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

Slow-wave oscillations in a corticothalamic model of sleep and wake

A physiologically-based corticothalamic neural field model is used to study slow wave oscillations including cortical UP and DOWN states in deep sleep by extending it to incorporate bursting dynamics of neurons in the thalamic reticular nucleus. The interplay of local bursting dynamics and network interactions produces the cortical UP and DOWN states of slow wave sleep while preserving previously verified model predictions in the wake state. Results show that EEG spectral features in wake and sleep are reproduced. The bursting is subthreshold but acts to intensify the amplitude of oscillations in slow wave sleep with deep UP/DOWN oscillations on the cortex emerging naturally. Furthermore, there is a continuous cycle between the two regimes, rather than a flip-flop between discrete states.

A computational study of stimulus driven epileptic seizure abatement

Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.

Anesthetic action on extra-synaptic receptors: effects in neural population models of EEG activity

The role of extra-synaptic receptors in the regulation of excitation and inhibition in the brain has attracted increasing attention. Because activity in the extra-synaptic receptors plays a role in regulating the level of excitation and inhibition in the brain, they may be important in determining the level of consciousness. This paper reviews briefly the literature on extra-synaptic GABA and NMDA receptors and their affinity to anesthetic drugs. We propose a neural population model that illustrates how the effect of the anesthetic drug propofol on GABAergic extra-synaptic receptors results in changes in neural population activity and the electroencephalogram (EEG). Our results show that increased tonic inhibition in inhibitory cortical neurons cause a dramatic increase in the power of both δ− and α− bands. Conversely, the effects of increased tonic inhibition in cortical excitatory neurons and thalamic relay neurons have the opposite effect and decrease the power in these bands. The increased δ-activity is in accord with observed data for deepening propofol anesthesia; but is absolutely dependent on the inclusion of extrasynaptic (tonic) GABA action in the model.

Control of absence seizures induced by the pathways connected to SRN in corticothalamic system

The cerebral cortex, thalamus and basal ganglia together form an important network in the brain, which is closely related to several nerve diseases, such as parkinson disease, epilepsy seizure and so on. Absence seizure can be characterized by 2-4 Hz oscillatory activity, and it can be induced by abnormal interactions between the cerebral cortex and thalamus. Many experimental results have also shown that basal ganglia are a key neural structure, which closely links the corticothalamic system in the brain. Presently, we use a corticothalamic-basal ganglia model to study which pathways in corticothalamic system can induce absence seizures and how these oscillatory activities can be controlled by projections from the substantia nigra pars reticulata (SNr) to the thalamic reticular nucleus (TRN) or the specific relay nuclei (SRN) of the thalamus. By tuning the projection strength of the pathway "Excitatory pyramidal cortex-SRN", "SRN-Excitatory pyramidal cortex" and "SRN-TRN" respectively, different firing states including absence seizures can appear. This indicates that absence seizures can be induced by tuning the connection strength of the considered pathway. In addition, typical absence epilepsy seizure state "spike-and-slow wave discharges" can be controlled by adjusting the activation level of the SNr as the pathways SNr-SRN and SNr-TRN open independently or together. Our results emphasize the importance of basal ganglia in controlling absence seizures in the corticothalamic system, and can provide a potential idea for the clinical treatment.

Construct validation of a DCM for resting state fMRI

Recently, there has been a lot of interest in characterising the connectivity of resting state brain networks. Most of the literature uses functional connectivity to examine these intrinsic brain networks. Functional connectivity has well documented limitations because of its inherent inability to identify causal interactions. Dynamic causal modelling (DCM) is a framework that allows for the identification of the causal (directed) connections among neuronal systems — known as effective connectivity. This technical note addresses the validity of a recently proposed DCM for resting state fMRI – as measured in terms of their complex cross spectral density – referred to as spectral DCM. Spectral DCM differs from (the alternative) stochastic DCM by parameterising neuronal fluctuations using scale free (i.e., power law) forms, rendering the stochastic model of neuronal activity deterministic. Spectral DCM not only furnishes an efficient estimation of model parameters but also enables the detection of group differences in effective connectivity, the form and amplitude of the neuronal fluctuations or both. We compare and contrast spectral and stochastic DCM models with endogenous fluctuations or state noise on hidden states. We used simulated data to first establish the face validity of both schemes and show that they can recover the model (and its parameters) that generated the data. We then used Monte Carlo simulations to assess the accuracy of both schemes in terms of their root mean square error. We also simulated group differences and compared the ability of spectral and stochastic DCMs to identify these differences. We show that spectral DCM was not only more accurate but also more sensitive to group differences. Finally, we performed a comparative evaluation using real resting state fMRI data (from an open access resource) to study the functional integration within default mode network using spectral and stochastic DCMs.

•

This paper provides construct validation of spectral DCM against stochastic DCM.

•

Spectral DCM is shown to be more accurate than stochastic DCM in terms of root mean square error.

•

Spectral DCM is shown to be more sensitive at identifying group differences.

Characterization of K-complexes and slow wave activity in a neural mass model

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

Determination of effective brain connectivity from functional connectivity using propagator-based interferometry and neural field theory with application to the corticothalamic system

It is shown how to compute both direct and total effective connection matrices (deCMs and teCMs), which embody the strengths of neural connections between regions, from correlation-based functional CMs using propagator-based interferometry, a method that stems from geophysics and acoustics, coupled with the recent identification of deCMs and teCMs with bare and dressed propagators, respectively. The approach incorporates excitatory and inhibitory connections, multiple structures and populations, and measurement effects. The propagator is found for a generalized scalar wave equation derived from neural field theory, and expressed in terms of neural activity correlations and covariances, and wave damping rates. It is then related to correlation matrices that are commonly used to express functional and effective connectivities in the brain. The results are illustrated in analytically tractable test cases.

Spatiotemporally varying visual hallucinations: II. Spectral classification and comparison with theory

In order to better understand the nature of visual hallucinations, and to test predictions of spatiotemporally oscillating hallucinations from a recent corticothalamic model of visual dynamics, clinical descriptions of hallucinations are used to establish boundaries on the spatiotemporal frequencies observed in various disorders. Detailed comparisons with hallucinations during migraine aura demonstrate that key features are consistent with corticothalamic origin and specific abnormalities, but underline the need for more detailed quantitative data to be obtained on temporally oscillating hallucinations more generally.

Structural connectivity based whole brain modelling in epilepsy

Epilepsy is a neurological condition characterised by the recurrence of seizures. During seizures multiple brain areas can behave abnormally. Rather than considering each abnormal area in isolation, one can consider them as an interconnected functional 'network'. Recently, there has been a shift in emphasis to consider epilepsy as a disorder involving more widespread functional brain networks than perhaps was previously thought. The basis for these functional networks is proposed to be the static structural brain network established through the connectivity of the white matter. Additionally, it has also been argued that time varying aspects of epilepsy are of crucial importance and as such computational models of these dynamical properties have recently advanced. We describe how dynamic computer models can be combined with static human in vivo connectivity obtained through diffusion weighted magnetic resonance imaging. We predict that in future the use of these two methods in concert will lead to predictions for optimal surgery and brain stimulation sites for epilepsy and other neurological disorders.

Dynamic mechanisms of neocortical focal seizure onset

Recent experimental and clinical studies have provided diverse insight into the mechanisms of human focal seizure initiation and propagation. Often these findings exist at different scales of observation, and are not reconciled into a common understanding. Here we develop a new, multiscale mathematical model of cortical electric activity with realistic mesoscopic connectivity. Relating the model dynamics to experimental and clinical findings leads us to propose three classes of dynamical mechanisms for the onset of focal seizures in a unified framework. These three classes are: (i) globally induced focal seizures; (ii) globally supported focal seizures; (iii) locally induced focal seizures. Using model simulations we illustrate these onset mechanisms and show how the three classes can be distinguished. Specifically, we find that although all focal seizures typically appear to arise from localised tissue, the mechanisms of onset could be due to either localised processes or processes on a larger spatial scale. We conclude that although focal seizures might have different patient-specific aetiologies and electrographic signatures, our model suggests that dynamically they can still be classified in a clinically useful way. Additionally, this novel classification according to the dynamical mechanisms is able to resolve some of the previously conflicting experimental and clinical findings.

According to the WHO fact sheet, epilepsy is a neurological disorder affecting about 50 million people worldwide. Even today 30% of epilepsy patients do not respond well to drug therapies. Neocortical focal epilepsy is a particular type of epilepsy in which drug treatments fail and surgical success rate is low. Hence, research is essential to improve the treatment of this type of epilepsy. Recent advances in brain recording methods have led to new observations regarding the nature of neocortical focal epilepsy. However, some of the observations appear to be contradictory. Here, we develop a computational modelling framework that can explain the different observations as different aspects of possible mechanisms that can all lead to seizure onset. Specifically, we classify three main conditions under which focal seizure onset can happen. This classification is clinically important, as our model predicts different treatment strategies for each class. We conclude that focal seizures are diverse, not only in their electrographic appearance and aetiology, but also in their onset mechanism. Combined multiscale recordings as well as stimulation studies are required to elucidate the onset mechanism in each patient. Our work provides the first classification of possible onset mechanism.

Determination of effective brain connectivity from functional connectivity with application to resting state connectivities

Neural field theory insights are used to derive effective brain connectivity matrices from the functional connectivity matrix defined by activity covariances. The symmetric case is exactly solved for a resting state system driven by white noise, in which strengths of connections, often termed effective connectivities, are inferred from functional data; these include strengths of connections that are underestimated or not detected by anatomical imaging. Proximity to criticality is calculated and found to be consistent with estimates obtainable from other methods. Links between anatomical, effective, and functional connectivity and resting state activity are quantified, with applicability to other complex networks. Proof-of-principle results are illustrated using published experimental data on anatomical connectivity and resting state functional connectivity. In particular, it is shown that functional connection matrices can be used to uncover the existence and strength of connections that are missed from anatomical connection matrices, including interhemispheric connections that are difficult to track with techniques such as diffusion spectrum imaging.

Scale-free bursting in human cortex following hypoxia at birth

The human brain is fragile in the face of oxygen deprivation. Even a brief interruption of metabolic supply at birth challenges an otherwise healthy neonatal cortex, leading to a cascade of homeostatic responses. During recovery from hypoxia, cortical activity exhibits a period of highly irregular electrical fluctuations known as burst suppression. Here we show that these bursts have fractal properties, with power-law scaling of burst sizes across a remarkable 5 orders of magnitude and a scale-free relationship between burst sizes and durations. Although burst waveforms vary greatly, their average shape converges to a simple form that is asymmetric at long time scales. Using a simple computational model, we argue that this asymmetry reflects activity-dependent changes in the excitatory-inhibitory balance of cortical neurons. Bursts become more symmetric following the resumption of normal activity, with a corresponding reorganization of burst scaling relationships. These findings place burst suppression in the broad class of scale-free physical processes termed crackling noise and suggest that the resumption of healthy activity reflects a fundamental reorganization in the relationship between neuronal activity and its underlying metabolic constraints.

Engineering a thalamo-cortico-thalamic circuit on SpiNNaker: a preliminary study toward modeling sleep and wakefulness

We present a preliminary study of a thalamo-cortico-thalamic (TCT) implementation on SpiNNaker (Spiking Neural Network architecture), a brain inspired hardware platform designed to incorporate the inherent biological properties of parallelism, fault tolerance and energy efficiency. These attributes make SpiNNaker an ideal platform for simulating biologically plausible computational models. Our focus in this work is to design a TCT framework that can be simulated on SpiNNaker to mimic dynamical behavior similar to Electroencephalogram (EEG) time and power-spectra signatures in sleep-wake transition. The scale of the model is minimized for simplicity in this proof-of-concept study; thus the total number of spiking neurons is ≈1000 and represents a "mini-column" of the thalamocortical tissue. All data on model structure, synaptic layout and parameters is inspired from previous studies and abstracted at a level that is appropriate to the aims of the current study as well as computationally suitable for model simulation on a small 4-chip SpiNNaker system. The initial results from selective deletion of synaptic connectivity parameters in the model show similarity with EEG power spectra characteristics of sleep and wakefulness. These observations provide a positive perspective and a basis for future implementation of a very large scale biologically plausible model of thalamo-cortico-thalamic interactivity-the essential brain circuit that regulates the biological sleep-wake cycle and associated EEG rhythms.

A physiologically based model of orexinergic stabilization of sleep and wake

The orexinergic neurons of the lateral hypothalamus (Orx) are essential for regulating sleep-wake dynamics, and their loss causes narcolepsy, a disorder characterized by severe instability of sleep and wake states. However, the mechanisms through which Orx stabilize sleep and wake are not well understood. In this work, an explanation of the stabilizing effects of Orx is presented using a quantitative model of important physiological connections between Orx and the sleep-wake switch. In addition to Orx and the sleep-wake switch, which is composed of mutually inhibitory wake-active monoaminergic neurons in brainstem and hypothalamus (MA) and the sleep-active ventrolateral preoptic neurons of the hypothalamus (VLPO), the model also includes the circadian and homeostatic sleep drives. It is shown that Orx stabilizes prolonged waking episodes via its excitatory input to MA and by relaying a circadian input to MA, thus sustaining MA firing activity during the circadian day. During sleep, both Orx and MA are inhibited by the VLPO, and the subsequent reduction in Orx input to the MA indirectly stabilizes sustained sleep episodes. Simulating a loss of Orx, the model produces dynamics resembling narcolepsy, including frequent transitions between states, reduced waking arousal levels, and a normal daily amount of total sleep. The model predicts a change in sleep timing with differences in orexin levels, with higher orexin levels delaying the normal sleep episode, suggesting that individual differences in Orx signaling may contribute to chronotype. Dynamics resembling sleep inertia also emerge from the model as a gradual sleep-to-wake transition on a timescale that varies with that of Orx dynamics. The quantitative, physiologically based model developed in this work thus provides a new explanation of how Orx stabilizes prolonged episodes of sleep and wake, and makes a range of experimentally testable predictions, including a role for Orx in chronotype and sleep inertia.

Bidirectional control of absence seizures by the basal ganglia: a computational evidence

Absence epilepsy is believed to be associated with the abnormal interactions between the cerebral cortex and thalamus. Besides the direct coupling, anatomical evidence indicates that the cerebral cortex and thalamus also communicate indirectly through an important intermediate bridge–basal ganglia. It has been thus postulated that the basal ganglia might play key roles in the modulation of absence seizures, but the relevant biophysical mechanisms are still not completely established. Using a biophysically based model, we demonstrate here that the typical absence seizure activities can be controlled and modulated by the direct GABAergic projections from the substantia nigra pars reticulata (SNr) to either the thalamic reticular nucleus (TRN) or the specific relay nuclei (SRN) of thalamus, through different biophysical mechanisms. Under certain conditions, these two types of seizure control are observed to coexist in the same network. More importantly, due to the competition between the inhibitory SNr-TRN and SNr-SRN pathways, we find that both decreasing and increasing the activation of SNr neurons from the normal level may considerably suppress the generation of spike-and-slow wave discharges in the coexistence region. Overall, these results highlight the bidirectional functional roles of basal ganglia in controlling and modulating absence seizures, and might provide novel insights into the therapeutic treatments of this brain disorder.

Epilepsy is a general term for conditions with recurring seizures. Absence seizures are one of several kinds of seizures, which are characterized by typical 2–4 Hz spike-and-slow wave discharges (SWDs). There is accumulating evidence that absence seizures are due to abnormal interactions between cerebral cortex and thalamus, and the basal ganglia may take part in controlling such brain disease via the indirect basal ganglia-thalamic pathway relaying at superior colliculus. Actually, the basal ganglia not only send indirect signals to thalamus, but also communicate with several key nuclei of thalamus through multiple direct GABAergic projections. Nevertheless, whether and how these direct pathways regulate absence seizure activities are still remain unknown. By computational modelling, we predicted that two direct inhibitory basal ganglia-thalamic pathways emitting from the substantia nigra pars reticulata may also participate in the control of absence seizures. Furthermore, we showed that these two types of seizure control can coexist in the same network, and depending on the instant network state, both lowing and increasing the activation of SNr neurons may inhibit the SWDs due to the existence of competition. Our findings emphasize the bidirectional modulation effects of basal ganglia on absence seizures, and might have physiological implications on the treatment of absence epilepsy.

Experimental observation of a theoretically predicted nonlinear sleep spindle harmonic in human EEG

OBJECTIVE

To investigate the properties of a sleep spindle harmonic oscillation previously predicted by a theoretical neural field model of the brain.

METHODS

Spindle oscillations were extracted from EEG data from nine subjects using an automated algorithm. The power and frequency of the spindle oscillation and the harmonic oscillation were compared across subjects. The bicoherence of the EEG was calculated to identify nonlinear coupling.

RESULTS

All subjects displayed a spindle harmonic at almost exactly twice the frequency of the spindle. The power of the harmonic scaled nonlinearly with that of the spindle peak, consistent with model predictions. Bicoherence was observed at the spindle frequency, confirming the nonlinear origin of the harmonic oscillation.

CONCLUSIONS

The properties of the sleep spindle harmonic were consistent with the theoretical modeling of the sleep spindle harmonic as a nonlinear phenomenon.

SIGNIFICANCE

Most models of sleep spindle generation are unable to produce a spindle harmonic oscillation, so the observation and theoretical explanation of the harmonic is a significant step in understanding the mechanisms of sleep spindle generation. Unlike seizures, sleep spindles produce nonlinear effects that can be observed in healthy controls, and unlike the alpha oscillation, there is no linearly generated harmonic that can obscure nonlinear effects. This makes the spindle harmonic a good candidate for future investigation of nonlinearity in the brain.

A thalamo-cortical neural mass model for the simulation of brain rhythms during sleep

Cortico-thalamic interactions are known to play a pivotal role in many brain phenomena, including sleep, attention, memory consolidation and rhythm generation. Hence, simple mathematical models that can simulate the dialogue between the cortex and the thalamus, at a mesoscopic level, have a great cognitive value. In the present work we describe a neural mass model of a cortico-thalamic module, based on neurophysiological mechanisms. The model includes two thalamic populations (a thalamo-cortical relay cell population, TCR, and its related thalamic reticular nucleus, TRN), and a cortical column consisting of four connected populations (pyramidal neurons, excitatory interneurons, inhibitory interneurons with slow and fast kinetics). Moreover, thalamic neurons exhibit two firing modes: bursting and tonic. Finally, cortical synapses among pyramidal neurons incorporate a disfacilitation mechanism following prolonged activity. Simulations show that the model is able to mimic the different patterns of rhythmic activity in cortical and thalamic neurons (beta and alpha waves, spindles, delta waves, K-complexes, slow sleep waves) and their progressive changes from wakefulness to deep sleep, by just acting on modulatory inputs. Moreover, simulations performed by providing short sensory inputs to the TCR show that brain rhythms during sleep preserve the cortex from external perturbations, still allowing a high cortical activity necessary to drive synaptic plasticity and memory consolidation. In perspective, the present model may be used within larger cortico-thalamic networks, to gain a deeper understanding of mechanisms beneath synaptic changes during sleep, to investigate the specific role of brain rhythms, and to explore cortical synchronization achieved via thalamic influences.

Modern concepts of seizure modeling

Seizures are complex phenomena spanning multiple spatial and temporal scales, from ion dynamics to communication between brain regions, from milliseconds (spikes) to days (interseizure intervals). Because of the existence of such multiple scales, the experimental evaluation of the mechanisms underlying the initiation, propagation, and termination of epileptic seizures is a difficult problem. Theoretical models and numerical simulations provide new tools to investigate seizure mechanisms at multiple scales. In this chapter, we review different theoretical approaches and their contributions to our understanding of seizure mechanisms.

Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status epilepticus

The EEG of patients in non-convulsive status epilepticus (NCSE) often displays delta oscillations or generalized spike-wave discharges. In some patients, these delta oscillations coexist with intermittent epileptic spikes. In this study we verify the prediction of a computational model of the thalamo-cortical system that these spikes are phase-locked to the delta oscillations. We subsequently describe the physiological mechanism underlying this observation as suggested by the model. It is suggested that the spikes reflect inhibitory stochastic fluctuations in the input to thalamo-cortical relay neurons and phase-locking is a consequence of differential excitability of relay neurons over the delta cycle. Further analysis shows that the observed phase-locking can be regarded as a stochastic precursor of generalized spike-wave discharges. This study thus provides an explanation of intermittent spikes during delta oscillations in NCSE and might be generalized to other encephathologies in which delta activity can be observed.

Prediction and verification of nonlinear sleep spindle harmonic oscillations

This paper examines nonlinear effects in a neural field model of the corticothalamic system to predict the EEG power spectrum of sleep spindles. Nonlinearity in the thalamic relay nuclei gives rise to a spindle harmonic visible in the cortical EEG. By deriving an analytic expression for nonlinear spectrum, the power in the spindle harmonic is predicted to scale quadratically with the power in the spindle oscillation. By isolating sleep spindles from background sleep in experimental EEG data, the spindle harmonic is directly observed.

Large-scale brain dynamics in disorders of consciousness

Brain injury profoundly affects global brain dynamics, and these changes are manifest in the electroencephalogram (EEG). Despite the heterogeneity of injury mechanisms and the modularity of brain function, there is a commonality of dynamical features that characterize the EEG along the gamut from coma to recovery. After severest injury, EEG activity is concentrated below 1 Hz. In minimally conscious state during wakefulness, there is a peak of activity in the 3-7 Hz range, often coherent across the brain, and often also activity in the beta (15-30 Hz) range. These spectral changes likely result from varying degrees of functional deafferentation at thalamic and cortical levels. EEG-based indices of brain dynamics that go beyond these simple spectral measures may provide further diagnostic information and physiologic insights.

Common resting brain dynamics indicate a possible mechanism underlying zolpidem response in severe brain injury

Zolpidem produces paradoxical recovery of speech, cognitive and motor functions in select subjects with severe brain injury but underlying mechanisms remain unknown. In three diverse patients with known zolpidem responses we identify a distinctive pattern of EEG dynamics that suggests a mechanistic model. In the absence of zolpidem, all subjects show a strong low frequency oscillatory peak ∼6–10 Hz in the EEG power spectrum most prominent over frontocentral regions and with high coherence (∼0.7–0.8) within and between hemispheres. Zolpidem administration sharply reduces EEG power and coherence at these low frequencies. The ∼6–10 Hz activity is proposed to arise from intrinsic membrane properties of pyramidal neurons that are passively entrained across the cortex by locally-generated spontaneous activity. Activation by zolpidem is proposed to arise from a combination of initial direct drug effects on cortical, striatal, and thalamic populations and further activation of underactive brain regions induced by restoration of cognitively-mediated behaviors.

DOI:http://dx.doi.org/10.7554/eLife.01157.001

Some individuals who experience severe brain damage are left with disorders of consciousness. While they can appear to be awake, these individuals lack awareness of their surroundings and cannot respond to events going on around them. Few treatments are available, but a minority of patients show striking improvements in speech, alertness and movement in response to the sleeping pill zolpidem.

Although the idea of a sleeping pill increasing consciousness is paradoxical, it is possible that in patients with impaired consciousness, zolpidem reduces the activity of an area of the brain that would otherwise inhibit activity in other regions of the brain. However, the precise mechanisms by which zolpidem increases consciousness in these patients, and the reasons why only a minority of individuals respond, are unknown.

Now, Williams et al. have used electrodes attached to the scalp to measure changes in brain activity in three patients known to respond to zolpidem. These measurements showed that before the drug was taken, there were two important differences between the brain activity of the patients and that of healthy subjects: first, the patients showed brain waves of a lower frequency than any seen in healthy subjects; second, these brain waves were much more synchronized than brain activity in healthy individuals. After taking zolpidem, this synchronicity was reduced and all of the patients also showed an increase in higher frequency brain waves.

Based on the effects of zolpidem on electrical activity throughout the brain, Williams et al. propose a new model to explain the therapeutic action of the drug in some minimally conscious patients. If the correlation between brain waves and zolpidem response holds up in future studies, this relation could be used to predict which patients might benefit from the drug. A better understanding of these processes should also help us to understand, diagnose and develop new treatments for disorders of consciousness.

DOI:http://dx.doi.org/10.7554/eLife.01157.002

Modulation of epileptic activity by deep brain stimulation: a model-based study of frequency-dependent effects

A number of studies showed that deep brain stimulation (DBS) can modulate the activity in the epileptic brain and that a decrease of seizures can be achieved in “responding” patients. In most of these studies, the choice of stimulation parameters is critical to obtain desired clinical effects. In particular, the stimulation frequency is a key parameter that is difficult to tune. A reason is that our knowledge about the frequency-dependant mechanisms according to which DBS indirectly impacts the dynamics of pathological neuronal systems located in the neocortex is still limited. We address this issue using both computational modeling and intracerebral EEG (iEEG) data. We developed a macroscopic (neural mass) model of the thalamocortical network. In line with already-existing models, it includes interconnected neocortical pyramidal cells and interneurons, thalamocortical cells and reticular neurons. The novelty was to introduce, in the thalamic compartment, the biophysical effects of direct stimulation. Regarding clinical data, we used a quite unique data set recorded in a patient (drug-resistant epilepsy) with a focal cortical dysplasia (FCD). In this patient, DBS strongly reduced the sustained epileptic activity of the FCD for low-frequency (LFS, < 2 Hz) and high-frequency stimulation (HFS, > 70 Hz) while intermediate-frequency stimulation (IFS, around 50 Hz) had no effect. Signal processing, clustering, and optimization techniques allowed us to identify the necessary conditions for reproducing, in the model, the observed frequency-dependent stimulation effects. Key elements which explain the suppression of epileptic activity in the FCD include: (a) feed-forward inhibition and synaptic short-term depression of thalamocortical connections at LFS, and (b) inhibition of the thalamic output at HFS. Conversely, modeling results indicate that IFS favors thalamic oscillations and entrains epileptic dynamics.

Modeling resting-state functional networks when the cortex falls asleep: local and global changes

The transition from wakefulness to sleep represents the most conspicuous change in behavior and the level of consciousness occurring in the healthy brain. It is accompanied by similarly conspicuous changes in neural dynamics, traditionally exemplified by the change from "desynchronized" electroencephalogram activity in wake to globally synchronized slow wave activity of early sleep. However, unit and local field recordings indicate that the transition is more gradual than it might appear: On one hand, local slow waves already appear during wake; on the other hand, slow sleep waves are only rarely global. Studies with functional magnetic resonance imaging also reveal changes in resting-state functional connectivity (FC) between wake and slow wave sleep. However, it remains unclear how resting-state networks may change during this transition period. Here, we employ large-scale modeling of the human cortico-cortical anatomical connectivity to evaluate changes in resting-state FC when the model "falls asleep" due to the progressive decrease in arousal-promoting neuromodulation. When cholinergic neuromodulation is parametrically decreased, local slow waves appear, while the overall organization of resting-state networks does not change. Furthermore, we show that these local slow waves are structured macroscopically in networks that resemble the resting-state networks. In contrast, when the neuromodulator decrease further to very low levels, slow waves become global and resting-state networks merge into a single undifferentiated, broadly synchronized network.

Implementing the cellular mechanisms of synaptic transmission in a neural mass model of the thalamo-cortical circuitry

A novel direction to existing neural mass modeling technique is proposed where the commonly used “alpha function” for representing synaptic transmission is replaced by a kinetic framework of neurotransmitter and receptor dynamics. The aim is to underpin neuro-transmission dynamics associated with abnormal brain rhythms commonly observed in neurological and psychiatric disorders. An existing thalamocortical neural mass model is modified by using the kinetic framework for modeling synaptic transmission mediated by glutamatergic and GABA (gamma-aminobutyric-acid)-ergic receptors. The model output is compared qualitatively with existing literature on in vitro experimental studies of ferret thalamic slices, as well as on single-neuron-level model based studies of neuro-receptor and transmitter dynamics in the thalamocortical tissue. The results are consistent with these studies: the activation of ligand-gated GABA receptors is essential for generation of spindle waves in the model, while blocking this pathway leads to low-frequency synchronized oscillations such as observed in slow-wave sleep; the frequency of spindle oscillations increase with increased levels of post-synaptic membrane conductance for AMPA (alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic-acid) receptors, and blocking this pathway effects a quiescent model output. In terms of computational efficiency, the simulation time is improved by a factor of 10 compared to a similar neural mass model based on alpha functions. This implies a dramatic improvement in computational resources for large-scale network simulation using this model. Thus, the model provides a platform for correlating high-level brain oscillatory activity with low-level synaptic attributes, and makes a significant contribution toward advancements in current neural mass modeling paradigm as a potential computational tool to better the understanding of brain oscillations in sickness and in health.

Cortical information flow in Parkinson's disease: a composite network/field model

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany Parkinson's disease (PD). Since motor commands originate in the cortex, an important question is how the basal ganglia influence cortical information flow, and how this influence becomes pathological in PD. To explore this, we developed a composite neuronal network/neural field model. The network model consisted of 4950 spiking neurons, divided into 15 excitatory and inhibitory cell populations in the thalamus and cortex. The field model consisted of the cortex, thalamus, striatum, subthalamic nucleus, and globus pallidus. Both models have been separately validated in previous work. Three field models were used: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. Spikes generated by these field models were then used to drive the network model. Compared to the network driven by the healthy model, the PD-driven network had lower firing rates, a shift in spectral power toward lower frequencies, and higher probability of bursting; each of these findings is consistent with empirical data on PD. In the healthy model, we found strong Granger causality between cortical layers in the beta and low gamma frequency bands, but this causality was largely absent in the PD model. In particular, the reduction in Granger causality from the main “input” layer of the cortex (layer 4) to the main “output” layer (layer 5) was pronounced. This may account for symptoms of PD that seem to reflect deficits in information flow, such as bradykinesia. In general, these results demonstrate that the brain's large-scale oscillatory environment, represented here by the field model, strongly influences the information processing that occurs within its subnetworks. Hence, it may be preferable to drive spiking network models with physiologically realistic inputs rather than pure white noise.

Stability constraints on large-scale structural brain networks

Stability is an important dynamical property of complex systems and underpins a broad range of coherent self-organized behavior. Based on evidence that some neurological disorders correspond to linear instabilities, we hypothesize that stability constrains the brain's electrical activity and influences its structure and physiology. Using a physiologically-based model of brain electrical activity, we investigated the stability and dispersion solutions of networks of neuronal populations with propagation time delays and dendritic time constants. We find that stability is determined by the spectrum of the network's matrix of connection strengths and is independent of the temporal damping rate of axonal propagation with stability restricting the spectrum to a region in the complex plane. Time delays and dendritic time constants modify the shape of this region but it always contains the unit disk. Instabilities resulting from changes in connection strength initially have frequencies less than a critical frequency. For physiologically plausible parameter values based on the corticothalamic system, this critical frequency is approximately 10 Hz. For excitatory networks and networks with randomly distributed excitatory and inhibitory connections, time delays and non-zero dendritic time constants have no impact on network stability but do effect dispersion frequencies. Random networks with both excitatory and inhibitory connections can have multiple marginally stable modes at low delta frequencies.

Synchronization regulation in a model of coupled neural masses

A model of coupled neural masses can generate seizure-like events and dynamics similar to those observed during interictal to ictal transitions and thus can be used for theoretical study of the control of epileptic seizures. In an effort to understand the mechanisms underlying epileptic seizures and how to avoid them, we added a control input to this model. Epileptic seizures are always accompanied by hypersynchronous firing of neurons, so research on synchronization among cortical areas is significant for seizure control. In this study, principal component analysis (PCA) was used to identify synchronization clusters composed of several neural masses. A method for calculating the synchronization cluster strength and participation rate is presented. The synchronization cluster strength can be used to identify synchronization clusters and the participation rate can be employed to identify neural masses that participate in the clusters. Each synchronization cluster is controlled as a whole using a proportional-integral-derivative (PID) controller. We illustrate these points using coupled neural mass models of synchronization to show their responses to increased (between node) coupling with and without control. Experiment results indicated that PID control can effectively regulate synchronization between neural masses and has the potential for seizure prevention.

Relationships between Electroencephalographic Spectral Peaks Across Frequency Bands

The degree to which electroencephalographic spectral peaks are independent, and the relationships between their frequencies have been debated. A novel fitting method was used to determine peak parameters in the range 2-35 Hz from a large sample of eyes-closed spectra, and their interrelationships were investigated. Findings were compared with a mean-field model of thalamocortical activity, which predicts near-harmonic relationships between peaks. The subject set consisted of 1424 healthy subjects from the Brain Resource International Database. Peaks in the theta range occurred on average near half the alpha peak frequency, while peaks in the beta range tended to occur near twice and three times the alpha peak frequency on an individual-subject basis. Moreover, for the majority of subjects, alpha peak frequencies were significantly positively correlated with frequencies of peaks in the theta and low and high beta ranges. Such a harmonic progression agrees semiquantitatively with theoretical predictions from the mean-field model. These findings indicate a common or analogous source for different rhythms, and help to define appropriate individual frequency bands for peak identification.

The epilepsies: complex challenges needing complex solutions

It is widely accepted that epilepsies are complex syndromes due to their multi-factorial origins and manifestations. Different mathematical and computational descriptions use appropriate methods to address nonlinear relationships, chaotic behaviors and emergent properties. These theoretical approaches can be divided into two major categories: descriptive, such as flowcharts, graphs and other statistical analyses, and explicative, which include both realistic and abstract models. Although these modeling tools have brought great advances, a common framework to guide their design, implementation and evaluation, with the goal of future integration, is still needed. In the current review, we discuss two examples of complexity analysis that can be performed with epilepsy data: behavioral sequences of temporal lobe seizures and alterations in an experimental cellular model. We also highlight the importance of the creation of model repositories for the epileptology field and encourage the development of mathematical descriptions of complex systems, together with more accurate simulation techniques.

Towards a large-scale model of patient-specific epileptic spike-wave discharges

Clinical electroencephalographic (EEG) recordings of the transition into generalised epileptic seizures show a sudden onset of spike-wave dynamics from a low-amplitude irregular background. In addition, non-trivial and variable spatio-temporal dynamics are widely reported in combined EEG/fMRI studies on the scale of the whole cortex. It is unknown whether these characteristics can be accounted for in a large-scale mathematical model with fixed heterogeneous long-range connectivities. Here, we develop a modelling framework with which to investigate such EEG features. We show that a neural field model composed of a few coupled compartments can serve as a low-dimensional prototype for the transition between irregular background dynamics and spike-wave activity. This prototype then serves as a node in a large-scale network with long-range connectivities derived from human diffusion-tensor imaging data. We examine multivariate properties in 42 clinical EEG seizure recordings from 10 patients diagnosed with typical absence epilepsy and 50 simulated seizures from the large-scale model using 10 DTI connectivity sets from humans. The model can reproduce the clinical feature of stereotypy where seizures are more similar within a patient than between patients, essentially creating a patient-specific fingerprint. We propose the approach as a feasible technique for the investigation of patient-specific large-scale epileptic features in space and time.

Thalamo-cortical mechanisms underlying changes in amplitude and frequency of human alpha oscillations

Although a large number of studies have been devoted to establishing correlations between changes in amplitude and frequency of EEG alpha oscillations and cognitive processes, it is currently unclear through which physiological mechanisms such changes are brought about. In this study we use a biophysical model of EEG generation to gain a fundamental understanding of the functional changes within the thalamo-cortical system that might underly such alpha responses. The main result of this study is that, although the physiology of the thalamo-cortical system is characterized by a large number of parameters, alpha responses effectively depend on only three variables. Physiologically, these variables determine the resonance properties of feedforward, cortico-thalamo-cortical, and intra-cortical circuits. By examining the effect of modulations of these resonances on the amplitude and frequency of EEG alpha oscillations, it is established that the model can reproduce the variety of experimentally observed alpha responses, as well as the experimental finding that changes in alpha amplitude are typically an order of magnitude larger than changes in alpha frequency. The modeling results are also in line with the fact that alpha responses often correlate linearly with indices characterizing cognitive processes. By investigating the effect of synaptic and intrinsic neuronal parameters, we find that alpha responses reflect changes in cortical activation, which is consistent with the hypothesis that alpha activity serves to selectively inhibit cortical regions during cognitive processing demands. As an example of how these analyses can be applied to specific experimental protocols, we reproduce benzodiazepine-induced alpha responses and clarify the putative underlying thalamo-cortical mechanisms. The findings reported in this study provide a fundamental physiological framework within which alpha responses observed in specific experimental protocols can be understood.

Neural field theory of plasticity in the cerebral cortex

A generalized timing-dependent plasticity rule is incorporated into a recent neural field theory to explore synaptic plasticity in the cerebral cortex, with both excitatory and inhibitory populations included. Analysis in the time and frequency domains reveals that cortical network behavior gives rise to a saddle-node bifurcation and resonant frequencies, including a gamma-band resonance. These system resonances constrain cortical synaptic dynamics and divide it into four classes, which depend on the type of synaptic plasticity window. Depending on the dynamical class, synaptic strengths can either have a stable fixed point, or can diverge in the absence of a separate saturation mechanism. Parameter exploration shows that time-asymmetric plasticity windows, which are signatures of spike-timing dependent plasticity, enable the richest variety of synaptic dynamics to occur. In particular, we predict a zone in parameter space which may allow brains to attain the marginal stability phenomena observed experimentally, although additional regulatory mechanisms may be required to maintain these parameters.

Critical fluctuations in cortical models near instability

Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human electroencephalography (EEG), however, have shown significant autocorrelation at time lags on the scale of minutes, indicating the need to consider regimes where non-linearities influence the dynamics. Statistical properties such as increased autocorrelation length, increased variance, power law scaling, and bistable switching have been suggested as generic indicators of the approach to bifurcation in non-linear dynamical systems. We study temporal fluctuations in a widely-employed computational model (the Jansen–Rit model) of cortical activity, examining the statistical signatures that accompany bifurcations. Approaching supercritical Hopf bifurcations through tuning of the background excitatory input, we find a dramatic increase in the autocorrelation length that depends sensitively on the direction in phase space of the input fluctuations and hence on which neuronal subpopulation is stochastically perturbed. Similar dependence on the input direction is found in the distribution of fluctuation size and duration, which show power law scaling that extends over four orders of magnitude at the Hopf bifurcation. We conjecture that the alignment in phase space between the input noise vector and the center manifold of the Hopf bifurcation is directly linked to these changes. These results are consistent with the possibility of statistical indicators of linear instability being detectable in real EEG time series. However, even in a simple cortical model, we find that these indicators may not necessarily be visible even when bifurcations are present because their expression can depend sensitively on the neuronal pathway of incoming fluctuations.

A canonical model of multistability and scale-invariance in biological systems

Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a system's fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena.

Biological systems are able to adapt to rapidly and widely changing environments. Many biological organisms employ two distinct mechanisms that improve their survival in these circumstances: Firstly they exhibit rapid, qualitative changes in their internal dynamics; secondly they possess the ability to respond to change that is not absolute, but scales in proportion to the underlying intensity of the environment. In this paper, we study a simple class of noisy, dynamical systems that mathematically represent a very broad range of more complex models. We hence show how a combination of nonlinear instabilities and state-dependent noise in this model is able to unify these two apparently distinct biological phenomena. To illustrate its unifying potential, this simple model is applied to two very distinct biological processes – the spontaneous activity of the human cortex (i.e. when subjects are at rest), and genetic regulation in a bacteriophage. We also provide proof of principle that our model can be inverted from empirical data, allowing estimation of the parameters that express the nonlinear and stochastic influences at play in the underlying system.

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

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

Computational modeling of epilepsy for an experimental neurologist

Computational modeling can be a powerful tool for an experimentalist, providing a rigorous mathematical model of the system you are studying. This can be valuable in testing your hypotheses and developing experimental protocols prior to experimenting. This paper reviews models of seizures and epilepsy at different scales, including cellular, network, cortical region, and brain scales by looking at how they have been used in conjunction with experimental data. At each scale, models with different levels of abstraction, the extraction of physiological detail, are presented. Varying levels of detail are necessary in different situations. Physiologically realistic models are valuable surrogates for experimental systems because, unlike in an experiment, every parameter can be changed and every variable can be observed. Abstract models are useful in determining essential parameters of a system, allowing the experimentalist to extract principles that explain the relationship between mechanisms and the behavior of the system. Modeling is becoming easier with the emergence of platforms dedicated to neuronal modeling and databases of models that can be downloaded. Modeling will never be a replacement for animal and clinical experiments, but it should be a starting point in designing experiments and understanding their results.

Neural field theory with variance dynamics

Previous neural field models have mostly been concerned with prediction of mean neural activity and with second order quantities such as its variance, but without feedback of second order quantities on the dynamics. Here the effects of feedback of the variance on the steady states and adiabatic dynamics of neural systems are calculated using linear neural field theory to estimate the neural voltage variance, then including this quantity in the total variance parameter of the nonlinear firing rate-voltage response function, and thus into determination of the fixed points and the variance itself. The general results further clarify the limits of validity of approaches with and without inclusion of variance dynamics. Specific applications show that stability against a saddle-node bifurcation is reduced in a purely cortical system, but can be either increased or decreased in the corticothalamic case, depending on the initial state. Estimates of critical variance scalings near saddle-node bifurcation are also found, including physiologically based normalizations and new scalings for mean firing rate and the position of the bifurcation.

Gap junctions modulate seizures in a mean-field model of general anesthesia for the cortex

During slow-wave sleep, general anesthesia, and generalized seizures, there is an absence of consciousness. These states are characterized by low-frequency large-amplitude traveling waves in scalp electroencephalogram. Therefore the oscillatory state might be an indication of failure to form coherent neuronal assemblies necessary for consciousness. A generalized seizure event is a pathological brain state that is the clearest manifestation of waves of synchronized neuronal activity. Since gap junctions provide a direct electrical connection between adjoining neurons, thus enhancing synchronous behavior, reducing gap-junction conductance should suppress seizures; however there is no clear experimental evidence for this. Here we report theoretical predictions for a physiologically-based cortical model that describes the general anesthetic phase transition from consciousness to coma, and includes both chemical synaptic and direct electrotonic synapses. The model dynamics exhibits both Hopf (temporal) and Turing (spatial) instabilities; the Hopf instability corresponds to the slow (≲8 Hz) oscillatory states similar to those seen in slow-wave sleep, general anesthesia, and seizures. We argue that a delicately balanced interplay between Hopf and Turing modes provides a canonical mechanism for the default non-cognitive rest state of the brain. We show that the Turing mode, set by gap-junction diffusion, is generally protective against entering oscillatory modes; and that weakening the Turing mode by reducing gap conduction can release an uncontrolled Hopf oscillation and hence an increased propensity for seizure and simultaneously an increased sensitivity to GABAergic anesthesia.

Scaling effects and spatio-temporal multilevel dynamics in epileptic seizures

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures.