Neurophysical theory of coherence and correlations of electroencephalographic and electrocorticographic signals

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

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

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

BACKGROUND

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

NEW METHOD

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

RESULTS

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

COMPARISON WITH EXISTING METHODS

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

CONCLUSION

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

Questionnaires based on natural language processing elicit immersive ruminative thinking in ruminators: Evidence from behavioral responses and EEG data

Rumination is closely related to mental disorders and can thus be used as a marker of their presence or a predictor of their development. The presence of masking and fabrication in psychological selection can lead to inaccurate detection of psychological disorders. Human language is considered crucial in eliciting specific conscious activities, and the use of natural language processing (NLP) in the development of questionnaires for psychological tests has the potential to elicit immersive ruminative thinking, leading to changes in neural activity. Electroencephalography (EEG) is commonly used to detect and record neural activity in the human brain and is sensitive to changes in brain activity. In this study, we used NLP to develop a questionnaire to induce ruminative thinking and then recorded the EEG signals in response to the questionnaire. The behavioral results revealed that ruminators exhibited higher arousal rates and longer reaction times, specifically in response to the ruminative items of the questionnaire. The EEG results showed no significant difference between the ruminators and the control group during the resting state; however, a significant alteration in the coherence of the entire brain of the ruminators existed while they were answering the ruminative items. No differences were found in the control participants while answering the two items. These behavioral and EEG results indicate that the questionnaire elicited immersive ruminative thinking, specifically in the ruminators. Therefore, the questionnaire designed using NLP is capable of eliciting ruminative thinking in ruminators, offering a promising approach for the early detection of mental disorders in psychological selection.

Discrete spectral eigenmode-resonance network of brain dynamics and connectivity

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

Determination of Dynamic Brain Connectivity via Spectral Analysis

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

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

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

Unified analysis of global and focal aspects of absence epilepsy via neural field theory of the corticothalamic system

Absence epilepsy is characterized by a sudden paroxysmal loss of consciousness accompanied by oscillatory activity propagating over many brain areas. Although primary generalized absence seizures are supported by the global corticothalamic system, converging experimental evidence supports a focal theory of absence epilepsy. Here a physiology-based corticothalamic model is investigated with spatial heterogeneity due to focal epilepsy to unify global and focal aspects of absence epilepsy. Numeric and analytic calculations are employed to investigate the emergent spatiotemporal dynamics as well as their underlying dynamical mechanisms. They can be categorized into three scenarios: suppressed epilepsy, focal seizures, or generalized seizures, as summarized from a phase diagram vs focal width and characteristic axon range. The corresponding temporal frequencies and spatial extents of cortical waves in generalized seizures and focal seizures agree well with experimental observations of global and focal aspects of absence epilepsy, respectively. The emergence of the spatiotemporal dynamics corresponding to focal seizures provides a biophysical explanation of the temporally higher frequency but spatially more localized cortical waves observed in genetic rat models that display characteristics of human absence epilepsy. Predictions are also presented for further experimental test.

Neural field theory of effects of brain modifications and lesions on functional connectivity: Acute effects, short-term homeostasis, and long-term plasticity

Neural field theory is used to predict the functional connectivity effects of lesions or other modifications to effective connectivity. Widespread initial changes are predicted after localized or diffuse changes to white or gray matter, consistent with observations, and enabling lesion severity indexes to be defined. It is shown how short-term homeostasis and longer-term plasticity can reduce perturbations while maintaining brain criticality under conditions where some connections remain fixed because of damage in the lesion core. The extent to which such effects can compensate for initial connectivity changes is then explored, showing that the strongest corrective changes are concentrated toward the edges of the perturbation if it is localized and its core is fixed. The results are applicable to inferring underlying connectivity changes and to interpreting and monitoring functional connectivity modifications after lesions, injury, surgery, drugs, or brain stimulation.

Physical brain connectomics

Brain connectivity and structure-function relationships are analyzed from a physical perspective in place of common graph-theoretic and statistical approaches that overwhelmingly ignore the brain's physical structure and geometry. Field theory is used to define connectivity tensors in terms of bare and dressed propagators, and discretized representations are implemented that respect the physical nature and dimensionality of the quantities involved, retain the correct continuum limit, and enable diagrammatic analysis. Eigenfunction analysis is used to simultaneously characterize and probe patterns of brain connectivity and activity, in place of statistical or phenomenological patterns. Physically based measures that characterize the connectivity are then developed in coordinate and spectral domains; some of which generalize or rectify graph-theoretic measures to implement correct dimensionality and continuum limits, and some replace graph-theoretic quantities. Traditional graph-based measures are shown to be highly prone to artifacts introduced by discretization and threshold, often because essential physical constraints have not been imposed, dimensionality has not been included, and/or distinctions between scalar, vector, and tensor quantities have not been considered. The results can replace them in ways that converge correctly and measure properties of brain structure, rather than of its discretization, and thus potentially enable physical interpretation of the many phenomenological results in the literature. Geometric effects are shown to dominate in determining many brain properties and care must be taken not to interpret geometric differences as differences in intrinsic neural connectivity. The results demonstrate the need to use systematic physical methods to analyze the brain and the potential of such methods to obtain new insights from data, make new predictions for experimental test, and go beyond phenomenological classification to dynamics and mechanisms.

Inter- and Intra-Hemispheric EEG Coherence Study in Adults with Neuropsychiatric Disorders

Functional connectivity between different regions of the brain in the resting state has been a recent topic of interest in neurophysiological research. EEG coherence happened to be an useful tool for measuring changes in neuro-psycho-physiological functioning which are not detectable by simply measuring amplitude or power spectra. The aim of our study was to investigate the changes in the EEG coherence in groups of different mental disorders such as: depression, general anxiety disorder, ADHD, Asperger syndrome and headaches, compared to control group. All measures were made in two conditions: eye opened (EO) and eyes closed (EC). The obtained results show that in EO condition there is a significantly lower coherence for delta waves between analyzed groups. For theta coherence only for Asperger syndrome we found lower coherence compared to control group, ADHD and headaches in parietal region (P3-P4). Obtained results for intrahemispheric coherence have shown that there was significantly lower coherence in both conditions for delta and theta bands in almost all sites for Asperger's syndrome, and opposite increased intrahemispheric coherence for patients with headaches (for delta band in the anterior regions and for theta band in the posterior regions). ADHD patients expressed lower delta inter-hemispheric coherence in frontal regions, and increased coherence of theta in central regions but increased delta coherence in posterior regions only in EO condition. For depressive and anxiety patients we found decreased intrahemispheric coherence for EO condition for delta brain waves all over the cortex. Concerning the coherence in anxiety patients in our current study we have obtained hypo coherence in centro-parieto-occipital region only for delta in inter-hemispheric coherence and also lower delta coherence through the cortex for intrahemispheric coherence. Our findings for interhemispheric hyper coherence in subjects with depression specifically for alpha and beta bands were confirmed in other studies. We suggest that EEG coherence analysis could be a sensitive parameter in the detection of electrophysiological abnormalities in patients with anxiety, depression, ADHD, Asperger syndrome and headaches. These results can confirm the development of QEEG state and trait biomarkers for psychiatric disorders.

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

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

Spectrum of connectivity fluctuations including the effect of activity-dependent feedback

The spatiotemporal spectrum of feedback-driven fluctuations of brain connectivity is investigated using nonlinear neural field theory of the corticothalamic system. Weakly nonlinear dynamics of neural feedbacks are expanded in terms of first order perturbations of neural activity relative to a fixed point. Susceptibilities are used to quantify the change in connectivity per unit change in presynaptic or postsynaptic activity caused by nonlinear feedbacks such as facilitation, depression, sensitization, potentiation, and the effects of discrete eigenmode structure are included for a spherical brain geometry. Spectral signatures such as resonances are identified that allow the presence of particular presynaptic and postsynaptic feedback effects to be inferred. These include additional resonances at high frequencies and shifts of existing spectral peaks, mostly visible in the lowest spatial modes of the response.

Neural field theory of perceptual echo and implications for estimating brain connectivity

Neural field theory is used to predict and analyze the phenomenon of perceptual echo in which random input stimuli at one location are correlated with electroencephalographic responses at other locations. It is shown that this echo correlation (EC) yields an estimate of the transfer function from the stimulated point to other locations. Modal analysis then explains the observed spatiotemporal structure of visually driven EC and the dominance of the alpha frequency; two eigenmodes of similar amplitude dominate the response, leading to temporal beating and a line of low correlation that runs from the crown of the head toward the ears. These effects result from mode splitting and symmetry breaking caused by interhemispheric coupling and cortical folding. It is shown how eigenmodes obtained from functional magnetic resonance imaging experiments can be combined with temporal dynamics from EC or other evoked responses to estimate the spatiotemporal transfer function between any two points and hence their effective connectivity.

Estimating cortical column sensory networks in rodents from micro-electrocorticograph (μECoG) recordings

Micro-electrocorticograph (μECoG) arrays offer the flexibility to record local field potentials (LFPs) from the surface of the cortex, using high density electrodes that are sub-mm in diameter. Research to date has not provided conclusive evidence for the underlying signal generation of μECoG recorded LFPs, or if μECoG arrays can capture network activity from the cortex. We studied the pervading view of the LFP signal by exploring the spatial scale at which the LFP can be considered elemental. We investigated the underlying signal generation and ability to capture functional networks by implanting, μECoG arrays to record sensory-evoked potentials in four rats. The organization of the sensory cortex was studied by analyzing the sensory-evoked potentials with two distinct modeling techniques: (1) The volume conduction model, that models the electrode LFPs with an electrostatic representation, generated by a single cortical generator, and (2) the dynamic causal model (DCM), that models the electrode LFPs with a network model, whose activity is generated by multiple interacting cortical sources. The volume conduction approach modeled activity from electrodes separated < 1000 μm, with reasonable accuracy but a network model like DCM was required to accurately capture activity > 1500 μm. The extrinsic network component in DCM was determined to be essential for accurate modeling of observed potentials. These results all point to the presence of a sensory network, and that μECoG arrays are able to capture network activity in the neocortex. The estimated DCM network models the functional organization of the cortex, as signal generators for the μECoG recorded LFPs, and provides hypothesis-testing tools to explore the brain.

Spectral signatures of activity-dependent neural feedback in the corticothalamic system

The modulation of neural quantities by presynaptic and postsynaptic activities via local feedback processes is investigated by incorporating nonlinear phenomena such as relative refractory period, synaptic enhancement, synaptic depression, and habituation. This is done by introducing susceptibilities, which quantify the response in either firing threshold or synaptic strength to unit change in either presynaptic or postsynaptic activity. Effects on the power spectra are then analyzed for a realistic corticothalamic model to determine the spectral signatures of various nonlinear processes and to what extent these are distinct. Depending on the feedback processes, there can be enhancements or reductions in low-frequency and/or alpha power, splitting of the alpha resonance, and/or appearance of new resonances at high frequencies. These features in the power spectra allow processes to be fully distinguished where they are unique, or partly distinguished if they are common to only a subset of feedbacks, and can potentially be used to constrain the types, strengths, and dynamics of feedbacks present.

Cortical geometry as a determinant of brain activity eigenmodes: Neural field analysis

Perturbation analysis of neural field theory is used to derive eigenmodes of neural activity on a cortical hemisphere, which have previously been calculated numerically and found to be close analogs of spherical harmonics, despite heavy cortical folding. The present perturbation method treats cortical folding as a first-order perturbation from a spherical geometry. The first nine spatial eigenmodes on a population-averaged cortical hemisphere are derived and compared with previous numerical solutions. These eigenmodes contribute most to brain activity patterns such as those seen in electroencephalography and functional magnetic resonance imaging. The eigenvalues of these eigenmodes are found to agree with the previous numerical solutions to within their uncertainties. Also in agreement with the previous numerics, all eigenmodes are found to closely resemble spherical harmonics. The first seven eigenmodes exhibit a one-to-one correspondence with their numerical counterparts, with overlaps that are close to unity. The next two eigenmodes overlap the corresponding pair of numerical eigenmodes, having been rotated within the subspace spanned by that pair, likely due to second-order effects. The spatial orientations of the eigenmodes are found to be fixed by gross cortical shape rather than finer-scale cortical properties, which is consistent with the observed intersubject consistency of functional connectivity patterns. However, the eigenvalues depend more sensitively on finer-scale cortical structure, implying that the eigenfrequencies and consequent dynamical properties of functional connectivity depend more strongly on details of individual cortical folding. Overall, these results imply that well-established tools from perturbation theory and spherical harmonic analysis can be used to calculate the main properties and dynamics of low-order brain eigenmodes.

Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

Eigenmodes of brain activity: Neural field theory predictions and comparison with experiment

Neural field theory of the corticothalamic system is applied to predict and analyze the activity eigenmodes of the bihemispheric brain, focusing particularly on their spatial structure. The eigenmodes of a single brain hemisphere are found to be close analogs of spherical harmonics, which are the natural modes of the sphere. Instead of multiple eigenvalues being equal, as in the spherical case, cortical folding splits them to have distinct values. Inclusion of interhemispheric connections between homologous regions via the corpus callosum leads to further splitting that depends on symmetry or antisymmetry of activity between brain hemispheres, and the strength and sign of the interhemispheric connections. Symmetry properties of the lowest observed eigenmodes strongly constrain the interhemispheric connectivity strengths and unihemispheric mode spectra, and it is predicted that most spontaneous brain activity will be symmetric between hemispheres, consistent with observations. Comparison with the eigenmodes of an experimental anatomical connectivity matrix confirms these results, permits the relative strengths of intrahemispheric and interhemispheric connectivities to be approximately inferred from their eigenvalues, and lays the foundation for further experimental tests. The results are consistent with brain activity being in corticothalamic eigenmodes, rather than discrete "networks" and open the way to new approaches to brain analysis.

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

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

Neural field theory of nonlinear wave-wave and wave-neuron processes

Systematic expansion of neural field theory equations in terms of nonlinear response functions is carried out to enable a wide variety of nonlinear wave-wave and wave-neuron processes to be treated systematically in systems involving multiple neural populations. The results are illustrated by analyzing second-harmonic generation, and they can also be applied to wave-wave coalescence, multiharmonic generation, facilitation, depression, refractoriness, and other nonlinear processes.

Construct validation of a DCM for resting state fMRI

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

•

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

•

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

•

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

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

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

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.

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.

Generator localization by current source density (CSD): implications of volume conduction and field closure at intracranial and scalp resolutions

The topographic ambiguity and reference-dependency that has plagued EEG/ERP research throughout its history are largely attributable to volume conduction, which may be concisely described by a vector form of Ohm's Law. This biophysical relationship is common to popular algorithms that infer neuronal generators via inverse solutions. It may be further simplified as Poisson's source equation, which identifies underlying current generators from estimates of the second spatial derivative of the field potential (Laplacian transformation). Intracranial current source density (CSD) studies have dissected the "cortical dipole" into intracortical sources and sinks, corresponding to physiologically-meaningful patterns of neuronal activity at a sublaminar resolution, much of which is locally cancelled (i.e., closed field). By virtue of the macroscopic scale of the scalp-recorded EEG, a surface Laplacian reflects the radial projections of these underlying currents, representing a unique, unambiguous measure of neuronal activity at scalp. Although the surface Laplacian requires minimal assumptions compared to complex, model-sensitive inverses, the resulting waveform topographies faithfully summarize and simplify essential constraints that must be placed on putative generators of a scalp potential topography, even if they arise from deep or partially-closed fields. CSD methods thereby provide a global empirical and biophysical context for generator localization, spanning scales from intracortical to scalp recordings.

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.

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.

Dynamic causal modeling with neural fields

The aim of this paper is twofold: first, to introduce a neural field model motivated by a well-known neural mass model; second, to show how one can estimate model parameters pertaining to spatial (anatomical) properties of neuronal sources based on EEG or LFP spectra using Bayesian inference. Specifically, we consider neural field models of cortical activity as generative models in the context of dynamic causal modeling (DCM). This paper considers the simplest case of a single cortical source modeled by the spatiotemporal dynamics of hidden neuronal states on a bounded cortical surface or manifold. We build this model using multiple layers, corresponding to cortical lamina in the real cortical manifold. These layers correspond to the populations considered in classical (Jansen and Rit) neural mass models. This allows us to formulate a neural field model that can be reduced to a neural mass model using appropriate constraints on its spatial parameters. In turn, this enables one to compare and contrast the predicted responses from equivalent neural field and mass models respectively. We pursue this using empirical LFP data from a single electrode to show that the parameters controlling the spatial dynamics of cortical activity can be recovered, using DCM, even in the absence of explicit spatial information in observed data.

Neural field theory of synaptic plasticity

Plasticity is crucial to neural development, learning, and memory. In the common in vivo situation where postsynaptic neural activity results from multiple presynaptic inputs, it is shown that a widely used class of correlation-dependent and spike-timing dependent plasticity rules can be written in a form that can be incorporated into neural field theory, which enables their system-level dynamics to be investigated. It is shown that the resulting plasticity dynamics depends strongly on the stimulus spectrum via overall system frequency responses. In the case of perturbations that are approximately linear, explicit formulas are found for the dynamics in terms of stimulus spectra via system transfer functions. The resulting theory is applied to a simple model system to reveal how collective effects, especially resonances, can drastically modify system-level plasticity dynamics from that implied by single-neuron analyses. The simplified model illustrates the potential relevance of these effects in applications to brain stimulation, synaptic homeostasis, and epilepsy.

Epilepsy as a dynamic disease: a tutorial of the past with an eye to the future

How can clinical epileptologists and computational neuroscientists learn to function together within the confines of interdisciplinary teams to develop new and more effective treatment strategies for epilepsy? Here we introduce epileptologists to the way modelers think about epilepsy as a dynamic disease. Not only is there terminology to be learned, but also it is necessary to identify those areas where clinical input might be expected to have the greatest impact. It is concluded that both groups have major roles to play in educating, evaluating, and shaping the direction of the efforts of each other.

Effects of the anesthetic agent propofol on neural populations

The neuronal mechanisms of general anesthesia are still poorly understood. Besides several characteristic features of anesthesia observed in experiments, a prominent effect is the bi-phasic change of power in the observed electroencephalogram (EEG), i.e. the initial increase and subsequent decrease of the EEG-power in several frequency bands while increasing the concentration of the anaesthetic agent. The present work aims to derive analytical conditions for this bi-phasic spectral behavior by the study of a neural population model. This model describes mathematically the effective membrane potential and involves excitatory and inhibitory synapses, excitatory and inhibitory cells, nonlocal spatial interactions and a finite axonal conduction speed. The work derives conditions for synaptic time constants based on experimental results and gives conditions on the resting state stability. Further the power spectrum of Local Field Potentials and EEG generated by the neural activity is derived analytically and allow for the detailed study of bi-spectral power changes. We find bi-phasic power changes both in monostable and bistable system regime, affirming the omnipresence of bi-spectral power changes in anesthesia. Further the work gives conditions for the strong increase of power in the δ-frequency band for large propofol concentrations as observed in experiments.

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.

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.

Regional networks underlying interhemispheric connectivity: an EEG and DTI study in healthy ageing and amnestic mild cognitive impairment

Interhemispheric coherence derived from electroencephalogram (EEG) recordings is a measure of functional interhemispheric connectivity. Diffusion tensor imaging (DTI) determines the integrity of subcortical fiber tracts. We studied the pattern of subcortical fiber tracts underlying interhemispheric coherence and its alteration in 16 subjects with amnestic mild cognitive impairment (MCI), an at risk syndrome for Alzheimer's disease, and 20 cognitively healthy elderly control subjects using resting state EEG and high resolution DTI at 3 T. We used a multivariate network approach based on principal component analysis to determine effects of coherence on the regional pattern of diffusivity. Temporo-parietal coherence in the alpha band was significantly correlated with diffusivity in predominantly posterior white matter tracts including posterior corpus callosum, parietal, temporal and occipital lobe white matter, thalamus, midbrain, pons, and cerebellum, both in MCI subjects and controls (P < 0.05). In MCI subjects, frontal coherence in the alpha band was significantly correlated with a predominately frontal pattern of diffusivity including fiber tracts of the anterior corpus callosum, frontal lobe white matter, thalamus, pons, and cerebellum (P < 0.05). The study provides a methodology to access specific networks of subcortical fiber tracts subserving the maintenance of interhemispheric resting state coherence in the human brain.

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.

Two-dimensional coherence for measurement of asymmetry in postural steadiness

Two-dimensional magnitude squared coherence (2D-MSC) is developed to compare the two-valued time series which represent the center of pressure (COP) under each foot. A sinusoidal multiple taper spectral estimator is used to reduce bias and improve spectral resolution. The measure is applied to evaluate symmetry in the dual-plate postural steadiness time series obtained from healthy young and elderly volunteers, and patients with Huntington's Disease (HD), a group in which asymmetries in postural steadiness are anticipated. The results demonstrate that the 2D-MSC is a robust measure of inter-limb coordination that may be of value in studies of aging and neurologic disease.

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.

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.

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.

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.

Principal components analysis of Laplacian waveforms as a generic method for identifying ERP generator patterns: I. Evaluation with auditory oddball tasks

OBJECTIVE

To evaluate the effectiveness and comparability of PCA-based simplifications of ERP waveforms versus their reference-free Laplacian transformations for separating task- and response-related ERP generator patterns during auditory oddball tasks.

METHODS

Nose-referenced ERPs (31 sites total) were recorded from 66 right-handed adults during oddball tasks using syllables or tones. Response mode (left press, right press, silent count) and task was varied within subjects. Spherical spline current source density (CSD) waveforms were computed to sharpen ERP scalp topographies and eliminate volume-conducted contributions. ERP and CSD data were submitted to separate covariance-based, unrestricted temporal PCAs (Varimax) to disentangle temporally and spatially overlapping ERP and CSD components.

RESULTS

Corresponding ERP and CSD factors were unambiguously related to known ERP components. For example, the dipolar organization of a central N1 was evident from factorized anterior sinks and posterior sources encompassing the Sylvian fissure. Factors associated with N2 were characterized by asymmetric frontolateral (tonal: frontotemporal R > L) and parietotemporal (phonetic: parietotemporal L > R) sinks for targets. A single ERP factor summarized parietal P3 activity, along with an anterior negativity. In contrast, two CSD factors peaking at 360 and 560 ms distinguished a parietal P3 source with an anterior sink from a centroparietal P3 source with a sharply localized Fz sink. A smaller parietal but larger left temporal P3 source was found for silent count compared to button press. Left or right press produced opposite, region-specific asymmetries originating from central sites, modulating the N2/P3 complex.

CONCLUSIONS

CSD transformation is shown to be a valuable preprocessing step for PCA of ERP data, providing a unique, physiologically meaningful solution to the ubiquitous reference problem. By reducing ERP redundancy and producing sharper, simpler topographies, and without losing or distorting any effects of interest, the CSD-PCA solution replicated and extended previous task- and response-related findings.

SIGNIFICANCE

Eliminating ambiguities of the recording reference, the combined CSD-PCA approach systematically bridges between montage-dependent scalp potentials and distinct, anatomically-relevant current generators, and shows promise as a comprehensive, generic strategy for ERP analysis.

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.

Propagator theory of brain dynamics

A physiologically based continuum model of brain dynamics is extended to incorporate arbitrary numbers of structures and neural populations, multiple outgoing fields of activity from a single population of neurons to various targets, improved treatment of converging or diverging projections and mesoscopic structure, and generalized connections to quantities observable via electroencephalography and other methods. The results are applied to study the corticothalamic system, predicting an intracortical resonance that leads to enhancements of electroencephalographic activity in the gamma (>30 Hz) range. This resonance involves feedback loops incorporating slow, short-range inhibitory fibers.