Estimation of neurophysiological parameters from the waking EEG using a biophysical model of brain dynamics

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.

Suppression of beta oscillations by delayed feedback in a cortex-basal ganglia-thalamus-pedunculopontine nucleus neural loop model

Excessive neural synchronization of neural populations in the beta (β) frequency range (12-35 Hz) is intimately related to the symptoms of hypokinesia in Parkinson's disease (PD). Studies have shown that delayed feedback stimulation strategies can interrupt excessive neural synchronization and effectively alleviate symptoms associated with PD dyskinesia. Work on optimizing delayed feedback algorithms continues to progress, yet it remains challenging to further improve the inhibitory effect with reduced energy expenditure. Therefore, we first established a neural mass model of the cortex-basal ganglia-thalamus-pedunculopontine nucleus (CBGTh-PPN) closed-loop system, which can reflect the internal properties of cortical and basal ganglia neurons and their intrinsic connections with thalamic and pedunculopontine nucleus neurons. Second, the inhibitory effects of three delayed feedback schemes based on the external globus pallidum (GPe) on β oscillations were investigated separately and compared with those based on the subthalamic nucleus (STN) only. Our results show that all four delayed feedback schemes achieve effective suppression of pathological β oscillations when using the linear delayed feedback algorithm. The comparison revealed that the three GPe-based delayed feedback stimulation strategies were able to have a greater range of oscillation suppression with reduced energy consumption, thus improving control performance effectively, suggesting that they may be more effective for the relief of Parkinson's motor symptoms in practical applications.

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.

Spectral slowing in chronic stroke reflects abnormalities in both periodic and aperiodic neural dynamics

Decades of electrophysiological work have demonstrated the presence of "spectral slowing" in stroke patients - a prominent shift in the power spectrum towards lower frequencies, most evident in the vicinity of the lesion itself. Despite the reliability of this slowing as a marker of dysfunctional tissue across patient groups as well as animal models, it has yet to be explained in terms of the pathophysiological processes of stroke. To do so requires clear understanding of the neural dynamics that these differences represent, acknowledging the often overlooked fact that spectral power reflects more than just the amplitude of neural oscillations. To accomplish this, we used a combination of frequency domain and time domain measures to disambiguate and quantify periodic (oscillatory) and aperiodic (non-oscillatory) neural dynamics in resting state magnetoencephalography (MEG) recordings from chronic stroke patients. We found that abnormally elevated low frequency power in these patients was best explained by a steepening of the aperiodic component of the power spectrum, rather than an enhancement of low frequency oscillations, as is often assumed. However, genuine oscillatory activity at higher frequencies was also found to be abnormal, with patients showing alpha slowing and diminished oscillatory activity in the beta band. These aperiodic and periodic abnormalities were found to covary, and could be detected even in the un-lesioned hemisphere, however they were most prominent in perilesional tissue, where their magnitude was predictive of cognitive impairment. This work redefines spectral slowing as a pattern of changes involving both aperiodic and periodic neural dynamics and narrows the gap in understanding between non-invasive markers of dysfunctional tissue and disease processes responsible for altered neural dynamics.

Dynamic causal modelling shows a prominent role of local inhibition in alpha power modulation in higher visual cortex

During resting-state EEG recordings, alpha activity is more prominent over the posterior cortex in eyes-closed (EC) conditions compared to eyes-open (EO). In this study, we characterized the difference in spectra between EO and EC conditions using dynamic causal modelling. Specifically, we investigated the role of intrinsic and extrinsic connectivity-within the visual cortex-in generating EC-EO alpha power differences over posterior electrodes. The primary visual cortex (V1) and the bilateral middle temporal visual areas (V5) were equipped with bidirectional extrinsic connections using a canonical microcircuit. The states of four intrinsically coupled subpopulations-within each occipital source-were also modelled. Using Bayesian model selection, we tested whether modulations of the intrinsic connections in V1, V5 or extrinsic connections (or a combination thereof) provided the best evidence for the data. In addition, using parametric empirical Bayes (PEB), we estimated group averages under the winning model. Bayesian model selection showed that the winning model contained both extrinsic connectivity modulations, as well as intrinsic connectivity modulations in all sources. The PEB analysis revealed increased extrinsic connectivity during EC. Overall, we found a reduction in the inhibitory intrinsic connections during EC. The results suggest that the intrinsic modulations in V5 played the most important role in producing EC-EO alpha differences, suggesting an intrinsic disinhibition in higher order visual cortex, during EC resting state.

Inference of brain networks with approximate Bayesian computation - assessing face validity with an example application in Parkinsonism

This paper describes and validates a novel framework using the Approximate Bayesian Computation (ABC) algorithm for parameter estimation and model selection in models of mesoscale brain network activity. We provide a proof of principle, first pass validation of this framework using a set of neural mass models of the cortico-basal ganglia thalamic circuit inverted upon spectral features from experimental, in vivo recordings. This optimization scheme relaxes an assumption of fixed-form posteriors (i.e. the Laplace approximation) taken in previous approaches to inverse modelling of spectral features. This enables the exploration of model dynamics beyond that approximated from local linearity assumptions and so fit to explicit, numerical solutions of the underlying non-linear system of equations. In this first paper, we establish a face validation of the optimization procedures in terms of: (i) the ability to approximate posterior densities over parameters that are plausible given the known causes of the data; (ii) the ability of the model comparison procedures to yield posterior model probabilities that can identify the model structure known to generate the data; and (iii) the robustness of these procedures to local minima in the face of different starting conditions. Finally, as an illustrative application we show (iv) that model comparison can yield plausible conclusions given the known neurobiology of the cortico-basal ganglia-thalamic circuit in Parkinsonism. These results lay the groundwork for future studies utilizing highly nonlinear or brittle models that can explain time dependant dynamics, such as oscillatory bursts, in terms of the underlying neural circuits.

A Connectome-Based, Corticothalamic Model of State- and Stimulation-Dependent Modulation of Rhythmic Neural Activity and Connectivity

Rhythmic activity in the brain fluctuates with behaviour and cognitive state, through a combination of coexisting and interacting frequencies. At large spatial scales such as those studied in human M/EEG, measured oscillatory dynamics are believed to arise primarily from a combination of cortical (intracolumnar) and corticothalamic rhythmogenic mechanisms. Whilst considerable progress has been made in characterizing these two types of neural circuit separately, relatively little work has been done that attempts to unify them into a single consistent picture. This is the aim of the present paper. We present and examine a whole-brain, connectome-based neural mass model with detailed long-range cortico-cortical connectivity and strong, recurrent corticothalamic circuitry. This system reproduces a variety of known features of human M/EEG recordings, including spectral peaks at canonical frequencies, and functional connectivity structure that is shaped by the underlying anatomical connectivity. Importantly, our model is able to capture state- (e.g., idling/active) dependent fluctuations in oscillatory activity and the coexistence of multiple oscillatory phenomena, as well as frequency-specific modulation of functional connectivity. We find that increasing the level of sensory drive to the thalamus triggers a suppression of the dominant low frequency rhythms generated by corticothalamic loops, and subsequent disinhibition of higher frequency endogenous rhythmic behaviour of intracolumnar microcircuits. These combine to yield simultaneous decreases in lower frequency and increases in higher frequency components of the M/EEG power spectrum during states of high sensory or cognitive drive. Building on this, we also explored the effect of pulsatile brain stimulation on ongoing oscillatory activity, and evaluated the impact of coexistent frequencies and state-dependent fluctuations on the response of cortical networks. Our results provide new insight into the role played by cortical and corticothalamic circuits in shaping intrinsic brain rhythms, and suggest new directions for brain stimulation therapies aimed at state-and frequency-specific control of oscillatory brain activity.

Estimation of Time-Varying Spectral Peaks and Decomposition of EEG Spectrograms

Detection of spectral peaks and estimation of their properties, including frequency and amplitude, are fundamental to many applications of signal processing. Electroencephalography (EEG) of sleep, in particular, displays characteristic oscillations that change continuously throughout the night. Capturing these dynamics is essential to understanding the sleep process and characterizing the heterogeneity observed across individuals. Most sleep EEG analyses rely on either time-averaged spectra or bandpassed amplitude/power. Unfortunately, these approaches obscure the time-variability of peak properties, require specification of a priori criteria, and cannot distinguish power from nearby oscillations. More sophisticated approaches, using various spectral models, have been proposed to better estimate oscillatory properties, but these too have limitations. We present an improved approach to spectrogram decomposition, tracking time-varying parameterized peak functions and dynamically estimating their parameters using a modified form of the iterated extended Kalman filter (IEKF) that incorporates discrete On/Off-switching of peak combinations and a sampling step to draw the initial reference trajectory. We evaluate this approach on two types of simulated examples-one nearly within the model class and one outside. We find excellent performance, in terms of spectral fits and accuracy of estimated states, for both simulation types. We then apply the approach to real EEG data of sleep onset, obtaining quality spectral estimates with estimated peak combinations closely matching the expert-scored sleep stages. This approach offers not only the ability to estimate time-varying parameters of spectral peaks but, moving forward, the potential to estimate the governing dynamics and analyze their variability across nights, subjects, and clinical groups.

Evoked response activity eigenmode analysis in a convoluted cortex via neural field theory

Neural field theory of the corticothalamic system is used to explore evoked response potentials (ERPs) caused by spatially localized impulse stimuli on the convoluted cortex and on a spherical cortex. Eigenfunctions are calculated analytically on the spherical cortex and numerically on the convoluted cortex via eigenfunction expansions. Eigenmodes on a convoluted cortex are similar to those of the spherical cortex, and a few such modes are found to be sufficient to reproduce the main ERP features. It is found that the ERP peak is stronger in spherical cortex than convoluted cortex, but in both cases the peak decreases monotonically with increasing distance from the stimulus point. In the convoluted case, cortical folding causes ERPs to differ between locations at the same distance from the stimulus point and spherical symmetries are only approximately preserved.

Neural Field Theory of Evoked Response Potentials With Attentional Gain Dynamics

A generalized neural field model of large-scale activity in the corticothalamic system is used to predict standard evoked potentials. This model embodies local feedbacks that modulate the gains of neural activity as part of the response to incoming stimuli and thus enables both activity changes and effective connectivity changes to be calculated as parts of a generalized evoked response, and their relative contributions to be determined. The results show that incorporation of gain modulations enables a compact and physically justifiable description of the differences in gain between background-EEG and standard-ERP conditions, with the latter able to be initiated from the background state, rather than requiring distinct parameters as in earlier work. In particular, top-down gains are found to be reduced during an ERP, consistent with recent theoretical suggestions that the role of internal models is diminished in favor of external inputs when the latter change suddenly. The static-gain and modulated-gain system transfer functions are analyzed via control theory in terms of system resonances that were recently shown to implement data filtering whose gain adjustments can be interpreted as attention. These filters are shown to govern early and late features in standard evoked responses and their gain parameters are shown to be dynamically adjusted in a way that implements a form of attention. The results show that dynamically modulated resonant filters responsible for the low-frequency oscillations in an evoked potential response have different parameters than those responsible for low-frequency resting EEG responses, while both responses share similar mid- and high-frequency resonant filters. These results provide a biophysical mechanism by which oscillatory activity in the theta, alpha, and beta frequency ranges of an evoked response are modulated as reflections of attention; notably theta is enhanced and alpha suppressed during the latter parts of the ERP. Furthermore, the model enables the part of the ERP response induced by gain modulations to be estimated and interpreted in terms of attention.

Gamma-band correlations in the primary visual cortex

This paper generalizes and extends previous work on using neural field theory to quantitatively analyze the two-dimensional (2D) spatiotemporal correlation properties of gamma-band (30-70 Hz) oscillations evoked by stimuli arriving at the primary visual cortex, and modulated by patchy connectivities that depend on orientation preference (OP). Correlation functions are derived analytically for general stimulus and measurement conditions. The theoretical results reproduce a range of published experimental results. These include (i) the existence of two-point oscillatory temporal cross correlations with zero time lag between neurons with similar OP; (ii) the influence of spatial separation of neurons on the strength of the correlations; and (iii) the effects of differing stimulus orientations. They go beyond prior work by incorporating experimentally observed patchy projection patterns to predict the 2D correlation structure including both OP and ocular dominance effects, thereby relaxing assumptions of translational invariance implicit in prior one-dimensional analysis.

Inferring a simple mechanism for alpha-blocking by fitting a neural population model to EEG spectra

Alpha blocking, a phenomenon where the alpha rhythm is reduced by attention to a visual, auditory, tactile or cognitive stimulus, is one of the most prominent features of human electroencephalography (EEG) signals. Here we identify a simple physiological mechanism by which opening of the eyes causes attenuation of the alpha rhythm. We fit a neural population model to EEG spectra from 82 subjects, each showing a different degree of alpha blocking upon opening of their eyes. Though it has been notoriously difficult to estimate parameters by fitting such models, we show how, by regularizing the differences in parameter estimates between eyes-closed and eyes-open states, we can reduce the uncertainties in these differences without significantly compromising fit quality. From this emerges a parsimonious explanation for the spectral differences between states: Changes to just a single parameter, p_ei, corresponding to the strength of a tonic excitatory input to the inhibitory cortical population, are sufficient to explain the reduction in alpha rhythm upon opening of the eyes. We detect this by comparing the shift in each model parameter between eyes-closed and eyes-open states. Whereas changes in most parameters are weak or negligible and do not scale with the degree of alpha attenuation across subjects, the change in p_ei increases monotonically with the degree of alpha blocking observed. These results indicate that opening of the eyes reduces alpha activity by increasing external input to the inhibitory cortical population.

One of the most striking features of the human electroencephalogram (EEG) is the presence of neural oscillations in the range of 8-13 Hz. It is well known that attenuation of these alpha oscillations, a process known as alpha blocking, arises from opening of the eyes, though the cause has remained obscure. In this study we infer the mechanism underlying alpha blocking by fitting a neural population model to EEG spectra from 82 different individuals. Although such models have long held the promise of being able to relate macroscopic recordings of brain activity to microscopic neural parameters, their utility has been limited by the difficulty of inferring these parameters from fits to data. Our approach involves fitting eyes-open and eyes-closed EEG spectra in a way that minimizes unnecessary differences in model parameters between the two states. Surprisingly, we find that changes in just one parameter, the level of external input to the inhibitory neurons in cortex, is sufficient to explain the attenuation of alpha oscillations. This indicates that opening of the eyes reduces alpha activity simply by increasing external inputs to the inhibitory neurons in the cortex.

Model-based robust suppression of epileptic seizures without sensory measurements

Uncontrolled seizures may lead to irreversible damages in the brain and various limitations in the patient's life. There exist experimental studies to stabilize the patient seizures. However, the experimental setups have many sensory devices to measure the dynamics of the brain cortex. These equipments prevent to produce small portable stabilizers for patients in everyday life. Recently, a comprehensive cortex model is introduced to apply model-based observers and controllers. However, this cortex model can be uncertain and have time-varying parameters. Therefore, in this paper, a robust Takagi-Sugeno (TS) controller and observer are designed to suppress the epileptic seizures without sensory measurements. The unavailable sensory measurements are provided by the designed nonlinear observer. The exponential convergence of the observer and controller is satisfied by the feedback parameter design using linear matrix inequalities. In addition, TS fuzzy observer-controller design has been compared with the conventional PID method in terms of control performance and design problem. The numerical computations show that the epileptic seizures are more effectively suppressed by the TS fuzzy observer-based controller under uncertain membrane potential dynamics.

Neural field theory of evoked response potentials in a spherical brain geometry

Evoked response potentials (ERPs) are calculated in spherical and planar geometries using neural field theory of the corticothalamic system. The ERP is modeled as an impulse response and the resulting modal effects of spherical corticothalamic dynamics are explored, showing that results for spherical and planar geometries converge in the limit of large brain size. Cortical modal effects can lead to a double-peak structure in the ERP time series. It is found that the main difference between infinite planar geometry and spherical geometry is that the ERP peak is sharper and stronger in the spherical geometry. It is also found that the magnitude of the response decreases with increasing spatial width of the stimulus at the cortex. The peak is slightly delayed at large angles from the stimulus point, corresponding to group velocities of 6-10 m s^{-1}. Strong modal effects are found in the spherical geometry, with the lowest few modes sufficing to describe the main features of ERPs, except very near to spatially narrow stimuli.

Parameter estimation and identifiability in a neural population model for electro-cortical activity

Electroencephalography (EEG) provides a non-invasive measure of brain electrical activity. Neural population models, where large numbers of interacting neurons are considered collectively as a macroscopic system, have long been used to understand features in EEG signals. By tuning dozens of input parameters describing the excitatory and inhibitory neuron populations, these models can reproduce prominent features of the EEG such as the alpha-rhythm. However, the inverse problem, of directly estimating the parameters from fits to EEG data, remains unsolved. Solving this multi-parameter non-linear fitting problem will potentially provide a real-time method for characterizing average neuronal properties in human subjects. Here we perform unbiased fits of a 22-parameter neural population model to EEG data from 82 individuals, using both particle swarm optimization and Markov chain Monte Carlo sampling. We estimate how much is learned about individual parameters by computing Kullback-Leibler divergences between posterior and prior distributions for each parameter. Results indicate that only a single parameter, that determining the dynamics of inhibitory synaptic activity, is directly identifiable, while other parameters have large, though correlated, uncertainties. We show that the eigenvalues of the Fisher information matrix are roughly uniformly spaced over a log scale, indicating that the model is sloppy, like many of the regulatory network models in systems biology. These eigenvalues indicate that the system can be modeled with a low effective dimensionality, with inhibitory synaptic activity being prominent in driving system behavior.

Optimal Model Parameter Estimation from EEG Power Spectrum Features Observed during General Anesthesia

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ - (0 - 4 Hz) and α - (8 - 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.

Power Spectrum and Diffusion of the Amari Neural Field

We study the power spectrum of a space-time dependent neural field which describes the average membrane potential of neurons in a single layer. This neural field is modelled by a dissipative integro-differential equation, the so-called Amari equation. By considering a small perturbation with respect to a stationary and uniform configuration of the neural field we derive a linearized equation which is solved for a generic external stimulus by using the Fourier transform into wavevector-freqency domain, finding an analytical formula for the power spectrum of the neural field. In addition, after proving that for large wavelengths the linearized Amari equation is equivalent to a diffusion equation which admits space-time dependent analytical solutions, we take into account the nonlinearity of the Amari equation. We find that for large wavelengths a weak nonlinearity in the Amari equation gives rise to a reaction-diffusion equation which can be formally derived from a neural action functional by introducing a dual neural field. For some initial conditions, we discuss analytical solutions of this reaction-diffusion equation.

Suppression of Parkinsonian Beta Oscillations by Deep Brain Stimulation: Determination of Effective Protocols

A neural field model of the corticothalamic-basal ganglia system is developed that describes enhanced beta activity within subthalamic and pallidal circuits in Parkinson's disease (PD) via system resonances. A model of deep brain stimulation (DBS) of typical clinical targets, the subthalamic nucleus (STN) and globus pallidus internus (GPi), is added and studied for several distinct stimulation protocols that are used for treatment of the motor symptoms of PD and that reduce pathological beta band activity (13-30 Hz) in the corticothalamic-basal ganglia network. The resulting impact of DBS on enhanced beta activity in the STN and GPi, as well as cortico-subthalamic and cortico-pallidal coherence, are studied. Both STN-DBS and GPi-DBS are found to be effective for suppressing peak STN and GPi power in the beta band, with GPi-DBS being slightly more effective in both the STN and the GPi for all stimulus protocols tested. The largest decrease in cortico-STN coherence is observed during STN-DBS, whereas GPi-DBS is most effective for reducing cortico-GPi coherence. A reduction of the pathologically large STN connection strengths that define the parkinsonian state results in enhanced 6 Hz activity and could thus represent a compensatory mechanism that has the side effect of driving parkinsonian tremor-like oscillations. This model provides a method for systematically testing effective DBS protocols that agrees with experimental and clinical findings. Furthermore, the model suggests GPi-DBS and STN-DBS have distinct impacts on elevated synchronization between the basal ganglia and motor cortex in PD.

Necessity of the sleep-wake cycle for synaptic homeostasis: system-level analysis of plasticity in the corticothalamic system

Neural field theory is used to study the system-level effects of plasticity in the corticothalamic system, where arousal states are represented parametrically by the connection strengths of the system, among other physiologically based parameters. It is found that the plasticity dynamics have no fixed points or closed cycles in the parameter space of the connection strengths, but parameter subregions exist where flows have opposite signs. Remarkably, these subregions coincide with previously identified regions that correspond to wake and slow-wave sleep, thus demonstrating state dependence of the sign of synaptic modification. We then show that a closed cycle in the parameter space is possible when the plasticity dynamics are driven by the ascending arousal system, which cycles the brain between sleep and wake to complete a closed loop that includes arcs through the opposite-flow subregions. Thus, it is concluded that both wake and sleep are necessary, and together are able to stabilize connection weights in the brain over the daily cycle, thereby providing quantitative realization of the synaptic homeostasis hypothesis.

Neural Field Theory of Corticothalamic Prediction With Control Systems Analysis

Neural field theory is used to model and analyze realistic corticothalamic responses to simple visual stimuli. This yields system transfer functions that embody key features in common with those of engineering control systems, which enables interpretation of brain dynamics in terms of data filters. In particular, these features assist in finding internal signals that represent input stimuli and their changes, which are exactly the types of quantities used in control systems to enable prediction of future input signals, and adjustment of gains which is argued to be the analog of attention in control theory. Corticothalamic dynamics are shown to be analogous to the classical proportional-integral-derivative (PID) filters that are widely used in engineering.

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

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

Numerical study of entrainment of the human circadian system and recovery by light treatment

Background

While the effects of light as a zeitgeber are well known, the way the effects are modulated by features of the sleep-wake system still remains to be studied in detail.

Methods

A mathematical model for disturbance and recovery of the human circadian system is presented. The model combines a circadian oscillator and a sleep-wake switch that includes the effects of orexin. By means of simulations, we characterize the period-locking zone of the model, where a stable 24-hour circadian rhythm exists, and the occurrence of circadian disruption due to both insufficient light and imbalance in orexin. We also investigate how daily bright light treatments of short duration can recover the normal circadian rhythm.

Results

It is found that the system exhibits continuous phase advance/delay at lower/higher orexin levels. Bright light treatment simulations disclose two optimal time windows, corresponding to morning and evening light treatments. Among the two, the morning light treatment is found effective in a wider range of parameter values, with shorter recovery time.

Conclusions

This approach offers a systematic way to determine the conditions under which circadian disruption occurs, and to evaluate the effects of light treatment. In particular, it could potentially offer a way to optimize light treatments for patients with circadian disruption, e.g., sleep and mood disorders, in clinical settings.

Quantitative theory of deep brain stimulation of the subthalamic nucleus for the suppression of pathological rhythms in Parkinson's disease

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is modeled to explore the mechanisms of this effective, but poorly understood, treatment for motor symptoms of drug-refractory Parkinson's disease and dystonia. First, a neural field model of the corticothalamic-basal ganglia (CTBG) system is developed that reproduces key clinical features of Parkinson's disease, including its characteristic 4-8 Hz and 13-30 Hz electrophysiological signatures. Deep brain stimulation of the STN is then modeled and shown to suppress the pathological 13-30 Hz (beta) activity for physiologically realistic and optimized stimulus parameters. This supports the idea that suppression of abnormally coherent activity in the CTBG system is a major factor in DBS therapy for Parkinson's disease, by permitting normal dynamics to resume. At high stimulus intensities, nonlinear effects in the target population mediate wave-wave interactions between resonant beta activity and the stimulus pulse train, leading to complex spectral structure that shows remarkable similarity to that seen in steady-state evoked potential experiments.

Multistability in the corticothalamic system

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

Unified neural field theory of brain dynamics underlying oscillations in Parkinson's disease and generalized epilepsies

The mechanisms underlying pathologically synchronized neural oscillations in Parkinson's disease (PD) and generalized epilepsies are explored in parallel via a physiologically-based neural field model of the corticothalamic-basal ganglia (CTBG) system. The basal ganglia (BG) are approximated as a single effective population and their roles in the modulation of oscillatory dynamics of the corticothalamic (CT) system and vice versa are analyzed. In addition to normal EEG rhythms, enhanced activity around 4 Hz and 20 Hz exists in the model, consistent with the characteristic frequencies observed in PD. These rhythms result from resonances in loops formed between the BG and CT populations, analogous to those that underlie epileptic oscillations in a previous CT model, and which are still present in the combined CTBG system. Dopamine depletion is argued to weaken the dampening of these loop resonances in PD, and network connections then explain the significant coherence observed between BG, thalamic, and cortical population activity around 4-8 Hz and 20 Hz. Parallels between the afferent and efferent connection sites of the thalamic reticular nucleus (TRN) and BG predict low dopamine to correspond to a reduced likelihood of tonic-clonic (grand mal) seizures, which agrees with experimental findings. Furthermore, the model predicts an increased likelihood of absence (petit mal) seizure resulting from pathologically low dopamine levels in accordance with experimental observations. Suppression of absence seizure activity is demonstrated when afferent and efferent BG connections to the CT system are strengthened, which is consistent with other CTBG modeling studies. The BG are demonstrated to have a suppressive effect on activity of the CTBG system near tonic-clonic seizure states, which provides insight into the reported efficacy of current treatments in BG circuits. Sleep states of the TRN are also found to suppress pathological PD activity in accordance with observations. Overall, the findings demonstrate strong parallels between coherent oscillations in generalized epilepsies and PD, and provide insights into possible comorbidities.

K-complexes, spindles, and ERPs as impulse responses: unification via neural field theory

To interrelate K-complexes, spindles, evoked response potentials (ERPs), and spontaneous electroencephalography (EEG) using neural field theory (NFT), physiology-based NFT of the corticothalamic system is used to model cortical excitatory and inhibitory populations and thalamic relay and reticular nuclei. The impulse response function of the model is used to predict the responses to impulses, which are compared with transient waveforms in sleep studies. Fits to empirical data then allow underlying brain physiology to be inferred and compared with other waves. Spontaneous K-complexes, spindles, and other transient waveforms can be reproduced using NFT by treating them as evoked responses to impulsive stimuli with brain parameters appropriate to spontaneous EEG in sleep stage 2. Using this approach, spontaneous K-complexes and sleep spindles can be analyzed using the same single theory as previously been used to account for waking ERPs and other EEG phenomena. As a result, NFT can explain a wide variety of transient waveforms that have only been phenomenologically classified to date. This enables noninvasive fitting to be used to infer underlying physiological parameters. This physiology-based model reproduces the time series of different transient EEG waveforms; it has previously reproduced experimental EEG spectra, and waking ERPs, and many other observations, thereby unifying transient sleep waveforms with these phenomena.

Inference of direct and multistep effective connectivities from functional connectivity of the brain and of relationships to cortical geometry

BACKGROUND

The problem of inferring effective brain connectivity from functional connectivity is under active investigation, and connectivity via multistep paths is poorly understood.

NEW METHOD

A method is presented to calculate the direct effective connection matrix (deCM), which embodies direct connection strengths between brain regions, from functional CMs (fCMs) by minimizing the difference between an experimental fCM and one calculated via neural field theory from an ansatz deCM based on an experimental anatomical CM.

RESULTS

The best match between fCMs occurs close to a critical point, consistent with independent published stability estimates. Residual mismatch between fCMs is identified to be largely due to interhemispheric connections that are poorly estimated in an initial ansatz deCM due to experimental limitations; improved ansatzes substantially reduce the mismatch and enable interhemispheric connections to be estimated. Various levels of significant multistep connections are then imaged via the neural field theory (NFT) result that these correspond to powers of the deCM; these are shown to be predictable from geometric distances between regions.

COMPARISON WITH EXISTING METHODS

This method gives insight into direct and multistep effective connectivity from fCMs and relating to physiology and brain geometry. This contrasts with other methods, which progressively adjust connections without an overarching physiologically based framework to deal with multistep or poorly estimated connections.

CONCLUSIONS

deCMs can be usefully estimated using this method and the results enable multistep connections to be investigated systematically.

Wilson-Cowan Equations for Neocortical Dynamics

In 1972-1973 Wilson and Cowan introduced a mathematical model of the population dynamics of synaptically coupled excitatory and inhibitory neurons in the neocortex. The model dealt only with the mean numbers of activated and quiescent excitatory and inhibitory neurons, and said nothing about fluctuations and correlations of such activity. However, in 1997 Ohira and Cowan, and then in 2007-2009 Buice and Cowan introduced Markov models of such activity that included fluctuation and correlation effects. Here we show how both models can be used to provide a quantitative account of the population dynamics of neocortical activity.We first describe how the Markov models account for many recent measurements of the resting or spontaneous activity of the neocortex. In particular we show that the power spectrum of large-scale neocortical activity has a Brownian motion baseline, and that the statistical structure of the random bursts of spiking activity found near the resting state indicates that such a state can be represented as a percolation process on a random graph, called directed percolation.Other data indicate that resting cortex exhibits pair correlations between neighboring populations of cells, the amplitudes of which decay slowly with distance, whereas stimulated cortex exhibits pair correlations which decay rapidly with distance. Here we show how the Markov model can account for the behavior of the pair correlations.Finally we show how the 1972-1973 Wilson-Cowan equations can account for recent data which indicates that there are at least two distinct modes of cortical responses to stimuli. In mode 1 a low intensity stimulus triggers a wave that propagates at a velocity of about 0.3 m/s, with an amplitude that decays exponentially. In mode 2 a high intensity stimulus triggers a larger response that remains local and does not propagate to neighboring regions.

A neural mass model of phase-amplitude coupling

Brain activity shows phase-amplitude coupling between its slow and fast oscillatory components. We study phase-amplitude coupling as recorded at individual sites, using a modified version of the well-known Wendling neural mass model. To the population of fast inhibitory interneurons of this model, we added external modulatory input and dynamic self-feedback. These two modifications together are sufficient to let the inhibitory population serve as a limit-cycle oscillator, with frequency characteristics comparable to the beta and gamma bands. The frequency and power of these oscillations can be tuned through the time constant of the dynamic and modulatory input. Alpha band activity is generated, as is usual in such models, as a result of interactions of pyramidal neurons and a population of slow inhibitory interneurons. The slow inhibitory population activity directly influences the fast oscillations via the synaptic gain between slow and fast inhibitory populations. As a result, the amplitude envelope of the fast oscillation is coupled to the phase of the slow activity; this result is consistent with the notion that phase-amplitude coupling is effectuated by interactions between inhibitory interneurons.

Real-time automated EEG tracking of brain states using neural field theory

A real-time fitting system is developed and used to fit the predictions of an established physiologically-based neural field model to electroencephalographic spectra, yielding a trajectory in a physiological parameter space that parametrizes intracortical, intrathalamic, and corticothalamic feedbacks as the arousal state evolves continuously over time. This avoids traditional sleep/wake staging (e.g., using Rechtschaffen-Kales stages), which is fundamentally limited because it forces classification of continuous dynamics into a few discrete categories that are neither physiologically informative nor individualized. The classification is also subject to substantial interobserver disagreement because traditional staging relies in part on subjective evaluations. The fitting routine objectively and robustly tracks arousal parameters over the course of a full night of sleep, and runs in real-time on a desktop computer. The system developed here supersedes discrete staging systems by representing arousal states in terms of physiology, and provides an objective measure of arousal state which solves the problem of interobserver disagreement. Discrete stages from traditional schemes can be expressed in terms of model parameters for backward compatibility with prior studies.

How the cortico-thalamic feedback affects the EEG power spectrum over frontal and occipital regions during propofol-induced sedation

Increasing concentrations of the anaesthetic agent propofol initially induces sedation before achieving full general anaesthesia. During this state of anaesthesia, the observed specific changes in electroencephalographic (EEG) rhythms comprise increased activity in the δ- (0.5-4 Hz) and α- (8-13 Hz) frequency bands over the frontal region, but increased δ- and decreased α-activity over the occipital region. It is known that the cortex, the thalamus, and the thalamo-cortical feedback loop contribute to some degree to the propofol-induced changes in the EEG power spectrum. However the precise role of each structure to the dynamics of the EEG is unknown. In this paper we apply a thalamo-cortical neuronal population model to reproduce the power spectrum changes in EEG during propofol-induced anaesthesia sedation. The model reproduces the power spectrum features observed experimentally both in frontal and occipital electrodes. Moreover, a detailed analysis of the model indicates the importance of multiple resting states in brain activity. The work suggests that the α-activity originates from the cortico-thalamic relay interaction, whereas the emergence of δ-activity results from the full cortico-reticular-relay-cortical feedback loop with a prominent enforced thalamic reticular-relay interaction. This model suggests an important role for synaptic GABAergic receptors at relay neurons and, more generally, for the thalamus in the generation of both the δ- and the α- EEG patterns that are seen during propofol anaesthesia sedation.

Physiologically based arousal state estimation and dynamics

A neural field model of the brain is used to represent brain states using physiologically based parameters rather than arbitrary, discrete sleep stages. Each brain state is represented as a point in a physiologically parametrized space. Over time, changes in brain state cause these points to trace continuous trajectories, unlike the artificial discrete jumps in sleep stage that occur with traditional sleep staging. The discrete Rechtschaffen and Kales sleep stages are associated with regions in the physiological parameter space based on their electroencephalographic features, which enables interpretation of traditional sleep stages in terms of physiological trajectories. Wake states are found to be associated with strong positive corticothalamic feedback compared to sleep. The existence of physiologically valid trajectories between brain states in the model is demonstrated. Actual trajectories for an individual can be determined by fitting the model using EEG alone, and enable analysis of the physiological differences between subjects.

Mean-field thalamocortical modeling of longitudinal EEG acquired during intensive meditation training

Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and anatomy into account, to formally model brain processes associated with intensive meditation training. The observed changes in model parameters inform theoretical accounts of attention training through meditation, and may motivate future study on the use of meditation in a variety of clinical populations.

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.

Diagnostic utility of quantitative EEG in un-medicated schizophrenia

The aim of the current study was to evaluate the quantitative electroencephalography (QEEG) characteristics of patients with un-medicated schizophrenia (SPR) and to investigate the diagnostic utility of QEEG in assessing such patients during resting conditions. The subjects included 90 patients with schizophrenia and 90 normal controls. Spectral analysis was performed on the absolute power of all of the electrodes across five frequency bands following artifact removal. We conducted a repeated-measures ANOVA to examine group differences within the five frequency bands across several brain regions and receiver operator characteristic (ROC) analyses to examine the discrimination ability of each frequency band. Compared with controls, patients with schizophrenia showed increased delta and theta activity and decreased alpha 2 activity, particularly in the frontocentral area. There were no significant differences in the alpha 1 and beta activity. The ROC analysis performed on the delta frequency band generated the best result, with an overall classification accuracy of 62.2%. The results of this study confirmed the characteristics of the QEEG power in un-medicated schizophrenia patients compared with normal controls. These findings suggest that a resting EEG test can be a supportive tool for evaluating patients with schizophrenia.

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.

Identification of BDNF sensitive electrophysiological markers of synaptic activity and their structural correlates in healthy subjects using a genetic approach utilizing the functional BDNF Val66Met polymorphism

Increasing evidence suggests that synaptic dysfunction is a core pathophysiological hallmark of neurodegenerative disorders. Brain-derived neurotropic factor (BDNF) is key synaptogenic molecule and targeting synaptic repair through modulation of BDNF signalling has been suggested as a potential drug discovery strategy. The development of such "synaptogenic" therapies depend on the availability of BDNF sensitive markers of synaptic function that could be utilized as biomarkers for examining target engagement or drug efficacy in humans. Here we have utilized the BDNF Val66Met genetic polymorphism to examine the effect of the polymorphism and genetic load (i.e. Met allele load) on electrophysiological (EEG) markers of synaptic activity and their structural (MRI) correlates. Sixty healthy adults were prospectively recruited into the three genetic groups (Val/Val, Val/Met, Met/Met). Subjects also underwent fMRI, tDCS/TMS, and cognitive assessments as part of a larger study. Overall, some of the EEG markers of synaptic activity and brain structure measured with MRI were the most sensitive markers of the polymorphism. Met carriers showed decreased oscillatory activity and synchrony in the neural network subserving error-processing, as measured during a flanker task (ERN); and showed increased slow-wave activity during resting. There was no evidence for a Met load effect on the EEG measures and the polymorphism had no effects on MMN and P300. Met carriers also showed reduced grey matter volume in the anterior cingulate and in the (left) prefrontal cortex. Furthermore, anterior cingulate grey matter volume, and oscillatory EEG power during the flanker task predicted subsequent behavioural adaptation, indicating a BDNF dependent link between brain structure, function and behaviour associated with error processing and monitoring. These findings suggest that EEG markers such as ERN and resting EEG could be used as BDNF sensitive functional markers in early clinical development to examine target engagement or drug related efficacy of synaptic repair therapies in humans.

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.

Attention-deficit/hyperactivity disorder: neurophysiology, information processing, arousal and drug development

In this review, we draw on literature from both animal and human neurophysiological studies to consider the neurochemical mechanisms underlying attention-deficit/ hyperactivity disorder (ADHD). Psychophysiological and neuropsychological research is used to propose possible etiological endophenotypes of ADHD. These are conceptualized as patients with distinct cortical-arousal, information-processing or maturational abnormalities, or a combination thereof, and how the endophenotypes can be used to help drug development and optimize treatment and management. To illustrate, the paper focuses on neuro- and psychophysiological evidence that suggests cholinergic mechanisms may underlie specific information-processing abnormalities that occur in ADHD. The clinical implications for a cholinergic hypothesis of ADHD are considered, along with its possible implications for treatment and pharmacological development.

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.

Dominant frequencies of resting human brain activity as measured by the electrocorticogram

The brain's spontaneous, intrinsic activity is increasingly being shown to reveal brain function, delineate large scale brain networks, and diagnose brain disorders. One of the most studied and clinically utilized types of intrinsic brain activity are oscillations in the electrocorticogram (ECoG), a relatively localized measure of cortical synaptic activity. Here we objectively characterize the types of ECoG oscillations commonly observed over particular cortical areas when an individual is awake and immobile with eyes closed, using a surface-based cortical atlas and cluster analysis. Both methods show that [1] there is generally substantial variability in the dominant frequencies of cortical regions and substantial overlap in dominant frequencies across the areas sampled (primarily lateral central, temporal, and frontal areas), [2] theta (4-8 Hz) is the most dominant type of oscillation in the areas sampled with a mode around 7 Hz, [3] alpha (8-13 Hz) is largely limited to parietal and occipital regions, and [4] beta (13-30 Hz) is prominent peri-Rolandically, over the middle frontal gyrus, and the pars opercularis. In addition, the cluster analysis revealed seven types of ECoG spectral power densities (SPDs). Six of these have peaks at 3, 5, 7 (narrow), 7 (broad), 10, and 17 Hz, while the remaining cluster is broadly distributed with less pronounced peaks at 8, 19, and 42 Hz. These categories largely corroborate conventional sub-gamma frequency band distinctions (delta, theta, alpha, and beta) and suggest multiple sub-types of theta. Finally, we note that gamma/high gamma activity (30+ Hz) was at times prominently observed, but was too infrequent and variable across individuals to be reliably characterized. These results should help identify abnormal patterns of ECoG oscillations, inform the interpretation of EEG/MEG intrinsic activity, and provide insight into the functions of these different oscillations and the networks that produce them. Specifically, our results support theories of the importance of theta oscillations in general cortical function, suggest that alpha activity is primarily related to sensory processing/attention, and demonstrate that beta networks extend far beyond primary sensorimotor regions.

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.

The Virtual Brain: a simulator of primate brain network dynamics

We present The Virtual Brain (TVB), a neuroinformatics platform for full brain network simulations using biologically realistic connectivity. This simulation environment enables the model-based inference of neurophysiological mechanisms across different brain scales that underlie the generation of macroscopic neuroimaging signals including functional MRI (fMRI), EEG and MEG. Researchers from different backgrounds can benefit from an integrative software platform including a supporting framework for data management (generation, organization, storage, integration and sharing) and a simulation core written in Python. TVB allows the reproduction and evaluation of personalized configurations of the brain by using individual subject data. This personalization facilitates an exploration of the consequences of pathological changes in the system, permitting to investigate potential ways to counteract such unfavorable processes. The architecture of TVB supports interaction with MATLAB packages, for example, the well known Brain Connectivity Toolbox. TVB can be used in a client-server configuration, such that it can be remotely accessed through the Internet thanks to its web-based HTML5, JS, and WebGL graphical user interface. TVB is also accessible as a standalone cross-platform Python library and application, and users can interact with the scientific core through the scripting interface IDLE, enabling easy modeling, development and debugging of the scientific kernel. This second interface makes TVB extensible by combining it with other libraries and modules developed by the Python scientific community. In this article, we describe the theoretical background and foundations that led to the development of TVB, the architecture and features of its major software components as well as potential neuroscience applications.

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.

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.