigenmodes, whose effect is enhanced by the near-critical state of the brain and whose sign is consistent with inferences from neural field theory. The topographies and blocking of the mu and tau rhythms within the alpha-band are explained analogously via eigenmodes. Moreover, the observation of three rhythms in the alpha band is due to there being exactly three members of the first family of spatially nonuniform modes. These results thus provide a simple, unified description of alpha band rhythms and enable experimental observations of spectral structure and topography to be linked directly to theory and underlying physiology.

Multi-scale modelling of the epileptic brain: advantages of computational therapy exploration

Objective: Epilepsy is a complex disease spanning across multiple scales, from ion channels in neurons to neuronal circuits across the entire brain. Over the past decades, computational models have been used to describe the pathophysiological activity of the epileptic brain from different aspects. Traditionally, each computational model can aid in optimizing therapeutic interventions, therefore, providing a particular view to design strategies for treating epilepsy. As a result, most studies are concerned with generating specific models of the epileptic brain that can help us understand the certain machinery of the pathological state. Those specific models vary in complexity and biological accuracy, with system-level models often lacking biological details.Approach: Here, we review various types of computational model of epilepsy and discuss their potential for different therapeutic approaches and scenarios, including drug discovery, surgical strategies, brain stimulation, and seizure prediction. We propose that we need to consider an integrated approach with a unified modelling framework across multiple scales to understand the epileptic brain. Our proposal is based on the recent increase in computational power, which has opened up the possibility of unifying those specific epileptic models into simulations with an unprecedented level of detail.Main results: A multi-scale epilepsy model can bridge the gap between biologically detailed models, used to address molecular and cellular questions, and brain-wide models based on abstract models which can account for complex neurological and behavioural observations.Significance: With these efforts, we move toward the next generation of epileptic brain models capable of connecting cellular features, such as ion channel properties, with standard clinical measures such as seizure severity.

Recruiting neural field theory for data augmentation in a motor imagery brain-computer interface

We introduce a novel approach to training data augmentation in brain-computer interfaces (BCIs) using neural field theory (NFT) applied to EEG data from motor imagery tasks. BCIs often suffer from limited accuracy due to a limited amount of training data. To address this, we leveraged a corticothalamic NFT model to generate artificial EEG time series as supplemental training data. We employed the BCI competition IV '2a' dataset to evaluate this augmentation technique. For each individual, we fitted the model to common spatial patterns of each motor imagery class, jittered the fitted parameters, and generated time series for data augmentation. Our method led to significant accuracy improvements of over 2% in classifying the "total power" feature, but not in the case of the "Higuchi fractal dimension" feature. This suggests that the fit NFT model may more favorably represent one feature than the other. These findings pave the way for further exploration of NFT-based data augmentation, highlighting the benefits of biophysically accurate artificial data.

The seizure classification of focal epilepsy based on the network motif analysis

Due to the complexity of focal epilepsy and its risk for transiting to the generalized epilepsy, the development of reliable classification methods to accurately predict and classify focal and generalized seizures is critical for the clinical management of patients with epilepsy. In order to holistically understand the seizure propagation behavior of focal epilepsy, we propose a three-node motif reduced network by respectively simplifying the focal region, surrounding healthy region and their critical regions as the single node. Because three-node motif can richly characterize information evolutions, the motif analysis method could comprehensively investigate the seizure behavior of focal epilepsy. Firstly, we define a new seizure propagation marker value to capture the seizure onsets and intensity. Based on the three-node motif analysis, it is shown that the focal seizure and spreading can be categorized as inhibitory seizure, focal seizure, focal-critical seizure and generalized seizures, respectively. The four types of seizures correspond to specific modal types respectively, reflecting the strong correlation between seizure behavior and information flow evolution. In addition, it is found that the intensity difference of outflow and inflow information from the critical node (connection heterogeneity) and the excitability of the critical node significantly affected the distribution and transition of the four seizure types. In particular, the method of local linear stability analysis also verifies the effectiveness of four types of seizures classification. In sum, this paper computationally confirms the complex dynamic behavior of focal seizures, and the study of criticality is helpful to propose novel seizure control strategies.

Neural field theory of adaptive effects on auditory evoked responses and mismatch negativity in multifrequency stimulus sequences

Physiologically based neural field theory (NFT) of the corticothalamic system, including adaptation, is used to calculate the responses evoked by trains of auditory stimuli that differ in frequency. In oddball paradigms, fully distinguishable frequencies lead to different standard (common stimulus) and deviant (rare stimulus) responses; the signal obtained by subtracting the standard response from the deviant is termed the mismatch negativity (MMN). In this analysis, deviant responses are found to correspond to unadapted cortex, whereas the part of auditory cortex that processes the standard stimuli adapts over several stimulus presentations until the final standard response form is achieved. No higher-order memory processes are invoked. In multifrequency experiments, the deviant response approaches the standard one as the deviant frequency approaches that of the standard and analytic criteria for this effect to be obtained. It is shown that these criteria can also be used to understand adaptation in random tone sequences. A method of probing MMNs and adaptation in random tone sequences is suggested to makes more use of such data.

Modelling and Controlling System Dynamics of the Brain: An Intersection of Machine Learning and Control Theory

The human brain, as a complex system, has long captivated multidisciplinary researchers aiming to decode its intricate structure and function. This intricate network has driven scientific pursuits to advance our understanding of cognition, behavior, and neurological disorders by delving into the complex mechanisms underlying brain function and dysfunction. Modelling brain dynamics using machine learning techniques deepens our comprehension of brain dynamics from a computational perspective. These computational models allow researchers to simulate and analyze neural interactions, facilitating the identification of dysfunctions in connectivity or activity patterns. Additionally, the trained dynamical system, serving as a surrogate model, optimizes neurostimulation strategies under the guidelines of control theory. In this chapter, we discuss the recent studies on modelling and controlling brain dynamics at the intersection of machine learning and control theory, providing a framework to understand and improve cognitive function, and treat neurological and psychiatric disorders.

Suppression of absence seizures by using different stimulations in a reduced corticothalamic-basal ganglion-pedunculopontine nucleus model

Coupled neural network models are playing an increasingly important part in the modulation of absence seizures today. However, it is currently unclear how basal ganglia, corticothalamic network and pedunculopontine nucleus can coordinate with each other to develop a whole coupling circuit, theoretically. In addition, it is still difficult to select effective parameters of electrical stimulation on the regulation of absence seizures in clinical trials. Therefore, to develop a coupled model and reduce computation cost, a new model constructed by a simplified basal ganglion, two corticothalamic circuits and a pedunculopontine nucleus was proposed. Further, to seek better inhibition therapy, three electrical stimulations, high frequency stimulation (HFS), 1:0 coordinate reset stimulation (CRS) and 3:2 CRS, were applied to the thalamic reticular nucleus (RE) in the first corticothalamic circuit in the coupled model. The simulation results revealed that increasing the frequency and pulse width of an electrical stimulation within a certain range can also suppress seizures. Under the same parameters of electrical stimulation, the inhibitory effect of HFS on seizures was better than that of 1:0 CRS and 3:2 CRS. The research established a reduced corticothalamic-basal ganglion-pedunculopontine nucleus model, which lays a theoretical foundation for future optimal parameters selection of electrical stimulation. We hope that the findings will provide new insights into the role of theoretical models in absence seizures.

Criticality of neuronal avalanches in human sleep and their relationship with sleep macro- and micro-architecture

Sleep plays a key role in preserving brain function, keeping brain networks in a state that ensures optimal computation. Empirical evidence indicates that this state is consistent with criticality, where scale-free neuronal avalanches emerge. However, the connection between sleep architecture and brain tuning to criticality remains poorly understood. Here, we characterize the critical behavior of avalanches and study their relationship with sleep macro- and micro-architectures, in particular, the cyclic alternating pattern (CAP). We show that avalanches exhibit robust scaling behaviors, with exponents obeying scaling relations consistent with the mean-field directed percolation universality class. We demonstrate that avalanche dynamics is modulated by the NREM-REM cycles and that, within NREM sleep, avalanche occurrence correlates with CAP activation phases-indicating a potential link between CAP and brain tuning to criticality. The results open new perspectives on the collective dynamics underlying CAP function, and on the relationship between sleep architecture, avalanches, and self-organization to criticality.

Method for quantifying arousal and consciousness in healthy states and severe brain injury via EEG-based measures of corticothalamic physiology

BACKGROUND

Characterization of normal arousal states has been achieved by fitting predictions of corticothalamic neural field theory (NFT) to electroencephalographic (EEG) spectra to yield relevant physiological parameters.

NEW METHOD

A prior fitting method is extended to distinguish conscious and unconscious states in healthy and brain injured subjects by identifying additional parameters and clusters in parameter space.

RESULTS

Fits of NFT predictions to EEG spectra are used to estimate neurophysiological parameters in healthy and brain injured subjects. Spectra are used from healthy subjects in wake and sleep and from patients with unresponsive wakefulness syndrome, in a minimally conscious state (MCS), and emerged from MCS. Subjects cluster into three groups in parameter space: conscious healthy (wake and REM), sleep, and brain injured. These are distinguished by the difference X-Y between corticocortical (X) and corticothalamic (Y) feedbacks, and by mean neural response rates α and β to incoming spikes. X-Y tracks consciousness in healthy individuals, with smaller values in wake/REM than sleep, but cannot distinguish between brain injuries. Parameters α and β differentiate deep sleep from wake/REM and brain injury.

COMPARISON WITH EXISTING METHODS

Other methods typically rely on laborious clinical assessment, manual EEG scoring, or evaluation of measures like Φ from integrated information theory, for which no efficient method exists. In contrast, the present method can be automated on a personal computer.

CONCLUSION

The method provides a means to quantify consciousness and arousal in healthy and brain injured subjects, but does not distinguish subtypes of brain injury.

The non-specific matrix thalamus facilitates the cortical information processing modes relevant for conscious awareness

The neurobiological mechanisms of arousal and anesthesia remain poorly understood. Recent evidence highlights the key role of interactions between the cerebral cortex and the diffusely projecting matrix thalamic nuclei. Here, we interrogate these processes in a whole-brain corticothalamic neural mass model endowed with targeted and diffusely projecting thalamocortical nuclei inferred from empirical data. This model captures key features seen in propofol anesthesia, including diminished network integration, lowered state diversity, impaired susceptibility to perturbation, and decreased corticocortical coherence. Collectively, these signatures reflect a suppression of information transfer across the cerebral cortex. We recover these signatures of conscious arousal by selectively stimulating the matrix thalamus, recapitulating empirical results in macaque, as well as wake-like information processing states that reflect the thalamic modulation of large-scale cortical attractor dynamics. Our results highlight the role of matrix thalamocortical projections in shaping many features of complex cortical dynamics to facilitate the unique communication states supporting conscious awareness.

Regulating epileptiform discharges by heterogeneous interneurons in thalamocortical model

Inhibitory interneurons in the cortex are abundant and have diverse roles, classified as parvalbumin (PV), somatostatin (SOM), and vasoactive intestinal polypeptide (VIP) according to chemically defined categories. Currently, their involvement with seizures has been partially uncovered in physiological terms. Here, we propose a corticothalamic model containing heterogeneous interneurons to study the effects of various interneurons on absence seizure dynamics by means of optogenetic stimulation. First, the important role of feedforward inhibition caused by SRN→PV→PN projections on seizures is verified. Then, we demonstrate that light activation targeting either PV or SOM INs can control seizures. Finally, with different inhibition contributions from PV INs and SOM INs, the possible disinhibitory effect of blue light acting on VIP INs is mainly discussed. The results suggest that depending on the inhibition degree of both types, the disinhibition brought about by the VIP INs will trigger seizures, will control seizures, and will not work or cause the PNs to tend toward a high saturation state with high excitability. The circuit mechanism and the related bifurcation characteristics in various cases are emphatically revealed. In the model presented, in addition to Hopf and saddle-node bifurcations, the system may also undergo period-doubling and torus bifurcations under stimulus action, with more complex dynamics. Our work may provide a theoretical basis for understanding and further exploring the role of heterogeneous interneurons, in particular, the VIP INs, a novel target, in absence seizures.

Neuronal avalanches: Sandpiles of self-organized criticality or critical dynamics of brain waves?

Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave dynamics [Phys. Rev. Research 2, 023061 (2020); J. Cognitive Neurosci. 32, 2178 (2020)] reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Biases in inverse Ising estimates of near-critical behavior

Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as pseudo-likelihood maximization (PLM), are biased. Using the Sherrington-Kirkpatrick model as a benchmark, we show that these biases are large in critical regimes close to phase boundaries, and they may alter the qualitative interpretation of the inferred model. In particular, we show that the small-sample bias causes models inferred through PLM to appear closer to criticality than one would expect from the data. Data-driven methods to correct this bias are explored and applied to a functional magnetic resonance imaging data set from neuroscience. Our results indicate that additional care should be taken when attributing criticality to real-world data sets.

Preservation of thalamocortical circuitry is essential for good recovery after cardiac arrest

Continuous electroencephalographam (EEG) monitoring contributes to prediction of neurological outcome in comatose cardiac arrest survivors. While the phenomenology of EEG abnormalities in postanoxic encephalopathy is well known, the pathophysiology, especially the presumed role of selective synaptic failure, is less understood. To further this understanding, we estimate biophysical model parameters from the EEG power spectra from individual patients with a good or poor recovery from a postanoxic encephalopathy. This biophysical model includes intracortical, intrathalamic, and corticothalamic synaptic strengths, as well as synaptic time constants and axonal conduction delays. We used continuous EEG measurements from hundred comatose patients recorded during the first 48 h postcardiac arrest, 50 with a poor neurological outcome [cerebral performance category ( CPC = 5 ) ] and 50 with a good neurological outcome ( CPC = 1 ). We only included patients that developed (dis-)continuous EEG activity within 48 h postcardiac arrest. For patients with a good outcome, we observed an initial relative excitation in the corticothalamic loop and corticothalamic propagation that subsequently evolved towards values observed in healthy controls. For patients with a poor outcome, we observed an initial increase in the cortical excitation-inhibition ratio, increased relative inhibition in the corticothalamic loop, delayed corticothalamic propagation of neuronal activity, and severely prolonged synaptic time constants that did not return to physiological values. We conclude that the abnormal EEG evolution in patients with a poor neurological recovery after cardiac arrest may result from persistent and selective synaptic failure that includes corticothalamic circuitry and also delayed corticothalamic propagation.

Dissociation between phase and power correlation networks in the human brain is driven by co-occurrent bursts

Well-known haemodynamic resting-state networks are better mirrored in power correlation networks than phase coupling networks in electrophysiological data. However, what do these power correlation networks reflect? We address this long-outstanding question in neuroscience using rigorous mathematical analysis, biophysical simulations with ground truth and application of these mathematical concepts to empirical magnetoencephalography (MEG) data. Our mathematical derivations show that for two non-Gaussian electrophysiological signals, their power correlation depends on their coherence, cokurtosis and conjugate-coherence. Only coherence and cokurtosis contribute to power correlation networks in MEG data, but cokurtosis is less affected by artefactual signal leakage and better mirrors haemodynamic resting-state networks. Simulations and MEG data show that cokurtosis may reflect co-occurrent bursting events. Our findings shed light on the origin of the complementary nature of power correlation networks to phase coupling networks and suggests that the origin of resting-state networks is partly reflected in co-occurent bursts in neuronal activity.

Control of epileptic activities in a cortex network of multiple coupled neural populations under electromagnetic induction

Epilepsy is believed to be associated with the abnormal synchronous neuronal activity in the brain, which results from large groups or circuits of neurons. In this paper, we choose to focus on the temporal lobe epilepsy, and establish a cortex network of multiple coupled neural populations to explore the epileptic activities under electromagnetic induction. We demonstrate that the epileptic activities can be controlled and modulated by electromagnetic induction and coupling among regions. In certain regions, these two types of control are observed to show exactly reverse effects. The results show that the strong electromagnetic induction is conducive to eliminating the epileptic seizures. The coupling among regions has a conduction effect that the previous normal background activity of the region gives way to the epileptic discharge, owing to coupling with spike wave discharge regions. Overall, these results highlight the role of electromagnetic induction and coupling among the regions in controlling and modulating epileptic activities, and might provide novel insights into the treatments of epilepsy.

Combined effect of stimulation and electromagnetic induction on absence seizure inhibition in coupled thalamocortical circuits

Deep brain stimulation (DBS) and electromagnetic induction are new techniques that are increasingly used in modern epilepsy treatments; however, the mechanism of action remains unclear. In this study, we constructed a bidirectional-coupled cortico-thalamic model, based on which we proposed three regulation schemes: isolated regulation of DBS, isolated regulation of electromagnetic induction and combined regulation of the previous two. In particular, we introduced DBS with a lower amplitude and considered the influence of electromagnetic induction caused by the transmembrane current on the membrane potential. The most striking finding of this study is that the three therapeutic schemes could effectively control abnormal discharge, and combined regulation could reduce the occurrence of epileptic seizures more effectively. The present study bridges the gap between the bidirectional coupling model and combined control. In this way, the damage induced by electrical stimulation of the patient's brain tissue could be reduced, and the abnormal physiological discharge pattern of the cerebral cortex was simultaneously regulated by different techniques. This work opens new avenues for improving brain dysfunction in patients with epilepsy, expands ideas for promoting the development of neuroscience and is meaningful for improving the health of modern society and developing the field of science.

Critical brain wave dynamics of neuronal avalanches

Analytical expressions for scaling of brain wave spectra derived from the general non-linear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent non-linear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different non-linear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order non-linear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Suppression of seizure in childhood absence epilepsy using robust control of deep brain stimulation: a simulation study

Deep brain stimulation (DBS) is a promising technique to relieve the symptoms in patients with intractable seizures. Although the DBS therapy for seizure suppression dates back more than 40 years, determining stimulation parameters is a significant challenge to the success of this technique. One solution to this challenge with application in a real DBS system is to design a closed-loop control system to regulate the stimulation intensity using computational models of epilepsy automatically. The main goal of the current study is to develop a robust control technique based on adaptive fuzzy terminal sliding mode control (AFTSMC) for eliminating the oscillatory spiking behavior in childhood absence epilepsy (CAE) dynamical model consisting of cortical, thalamic relay, and reticular nuclei neurons. To this end, the membrane voltage dynamics of the three coupled neurons are considered as a three-input three-output nonlinear state delay system. A fuzzy logic system is developed to estimate the unknown nonlinear dynamics of the current and delayed states of the model embedded in the control input. Chattering-free control input (continuous DBS pulses) without any singularity problem is the superiority of the proposed control method. To guarantee the bounded stability of the closed-loop system in a finite time, the upper bounds of the external disturbance and minimum estimation errors are updated online with adaptive laws without any offline tuning phase. Simulation results are provided to show the robustness of AFTSMC in the presence of uncertainty and external disturbances.

The adjustment mechanism of the spike and wave discharges in thalamic neurons: a simulation analysis

Different from many previous theoretical studies, this paper explores the regulatory mechanism of the spike and wave discharges (SWDs) in the reticular thalamic nucleus (TRN) by a dynamic computational model. We observe that the SWDs appears in the TRN by changing the coupling weights and delays in the thalamocortical circuit. The abundant poly-spikes wave discharges is also induced when the delay increases to large enough. These discharges can be inhibited by tuning the inhibitory output from the basal ganglia to the thalamus. The mechanisms of these waves can be explained in this model together with simulation results, which are different from the mechanisms in the cortex. The TRN is an important target in treating epilepsy, and the results may be a theoretical evidence for experimental study in the future.

Inhibitory synaptic loss drives network changes in multiple sclerosis: An ex vivo to in silico translational study

Background:

Synaptic and neuronal loss contribute to network dysfunction and disability in multiple sclerosis (MS). However, it is unknown whether excitatory or inhibitory synapses and neurons are more vulnerable and how their losses impact network functioning.

Objective:

To quantify excitatory and inhibitory synapses and neurons and to investigate how synaptic loss affects network functioning through computational modeling.

Methods:

Using immunofluorescent staining and confocal microscopy, densities of glutamatergic and GABAergic synapses and neurons were compared between post-mortem MS and non-neurological control cases. Then, a corticothalamic biophysical model was employed to study how MS-induced excitatory and inhibitory synaptic loss affect network functioning.

Results:

In layer VI of normal-appearing MS cortex, excitatory and inhibitory synaptic densities were significantly lower than controls (reductions up to 14.9%), but demyelinated cortex showed larger losses of inhibitory synapses (29%). In our computational model, reducing inhibitory synapses impacted the network most, leading to a disinhibitory increase in neuronal activity and connectivity.

Conclusion:

In MS, excitatory and inhibitory synaptic losses were observed, predominantly for inhibitory synapses in demyelinated cortex. Inhibitory synaptic loss affected network functioning most, leading to increased neuronal activity and connectivity. As network disinhibition relates to cognitive impairment, inhibitory synaptic loss seems particularly relevant in MS.

Regulating absence seizures by tri-phase delay stimulation applied to globus pallidus internal

In this paper, a reduced globus pallidus internal (GPI)-corticothalamic (GCT) model is developed, and a tri-phase delay stimulation (TPDS) with sequentially applying three pulses on the GPI representing the inputs from the striatal D ₁ neurons, subthalamic nucleus (STN), and globus pallidus external (GPE), respectively, is proposed. The GPI is evidenced to control absence seizures characterized by 2 Hz-4 Hz spike and wave discharge (SWD). Hence, based on the basal ganglia-thalamocortical (BGCT) model, we firstly explore the triple effects of D _l-GPI, GPE-GPI, and STN-GPI pathways on seizure patterns. Then, using the GCT model, we apply the TPDS on the GPI to potentially investigate the alternative and improved approach if these pathways to the GPI are blocked. The results show that the striatum D ₁, GPE, and STN can indeed jointly and significantly affect seizure patterns. In particular, the TPDS can effectively reproduce the seizure pattern if the D ₁-GPI, GPE-GPI, and STN-GPI pathways are cut off. In addition, the seizure abatement can be obtained by well tuning the TPDS stimulation parameters. This implies that the TPDS can play the surrogate role similar to the modulation of basal ganglia, which hopefully can be helpful for the development of the brain-computer interface in the clinical application of epilepsy.

Classification of EEG Signals for Prediction of Epileptic Seizures

Epilepsy is a common brain disorder that causes patients to face multiple seizures in a single day. Around 65 million people are affected by epilepsy worldwide. Patients with focal epilepsy can be treated with surgery, whereas generalized epileptic seizures can be managed with medications. It has been noted that in more than 30% of cases, these medications fail to control epileptic seizures, resulting in accidents and limiting the patient’s life. Predicting epileptic seizures in such patients prior to the commencement of an oncoming seizure is critical so that the seizure can be treated with preventive medicines before it occurs. Electroencephalogram (EEG) signals of patients recorded to observe brain electrical activity during a seizure can be quite helpful in predicting seizures. Researchers have proposed methods that use machine and/or deep learning techniques to predict epileptic seizures using scalp EEG signals; however, prediction of seizures with increased accuracy is still a challenge. Therefore, we propose a three-step approach. It includes preprocessing of scalp EEG signals with PREP pipeline, which is a more sophisticated alternative to basic notch filtering. This method uses a regression-based technique to further enhance the SNR, with a combination of handcrafted, i.e., statistical features such as temporal mean, variance, and skewness, and automated features using CNN, followed by classification of interictal state and preictal state segments using LSTM to predict seizures. We train and validate our proposed technique on the CHB-MIT scalp EEG dataset and achieve accuracy of 94%, sensitivity of 93.8%, and 91.2% specificity. The proposed technique achieves better sensitivity and specificity than existing methods.

Role of coupling distances in a coupled thalamocortical network for regulation of epilepsy

The recent theoretical modeling of coupled cortical thalamic network is an important advance toward the spatiotemporal dynamics of the brain. However, the diversity of coupling distances is ignored, and the better choice of deep brain stimulation (DBS) parameters to control epilepsy is still a challenge so far. A modeling object of this paper is to establish a coupled cortical thalamic model with uncertain coupling distances including nine combinations. Based on the pathways formed by pyramidal neuronal population (PY), thalamic reticular nucleus (RE) and thalamic relay nucleus (TC), we simulate the spike-wave discharges (SWD) at 2-4Hz which are the main manifestations of absence episodes. It is demonstrated that combination (1/3, 1/9) between the left and right ventricles is the optimal coupling distance of the proposed model by analyzing the percentage of SWD. A stimulating object of this paper is to find an optimum parameter range of DBS. One of the important results is that the number of SWD is inversely proportional to the amplitude, another one is that the number of SWD shows a U-shaped trend with the change of frequency. The present study has laidtheoryfoundationforthebrainplasticity, which will provide an important theoretical basis and direction for the treatment of absence epilepsy in the future. In brief, hopefully our simulation results will provide some help to patients.

Cross-Frequency Slow Oscillation–Spindle Coupling in a Biophysically Realistic Thalamocortical Neural Mass Model

Sleep manifests itself by the spontaneous emergence of characteristic oscillatory rhythms, which often time-lock and are implicated in memory formation. Here, we analyze a neural mass model of the thalamocortical loop in which the cortical node can generate slow oscillations (approximately 1 Hz) while its thalamic component can generate fast sleep spindles of σ-band activity (12–15 Hz). We study the dynamics for different coupling strengths between the thalamic and cortical nodes, for different conductance values of the thalamic node's potassium leak and hyperpolarization-activated cation-nonselective currents, and for different parameter regimes of the cortical node. The latter are listed as follows: (1) a low activity (DOWN) state with noise-induced, transient excursions into a high activity (UP) state, (2) an adaptation induced slow oscillation limit cycle with alternating UP and DOWN states, and (3) a high activity (UP) state with noise-induced, transient excursions into the low activity (DOWN) state. During UP states, thalamic spindling is abolished or reduced. During DOWN states, the thalamic node generates sleep spindles, which in turn can cause DOWN to UP transitions in the cortical node. Consequently, this leads to spindle-induced UP state transitions in parameter regime (1), thalamic spindles induced in some but not all DOWN states in regime (2), and thalamic spindles following UP to DOWN transitions in regime (3). The spindle-induced σ-band activity in the cortical node, however, is typically the strongest during the UP state, which follows a DOWN state “window of opportunity” for spindling. When the cortical node is parametrized in regime (3), the model well explains the interactions between slow oscillations and sleep spindles observed experimentally during Non-Rapid Eye Movement sleep. The model is computationally efficient and can be integrated into large-scale modeling frameworks to study spatial aspects like sleep wave propagation.

Mechanism analysis for excitatory interneurons dominating poly-spike wave and optimization of electrical stimulation

In addition to inhibitory interneurons, there exist excitatory interneurons (EINs) in the cortex, which mainly have excitatory projections to pyramidal neurons. In this study, we improve a thalamocortical model by introducing EIN, investigate the dominant role of EIN in generating spike and slow wave discharges (SWDs), and consider a non-rectangular pulse to control absence seizures. First, we display here that the improved model can reproduce typical SWDs of absence seizures. Moreover, we focus on the function of EIN by means of bifurcation analysis and find that EIN can induce transition behaviors under Hopf-type and fold limit cycle bifurcations. Specifically, the system has three stable solutions composing a tri-stable region. In this region, there are three attraction basins, which hints that external stimulation can drive the system trajectory from one basin to another, thereby eliminating abnormal oscillations. Furthermore, we compare the increasing ramp with rectangular pulse and optimize stimulation waveforms from the perspective of electrical charges input. The controlling role of the single increasing ramp to absence seizures is remarkable and the optimal stimulus parameters have been found theoretically. This work provides a computational model containing EIN and a theoretical basis for future physiological experiments and clinical research studies.

Virtual intracranial EEG signals reconstructed from MEG with potential for epilepsy surgery

Modelling the interactions that arise from neural dynamics in seizure genesis is challenging but important in the effort to improve the success of epilepsy surgery. Dynamical network models developed from physiological evidence offer insights into rapidly evolving brain networks in the epileptic seizure. A limitation of previous studies in this field is the dependence on invasive cortical recordings with constrained spatial sampling of brain regions that might be involved in seizure dynamics. Here, we propose virtual intracranial electroencephalography (ViEEG), which combines non-invasive ictal magnetoencephalographic imaging (MEG), dynamical network models and a virtual resection technique. In this proof-of-concept study, we show that ViEEG signals reconstructed from MEG alone preserve critical temporospatial characteristics for dynamical approaches to identify brain areas involved in seizure generation. We show the non-invasive ViEEG approach may have some advantage over intracranial electroencephalography (iEEG). Future work may be designed to test the potential of the virtual iEEG approach for use in surgical management of epilepsy.

Generalized neural field theory of cortical plasticity illustrated by an application to the linear phase of ocular dominance column formation in primary visual cortex

Physiologically based neural field theory (NFT) is extended to encompass cortical plasticity dynamics. An illustrative application is provided which treats the evolution of the connectivity of left- and right-eye visual stimuli to neuronal populations in the primary visual cortex (V1), and the initial, linear phase of formation of approximately one-dimensional (1D) ocular dominance columns (ODCs) that sets their transverse spatial scale. This links V1 activity, structure, and physiology within a single theory that already accounts for a range of other brain activity and connectivity phenomena, thereby enabling ODC formation and many other phenomena to be interrelated and cortical parameters to be constrained across multiple domains. The results accord with experimental ODC widths for realistic cortical parameters and are based directly on a unified description of the neuronal populations involved, their connection strengths, and the neuronal activity they support. Other key results include simple analytic approximations for ODC widths and the parameters of maximum growth rate, constraints on cortical excitatory and inhibitory gains, elucidation of the roles of specific poles of the V1 response function, and the fact that ODCs are not formed when input stimuli are fully correlated between eyes. This work provides a basis for further generalization of NFT to model other plasticity phenomena, thereby linking them to the range multiscale phenomena accounted for by NFT.

The Relationship Between the Rhythmic Components of the Brain Electrical Activity During the Development of Status Epilepticus: An Operational Model of Brain Rhythms Generation

Background/Introduction: Despite the fact that brain rhythms are widely studied and officially classified, there is no consensus on their relationship, which can shed light on the genesis of rhythmic activity, its synchronization, functional role, and the formation of pathological reactions. Using the experimental status epilepticus (SE) as a model of brain in a hypersynchronized state with well-defined rhythms, we aimed to study the relationship between the rhythmic components of the brain electrical activity. Materials and Methods: Local field potentials (LFPs) were recorded simultaneously from the hippocampus, entorhinal cortex, medial septum, and amygdala during normal conditions and after kainic acid (KA) administration in waking guinea pigs. The dynamical spectral LFP properties were analyzed with the aid of Fast Fourier transform. Results: KA induces prominent SE with periodic combination of epileptiform discharge complexes and relatively quiet interdischarge intervals in the electrical activity of the brain. We have shown that new components appeared in the LFP spectra during the development of SE, representing a sequential doubling of the frequency, which had initially been dominating in the background records. Discussion: The phenomenon of frequency doubling can be interpreted as the octave principle of the LFP spectrum rhythmic carcass structure. The spectra of discharge complexes represent an alternation of harmonic spectra, where fundamental frequency coincides with one of the doubled frequencies dominating in the interdischarge activity. Using a nonlinear recurrent operation of rhythm multiplication and the obtained data we propose an operational model of the generation of rhythms and pathological discharges in the brain based on the octave principle. Impact statement In this study, we examined the relationship between the rhythmic components of the electrical activity of the limbic structures during the experimental status epilepticus and propose an operational model of brain rhythms generation based on the octave principle. Our study demonstrates that using fundamental principles (nonlinearity and the presence of recurrence), it is possible to explain the genesis and phenomenology of the electrical activity of brain structures in normal and pathological conditions.

Discrete spectral eigenmode-resonance network of brain dynamics and connectivity

The problem of finding a compact natural representation of brain dynamics and connectivity is addressed using an expansion in terms of physical spatial eigenmodes and their frequency resonances. It is demonstrated that this discrete expansion via the system transfer function enables linear and nonlinear dynamics to be analyzed in compact form in terms of natural dynamic "atoms," each of which is a frequency resonance of an eigenmode. Because these modal resonances are determined by the system dynamics, not the investigator, they are privileged over widely used phenomenological patterns, and obviate the need for artificial discretizations and thresholding in coordinate space. It is shown that modal resonances participate as nodes of a discrete spectral network, are noninteracting in the linear regime, but are linked nonlinearly by wave-wave coalescence and decay processes. The modal resonance formulation is shown to be capable of speeding numerical calculations of strongly nonlinear interactions. Recent work in brain dynamics, especially based on neural field theory (NFT) approaches, allows eigenmodes and their resonances to be estimated from data without assuming a specific brain model. This means that dynamic equations can be inferred using system identification methods from control theory, rather than being assumed, and resonances can be interpreted as control-systems data filters. The results link brain activity and connectivity with control-systems functions such as prediction and attention via gain control and can also be linked to specific NFT predictions if desired, thereby providing a convenient bridge between physiologically based theories and experiment. Amplitudes of modes and resonances can also be tracked to provide a more direct and temporally localized representation of the dynamics than correlations and covariances, which are widely used in the field. By synthesizing many different lines of research, this work provides a way to link quantitative electrophysiological and imaging measurements, connectivity, brain dynamics, and function. This underlines the need to move between coordinate and spectral representations as required. Moreover, standard theoretical-physics approaches and mathematical methods can be used in place of ad hoc statistical measures such as those based on graph theory of artificially discretized and decimated networks, which are highly prone to selection effects and artifacts.

Neural Field Theory of Evoked Response Sequences and Mismatch Negativity With Adaptation

Physiologically based neural field theory of the corticothalamic system is used to calculate the responses evoked by trains of auditory stimuli that correspond to different cortical locations via the tonotopic map. The results are shown to account for standard and deviant evoked responses to frequent and rare stimuli, respectively, in the auditory oddball paradigms widely used in human cognitive studies, and the so-called mismatch negativity between them. It also reproduces a wide range of other effects and variants, including the mechanism by which a change in standard responses relative to deviants can develop through adaptation, different responses when two deviants are presented in a row or a standard is presented after two deviants, relaxation of standard responses back to deviant form after a stimulus-free period, and more complex sequences. Some cases are identified in which adaptation does not account for the whole difference between standard and deviant responses. The results thus provide a systematic means to determine how much of the response is due to adaptation in the system comprising the primary auditory cortex and medial geniculate nucleus, and how much requires involvement of higher-level processing.

Determination of Dynamic Brain Connectivity via Spectral Analysis

Spectral analysis based on neural field theory is used to analyze dynamic connectivity via methods based on the physical eigenmodes that are the building blocks of brain dynamics. These approaches integrate over space instead of averaging over time and thereby greatly reduce or remove the temporal averaging effects, windowing artifacts, and noise at fine spatial scales that have bedeviled the analysis of dynamical functional connectivity (FC). The dependences of FC on dynamics at various timescales, and on windowing, are clarified and the results are demonstrated on simple test cases, demonstrating how modes provide directly interpretable insights that can be related to brain structure and function. It is shown that FC is dynamic even when the brain structure and effective connectivity are fixed, and that the observed patterns of FC are dominated by relatively few eigenmodes. Common artifacts introduced by statistical analyses that do not incorporate the physical nature of the brain are discussed and it is shown that these are avoided by spectral analysis using eigenmodes. Unlike most published artificially discretized “resting state networks” and other statistically-derived patterns, eigenmodes overlap, with every mode extending across the whole brain and every region participating in every mode—just like the vibrations that give rise to notes of a musical instrument. Despite this, modes are independent and do not interact in the linear limit. It is argued that for many purposes the intrinsic limitations of covariance-based FC instead favor the alternative of tracking eigenmode coefficients vs. time, which provide a compact representation that is directly related to biophysical brain dynamics.

Modal-Polar Representation of Evoked Response Potentials in Multiple Arousal States

An expansion of the corticothalamic transfer function into eigenmodes and resonant poles is used to derive a simple formula for evoked response potentials (ERPs) in various states of arousal. The transfer function corresponds to the cortical response to an external stimulus, which encodes all the information and properties of the linear system. This approach links experimental observations of resonances and characteristic timescales in brain activity with physically based neural field theory (NFT). The present work greatly simplifies the formula of the analytical ERP, and separates its spatial part (eigenmodes) from the temporal part (poles). Within this framework, calculations involve contour integrations that yield an explicit expression for ERPs. The dominant global mode is considered explicitly in more detail to study how the ERP varies with time in this mode and to illustrate the method. For each arousal state in sleep and wake, the resonances of the system are determined and it is found that five poles are sufficient to study the main dynamics of the system in waking eyes-open and eyes-closed states. Similarly, it is shown that six poles suffice to reproduce ERPs in rapid-eye movement sleep, sleep state 1, and sleep state 2 states, whereas just four poles suffice to reproduce the dynamics in slow wave sleep. Thus, six poles are sufficient to preserve the main global ERP dynamics of the system for all states of arousal. These six poles correspond to the dominant resonances of the system at slow-wave, alpha, and beta frequencies. These results provide the basis for simplified analytic treatment of brain dynamics and link observations more closely to theory.

Neural field theory of neural avalanche exponents

The power-law exponents of observed size and lifetime distributions of near-critical neural avalanches are calculated from neural field theory using diagrammatic methods. This brings neural avalanches within the ambit of neural field theory, which has also previously explained near-critical 1/f spectra and many other observed features of neural activity. This strengthens the case for near-criticality of the brain and opens the way for these other phenomena to be interrelated with avalanches and their dynamics.

Brain dynamics and structure-function relationships via spectral factorization and the transfer function

It is shown how the brain's linear transfer function provides a means to systematically analyze brain connectivity and dynamics, and to infer connectivity, eigenmodes, and activity measures such as spectra, evoked responses, coherence, and causality, all of which are widely used in brain monitoring. In particular, the Wilson spectral factorization algorithm is outlined and used to efficiently obtain linear transfer functions from experimental two-point correlation functions. The algorithm is tested on a series of brain-like structures of increasing complexity which include time delays, asymmetry, two-dimensionality, and complex network connectivity. These tests are used to verify the algorithm is suitable for application to brain dynamics, specify sampling requirements for experimental time series, and to verify that its runtime is short enough to obtain accurate results for systems of similar size to current experiments. The results can equally well be applied to inference of the transfer function in complex linear systems other than brains.