Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment

Directed cortical information flow during human object recognition: analyzing induced EEG gamma-band responses in brain's source space

The increase of induced gamma-band responses (iGBRs; oscillations >30 Hz) elicited by familiar (meaningful) objects is well established in electroencephalogram (EEG) research. This frequency-specific change at distinct locations is thought to indicate the dynamic formation of local neuronal assemblies during the activation of cortical object representations. As analytically power increase is just a property of a single location, phase-synchrony was introduced to investigate the formation of large-scale networks between spatially distant brain sites. However, classical phase-synchrony reveals symmetric, pair-wise correlations and is not suited to uncover the directionality of interactions. Here, we investigated the neural mechanism of visual object processing by means of directional coupling analysis going beyond recording sites, but rather assessing the directionality of oscillatory interactions between brain areas directly. This study is the first to identify the directionality of oscillatory brain interactions in source space during human object recognition and suggests that familiar, but not unfamiliar, objects engage widespread reciprocal information flow. Directionality of cortical information-flow was calculated based upon an established Granger-Causality coupling-measure (partial-directed coherence; PDC) using autoregressive modeling. To enable comparison with previous coupling studies lacking directional information, phase-locking analysis was applied, using wavelet-based signal decompositions. Both, autoregressive modeling and wavelet analysis, revealed an augmentation of iGBRs during the presentation of familiar objects relative to unfamiliar controls, which was localized to inferior-temporal, superior-parietal and frontal brain areas by means of distributed source reconstruction. The multivariate analysis of PDC evaluated each possible direction of brain interaction and revealed widespread reciprocal information-transfer during familiar object processing. In contrast, unfamiliar objects entailed a sparse number of only unidirectional connections converging to parietal areas. Considering the directionality of brain interactions, the current results might indicate that successful activation of object representations is realized through reciprocal (feed-forward and feed-backward) information-transfer of oscillatory connections between distant, functionally specific brain areas.

Estimate of causality between independent cortical spatial patterns during movement volition in spinal cord injured patients

Static hemodynamic or neuroelectric images of brain regions activated during particular tasks do not convey the information of how these regions communicate to each other. Cortical connectivity estimation aims at describing these interactions as connectivity patterns which hold the direction and strength of the information flow between cortical areas. In this study, we attempted to estimate the causality between distributed cortical systems during a movement volition task in preparation for execution of simple movements by a group of normal healthy subjects and by a group of Spinal Cord Injured (SCI) patients. To estimate the causality between the spatial distributed patterns of cortical activity in the frequency domain, we applied a series of processing steps on the recorded EEG data. From the high-resolution EEG recordings we estimated the cortical waveforms for the regions of interest (ROIs), each representing a selected sensor group population. The solutions of the linear inverse problem returned a series of cortical waveforms for each ROI considered and for each trial analyzed. For each subject, the cortical waveforms were then subjected to Independent Component Analysis (ICA) pre-processing. The independent components obtained by the application of the ThinICA algorithm were further processed by a Partial Directed Coherence algorithm, in order to extract the causality between spatial cortical patterns of the estimated data. The source-target cortical dependencies found in the group of normal subjects were relatively similar in all frequency bands analyzed. For the normal subjects we observed a common source pattern in an ensemble of cortical areas including the right parietal and right lip primary motor areas and bilaterally the primary foot and posterior SMA areas. The target of this cortical network, in the Granger-sense of causality, was shown to be a smaller network composed mostly by the primary foot motor areas and the posterior SMA bilaterally. In the case of the SCI population, both the source and the target cortical patterns had larger sizes than in the normal population. The source cortical areas included always the primary foot and lip motor areas, often bilaterally. In addition, the right parietal area and the bilateral premotor area 6 were also involved. Again, the patterns remained substantially stable across the different frequency bands analyzed. The target cortical patterns observed in the SCI population had larger extensions when compared to the normal ones, since in most cases they involved the bilateral activation of the primary foot movement areas as well as the SMA, the primary lip areas and the parietal cortical areas.

Functional connections between auditory cortical fields in humans revealed by Granger causality analysis of intra-cranial evoked potentials to sounds: Comparison of two methods

Knowledge of neural interactions amongst cortical sites is important for understanding higher brain function. We studied such interactions using Granger causality (GC) to analyze auditory event-related potentials (ERPs) recorded directly and simultaneously from two physiologically identified and functionally interconnected auditory areas of cerebral cortex in human neurosurgical patients. Two methods of GC analysis were used and the results compared. Both approaches involved adaptive autoregressive modeling but differed from each other in other ways. Results obtained by using the two methods also differed. Fewer false-positive results were obtained using the method that suppressed the ERP non-stationarity and that expressed the GC as the sum of model coefficients, which suggests that this is the more appropriate approach for analyzing ERPs recorded directly from the human cortex.

Comparison of different cortical connectivity estimators for high-resolution EEG recordings

The aim of this work is to characterize quantitatively the performance of a body of techniques in the frequency domain for the estimation of cortical connectivity from high-resolution EEG recordings in different operative conditions commonly encountered in practice. Connectivity pattern estimators investigated are the Directed Transfer Function (DTF), its modification known as direct DTF (dDTF) and the Partial Directed Coherence (PDC). Predefined patterns of cortical connectivity were simulated and then retrieved by the application of the DTF, dDTF, and PDC methods. Signal-to-noise ratio (SNR) and length (LENGTH) of EEG epochs were studied as factors affecting the reconstruction of the imposed connectivity patterns. Reconstruction quality and error rate in estimated connectivity patterns were evaluated by means of some indexes of quality for the reconstructed connectivity pattern. The error functions were statistically analyzed with analysis of variance (ANOVA). The whole methodology was then applied to high-resolution EEG data recorded during the well-known Stroop paradigm. Simulations indicated that all three methods correctly estimated the simulated connectivity patterns under reasonable conditions. However, performance of the methods differed somewhat as a function of SNR and LENGTH factors. The methods were generally equivalent when applied to the Stroop data. In general, the amount of available EEG affected the accuracy of connectivity pattern estimations. Analysis of 27 s of nonconsecutive recordings with an SNR of 3 or more ensured that the connectivity pattern could be accurately recovered with an error below 7% for the PDC and 5% for the DTF. In conclusion, functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in most EEG recordings by combining high-resolution EEG techniques, linear inverse estimation of the cortical activity, and frequency domain multivariate methods such as PDC, DTF, and dDTF.

Causal influences in the human brain during face discrimination: a short-window directed transfer function approach

In this letter, we considered the application of parametric spectral analysis, namely a short-window directed transfer function (DTF) approach, to multichannel electroencephalography (EEG) data during a face discrimination task. We identified causal influences between occipitoparietal and centrofrontal electrode sites, the timing of which corresponded to previously reported EEG face-selective components. More importantly we present evidence that there are both feedforward and feedback influences, a finding that is in direct contrast to current computational models of perceptual discrimination and decision making which tend to favor a purely feedforward processing scheme.

Cortical functional network organization from autoregressive modeling of local field potential oscillations

A framework is presented for quantifying functional network organization in the brain by spectral analysis based on autoregressive modeling. Local field potentials (LFPs), simultaneously recorded from distributed sites in the cerebral cortex of monkeys, are treated as signals generated by local neuronal assemblies. During the delay period of a visual pattern discrimination task, oscillatory assembly activity is manifested in the LFPs in the beta-frequency range (14-30 Hz). Coherence analysis has shown that these oscillations are phase synchronized in functional networks in the sensorimotor cortex in relation to maintenance of contralateral hand position, and in the visual cortex in relation to anticipation of the visual stimulus. Granger causality analysis has revealed information flow in the sensorimotor network that is consistent with a peripheral sensorimotor feedback loop, and in the visual network that is consistent with top-down anticipatory modulation of assemblies in the primary visual cortex.

Perspectives on the Neuroscience of Cognition and Consciousness

The origin and current use of the concepts of computation, representation and information in Neuroscience are examined and conceptual flaws are identified which vitiate their usefulness for addressing the problem of the neural basis of Cognition and Consciousness. In contrast, a convergence of views is presented to support the characterization of the Nervous System as a complex dynamical system operating in a metastable regime, and capable of evolving to configurations and transitions in phase space with potential relevance for Cognition and Consciousness.

Metastability, criticality and phase transitions in brain and its models

This survey of experimental findings and theoretical insights of the past 25 years places the brain firmly into the conceptual framework of nonlinear dynamics, operating at the brink of criticality, which is achieved and maintained by self-organization. It is here the basis for proposing that the application of the twin concepts of scaling and universality of the theory of non-equilibrium phase transitions can serve as an informative approach for elucidating the nature of underlying neural-mechanisms, with emphasis on the dynamics of recursively reentrant activity flow in intracortical and cortico-subcortical neuronal loops.

Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data

The aim of this paper is to test a technique called partial directed coherence (PDC) and its modification (squared PDC; sPDC) for the estimation of human cortical connectivity by means of simulation study, in which both PDC and sPDC were studied by analysis of variance. The statistical analysis performed returned that both PDC and sPDC are able to estimate correctly the imposed connectivity patterns when data exhibit a signal-to-noise ratio of at least 3 and a length of at least 27 s of nonconsecutive recordings at 250 Hz of sampling rate, equivalent, more generally, to 6750 data samples.

Linear and nonlinear causality between signals: methods, examples and neurophysiological applications

In this paper, we will present and review the most usual methods to detect linear and nonlinear causality between signals: linear Granger causality test (Geweke in J Am Stat Assoc 77:304-313, 1982) extended to direct causality in multivariate case (LGC), directed coherence (DCOH, Saito and Harashima in Recent advances in EEG and EMG data processing, Elsevier, Amsterdam, 1981), partial directed coherence (PDC, Sameshima and Baccala 1999) and nonlinear Granger causality test of Baek and Brock (in Working Paper University of Iowa, 1992) extended to direct causality in multivariate case (partial nonlinear Granger causality, PNGC). All these methods are tested and compared on several ARX, Poisson and nonlinear models, and on neurophysiological data (depth EEG). The results show that LGC, DCOH and PDC are not very robust in relation to nonlinear linkages but they seem to correctly find linear linkages if only the autoregressive parts are nonlinear. PNGC is extremely dependent on the choice of parameters. Moreover, LGC and PNGC may give misleading results in the case of causality on a spectral band, which is illustrated by our neurophysiological database.

Dynamic changes in the direction of the theta rhythmic drive between supramammillary nucleus and the septohippocampal system

Neurons in the supramammillary nucleus (SUM) of urethane-anesthetized rats fire rhythmically in synchrony with hippocampal theta rhythm. As these neurons project to the septum and hippocampus, it is generally assumed that their role is to mediate ascending activation, leading to the hippocampal theta rhythm. However, the connections between SUM and the septohippocampal system are reciprocal; there is strong evidence that theta remains in the hippocampus after SUM lesions and in the SUM after lesioning the medial septum. The present study examines the dynamics of coupling between rhythmic discharge in the SUM and hippocampal field potential oscillations, using the directionality information carried by the two signals. Using directed transfer function analysis, we demonstrate that during sensory-elicited theta rhythm and also during short episodes of theta acceleration of spontaneous oscillations, the spike train of a subpopulation of SUM neurons contains information predicting future variations in rhythmic field potentials in the hippocampus. In contrast, during slow spontaneous theta rhythm, it is the SUM spike signal that can be predicted from the preceding segment of the electrical signal recorded in the hippocampus. These findings indicate that, in the anesthetized rat, SUM neurons effectively drive theta oscillations in the hippocampus during epochs of sensory-elicited theta rhythm and short episodes of theta acceleration, whereas spontaneous slow theta in the SUM is controlled by descending input from the septohippocampal system. Thus, in certain states, rhythmically firing SUM neurons function to accelerate the septal theta oscillator, and in others, they are entrained by a superordinate oscillatory network.

Stochastic modeling of neurobiological time series: power, coherence, Granger causality, and separation of evoked responses from ongoing activity

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.

Synchronous dynamic brain networks revealed by magnetoencephalography

We visualized synchronous dynamic brain networks by using prewhitened (stationary) magnetoencephalography signals. Data were acquired from 248 axial gradiometers while 10 subjects fixated on a spot of light for 45 s. After fitting an autoregressive integrative moving average model and taking the residuals, all pairwise, zero-lag, partial cross-correlations (PCC(ij)(0)) between the i and j sensors were calculated, providing estimates of the strength and sign (positive and negative) of direct synchronous coupling between neuronal populations at a 1-ms temporal resolution. Overall, 51.4% of PCC(ij)(0) were positive, and 48.6% were negative. Positive PCC(ij)(0) occurred more frequently at shorter intersensor distances and were 72% stronger than negative ones, on the average. On the basis of the estimated PCC(ij)(0), dynamic neural networks were constructed (one per subject) that showed distinct features, including several local interactions. These features were robust across subjects and could serve as a blueprint for evaluating dynamic brain function.

Dynamic sculpting of brain functional connectivity and mental rotation aptitude

Changes in long-range synchronization are considered a key mechanism for the integration and segregation of cortical regions mediating cognitive processes. Such synchronization or functional connectivity is reflected in human electroencephalographic (EEG) coherence and in steady-state visually evoked potential (SSVEP) coherence. In this chapter, the relationship between cognitive proficiency in the mental rotation task (MRT) and functional connectivity reflected in SSVEP event-related partial coherence is described. The capacity to estimate changing levels of functional connectivity with a relatively high temporal resolution makes it possible to examine the relationship between functional connectivity at various points in time and aptitude. In the current study, the relationships between functional connectivity and two mental rotation aptitude measures, mental rotation speed and mental rotation accuracy, are described. We observed that functional connectivity was correlated with proficiency and that this correlation was both positive and negative for various regions and points in time. It is suggested that cognitive aptitude is related to the brain's capacity to enhance functional connectivity or communication between cortical regions that are relevant to the cognitive demands while attenuating irrelevant communication. This capacity is termed functional connectivity sculpting, and it is proposed that functional connectivity sculpting may constitute an important functional component of the neural substrate of learning and aptitude.

Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data

It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger causality analysis may not clearly distinguish between direct causal influences from one time series to another and indirect ones acting through a third time series. In order to differentiate direct from indirect Granger causality, a conditional Granger causality measure in the frequency domain is derived based on a partition matrix technique. Simulations and an application to neural field potential time series are demonstrated to validate the method.

High-frequency gamma oscillations and human brain mapping with electrocorticography

Invasive EEG recordings with depth and/or subdural electrodes are occasionally necessary for the surgical management of patients with epilepsy refractory to medications. In addition to their vital clinical utility, electrocorticographic (ECoG) recordings provide an unprecedented opportunity to study the electrophysiological correlates of functional brain activation in greater detail than non-invasive recordings. The proximity of ECoG electrodes to the cortical sources of EEG activity enhances their spatial resolution, as well as their sensitivity and signal-to-noise ratio, particularly for high-frequency EEG activity. ECoG recordings have, therefore, been used to study the event-related dynamics of brain oscillations in a variety of frequency ranges, and in a variety of functional-neuroanatomic systems, including somatosensory and somatomotor systems, visual and auditory perceptual systems, and cortical networks responsible for language. These ECoG studies have confirmed and extended the original non-invasive observations of ERD/ERS phenomena in lower frequencies, and have discovered novel event-related responses in gamma frequencies higher than those previously observed in non-invasive recordings. In particular, broadband event-related gamma responses greater than 60 Hz, extending up to approximately 200 Hz, have been observed in a variety of functional brain systems. The observation of these "high gamma" responses requires a recording system with an adequate sampling rate and dynamic range (we use 1000 Hz at 16-bit A/D resolution) and is facilitated by event-related time-frequency analyses of the recorded signals. The functional response properties of high-gamma activity are distinct from those of ERD/ERS phenomena in lower frequencies. In particular, the timing and spatial localization of high-gamma ERS often appear to be more specific to the putative timing and localization of functional brain activation than alpha or beta ERD/ERS. These findings are consistent with the proposed role of synchronized gamma oscillations in models of neural computation, which have in turn been inspired by observations of gamma activity in animal preparations, albeit at somewhat lower frequencies. Although ECoG recordings cannot directly measure the synchronization of action potentials among assemblies of neurons, they may demonstrate event-related interactions between gamma oscillations in macroscopic local field potentials (LFP) generated by different large-scale populations of neurons engaged by the same functional task. Indeed, preliminary studies suggest that such interactions do occur in gamma frequencies, including high-gamma frequencies, at latencies consistent with the timing of task performance. The neuronal mechanisms underlying high-gamma activity and its unique response properties in humans are still largely unknown, but their investigation through invasive methods is expected to facilitate and expand their potential clinical and research applications, including functional brain mapping, brain-computer interfaces, and neurophysiological studies of human cognition.

Nonlinear multivariate analysis of neurophysiological signals

Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from time series. In this work, we first describe the multivariate linear methods most commonly used in neurophysiology and show that they can be extended to assess the existence of nonlinear interdependence between signals. We then review the concepts of entropy and mutual information followed by a detailed description of nonlinear methods based on the concepts of phase synchronization, generalized synchronization and event synchronization. In all cases, we show how to apply these methods to study different kinds of neurophysiological data. Finally, we illustrate the use of multivariate surrogate data test for the assessment of the strength (strong or weak) and the type (linear or nonlinear) of interdependence between neurophysiological signals.

Time series analysis of magnetoencephalographic data during copying

We used standard time series modeling to analyze magnetoencephalographic (MEG) data acquired during three tasks. Each task lasted 45 s, for a total data acquisition period of 135 s. Ten healthy human subjects fixated their eyes on a central blue point for 45 s (fixation only, "F" task). Then a pentagon (visual template) appeared surrounding the fixation point which simultaneously became red (fixation + template, "FT" task). After 45 s, the fixation point changed to green, which was the "go" signal for the subjects to begin continuously copying the pentagon for 45 s using a joystick and without visual feedback of their movement trajectory (fixation + template + copying, "FTC" task). MEG data were acquired continuously from 248 axial gradiometers at a sampling rate of 1017.25 Hz. After removal of cardiac artifacts and rejection of records with eyeblink artifacts, a Box-Jenkins autoregressive integrative moving average (ARIMA) analysis was applied to the unsmoothed, unaveraged MEG time series for model identification and estimation within 25 time lags (approximately 25 ms). We found that an ARIMA model of 25th order autoregressive, first order differencing, and first order moving average (p=25, d=1, q=1) adequately modeled the series and yielded residuals practically stationary with respect to their mean, variance, and autocorrelation structure. These "prewhitened" residuals were then used for assessing pairwise associations between series using crosscorrelation analysis with +/-25 time lags (approximately +/-25 ms). The cross-correlograms thus obtained revealed rich and consistent patterns of interactions between series with respect to positive and/or negative correlations. The overall prevalence of these patterns was very similar in the three tasks used, and, for particular sensor pairs, they tended to be preserved across tasks.

Assessing cortical functional connectivity by linear inverse estimation and directed transfer function: simulations and application to real data

OBJECTIVE

To test a technique called Directed Transfer Function (DTF) for the estimation of human cortical connectivity, by means of simulation study and human study, using high resolution EEG recordings related to finger movements.

METHODS

The method of the Directed Transfer Function (DTF) is a frequency-domain approach, based on a multivariate autoregressive modeling of time series and on the concept of Granger causality. Since the spreading of the potential from the cortex to the sensors makes it difficult to infer the relation between the spatial patterns on the sensor space and those on the cortical sites, we propose the use of the DTF method on cortical signals estimated from high resolution EEG recordings, which exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. The simulation study was followed by an analysis of variance (ANOVA) of the results obtained for different levels of Signal to Noise Ratio (SNR) and temporal length, as they have been systematically imposed on simulated signals. The whole methodology was then applied to high resolution EEG data recorded during a visually paced finger movement.

RESULTS

The statistical analysis performed returns that during simulations, DTF is able to estimate correctly the imposed connectivity patterns under reasonable operative conditions, i.e. when data exhibit a SNR of at least 3 and a length of at least 75 s of non-consecutive recordings at 64 Hz of sampling rate, equivalent, more generally, to 4800 data samples.

CONCLUSIONS

Functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high resolution EEG techniques, linear inverse estimation and the DTF method.

SIGNIFICANCE

The estimation of cortical connectivity can be performed not only with hemodynamic measurements, by using functional MRI recordings, but also with modern EEG recordings treated with advanced computational techniques.

Inferential constraint sets in the organization of visual expectation

Many lines of evidence indicate that considering visual perception as a passive, stimulus-driven, feedforward decoding process is no longer tenable. Visual perception naturally occurs within the context of an integrated array of ongoing cognitive processes involving memory, perception in other modalities, and motor control. In many situations, these processes allow expectations to be formed for likely visual events. This article explores the idea that the formation of visual expectations involves the active organization of visual cortical areas, providing a framework of contextual information within which expected events are interpreted. Retinal inputs are treated as constraints that feed into a complex system of interacting visual cortical areas and thalamic nuclei, which are concurrently imposing constraints on one another. Although the nature of expectational organization in the visual cortex is not well-understood, a reasonable hypothesis is that expectation involves the mutual constraint of spatiotemporal activity patterns in multiple visual cortical areas. In this scenario, expectation is instantiated by a set of activity patterns in high-level visual cortical areas that impose constraints on one another as well as on low-level areas according to the partial information that is available about expected retinal inputs. One approach to testing this proposal is through the analysis of simultaneously recorded local field potentials (LFPs) from local neuronal assemblies in multiple visual cortical areas. Analysis of LFPs by multivariate autoregressive modeling is showing promise in revealing the organization of expectation in visual cortex.

Determination of EEG activity propagation: pair-wise versus multichannel estimate

Performance of different estimators describing propagation of electroencephalogram (EEG) activity, namely: Granger causality, directed transfer function (DTF), direct DTF (dDTF), short-time DTF (SDTF), bivariate coherence, and partial directed coherence are compared by means of simulations and on the examples of experimental signals. In particular, the differences between pair-wise and multichannel estimates are studied. The results show unequivocally that in most cases, the pair-wise estimates are incorrect and a complete set of signals involved in a given process has to be used to obtain the correct pattern of EEG flows. Different performance of multivariate estimators of propagation depending on their normalization is discussed. Advantages of multivariate autoregressive model are pointed out.

Directed interactions between visual areas and their role in processing image structure and expectancy

During sensory processing, cortical areas continuously exchange information in different directions along the hierarchy. The functional role of such interactions, however, has been the subject of various proposals. Here, we investigate the role of bottom-up and top-down interactions in processing stimulus structure and their relation to expected events. Applying multivariate autoregressive methods to local field potentials recorded in alert cats, we quantify directed interactions between primary (A17/18) and higher (A21) visual areas. A trial-by-trial analysis yields the following findings. To assess the role of interareal interactions in processing stimulus structure, we recorded in naïve animals during stimulation with natural movies and pink noise stimuli. The overall interactions decrease compared with baseline for both stimuli. To investigate whether forthcoming events modulate interactions, we recorded in trained animals viewing two stimuli, one of which had been associated with a reward. Several results support such modulations. First, the interactions increase compared with baseline and this increase is not observed in a context where food was not delivered. Second, these stimuli have a differential effect on top-down and bottom-up components. This difference is emphasized during the stimulus presentation and is maximal shortly before the possible reward. Furthermore, a spectral decomposition of the interactions shows that this asymmetry is most dominant in the gamma frequency range. Concluding, these results support the notion that interareal interactions are more related to an expectancy state rather than to processing of stimulus structure.

Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality

Previous studies have shown that synchronized beta frequency (14-30 Hz) oscillations in the primary motor cortex are involved in maintaining steady contractions of contralateral arm and hand muscles. However, little is known about the role of postcentral cortical areas in motor maintenance and their patterns of interaction with motor cortex. We investigated the functional relations of beta-synchronized neuronal assemblies in pre- and postcentral areas of two monkeys as they pressed a hand lever during the wait period of a visual discrimination task. By using power and coherence spectral analysis, we identified a beta-synchronized large-scale network linking pre- and postcentral areas. We then used Granger causality spectra to measure directional influences among recording sites. In both monkeys, strong Granger causal influences were observed from primary somatosensory cortex to both motor cortex and inferior posterior parietal cortex, with the latter area also exerting Granger causal influences on motor cortex. Granger causal influences from motor cortex to postcentral sites, however, were weak in one monkey and not observed in the other. These results are the first, to our knowledge, to demonstrate in awake monkeys that synchronized beta oscillations bind multiple sensorimotor areas into a large-scale network during motor maintenance behavior and carry Granger causal influences from primary somatosensory and inferior posterior parietal cortices to motor cortex.

Probing Changes in Neural Interaction During Adaptation

A procedure is developed to probe the changes in the functional interactions among neurons in primary motor cortex of the monkey brain during adaptation. A monkey is trained to learn a new skill, moving its arm to reach a target under the influence of external perturbations. The spike trains of multiple neurons in the primary motor cortex are recorded simultaneously. We utilize the methodology of directed transfer function, derived from a class of linear stochastic models, to quantify the causal interactions between the neurons. We find that the coupling between the motor neurons tends to increase during the adaptation but return to the original level after the adaptation. Furthermore, there is evidence that adaptation tends to affect the topology of the neural network, despite the approximate conservation of the average coupling strength in the network before and after the adaptation.

Spatial spectra of scalp EEG and EMG from awake humans

OBJECTIVE

Evaluate spectral scaling properties of scalp electroencephalogram (EEG) and electromyogram (EMG), optimal spacing of electrodes, and strategies for mitigating EMG.

METHODS

EEG was recorded referentially from 9 subjects with a 64 channel linear array (electrodes 3mm apart) placed parasagittally or transversely on forehead or occiput, at rest with eyes open or closed, or with deliberate EMG. Temporal (PSD(t)) and spatial (PSD(x)) power spectral densities were calculated with one-dimensional fast Fourier transform (FFT) for comparison with earlier analyses of intracranial EEG.

RESULTS

Scaling of PSD(t) from scalp resembled that from pia: near-linear decrease in log power with increasing log frequency (1/f(alpha)). Scalp PSD(x) decreased non-linearly and more rapidly than PSD(x) from pia. Peaks in PSD(t) (especially 4-12Hz) and PSD(x) (especially 0.1-0.4 cycles/cm) revealed departures from 1/f(alpha). EMG power in PSD(t) was more "white" than 1/f(alpha).

CONCLUSIONS

Smearing by dura-skull-scalp distorts PSD(x) more than PSD(t) of scalp EEG from 1/f(alpha) scaling at the pia. Spatial spectral peaks suggest that optimal scalp electrode spacing might be approximately 1cm to capture non-local EEG components having the texture of gyri. Mitigation of EMG by filtering is unsatisfactory. A criterion for measuring EMG may support biofeedback for training subjects to reduce their EMG.

SIGNIFICANCE

High-density recording and log-log spectral display of EEG provide a foundation for holist studies of global human brain function, as an alternative to network approaches that decompose EEG into localized, modular signals for correlation and coherence.

The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies

Understanding of brain functioning requires the investigation of activated cortical networks, in particular the detection of interactions between different cortical sites. Commonly, coherence and correlation are used to describe interrelations between EEG signals. However, on this basis, no statements on causality or the direction of their interrelations are possible. Causality between two signals may be expressed in terms of upgrading the predictability of one signal by the knowledge of the immediate past of the other signal. The best-established approach in this context is the so-called Granger causality. The classical estimation of Granger causality requires the stationarity of the signals. In this way, transient pathways of information transfer stay hidden. The study presents an adaptive estimation of Granger causality. Simulations demonstrate the usefulness of the time-variant Granger causality for detecting dynamic causal relations within time intervals of less than 100 ms. The time-variant Granger causality is applied to EEG data from the Stroop task. It was shown that conflict situations generate dense webs of interactions directed from posterior to anterior cortical sites. The web of directed interactions occurs mainly 400 ms after the stimulus onset and lasts up to the end of the task.

Fronto-parietal evoked potential synchronization is increased during mental rotation

We used steady state visually evoked potential event related partial coherence (SSVEP-ERPC) to examine the SSVEP synchronization between brain regions while 22 males undertook a sequential version of the Shepard and Metzler mental rotation task. Compared to the 60 degrees rotation, the 180 degrees rotation was associated with increased synchronization between bilateral prefrontal and parieto-occipital sites, between left frontal and right parietal sites and between bilateral parietal and occipital sites. We suggest that the increased synchronization between prefrontal and parieto-occipital regions may be associated with the working memory components of the task, while the left frontal to right parietal synchronization may represent the increased interaction between these regions thought to occur in a variety of visuo-motor tasks.

Synchronized activity in prefrontal cortex during anticipation of visuomotor processing

It is commonly presumed, though not well established, that the prefrontal cortex exerts top-down control of sensory processing. One aspect of this control is thought to be a facilitation of sensory pathways in anticipation of such processing. To investigate the possible involvement of prefrontal cortex in anticipatory top-down control, we studied the statistical relations between prefrontal activity, recorded while a macaque monkey waited for presentation of a visual stimulus, and subsequent sensory and motor events. Local field potentials were simultaneously recorded from prefrontal, motor, occipital and temporal cortical sites in the left cerebral hemisphere. Spectral power and coherence analysis revealed that during stimulus anticipation three of five prefrontal sites participated in a coherent oscillatory network synchronized in the beta-frequency range. Pre-stimulus network power and coherence were highly correlated with the amplitude and latency of early visual evoked potential components in visual cortical areas, and with response time. The results suggest that synchronized oscillatory networks in prefrontal cortex are involved in top-down anticipatory mechanisms that facilitate subsequent sensory processing in visual cortex. They further imply that stronger top-down control leads to larger and faster sensory responses, and a subsequently faster motor response.

Trial-to-trial variability of cortical evoked responses: implications for the analysis of functional connectivity

OBJECTIVES

The time series of single trial cortical evoked potentials typically have a random appearance, and their trial-to-trial variability is commonly explained by a model in which random ongoing background noise activity is linearly combined with a stereotyped evoked response. In this paper, we demonstrate that more realistic models, incorporating amplitude and latency variability of the evoked response itself, can explain statistical properties of cortical potentials that have often been attributed to stimulus-related changes in functional connectivity or other intrinsic neural parameters.

METHODS

Implications of trial-to-trial evoked potential variability for variance, power spectrum, and interdependence measures like cross-correlation and spectral coherence, are first derived analytically. These implications are then illustrated using model simulations and verified experimentally by the analysis of intracortical local field potentials recorded from monkeys performing a visual pattern discrimination task. To further investigate the effects of trial-to-trial variability on the aforementioned statistical measures, a Bayesian inference technique is used to separate single-trial evoked responses from the ongoing background activity.

RESULTS

We show that, when the average event-related potential (AERP) is subtracted from single-trial local field potential time series, a stimulus phase-locked component remains in the residual time series, in stark contrast to the assumption of the common model that no such phase-locked component should exist. Two main consequences of this observation are demonstrated for statistical measures that are computed on the residual time series. First, even though the AERP has been subtracted, the power spectral density, computed as a function of time with a short sliding window, can nonetheless show signs of modulation by the AERP waveform. Second, if the residual time series of two channels co-vary, then their cross-correlation and spectral coherence time functions can also be modulated according to the shape of the AERP waveform. Bayesian estimation of single-trial evoked responses provides further proof that these time-dependent statistical changes are due to remnants of the evoked phase-locked component in the residual time series.

CONCLUSIONS

Because trial-to-trial variability of the evoked response is commonly ignored as a contributing factor in evoked potential studies, stimulus-related modulations of power spectral density, cross-correlation, and spectral coherence measures is often attributed to dynamic changes of the connectivity within and among neural populations. This work demonstrates that trial-to-trial variability of the evoked response must be considered as a possible explanation of such modulation.

Phase and amplitude analysis in time-frequency space--application to voluntary finger movement

Two methods operating in time-frequency space were applied to analysis of EEG activity accompanying voluntary finger movements. The first one, based on matching pursuit approach provided high-resolution distributions of power in time-frequency space. The phenomena of event related desynchronization (ERD) and synchronization (ERS) were investigated without the need of band-pass filtering. Time evolution of mu- and beta-components was observed in a detailed way. The second method was based on a multichannel autoregressive model (MVAR) adapted for investigation of short-time changes in EEG signal. The direction and spectral content of the EEG activity propagation was estimated by means of short-time directed transfer function (SDTF). The evidence of 'cross-talk' between different areas of motor and sensory cortex was found. The earlier known phenomena, connected with voluntary movements, were confirmed and a new evidence concerning focal ERD/surround ERS and beta activity post-movement synchronization was found.

The brainweb: phase synchronization and large-scale integration

The emergence of a unified cognitive moment relies on the coordination of scattered mosaics of functionally specialized brain regions. Here we review the mechanisms of large-scale integration that counterbalance the distributed anatomical and functional organization of brain activity to enable the emergence of coherent behaviour and cognition. Although the mechanisms involved in large-scale integration are still largely unknown, we argue that the most plausible candidate is the formation of dynamic links mediated by synchrony over multiple frequency bands.

Segmentation and tracking of the electro-encephalogram signal using an adaptive recursive bandpass filter

An adaptive filtering approach for the segmentation and tracking of electro-encephalogram (EEG) signal waves is described. In this approach, an adaptive recursive bandpass filter is employed for estimating and tracking the centre frequency associated with each EEG wave. The main advantage inherent in the approach is that the employed adaptive filter has only one unknown coefficient to be updated. This coefficient, having an absolute value less than 1, represents an efficient distinct feature for each EEG specific wave, and its time function reflects the non-stationarity behaviour of the EEG signal. Therefore the proposed approach is simple and accurate in comparison with existing multivariate adaptive approaches. The approach is examined using extensive computer simulations. It is applied to computer-generated EEG signals composed of different waves. The adaptive filter coefficient (i.e. the segmentation parameter) is -0.492 for the delta wave, -0.360 for the theta wave, -0.191 for the alpha wave, -0.027 for the sigma wave, 0.138 for the beta wave and 0.605 for the gamma wave. This implies that the segmentation parameter increases with the increase in the centre frequency of the EEG waves, which provides fast on-line information about the behaviour of the EEG signal. The approach is also applied to real-world EEG data for the detection of sleep spindles.

Instantaneous multivariate EEG coherence analysis by means of adaptive high-dimensional autoregressive models

This study presents an efficient algorithm for the fitting of multivariate autoregressive models (MVAR) with time-dependent parameters to multidimensional signals. Thereby, the dimension of the model may be chosen to equal the number of signal channels. The autoregressive (AR) parameter matrices are estimated by an extension of the recursive least squares (RLS) algorithm with forgetting factor. The estimation procedure includes a single trial as well as an ensemble mean approach. The latter approach allows the simultaneous fit of one mean MVAR model to a set of single trials, each of them representing the measurement of the same task. A particular advantage of this ensemble mean approach is that it requires only a low computation effort in comparison to well known procedures applied to single trials. Furthermore, the ensemble mean approach is linked with a high adaptation capability. The properties of the estimator are investigated using simulated time series. It can be demonstrated that the adaptation capability of the estimation (measured by its adaptation speed and variance) does not depend on the model dimension. The mean MVAR fit is applied to 19-dimensional EEG data, recorded during an elementary comparison procedure. The calculation of ordinary and multiple coherence is discussed. The sensitivity of the multiple instantaneous EEG coherence will be demonstrated.

Cortical coordination dynamics and cognition

New imaging techniques in cognitive neuroscience have produced a deluge of information correlating cognitive and neural phenomena. Yet our understanding of the inter-relationship between brain and mind remains hampered by the lack of a theoretical language for expressing cognitive functions in neural terms. We propose an approach to understanding operational laws in cognition based on principles of coordination dynamics that are derived from a simple and experimentally verified theoretical model. When applied to the dynamical properties of cortical areas and their coordination, these principles support a mechanism of adaptive inter-area pattern constraint that we postulate underlies cognitive operations generally.

Connectivity and complexity: the relationship between neuroanatomy and brain dynamics

Nervous systems facing complex environments have to balance two seemingly opposing requirements. First, there is a need quickly and reliably to extract important features from sensory inputs. This is accomplished by functionally segregated (specialized) sets of neurons, e.g. those found in different cortical areas. Second, there is a need to generate coherent perceptual and cognitive states allowing an organism to respond to objects and events, which represent conjunctions of numerous individual features. This need is accomplished by functional integration of the activity of specialized neurons through their dynamic interactions. These interactions produce patterns of temporal correlations or functional connectivity involving distributed neuronal populations, both within and across cortical areas. Empirical and computational studies suggest that changes in functional connectivity may underlie specific perceptual and cognitive states and involve the integration of information across specialized areas of the brain. The interplay between functional segregation and integration can be quantitatively captured using concepts from statistical information theory, in particular by defining a measure of neural complexity. Complexity measures the extent to which a pattern of functional connectivity produced by units or areas within a neural system combines the dual requirements of functional segregation and integration. We find that specific neuroanatomical motifs are uniquely associated with high levels of complexity and that such motifs are embedded in the pattern of long-range cortico-cortical pathways linking segregated areas of the mammalian cerebral cortex. Our theoretical findings offer new insight into the intricate relationship between connectivity and complexity in the nervous system.