Prediction of electroencephalographic spectra from neurophysiology

Applying EEG phase synchronization measures to non-linearly coupled neural mass models

BACKGROUND

Recent neuroimaging analyses aim to understand how information is integrated across brain regions that have traditionally been studied in isolation; however, detecting functional connectivity networks in experimental EEG recordings is a non-trivial task.

NEW METHOD

We use neural mass models to simulate 10-s trials with coupling between 1-3 and 5-8s and compare how well three phase-based connectivity measures recover this connectivity pattern across a set of experimentally relevant conditions: variable oscillation frequency and power spectrum, feed forward connections with or without feedback, and simulated signals with and without volume conduction.

RESULTS

Overall, the results highlight successful detection of the onset and offset of significant synchronizations for a majority of the 28 simulated configurations; however, the tested phase measures sometimes differ in their sensitivity and specificity to the underlying connectivity.

COMPARISON WITH EXISTING METHODS

Prior work has shown that these phase measures perform well on signals generated by a computational model of coupled oscillators. In this work we extend previous studies by exploring the performance of these measures on a different class of computational models, and we compare the methods on 28 variations that capture a set of experimentally relevant conditions.

CONCLUSIONS

Our results underscore that no single phase synchronization measure is substantially better than all others, and experimental investigations will likely benefit from combining a set of measures together that are chosen based on both the experimental question of interest, the signal to noise ratio in the EEG data, and the approach used for statistical significance.

Information gain in the brain's resting state: A new perspective on autism

Along with the study of brain activity evoked by external stimuli, an increased interest in the research of background, “noisy” brain activity is fast developing in current neuroscience. It is becoming apparent that this “resting-state” activity is a major factor determining other, more particular, responses to stimuli and hence it can be argued that background activity carries important information used by the nervous systems for adaptive behaviors. In this context, we investigated the generation of information in ongoing brain activity recorded with magnetoencephalography (MEG) in children with autism spectrum disorder (ASD) and non-autistic children. Using a stochastic dynamical model of brain dynamics, we were able to resolve not only the deterministic interactions between brain regions, i.e., the brain's functional connectivity, but also the stochastic inputs to the brain in the resting state; an important component of large-scale neural dynamics that no other method can resolve to date. We then computed the Kullback-Leibler (KLD) divergence, also known as information gain or relative entropy, between the stochastic inputs and the brain activity at different locations (outputs) in children with ASD compared to controls. The divergence between the input noise and the brain's ongoing activity extracted from our stochastic model was significantly higher in autistic relative to non-autistic children. This suggests that brains of subjects with autism create more information at rest. We propose that the excessive production of information in the absence of relevant sensory stimuli or attention to external cues underlies the cognitive differences between individuals with and without autism. We conclude that the information gain in the brain's resting state provides quantitative evidence for perhaps the most typical characteristic in autism: withdrawal into one's inner world.

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

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

Seizure prediction in hippocampal and neocortical epilepsy using a model-based approach

OBJECTIVES

The aim of this study is to develop a model based seizure prediction method.

METHODS

A neural mass model was used to simulate the macro-scale dynamics of intracranial EEG data. The model was composed of pyramidal cells, excitatory and inhibitory interneurons described through state equations. Twelve model's parameters were estimated by fitting the model to the power spectral density of intracranial EEG signals and then integrated based on information obtained by investigating changes in the parameters prior to seizures. Twenty-one patients with medically intractable hippocampal and neocortical focal epilepsy were studied.

RESULTS

Tuned to obtain maximum sensitivity, an average sensitivity of 87.07% and 92.6% with an average false prediction rate of 0.2 and 0.15/h were achieved using maximum seizure occurrence periods of 30 and 50 min and a minimum seizure prediction horizon of 10s, respectively. Under maximum specificity conditions, the system sensitivity decreased to 82.9% and 90.05% and the false prediction rates were reduced to 0.16 and 0.12/h using maximum seizure occurrence periods of 30 and 50 min, respectively.

CONCLUSIONS

The spatio-temporal changes in the parameters demonstrated patient-specific preictal signatures that could be used for seizure prediction.

SIGNIFICANCE

The present findings suggest that the model-based approach may aid prediction of seizures.

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.

Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations

Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

Stimulus detection rate and latency, firing rates and 1-40Hz oscillatory power are modulated by infra-slow fluctuations in a bistable attractor network model

Recordings of membrane and field potentials, firing rates, and oscillation amplitude dynamics show that neuronal activity levels in cortical and subcortical structures exhibit infra-slow fluctuations (ISFs) on time scales from seconds to hundreds of seconds. Similar ISFs are salient also in blood-oxygenation-level dependent (BOLD) signals as well as in psychophysical time series. Functional consequences of ISFs are not fully understood. Here, they were investigated along with dynamical implications of ISFs in large-scale simulations of cortical network activity. For this purpose, a biophysically detailed hierarchical attractor network model displaying bistability and operating in an oscillatory regime was used. ISFs were imposed as slow fluctuations in either the amplitude or frequency of fast synaptic noise. We found that both mechanisms produced an ISF component in the synthetic local field potentials (LFPs) and modulated the power of 1-40Hz oscillations. Crucially, in a simulated threshold-stimulus detection task (TSDT), these ISFs were strongly correlated with stimulus detection probabilities and latencies. The results thus show that several phenomena observed in many empirical studies emerge concurrently in the model dynamics, which yields mechanistic insight into how infra-slow excitability fluctuations in large-scale neuronal networks may modulate fast oscillations and perceptual processing. The model also makes several novel predictions that can be experimentally tested in future studies.

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.

Neural masses and fields in dynamic causal modeling

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models-that consider the dynamics of specific ion-channels-present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity-through local lateral interactions among cortical layers-may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure-function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class.

A model of functional brain connectivity and background noise as a biomarker for cognitive phenotypes: application to autism

We present an efficient approach to discriminate between typical and atypical brains from macroscopic neural dynamics recorded as magnetoencephalograms (MEG). Our approach is based on the fact that spontaneous brain activity can be accurately described with stochastic dynamics, as a multivariate Ornstein-Uhlenbeck process (mOUP). By fitting the data to a mOUP we obtain: 1) the functional connectivity matrix, corresponding to the drift operator, and 2) the traces of background stochastic activity (noise) driving the brain. We applied this method to investigate functional connectivity and background noise in juvenile patients (n = 9) with Asperger's syndrome, a form of autism spectrum disorder (ASD), and compared them to age-matched juvenile control subjects (n = 10). Our analysis reveals significant alterations in both functional brain connectivity and background noise in ASD patients. The dominant connectivity change in ASD relative to control shows enhanced functional excitation from occipital to frontal areas along a parasagittal axis. Background noise in ASD patients is spatially correlated over wide areas, as opposed to control, where areas driven by correlated noise form smaller patches. An analysis of the spatial complexity reveals that it is significantly lower in ASD subjects. Although the detailed physiological mechanisms underlying these alterations cannot be determined from macroscopic brain recordings, we speculate that enhanced occipital-frontal excitation may result from changes in white matter density in ASD, as suggested in previous studies. We also venture that long-range spatial correlations in the background noise may result from less specificity (or more promiscuity) of thalamo-cortical projections. All the calculations involved in our analysis are highly efficient and outperform other algorithms to discriminate typical and atypical brains with a comparable level of accuracy. Altogether our results demonstrate a promising potential of our approach as an efficient biomarker for altered brain dynamics associated with a cognitive phenotype.

Stability constraints on large-scale structural brain networks

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

Statistical method for detecting phase shifts in alpha rhythm from human electroencephalogram data

We developed a statistical method for detecting discontinuous phase changes (phase shifts) in fluctuating alpha rhythms in the human brain from electroencephalogram (EEG) data obtained in a single trial. This method uses the state space models and the line process technique, which is a Bayesian method for detecting discontinuity in an image. By applying this method to simulated data, we were able to detect the phase and amplitude shifts in a single simulated trial. Further, we demonstrated that this method can detect phase shifts caused by a visual stimulus in the alpha rhythm from experimental EEG data even in a single trial. The results for the experimental data showed that the timings of the phase shifts in the early latency period were similar between many of the trials, and that those in the late latency period were different between the trials. The conventional averaging method can only detect phase shifts that occur at similar timings between many of the trials, and therefore, the phase shifts that occur at differing timings cannot be detected using the conventional method. Consequently, our obtained results indicate the practicality of our method. Thus, we believe that our method will contribute to studies examining the phase dynamics of nonlinear alpha rhythm oscillators.

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.

On the dynamics of cortical development: synchrony and synaptic self-organization

We describe a model for cortical development that resolves long-standing difficulties of earlier models. It is proposed that, during embryonic development, synchronous firing of neurons and their competition for limited metabolic resources leads to selection of an array of neurons with ultra-small-world characteristics. Consequently, in the visual cortex, macrocolumns linked by superficial patchy connections emerge in anatomically realistic patterns, with an ante-natal arrangement which projects signals from the surrounding cortex onto each macrocolumn in a form analogous to the projection of a Euclidean plane onto a Möbius strip. This configuration reproduces typical cortical response maps, and simulations of signal flow explain cortical responses to moving lines as functions of stimulus velocity, length, and orientation. With the introduction of direct visual inputs, under the operation of Hebbian learning, development of mature selective response “tuning” to stimuli of given orientation, spatial frequency, and temporal frequency would then take place, overwriting the earlier ante-natal configuration. The model is provisionally extended to hierarchical interactions of the visual cortex with higher centers, and a general principle for cortical processing of spatio-temporal images is sketched.

The value of spontaneous EEG oscillations in distinguishing patients in vegetative and minimally conscious states

OBJECTIVE

The value of spontaneous electroencephalography (EEG) oscillations in distinguishing patients in vegetative state (VS) and minimally conscious states (MCS) was studied.

METHODS

We quantified dynamic repertoire of EEG oscillations in resting condition with closed eyes in patients in VS and MCS. The exact composition of EEG oscillations was assessed by the probability-classification analysis of short-term EEG spectral patterns.

RESULTS

The probability of delta, theta, and slow-alpha oscillations occurrence was smaller for patients in MCS than for VS. Additionally, only patients in MCS demonstrated fast-alpha oscillation occurrence. Depending on the type and composition of EEG oscillations, the probability of their occurrence was either etiology dependent or independent. The probability of EEG oscillations occurrence differentiated brain injuries with different etiologies.

CONCLUSIONS

Spontaneous EEG oscillations have a potential value in distinguishing patients in VS and MCS.

SIGNIFICANCE

This work may have implications for clinical care, rehabilitative programs, and medical-legal decisions in patients with impaired consciousness states following coma due to acute brain injuries.

HIGHLIGHTS

The probability of delta, theta, and slow-alpha oscillations occurrence was smaller and the probability of fast-alpha oscillations occurrence was higher for patients in MCS than for patients in VS. The probability of EEG oscillations occurrence differentiated brain injuries with different etiologies. Spontaneous EEG has a potential value in distinguishing patients in VS and MCS.

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.

Traveling pulses in a stochastic neural field model of direction selectivity

We analyze the effects of extrinsic noise on traveling pulses in a neural field model of direction selectivity. The model consists of a one-dimensional scalar neural field with an asymmetric weight distribution consisting of an offset Mexican hat function. We first show how, in the absence of any noise, the system supports spontaneously propagating traveling pulses that can lock to externally moving stimuli. Using a separation of time-scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the wave from its uniformly translating position at long time-scales, and fluctuations in the wave profile around its instantaneous position at short time-scales. In the case of freely propagating pulses, the wandering is characterized by pure Brownian motion, whereas in the case of stimulus-locked pulses, it is given by an Ornstein–Uhlenbeck process. This establishes that stimulus-locked pulses are more robust to noise.

Neural field theory of plasticity in the cerebral cortex

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

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

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

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

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

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

Connectivity changes underlying spectral EEG changes during propofol-induced loss of consciousness

The mechanisms underlying anesthesia-induced loss of consciousness remain a matter of debate. Recent electrophysiological reports suggest that while initial propofol infusion provokes an increase in fast rhythms (from beta to gamma range), slow activity (from delta to alpha range) rises selectively during loss of consciousness. Dynamic causal modeling was used to investigate the neural mechanisms mediating these changes in spectral power in humans. We analyzed source-reconstructed data from frontal and parietal cortices during normal wakefulness, propofol-induced mild sedation, and loss of consciousness. Bayesian model selection revealed that the best model for explaining spectral changes across the three states involved changes in corticothalamic interactions. Compared with wakefulness, mild sedation was accounted for by an increase in thalamic excitability, which did not further increase during loss of consciousness. In contrast, loss of consciousness per se was accompanied by a decrease in backward corticocortical connectivity from frontal to parietal cortices, while thalamocortical connectivity remained unchanged. These results emphasize the importance of recurrent corticocortical communication in the maintenance of consciousness and suggest a direct effect of propofol on cortical dynamics.

Neural field theory with variance dynamics

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

Hemodynamic traveling waves in human visual cortex

Functional MRI (fMRI) experiments rely on precise characterization of the blood oxygen level dependent (BOLD) signal. As the spatial resolution of fMRI reaches the sub-millimeter range, the need for quantitative modelling of spatiotemporal properties of this hemodynamic signal has become pressing. Here, we find that a detailed physiologically-based model of spatiotemporal BOLD responses predicts traveling waves with velocities and spatial ranges in empirically observable ranges. Two measurable parameters, related to physiology, characterize these waves: wave velocity and damping rate. To test these predictions, high-resolution fMRI data are acquired from subjects viewing discrete visual stimuli. Predictions and experiment show strong agreement, in particular confirming BOLD waves propagating for at least 5–10 mm across the cortical surface at speeds of 2–12 mm s-1. These observations enable fundamentally new approaches to fMRI analysis, crucial for fMRI data acquired at high spatial resolution.

Functional magnetic resonance imaging (fMRI) experiments have advanced our understanding of the structure and function of the human brain. Dynamic changes in the flow and concentration of oxygen in blood are observed experimentally in fMRI data via the blood oxygen level dependent (BOLD) signal. Since neuronal activity induces this hemodynamic response, the BOLD signal provides a noninvasive measure of neuronal activity. Understanding the mechanisms that drive this BOLD response is fundamental for accurately inferring the underlying neuronal activity. The goal of this study is to systematically predict spatiotemporal hemodynamics from a biophysical model, then test these in a high resolution fMRI study of the visual cortex. Using this theory, we predict and empirically confirm the existence of hemodynamic waves in cortex – a striking and novel finding.

Corticothalamic dynamics: structure of parameter space, spectra, instabilities, and reduced model

Linear instabilities are analyzed in a physiologically based mean-field corticothalamic model and a reduced-parameter model derived from it. In both models, the stable zone corresponding to normal arousal states is bounded by a series of surfaces demarcating the onsets of instabilities. The stable zone is found to depend on delay and rate parameters, whose values have a simple relationship to the number of instabilities and dominant frequencies on the stable zone's boundary. The dominant frequencies of linear activity inside the stable zone are found to lie in clearly delineated regions, each corresponding to an instability surface on its boundary and having approximately the same dominant frequency. These regions are ordered in parameter space according to their dominant frequencies, and an instability associated with the intrathalamic loop is shown to have the highest frequency that can become unstable. This reveals an important role for the thalamus in controlling the stability and bandwidth of dynamics in the corticothalamic system as a whole. The reduced model is found to agree well with the full model in a wide region of parameter space and, thus, is a useful guide to the full model's dynamics.

Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory

It is shown how to compute effective and functional connection matrices (eCMs and fCMs) from anatomical CMs (aCMs) and corresponding strength-of-connection matrices (sCMs) using propagator methods in which neural interactions play the role of scatterings. This analysis demonstrates how network effects dress the bare propagators (the sCMs) to yield effective propagators (the eCMs) that can be used to compute the covariances customarily used to define fCMs. The results incorporate excitatory and inhibitory connections, multiple structures and populations, asymmetries, time delays, and measurement effects. They can also be postprocessed in the same manner as experimental measurements for direct comparison with data and thereby give insights into the role of coarse-graining, thresholding, and other effects in determining the structure of CMs. The spatiotemporal results show how to generalize CMs to include time delays and how natural network modes give rise to long-range coherence at resonant frequencies. The results are demonstrated using tractable analytic cases via neural field theory of cortical and corticothalamic systems. These also demonstrate close connections between the structure of CMs and proximity to critical points of the system, highlight the importance of indirect links between brain regions and raise the possibility of imaging specific levels of indirect connectivity. Aside from the results presented explicitly here, the expression of the connections among aCMs, sCMs, eCMs, and fCMs in terms of propagators opens the way for propagator theory to be further applied to analysis of connectivity.

Quantitative modelling of sleep dynamics

Arousal is largely controlled by the ascending arousal system of the hypothalamus and brainstem, which projects to the corticothalamic system responsible for electroencephalographic (EEG) signatures of sleep. Quantitative physiologically based modelling of brainstem dynamics theory is described here, using realistic parameters, and links to EEG are outlined. Verification against a wide range of experimental data is described, including arousal dynamics under normal conditions, sleep deprivation, stimuli, stimulants and jetlag, plus key features of wake and sleep EEGs.

Life or death: prognostic value of a resting EEG with regards to survival in patients in vegetative and minimally conscious States

OBJECTIVE

To investigate the potentially prognostic value of a resting state electroencephalogram (EEG) with regards to the clinical outcome from vegetative and minimally conscious states (VS and MCS) in terms of survival six months after a brain injury.

METHODS

We quantified a dynamic repertoire of EEG oscillations in resting condition with eyes closed in patients in VS and MCS. The exact composition of EEG oscillations was assessed by analysing the probability-classification of short-term EEG spectral patterns.

RESULTS

Results demonstrated that (a) the diversity and the variability of EEG for Non-Survivors were significantly lower than for Survivors; and (b) a higher probability of mostly delta and slow-theta oscillations occurring either alone or in combination were found during the first assessment for patients with a bad outcome (i.e., those who died) within six months of an injury compared to patients who survived. At the same time, patients with a good outcome (i.e., those who survived) after six months post-injury had a higher probability of mostly fast-theta and alpha oscillations occurring either alone or in combination during the first assessment when compared to patients who died within six months of an injury.

CONCLUSIONS

Resting state EEGs properly analysed may have a potentially prognostic value with regards to the outcome from VS or MCS in terms of survival six months after a brain injury.

SIGNIFICANCE

This work may have implications for clinical care, rehabilitative programmes and medical-legal decisions for patients with impaired consciousness states after being in a coma due to acute brain injuries.

Brain rhythms reveal a hierarchical network organization

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or "virtual brains", whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.

Biophysical mechanisms of multistability in resting-state cortical rhythms

The human alpha (8-12 Hz) rhythm is one of the most prominent, robust, and widely studied attributes of ongoing cortical activity. Contrary to the prevalent notion that it simply "waxes and wanes," spontaneous alpha activity bursts erratically between two distinct modes of activity. We now establish a mechanism for this multistable phenomenon in resting-state cortical recordings by characterizing the complex dynamics of a biophysical model of macroscopic corticothalamic activity. This is achieved by studying the predicted activity of cortical and thalamic neuronal populations in this model as a function of its dynamic stability and the role of nonspecific synaptic noise. We hence find that fluctuating noisy inputs into thalamic neurons elicit spontaneous bursts between low- and high-amplitude alpha oscillations when the system is near a particular type of dynamical instability, namely a subcritical Hopf bifurcation. When the postsynaptic potentials associated with these noisy inputs are modulated by cortical feedback, the SD of power within each of these modes scale in proportion to their mean, showing remarkable concordance with empirical data. Our state-dependent corticothalamic model hence exhibits multistability and scale-invariant fluctuations-key features of resting-state cortical activity and indeed, of human perception, cognition, and behavior-thus providing a unified account of these apparently divergent phenomena.

Thalamocortical changes in major depression probed by deconvolution and physiology-based modeling

Auditory event-related potentials (ERPs) have been extensively studied in patients with depression, but most studies have focused on purely phenomenological analysis methods, such as component scoring. In contrast, this study applies two recently developed physiology-based methods-fitting using a thalamocortical model of neuronal activity and waveform deconvolution - to data from a selective-attention task in four subject groups (49 patients with melancholic depression, 34 patients with non-melancholic depression, 111 participants with subclinical depressed mood, and 98 healthy controls), to yield insight into physiological differences in attentional processing between participants with major depression and controls. This approach found evidence that: participants with depressed mood, regardless of clinical status, shift from excitation in the thalamocortical system towards inhibition; that clinically depressed participants have decreased relative response amplitude between target and standard waveforms; and that patients with melancholic depression also have increased thalamocortical delays. These findings suggest possible physiological mechanisms underlying different depression subtypes, and may eventually prove useful in motivating new physiology-based diagnostic methods.

Central thalamic deep brain stimulation for cognitive neuromodulation - a review of proposed mechanisms and investigational studies

We review the history of efforts to apply central thalamic deep brain stimulation (CT/DBS) to restore consciousness in patients in a coma or vegetative state by changing the arousal state. Early experimental and clinical studies, and the results of a recent single-subject human study that demonstrated both immediate behavioral facilitation and carry-over effects of CT/DBS are reviewed. We consider possible mechanisms underlying CT/DBS effects on cognitively-mediated behaviors in conscious patients in light of the anatomical connectivity and physiological specializations of the central thalamus. Immediate and carry-over effects of CT/DBS are discussed within the context of possible effects on neuronal plasticity and gene expression. We conclude that CT/DBS should be studied as a therapeutic intervention to improve impaired cognitive function in severely brain-injured patients who, in addition to demonstrating clinical evidence of consciousness and goal-directed behavior, retain sufficient preservation of large-scale cerebral networks within the anterior forebrain. Although available data provide evidence for proof-of-concept, very significant challenges for study design and development of CT/DBS for clinical use are identified.

Beta-band activity during motor planning reflects response uncertainty

It has been known for many years that the power of beta-band oscillatory activity in motor-related brain regions decreases during the preparation and execution of voluntary movements. However, it is not clear yet whether the amplitude of this desynchronization is modulated by any parameter of the motor task. Here, we examined whether the degree of uncertainty about the upcoming movement direction modulated beta-band desynchronization during motor preparation. To this end, we recorded whole-head neuromagnetic signals while human subjects performed an instructed-delay reaching task with one, two, or three possible target directions. We found that the reduction of power of beta-band activity (16-28 Hz) during motor preparation was scaled relative to directional uncertainty. Furthermore, we show that the change of beta-band power correlates with the change of latency of response associated with response uncertainty. Finally, we show that the main source of beta-band desynchronization was located in the peri-Rolandic region. The results establish directional uncertainty as an important determinant of beta-band power during motor preparation and indicate that neural activity in the sensorimotor cortex during motor preparation covaries with directional uncertainty.

Influence of coherence between multiple cortical columns on alpha rhythm: a computational modeling study

In electroencephalographic (EEG) and magnetoencephalographic (MEG) signals, stimulus-induced amplitude increase and decrease in the alpha rhythm, known as event-related synchronization and desynchronization (ERS/ERD), emerge after a task onset. ERS/ERD is assumed to reflect neural processes relevant to cognitive tasks. Previous studies suggest that several sources of alpha rhythm, each of which can serve as an alpha rhythm generator, exist in the cortex. Since EEG/MEG signals represent spatially summed neural activities, ERS/ERD of the alpha rhythm may reflect the consequence of the interactions between multiple alpha rhythm generators. Two candidates modulate the magnitude of ERS/ERD: (1) coherence between the activities of the alpha rhythm generators and (2) mean amplitude of the activities of the alpha rhythm generators. In this study, we use a computational model of multiple alpha rhythm generators to determine the factor that dominantly causes ERS/ERD. Each alpha rhythm generator is modeled based on local column circuits in the primary visual cortex and made to interact with the neighboring generators through excitatory connections. We observe that the model consistently reproduces spontaneous alpha rhythms, event-related potentials, phase-locked alpha rhythms, and ERS/ERD in a specific range of connectivity coefficients. Independent analyses of the coherence and amplitude of multiple alpha rhythm generators reveal that the ERS/ERD in the simulated data is dominantly caused by stimulus-induced changes in the coherence between multiple alpha rhythm generators. Nonlinear phenomena such as phase-resetting and entrainment of the alpha rhythm are related to the neural mechanism underlying ERS/ERD.

Inference in alpha rhythm phase and amplitude modeled on Markov random field using belief propagation from electroencephalograms

Alpha rhythm is a major component of spontaneous electroencephalographic (EEG) data. We develop a novel method that can be used to estimate the instantaneous phases and amplitudes of the alpha rhythm with high accuracy by modeling the alpha rhythm phase and amplitude as Markov random field (MRF) models. By using a belief propagation technique, we construct an exact-inference algorithm that can be used to estimate instantaneous phases and amplitudes and calculate the marginal likelihood. Maximizing the marginal likelihood enables us to estimate the hyperparameters on the basis of type-II maximum likelihood estimation. We prove that the instantaneous phase and amplitude estimation by our method is consistent with that by the Hilbert transform, which has been commonly used to estimate instantaneous phases and amplitudes, of a signal filtered from observed data in the limited case that the observed data consist of only one frequency signal whose amplitude is constant and a Gaussian noise. Comparison of the performances of observation noise reduction by our method and by a Gaussian MRF model of alpha rhythm signal indicates that our method reduces observation noise more efficiently. Moreover, the instantaneous phase and amplitude estimates obtained using our method are more accurate than those obtained by the Hilbert transform. Application of our method to experimental EEG data also demonstrates that the relationship between the alpha rhythm phase and the reaction time emerges more clearly by using our method than the Hilbert transform. This indicates our method's practical usefulness. Therefore, applying our method to experimental EEG data will enable us to estimate the instantaneous phases and amplitudes of the alpha rhythm more precisely.

Fluctuation of gamma-band phase synchronization within the auditory cortex in schizophrenia

OBJECTIVE

To study the phase stability of the 40Hz auditory steady-state response (ASSR) in Sz, and in addition, to investigate inter-hemispheric phase synchronization using ipsilateral and contralateral hemisphere gamma band ASSRs.

METHODS

Whole head magnetoencephalography (MEG) was used to detect ASSR from both hemispheres in Sz patients and their control counterparts. Source localization, spatial and temporal filtering were performed to infer gamma band activity from the neural generators of the ASSR. The response gamma band phase stability relative to a reference signal was quantified using the phase synchronization index (PSI).

RESULTS

Results indicated reduced phase synchronization of the ASSR and the stimulus reference signal in Sz patients compared to control subjects, in addition to reduced inter-hemispheric phase synchronization between contralateral and ipsilateral hemispheric responses in Sz patients.

CONCLUSIONS

Greater intra and inter hemispheric fluctuations of ASSR gamma band phase synchronization in Sz add to previous studies suggesting timing deficiencies within neural populations, possibly caused by impairments of neural network parameters.

SIGNIFICANCE

This study provides experimental support that may aid in understanding the dynamics of neural phase synchrony caused by modifications of underlying neurotransmitter systems, as reflected in disease states such as schizophrenia.

The generation of rhythms within a cortical region: analysis of a neural mass model

Rhythms in brain electrical activity are assumed to play a significant role in many cognitive and perceptual processes. It is thus of great value to analyze these rhythms and their mutual relationships in large scale models of cortical regions. In the present work, we modified the neural mass model by Wendling et al. (Eur. J. Neurosci. 15 (2002) 1499-1508) by including a new inhibitory self-loop among GABAA,fast interneurons. A theoretical analysis was performed to demonstrate that, thanks to this loop, GABAA,fast interneurons can produce a gamma rhythm in the power spectral density (PSD) even without the participation of the other neural populations. Then, the model of a whole cortical region, built upon four interconnected neural populations (pyramidal cells, excitatory, GABAA,slow and GABAA,fast interneurons) was investigated by changing the internal connectivity parameters. Results show that different rhythm combinations (beta and gamma, alpha and gamma, or a wide spectrum) can be obtained within the same region by simply altering connectivity values, without the need to change synaptic kinetics. Finally, two or three cortical regions were connected by using different topologies of long range connections. Results show that long-range connections directed from pyramidal neurons to GABAA,fast interneurons are the most efficient to transmit rhythms from one region to another. In this way, PSD with three or four peaks can be obtained using simple connectivity patterns. The model can be of value to gain a deeper insight into the mechanisms involved in the generation of gamma rhythms and provide a better understanding of cortical EEG spectra.

High-frequency Broadband Modulations of Electroencephalographic Spectra

High-frequency cortical potentials in electroencephalographic (EEG) scalp recordings have low amplitudes and may be confounded with scalp muscle activities. EEG data from an eyes-closed emotion imagination task were linearly decomposed using independent component analysis (ICA) into maximally independent component (IC) processes. Joint decomposition of IC log spectrograms into source- and frequency-independent modulator (IM) processes revealed three distinct classes of IMs that separately modulated broadband high-frequency (∼15–200 Hz) power of brain, scalp muscle, and likely ocular motor IC processes. Multi-dimensional scaling revealed significant but spatially complex relationships between mean broadband brain IM effects and the valence of the imagined emotions. Thus, contrary to prevalent assumption, unitary modes of spectral modulation of frequencies encompassing the beta, gamma, and high gamma frequency ranges can be isolated from scalp-recorded EEG data and may be differentially associated with brain sources and cognitive activities.

Morphology and dynamic repertoire of EEG short-term spectral patterns in rest: explorative study

In the present explorative experimental study, we examined the diversity of electroencephalographic (EEG) short-term spectral patterns (SPs) within a broad frequency band (1.5-30Hz) for healthy adult subjects during closed eyes and open eyes resting conditions. The types of EEG SPs were assessed by counting all identical SPs with peaks in the same frequency bins from the pools of SPs, which were built from all the SPs of the entire EEG signal (all locations) for all subjects separately for closed and open eyes conditions. This study demonstrated that independently of the resting functional state of the brain (closed eyes vs. open eyes) (a) the diversity of short-term EEG SP types was limited, (b) the percent distribution of SP types among different categories of SPs (based on morphology of SPs) was constant and (c) the most preferred frequencies were restricted to delta-theta and alpha bands. At the same time, closed eyes and open eyes conditions differed from each other by the percent distribution of different types of SPs. The probabilities for the occurrence of particular SP types were typical for each of the examined conditions with domination of alpha-rhythmical SPs during closed eyes condition and domination of delta-theta-rhythmical SPs during open eyes condition. The findings suggest that the diversity of SPs varies as a function of functional state of the brain during resting conditions. Understanding of the diversity of short-term EEG SP types is important theoretically and practically, and is significant for advancing the interpretation of the EEG signal.

Neurophysiological changes with age probed by inverse modeling of EEG spectra

OBJECTIVE

To investigate age-associated changes in physiologically-based EEG spectral parameters in the healthy population.

METHODS

Eyes-closed EEG spectra of 1498 healthy subjects aged 6-86 years were fitted to a mean-field model of thalamocortical dynamics in a cross-sectional study. Parameters were synaptodendritic rates, cortical wave decay rates, connection strengths (gains), axonal delays for thalamocortical loops, and power normalizations. Age trends were approximated using smooth asymptotically linear functions with a single turning point. We also considered sex differences and relationships between model parameters and traditional quantitative EEG measures.

RESULTS

The cross-sectional data suggest that changes tend to be most rapid in childhood, generally leveling off at age 15-20 years. Most gains decrease in magnitude with age, as does power normalization. Axonal and dendritic delays decrease in childhood and then increase. Axonal delays and gains show small but significant sex differences.

CONCLUSIONS

Mean-field brain modeling allows interpretation of age-associated EEG trends in terms of physiological processes, including the growth and regression of white matter, influencing axonal delays, and the establishment and pruning of synaptic connections, influencing gains.

SIGNIFICANCE

This study demonstrates the feasibility of inverse modeling of EEG spectra as a noninvasive method for investigating large-scale corticothalamic dynamics, and provides a basis for future comparisons.

Dimensional reduction for the inverse problem of neural field theory

Inverse problems in computational neuroscience comprise the determination of synaptic weight matrices or kernels for neural networks or neural fields respectively. Here, we reduce multi-dimensional inverse problems to inverse problems in lower dimensions which can be solved in an easier way or even explicitly through kernel construction. In particular, we discuss a range of embedding techniques and analyze their properties. We study the Amari equation as a particular example of a neural field theory. We obtain a solution of the full 2D or 3D problem by embedding 0D or 1D kernels into the domain of the Amari equation using a suitable path parametrization and basis transformations. Pulses are interconnected at branching points via path gluing. As instructive examples we construct logical gates, such as the persistent XOR and binary addition in neural fields. In addition, we compare results of inversion by dimensional reduction with a recently proposed global inversion scheme for neural fields based on Tikhonov–Hebbian learning. The results show that stable construction of complex distributed processes is possible via neural field dynamics. This is an important first step to study the properties of such constructions and to analyze natural or artificial realizations of neural field architectures.