Prediction of electroencephalographic spectra from neurophysiology

Spike-timing-dependent plasticity leads to gamma band responses in a neural network

Early gamma band responses of the human electroencephalogram have been identified as an early interface linking top-down and bottom-up processing. This was based on findings that observed strong sensitivity of this signal to stimulus size and at the same time, to processes of attention and memory. Here, we simulate these findings in a simple random network of biologically plausible spiking neurons. During a learning phase, different stimuli were presented to the network and the synaptic connections were modified according to a spike-timing-dependent plasticity learning rule. In a subsequent test phase, we stimulated the network with (i) patterns of different sizes to simulate bottom-up effects and (ii) with patterns that were or were not presented during the learning phase. The network displayed qualitatively similar behavior as early gamma band responses measured from the scalp of human subjects: there was a general increase in response strength with increasing stimulus size and stronger responses for learned stimuli. We demonstrated that within one neural architecture early gamma band responses can be modulated both by bottom-up factors and by basal learning mechanisms mediated via spike-timing-dependent plasticity.

Comparative study of nonlinear properties of EEG signals of normal persons and epileptic patients

BACKGROUND

Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent.

RESULTS

Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak et al. [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases.

CONCLUSION

In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation.

Bistability and non-Gaussian fluctuations in spontaneous cortical activity

The brain is widely assumed to be a paradigmatic example of a complex, self-organizing system. As such, it should exhibit the classic hallmarks of nonlinearity, multistability, and "nondiffusivity" (large coherent fluctuations). Surprisingly, at least at the very large scale of neocortical dynamics, there is little empirical evidence to support this, and hence most computational and methodological frameworks for healthy brain activity have proceeded very reasonably from a purely linear and diffusive perspective. By studying the temporal fluctuations of power in human resting-state electroencephalograms, we show that, although these simple properties may hold true at some temporal scales, there is strong evidence for bistability and nondiffusivity in key brain rhythms. Bistability is manifest as nonclassic bursting between high- and low-amplitude modes in the alpha rhythm. Nondiffusivity is expressed through the irregular appearance of high amplitude "extremal" events in beta rhythm power fluctuations. The statistical robustness of these observations was confirmed through comparison with Gaussian-rendered phase-randomized surrogate data. Although there is a good conceptual framework for understanding bistability in cortical dynamics, the implications of the extremal events challenge existing frameworks for understanding large-scale brain systems.

Transitions to spike-wave oscillations and epileptic dynamics in a human cortico-thalamic mean-field model

In this paper we present a detailed theoretical analysis of the onset of spike-wave activity in a model of human electroencephalogram (EEG) activity, relating this to clinical recordings from patients with absence seizures. We present a complete explanation of the transition from inter-ictal activity to spike and wave using a combination of bifurcation theory, numerical continuation and techniques for detecting the occurrence of inflection points in systems of delay differential equations (DDEs). We demonstrate that the initial transition to oscillatory behaviour occurs as a result of a Hopf bifurcation, whereas the addition of spikes arises as a result of an inflection point of the vector field. Strikingly these findings are consistent with EEG data recorded from patients with absence seizures and we present a discussion of the clinical significance of these results, suggesting potential new techniques for detection and anticipation of seizures.

Mean-field modeling of the basal ganglia-thalamocortical system. I Firing rates in healthy and parkinsonian states

Parkinsonism leads to various electrophysiological changes in the basal ganglia-thalamocortical system (BGTCS), often including elevated discharge rates of the subthalamic nucleus (STN) and the output nuclei, and reduced activity of the globus pallidus external (GPe) segment. These rate changes have been explained qualitatively in terms of the direct/indirect pathway model, involving projections of distinct striatal populations to the output nuclei and GPe. Although these populations partly overlap, evidence suggests dopamine depletion differentially affects cortico-striato-pallidal connection strengths to the two pallidal segments. Dopamine loss may also decrease the striatal signal-to-noise ratio, reducing both corticostriatal coupling and striatal firing thresholds. Additionally, nigrostriatal degeneration may cause secondary changes including weakened lateral inhibition in the GPe, and mesocortical dopamine loss may decrease intracortical excitation and especially inhibition. Here a mean-field model of the BGTCS is presented with structure and parameter estimates closely based on physiology and anatomy. Changes in model rates due to the possible effects of dopamine loss listed above are compared with experiment. Our results suggest that a stronger indirect pathway, possibly combined with a weakened direct pathway, is compatible with empirical evidence. However, altered corticostriatal connection strengths are probably not solely responsible for substantially increased STN activity often found. A lower STN firing threshold, weaker intracortical inhibition, and stronger striato-GPe inhibition help explain the relatively large increase in STN rate. Reduced GPe-GPe inhibition and a lower GPe firing threshold can account for the comparatively small decrease in GPe rate frequently observed. Changes in cortex, GPe, and STN help normalize the cortical rate, also in accord with experiments. The model integrates the basal ganglia into a unified framework along with an existing thalamocortical model that already accounts for a wide range of electrophysiological phenomena. A companion paper discusses the dynamics and oscillations of this combined system.

Mean-field modeling of the basal ganglia-thalamocortical system. II Dynamics of parkinsonian oscillations

Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker intracortical connections in parkinsonian patients. Strict separation of the direct and indirect pathways is not necessary to obtain these results.

Modeling brain activation patterns for the default and cognitive states

We argue that spatial patterns of cortical activation observed with EEG, MEG and fMRI might arise from spontaneous self-organisation of interacting populations of excitatory and inhibitory neurons. We examine the dynamical behavior of a mean-field cortical model that includes chemical and electrical (gap-junction) synapses, focusing on two limiting cases: the "slow-soma" limit with slow voltage feedback from soma to dendrite, and the "fast-soma" limit in which the feedback action of soma voltage onto dendrite reversal potentials is instantaneous. For slow soma-dendrite feedback, we find a low-frequency (approximately 1 Hz) dynamic Hopf instability, and a stationary Turing instability that catalyzes formation of patterned distributions of cortical firing-rate activity with pattern wavelength approximately 2 cm. Turing instability can only be triggered when gap-junction diffusion between inhibitory neurons is strong, but patterning is destroyed if the tonic level of subcortical excitation is raised sufficiently. Interaction between the Hopf and Turing instabilities may describe the non-cognitive background or "default" state of the brain, as observed by BOLD imaging. In the fast-soma limit, the model predicts a high-frequency Hopf (approximately 35 Hz) instability, and a traveling-wave gamma-band instability that manifests as a 2-D standing-wave pattern oscillating in place at approximately 30 Hz. Small levels of inhibitory diffusion enhance and broaden the definition of the gamma antinodal regions by suppressing higher-frequency spatial modes, but gamma emergence is not contingent on the presence of inhibitory gap junctions; higher levels of diffusion suppress gamma activity. Fast-soma instabilities are enhanced by increased subcortical stimulation. Prompt soma-dendrite feedback may be an essential component of the genesis and large-scale cortical synchrony of gamma activity observed at the point of cognition.

Generation and control of cortical gamma: findings from simulation at two scales

A continuum model of electrocortical activity was applied separately at centimetric and macrocolumnar scales, permitting analysis of interaction between scales. State equations included effects of retrograde action potential propagation in dendritic trees, and kinetics of AMPA, GABA and NMDA receptors. Parameter values were provided from independent physiological and anatomical estimates. Realistic field potentials and pulse rates were obtained, including resonances in the alpha/theta and gamma ranges, 1/f(2) background activity, and autonomous gamma activity. Zero-lag synchrony and travelling waves occurred as complementary aspects of cortical transmission, and lead/lag relations between excitatory and inhibitory cell populations varied systematically around transition to autonomous gamma oscillation. Properties of the simulations can account for generation and control of gamma activity. All factors acting on excitatory/inhibitory balance controlled the onset and offset of gamma oscillation. Autonomous gamma was initiated by focal excitation of excitatory cells, and suppressed by laterally spreading trans-cortical excitation, which acted on both excitatory and inhibitory cell populations. Consequently, although spatially extensive non-specific reticular activation tended to suppress autonomous gamma, spatial variation of reticular activation could preferentially select fields of synchrony.

Modeling distributed axonal delays in mean-field brain dynamics

The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.

A study on the possible usefulness of detrended fluctuation analysis of the electroencephalogram background activity in Alzheimer's disease

We studied the EEG background activity of Alzheimer's disease (AD) patients with detrended fluctuation analysis (DFA). DFA provides an estimation of the scaling information and long-range correlations in time series. We recorded the EEG in 11 AD patients and 11 age-matched controls. Our results showed two scaling regions in all subjects' channels (for limited time scales from 0.01 to 0.04 s and from 0.08 to 0.43 s, respectively), with a clear bend when their corresponding slopes (alpha(1) and alpha(2)) were different. No significant differences between groups were found with alpha(1). However, alpha(2) values were significantly lower in control subjects at electrodes T5, T6, and O1 (p < 0.01, Student's t-test). These findings suggest that the scaling behavior of the EEG is sensitive to AD. Although alpha(2) values allowed us to separate AD patients and controls, accuracies were lower than with spectral analysis. However, a forward stepwise linear discriminant analysis with a leave-one-out cross-validation procedure showed that the combined use of DFA and spectral analysis could improve the diagnostic accuracy of each individual technique. Thus, although spectral analysis outperforms DFA, the combined use of both techniques may increase the insight into brain dysfunction in AD.

The dynamic brain: from spiking neurons to neural masses and cortical fields

The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

Mean field model of acetylcholine mediated dynamics in the thalamocortical system

A recent continuum model of the large scale electrical activity of the thalamocortical system is generalized to include cholinergic modulation. The model is examined analytically and numerically to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses. Changing the ACh concentration moves the system between zones of one, three, and five steady states, showing that neuromodulation of synaptic strength is a possible mechanism by which multiple steady states emerge in the brain. The lowest firing rate steady state is always stable, and subsequent fixed points alternate between stable and unstable. Increasing ACh concentration changes the form of the spectrum. Increasing the tonic level of ACh concentration increases the magnitudes of the N100 and P200 in the evoked response potential (ERP), without changing the timing of these peaks. Driving the system with a pulse of cholinergic activity results in a transient increase in the firing rate of cortical neurons that lasts over 10s. Step-like increases in cortical ACh concentration cause increases in the firing rate of cortical neurons, with rapid responses due to fast acting nicotinic receptors and slower responses due to muscarinic receptor suppression of intracortical connections.

Anticipation of natural stimuli modulates EEG dynamics: physiology and simulation

In everyday life we often encounter situations in which we can expect a visual stimulus before we actually see it. Here, we study the impact of such stimulus anticipation on the actual response to a visual stimulus. Participants were to indicate the sex of deer and cattle on photographs of the respective animals. On some trials, participants were cued on the species of the upcoming animal whereas on other trials this was not the case. Time frequency analysis of the simultaneously recorded EEG revealed modulations by this cue stimulus in two time windows. Early [Formula: see text] spectral responses [Formula: see text] displayed strongest stimulus-locking for stimuli that were preceded by a cue if they were sufficiently large. Late [Formula: see text] responses displayed enhanced amplitudes in response to large stimuli and to stimuli that were preceded by a cue. For late responses, however, no interaction between cue and stimulus size was observed. We were able to explain these results in a simulation by prestimulus gain modulations (early response) and by decreased response thresholds (late response). Thus, it seems plausible, that stimulus anticipation results in a pretuning of local neural populations.

Population dynamics: variance and the sigmoid activation function

This paper demonstrates how the sigmoid activation function of neural-mass models can be understood in terms of the variance or dispersion of neuronal states. We use this relationship to estimate the probability density on hidden neuronal states, using non-invasive electrophysiological (EEG) measures and dynamic casual modelling. The importance of implicit variance in neuronal states for neural-mass models of cortical dynamics is illustrated using both synthetic data and real EEG measurements of sensory evoked responses.

Rapid interactions between the ventral visual stream and emotion-related structures rely on a two-pathway architecture

Visual attention can be driven by the affective significance of visual stimuli before full-fledged processing of the stimuli. Two kinds of models have been proposed to explain this phenomenon: models involving sequential processing along the ventral visual stream, with secondary feedback from emotion-related structures ("two-stage models"); and models including additional short-cut pathways directly reaching the emotion-related structures ("two-pathway models"). We tested which type of model would best predict real magnetoencephalographic responses in subjects presented with arousing visual stimuli, using realistic models of large-scale cerebral architecture and neural biophysics. The results strongly support a "two-pathway" hypothesis. Both standard models including the retinotectal pathway and nonstandard models including cortical-cortical long-range fasciculi appear plausible.

Physiology-based modeling of cortical auditory evoked potentials

Evoked potentials are the transient electrical responses caused by changes in the brain following stimuli. This work uses a physiology-based continuum model of neuronal activity in the human brain to calculate theoretical cortical auditory evoked potentials (CAEPs) from the model's linearized response. These are fitted to experimental data, allowing the fitted parameters to be related to brain physiology. This approach yields excellent fits to CAEP data, which can then be compared to fits of EEG spectra. It is shown that the differences between resting eyes-open EEG and standard CAEPs can be explained by changes in the physiology of populations of neurons in corticothalamic pathways, with notable similarities to certain aspects of slow-wave sleep. This pilot study demonstrates the ability of our model-based fitting method to provide information on the underlying physiology of the brain that is not available using standard methods.

Physiologically based calculation of steady-state evoked potentials and cortical wave velocities

Steady-state evoked potentials (SSEPs) elicited by sinusoidal stimuli are predicted from a physiologically-based model, including bielectrode and volume conduction effects. Comparison with visual SSEPs yields constraints on phase and latency of the retinothalamic transfer function that are consistent with experiment. Predictions of phase velocities measured as SSEPs cross the cortex are consistent with low values measured for slow waves in sleep, while resonant behavior induced by corticothalamic loops, especially near the alpha peak, contributes to wide scatter in waking-state phase velocity measurements comparable to effects from volume conduction. The common use of bielectrode derivations to compensate for volume conduction effects is examined and shown to be incomplete, tending to lead to underestimates of phase velocity, especially at low frequencies and near the alpha peak, due to incorrect elimination of true long-wavelength contributions to the SSEP.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat "patchy" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Neural rate equations for bursting dynamics derived from conductance-based equations

A method of obtaining rate equations from conductance-based equations is developed and applied to fast-spiking and bursting neocortical neurons. It involves splitting systems of conductance-based equations into fast and slow subsystems, and averaging the effects of fast terms that drive the slowly varying quantities by showing that their average is closely proportional to the firing rate. The dependence of the firing rate on the injected current is then approximated in the analysis. The resulting behavior of the slow variables is then substituted back into the fast equations, with the further approximation of replacing the fast voltages in these terms by effective values. For bursting neurons the method yields two coupled limit-cycle oscillators: a self-exciting oscillator for the slow variables that commences limit-cycle oscillations at a critical current and modulates a fast spike-generating oscillator, thereby leading to slowly modulated bursts with a group of spikes in each burst. The dynamics of these coupled oscillators are then verified against those of the conductance-based equations. Finally, it is shown how to place the results in a form suitable for use in mean-field equations for neural population dynamics.

Visual gamma oscillations: waves, correlations, and other phenomena, including comparison with experimental data

Mean-field theory of brain dynamics is applied to explain the properties of gamma (> or approximately 30 Hz) oscillations of cortical activity often seen during vision experiments. It is shown that mm-scale patchy connections in the primary visual cortex can support collective gamma oscillations with the correct frequencies and spatial structure, even when driven by uncorrelated inputs. This occurs via resonances associated with the the periodic modulation of the network connections, rather than being due to single-cell properties alone. Near-resonant gamma waves are shown to obey the Schrödinger equation, which enables techniques and insights from quantum theory to be used in exploring these classical oscillations. Resulting predictions for gamma responses to stimuli account in a unified way for a wide range of experimental results, including why oscillations and zero-lag synchrony are associated, and variations in correlation functions with time delay, intercellular distance, and stimulus features. They also imply that gamma oscillations may enable a form of frequency multiplexing of neural signals. Most importantly, it is shown that correlations reproduce experimental results that show maximal correlations between cells that respond to related features, but little correlation with other cells, an effect that has been argued to be associated with segmentation of a scene into separate objects. Consistency with infill of missing contours and increase in response with length of bar-shaped stimuli are discussed. Background correlations expected in the absence of stimulation are also calculated and shown to be consistent in form with experimental measurements and similar to stimulus-induced correlations in structure. Finally, possible links of gamma instabilities to certain classes of photically induced seizures and visual hallucinations are discussed.

Dynamic causal models of neural system dynamics:current state and future extensions

Complex processes resulting from interaction of multiple elements can rarely be understood by analytical scientific approaches alone; additional, mathematical models of system dynamics are required. This insight, which disciplines like physics have embraced for a long time already, is gradually gaining importance in the study of cognitive processes by functional neuroimaging. In this field, causal mechanisms in neural systems are described in terms of effective connectivity. Recently, dynamic causal modelling (DCM) was introduced as a generic method to estimate effective connectivity from neuroimaging data in a Bayesian fashion. One of the key advantages of DCM over previous methods is that it distinguishes between neural state equations and modality-specific forward models that translate neural activity into a measured signal. Another strength is its natural relation to Bayesian model selection (BMS) procedures. In this article, we review the conceptual and mathematical basis of DCM and its implementation for functional magnetic resonance imaging data and event-related potentials. After introducing the application of BMS in the context of DCM, we conclude with an outlook to future extensions of DCM. These extensions are guided by the long-term goal of using dynamic system models for pharmacological and clinical applications, particularly with regard to synaptic plasticity.

A comparative study of different artefact removal algorithms for EEG signals acquired during functional MRI

In electroencephalographic (EEG) measurements performed during functional Magnetic Resonance Imaging (fMRI), imaging and cardiac artefacts strongly contaminate the EEG signal. Several algorithms have been proposed to suppress these artefacts and most of them have shown important improvements with respect to uncorrected signals. However, the relative performances of these algorithms have not been properly assessed. In particular, it is not known to what extent such algorithms deteriorate the EEG signal of interest. In this study, we propose to cross-validate different methods proposed for artefact correction, using a forward model to generate EEG and MR-related artefacts. The methods are assessed under various experimental conditions (described in terms of EEG sampling rate, artefacts amplitude, frequency band of interest, etc.). Using experimental data, we also tested the performance of the correction methods for alpha rhythm imaging and for epileptic spike reconstruction. Results show that most of the methods allow the observation of the modulation of alpha rhythms and the identification of spikes, despite subtle differences between algorithms. They also show that over-filtering the data may degrade the EEG. Our results indicate that the optimal artefact removal technique should be chosen according to whether one is interested in fast (>10 Hz) vs. slow (<10 Hz) oscillations or in evoked vs. ongoing activity.

Gap junctions mediate large-scale Turing structures in a mean-field cortex driven by subcortical noise

One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a cooperative phenomenon of multiply-interacting populations of neurons. Therefore a fruitful modeling approach is to picture the cerebral cortex as a continuum characterized by parameters that have been averaged over a small volume of cortical tissue. Such mean-field cortical models have been used to investigate gross patterns of brain behavior such as anesthesia, the cycles of natural sleep, memory and erasure in slow-wave sleep, and epilepsy. There is persuasive and accumulating evidence that direct gap-junction connections between inhibitory neurons promote synchronous oscillatory behavior both locally and across distances of some centimeters, but, to date, continuum models have ignored gap-junction connectivity. In this paper we employ simple mean-field arguments to derive an expression for D2, the diffusive coupling strength arising from gap-junction connections between inhibitory neurons. Using recent neurophysiological measurements reported by Fukuda [J. Neurosci. 26, 3434 (2006)], we estimate an upper limit of D2 approximately 0.6cm2. We apply a linear stability analysis to a standard mean-field cortical model, augmented with gap-junction diffusion, and find this value for the diffusive coupling strength to be close to the critical value required to destabilize the homogeneous steady state. Computer simulations demonstrate that larger values of D2 cause the noise-driven model cortex to spontaneously crystalize into random mazelike Turing structures: centimeter-scale spatial patterns in which regions of high-firing activity are intermixed with regions of low-firing activity. These structures are consistent with the spatial variations in brain activity patterns detected with the BOLD (blood oxygen-level-dependent) signal detected with magnetic resonance imaging, and may provide a natural substrate for synchronous gamma-band rhythms observed across separated EEG (electroencephalogram) electrodes.

Going beyond a mean-field model for the learning cortex: second-order statistics

Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the "up" and "down" states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories.

A neural mass model of spectral responses in electrophysiology

We present a neural mass model of steady-state membrane potentials measured with local field potentials or electroencephalography in the frequency domain. This model is an extended version of previous dynamic causal models for investigating event-related potentials in the time-domain. In this paper, we augment the previous formulation with parameters that mediate spike-rate adaptation and recurrent intrinsic inhibitory connections. We then use linear systems analysis to show how the model's spectral response changes with its neurophysiological parameters. We demonstrate that much of the interesting behaviour depends on the non-linearity which couples mean membrane potential to mean spiking rate. This non-linearity is analogous, at the population level, to the firing rate–input curves often used to characterize single-cell responses. This function depends on the model's gain and adaptation currents which, neurobiologically, are influenced by the activity of modulatory neurotransmitters. The key contribution of this paper is to show how neuromodulatory effects can be modelled by adding adaptation currents to a simple phenomenological model of EEG. Critically, we show that these effects are expressed in a systematic way in the spectral density of EEG recordings. Inversion of the model, given such non-invasive recordings, should allow one to quantify pharmacologically induced changes in adaptation currents. In short, this work establishes a forward or generative model of electrophysiological recordings for psychopharmacological studies.

Nonlinear local electrovascular coupling. II: From data to neuronal masses

In the companion article a local electrovascular coupling (LEVC) model was proposed to explain the continuous dynamics of electrical and vascular states within a cortical unit. These states produce certain mesoscopic reflections whose discrete time series can be reconstructed from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). In this article we develop a recursive optimization algorithm based on the local linearization (LL) filter and an innovation method to make statistical inferences about the LEVC model from both EEG and fMRI data, i.e., to estimate the unobserved states and the unknown parameters of the model. For a better understanding, the LL filter is described from a Bayesian point of view, providing the particulars for the case of hybrid data (e.g., EEG and fMRI), which could be sampled at different rates. The dynamics of the exogenous synaptic inputs going into the cortical unit are also estimated by introducing a set of Gaussian radial basis functions. In order to study the dynamics of the electrical and vascular states in the striate cortex of humans as well as their local interrelationships, we applied this algorithm to EEG and fMRI recordings obtained concurrently from two subjects while passively observing a radial checkerboard with a white/black pattern reversal. The EEG and fMRI data from the first subject was used to estimate the electrical/vascular states and parameters of the LEVC model in V1 for a 4.0 Hz reversion frequency. We used the EEG data from the second subject to investigate the changes in the dynamics of the electrical states when the frequency of reversion is varied from 0.5-4.0 Hz. Then we made use of the estimated electrical states to predict the effects on the vasculature that such variations produce.

Functional modulation of power-law distribution in visual perception

Neuronal activities have recently been reported to exhibit power-law scaling behavior. However, it has not been demonstrated that the power-law component can play an important role in human perceptual functions. Here, we demonstrate that the power spectrum of magnetoencephalograph recordings of brain activity varies in coordination with perception of subthreshold visual stimuli. We observed that perceptual performance could be better explained by modulation of the power-law component than by modulation of the peak power in particular narrow frequency ranges. The results suggest that the brain operates in a state of self-organized criticality, modulating the power spectral exponent of its activity to optimize its internal state for response to external stimuli.

Compact dynamical model of brain activity

A compact physiologically based mean-field formulation of brain dynamics is proposed to model observed brain activity and electroencephalographic (EEG) signals. In contrast to existing formulations, which are more detailed and complicated, our model is described by a single second-order delay differential equation that encapsulates salient aspects of the physiology. The model captures essential features of activity mediated by fast corticocortical connections and delayed feedbacks via extracortical pathways and external stimuli. In the linear regime, these features can be simply expressed by three coefficients derived from the properties of these physiological pathways and explicit nonlinear approximations are also derived. This compact model successfully reproduces the main features of experimental EEG's and the predictions of previous models, including resonance peaks in EEG spectra and nonlinear dynamics. As an illustration, key features of the dynamics of epileptic seizures are shown to be reproduced by the model. Due to its compact form, the model will facilitate insight into nonlinear brain dynamics via standard nonlinear techniques and will guide analysis and investigation of more complex models. It is thus a useful tool for analyzing complex brain activity, especially when it exhibits low-dimensional dynamics.

Reorganization of the composition of brain oscillations and their temporal characteristics in opioid dependent patients

In the present study, we examined the composition of electroencephalographic (EEG) brain oscillations in broad frequency band (0.5-30 Hz) in 22 opioid-dependent patients and 14 healthy subjects during resting condition (closed eyes). The exact compositions of brain oscillations and their temporal behavior were assessed by the probability-classification analysis of short-term EEG spectral patterns. It was demonstrated that EEG of patients with opioid dependence was characterized by (a) significant reorganization of brain oscillations with increase in the percentage of beta- and mostly fast-alpha-rhythmic segments, (b) longer periods of temporal stabilization for alpha and beta brain oscillations and by shorter periods of temporal stabilization for theta and polyrhythmic activity when compared with control subjects, and (c) right-sided dominance (significantly larger relative presence of particular spectral patterns in EEG channels of the right hemisphere). These effects were widely distributed across the cortex with the maximum magnitude in the occipital, right parietal, temporal, and frontal areas. Taken together the present study suggested (a) an allostatic state with neuronal activation, and (b) high sensitivity of the right hemisphere to adverse opioid effects.

Does the 1/f frequency scaling of brain signals reflect self-organized critical states?

Many complex systems display self-organized critical states characterized by 1/f frequency scaling of power spectra. Global variables such as the electroencephalogram, scale as 1/f, which could be the sign of self-organized critical states in neuronal activity. By analyzing simultaneous recordings of global and neuronal activities, we confirm the 1/f scaling of global variables for selected frequency bands, but show that neuronal activity is not consistent with critical states. We propose a model of 1/f scaling which does not rely on critical states, and which is testable experimentally.

Human auditory steady-state responses to changes in interaural correlation

Steady-state responses were evoked by noise stimuli that alternated between two levels of interaural correlation rho at a frequency fm. With rho alternating between +1 and 0, responses at fm dropped steeply above 4 Hz, but persisted up to 64 Hz. Two time constants of 47 and 4.4 ms with delays of 198 and 36 ms, respectively, were obtained by fitting responses to a transfer function based on symmetric exponential windows. The longer time constant, possibly reflecting cortical integration, is consistent with perceptual binaural "sluggishness". The shorter time constant may reflect running cross-correlation in the high brainstem or primary auditory cortex. Responses at 2fm peaked with an amplitude of 848+/-479 nV (fm=4 Hz). Investigation of this robust response revealed that: (1) changes in rho and lateralization evoked similar responses, suggesting a common neural origin, (2) response was most dependent on stimulus frequencies below 1000 Hz, but frequencies up to 4000 Hz also contributed, and (3) when rho alternated between [0.2-1] and 0, response amplitude varied linearly with rho, and the physiological response threshold was close to the average behavioral threshold (rho=0.31). This steady-state response may prove useful in the objective investigation of binaural hearing.

Integrated MEG/EEG and fMRI model based on neural masses

We introduce a bottom-up model for integrating electroencephalography (EEG) or magnetoencephalography (MEG) with functional magnetic resonance imaging (fMRI). An extended neural mass model is proposed based on the physiological principles of cortical minicolumns and their connections. The fMRI signal is extracted from the proposed neural mass model by introducing a relationship between the stimulus and the neural activity and using the resultant neural activity as input of the extended Balloon model. The proposed model, validated using simulations, is instrumental in evaluating the upcoming combined methods for simultaneous analysis of MEG/EEG and fMRI.

Mechanisms of evoked and induced responses in MEG/EEG

Cortical responses, recorded by electroencephalography and magnetoencephalography, can be characterized in the time domain, to study event-related potentials/fields, or in the time-frequency domain, to study oscillatory activity. In the literature, there is a common conception that evoked, induced, and on-going oscillations reflect different neuronal processes and mechanisms. In this work, we consider the relationship between the mechanisms generating neuronal transients and how they are expressed in terms of evoked and induced power. This relationship is addressed using a neuronally realistic model of interacting neuronal subpopulations. Neuronal transients were generated by changing neuronal input (a dynamic mechanism) or by perturbing the systems coupling parameters (a structural mechanism) to produce induced responses. By applying conventional time-frequency analyses, we show that, in contradistinction to common conceptions, induced and evoked oscillations are perhaps more related than previously reported. Specifically, structural mechanisms normally associated with induced responses can be expressed in evoked power. Conversely, dynamic mechanisms posited for evoked responses can induce responses, if there is variation in neuronal input. We conclude, it may be better to consider evoked responses as the results of mixed dynamic and structural effects. We introduce adjusted power to complement induced power. Adjusted power is unaffected by trial-to-trial variations in input and can be attributed to structural perturbations without ambiguity.

Multielectrode electroencephalogram power spectra: theory and application to approximate correction of volume conduction effects

Using a physiologically based model of brain activity, electroencephalogram (EEG) power spectra are calculated for signals derived from general linear combinations of voltages from multiple electrodes, with and without filtering by volume conduction. Two simple methods of combining scalp measurements to estimate unfiltered EEG power spectra are then proposed and their accuracy and robustness are explored, using the model predictions as an illustration. It is found that these methods, including a case that uses just three electrodes, enable improved estimation of the underlying spectrum relative to each of several widely used combinations alone.

Dynamic causal modeling of evoked responses in EEG and MEG

Neuronally plausible, generative or forward models are essential for understanding how event-related fields (ERFs) and potentials (ERPs) are generated. In this paper, we present a new approach to modeling event-related responses measured with EEG or MEG. This approach uses a biologically informed model to make inferences about the underlying neuronal networks generating responses. The approach can be regarded as a neurobiologically constrained source reconstruction scheme, in which the parameters of the reconstruction have an explicit neuronal interpretation. Specifically, these parameters encode, among other things, the coupling among sources and how that coupling depends upon stimulus attributes or experimental context. The basic idea is to supplement conventional electromagnetic forward models, of how sources are expressed in measurement space, with a model of how source activity is generated by neuronal dynamics. A single inversion of this extended forward model enables inference about both the spatial deployment of sources and the underlying neuronal architecture generating them. Critically, this inference covers long-range connections among well-defined neuronal subpopulations. In a previous paper, we simulated ERPs using a hierarchical neural-mass model that embodied bottom-up, top-down and lateral connections among remote regions. In this paper, we describe a Bayesian procedure to estimate the parameters of this model using empirical data. We demonstrate this procedure by characterizing the role of changes in cortico-cortical coupling, in the genesis of ERPs. In the first experiment, ERPs recorded during the perception of faces and houses were modeled as distinct cortical sources in the ventral visual pathway. Category-selectivity, as indexed by the face-selective N170, could be explained by category-specific differences in forward connections from sensory to higher areas in the ventral stream. We were able to quantify and make inferences about these effects using conditional estimates of connectivity. This allowed us to identify where, in the processing stream, category-selectivity emerged. In the second experiment, we used an auditory oddball paradigm to show that the mismatch negativity can be explained by changes in connectivity. Specifically, using Bayesian model selection, we assessed changes in backward connections, above and beyond changes in forward connections. In accord with theoretical predictions, there was strong evidence for learning-related changes in both forward and backward coupling. These examples show that category- or context-specific coupling among cortical regions can be assessed explicitly, within a mechanistic, biologically motivated inference framework.

Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations

Propagator theory of brain dynamics is generalized to incorporate a new class of patchy propagators that enable treatment of approximately periodic structures such as are seen in the visual cortex. Complex response fields are also incorporated to allow for features such as orientation preference and wave-number selectivity. The results are applied to the corticothalamic system associated with the primary visual cortex. It is found that this system can generate gamma ( > or = 30 Hz) oscillations during stimulation, whose properties are consistent with experimental findings on gamma frequency and bandwidth, and existence of fine-scale spatial structure. It is found that a potential resonance is associated with each reciprocal lattice vector corresponding to periodic modulations of the propagators. It is found that the lowest resonances are the most likely to give rise to noticeable spectral peaks and increases of correlation amplitude, length, and time, and that these aspects are prominent only if the system is close to marginal stability, in accord with previous measurements and discussions of cortical stability. These features also enable gamma resonances to be stimulus-evoked, with substantial resonance sharpening for relatively small changes in mean neural firing rate. The results also imply dependence of gamma frequency on stimulus features.

EEG MARKERS FOR COGNITIVE DECLINE IN ELDERLY SUBJECTS WITH SUBJECTIVE MEMORY COMPLAINTS

New treatments for Alzheimer's disease require early detection of cognitive decline. Most studies seeking to identify markers of early cognitive decline have focused on a limited number of measures. We sought to establish the profile of brain function measures which best define early neuropsychological decline. We compared subjects with subjective memory complaints to normative controls on a wide range of EEG derived measures, including a new measure of event-related spatio-temporal waves and biophysical modeling, which derives anatomical and physiological parameters based on subject's EEG measurements. Measures that distinguished the groups were then related to cognitive performance on a variety of learning and executive function tasks. The EEG measures include standard power measures, peak alpha frequency, EEG desynchronization to eyes-opening, and global phase synchrony. The most prominent differences in subjective memory complaint subjects were elevated alpha power and an increased number of spatio-temporal wave events. Higher alpha power and changes in wave activity related most strongly to a decline in verbal memory performance in subjects with subjective memory complaints, and also declines in maze performance and working memory reaction time. Interestingly, higher alpha power and wave activity were correlated with improved performance in reverse digit span in the subjective memory complaint group. The modeling results suggest that differences in the subjective memory complaint subjects were due to a decrease in cortical and thalamic inhibitory gains and slowed dendritic time-constants. The complementary profile that emerges from the variety of measures and analyses points to a nonlinear progression in electrophysiological changes from early neuropsychological decline to late-stage dementia, and electrophysiological changes in subjective memory complaint that vary in their relationships to a range of memory-related tasks.

The nonlinear theory of schizophrenia

OBJECTIVE

Nonlinear properties exist within the brain across a hierarchy of scales and within a variety of critical neural processes. Only a few studies of brain activity in schizophrenia, however, have used nonlinear methods. This review paper evaluates the contribution of the nonlinear sciences towards understanding schizophrenia.

METHOD

Applications of nonlinear methods to the study of schizophrenia symptoms and to healthy and schizophrenia functional neuroscience data are reviewed. The main flaws of nonlinear algorithms and recent methods to correct these are also appraised.

RESULTS

Initial research methods utilized in the study of nonlinearity in schizophrenia have fundamental methodological limitations. In the last decade, many of these problems have been addressed, facilitating future progress. Research incorporating these improvements has been applied to normal electroencephalogram (EEG) data and to the symptoms of schizophrenia, but not systematically to brain imaging data collected from patients with schizophrenia.

CONCLUSION

There is strong statistical evidence for weak nonlinearity in normal EEG and in the fluctuations of the symptoms of schizophrenia. However, the contribution of nonlinear processes to brain dysfunction in schizophrenia is yet to be properly established or accurately quantified. Despite this, recent methodological advances suggest that a 'nonlinear theory' of schizophrenia may be helpful in understanding this disorder.

A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis

The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain's mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology, and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific predictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions. Hence, we argue that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted and interrelated by the global bifurcation diagram of the model's dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain.

Multiscale brain modelling

A central difficulty of brain modelling is to span the range of spatio-temporal scales from synapses to the whole brain. This paper overviews results from a recent model of the generation of brain electrical activity that incorporates both basic microscopic neurophysiology and large-scale brain anatomy to predict brain electrical activity at scales from a few tenths of a millimetre to the whole brain. This model incorporates synaptic and dendritic dynamics, nonlinearity of the firing response, axonal propagation and corticocortical and corticothalamic pathways. Its relatively few parameters measure quantities such as synaptic strengths, corticothalamic delays, synaptic and dendritic time constants, and axonal ranges, and are all constrained by independent physiological measurements. It reproduces quantitative forms of electroencephalograms seen in various states of arousal, evoked response potentials, coherence functions, seizure dynamics and other phenomena. Fitting model predictions to experimental data enables underlying physiological parameters to be inferred, giving a new non-invasive window into brain function that complements slower, but finer-resolution, techniques such as fMRI. Because the parameters measure physiological quantities relating to multiple scales, and probe deep structures such as the thalamus, this will permit the testing of a range of hypotheses about vigilance, cognition, drug action and brain function. In addition, referencing to a standardized database of subjects adds strength and specificity to characterizations obtained.