Phase-amplitude Coupling Measures Research Articles

Modulation index predicts the effect of ethosuximide on developmental and epileptic encephalopathy with spike-and-wave activation in sleep

PurposeIn developmental and epileptic encephalopathy with spike-and-wave activation in sleep (DEE-SWAS), the thalamocortical network is suggested to play an important role in the pathophysiology of the progression from focal epilepsy to DEE-SWAS. Ethosuximide (ESM) exerts effects by blocking T-type calcium channels in thalamic neurons. With the thalamocortical network in mind, we studied the prediction of ESM effectiveness in DEE-SWAS treatment using phase-amplitude coupling (PAC) analysis. MethodsWe retrospectively enrolled children with DEE-SWAS who had an electroencephalogram (EEG) recorded between January 2009 and September 2022 and were prescribed ESM at Okayama University Hospital. Only patients whose EEG showed continuous spike-and-wave during sleep were included. We extracted 5-min non-rapid eye movement sleep stage N2 segments from EEG recorded before starting ESM. We calculated the modulation index (MI) as the measure of PAC in pair combination comprising one of two fast oscillation types (gamma, 40–80 Hz; ripples, 80–150 Hz) and one of five slow-wave bands (delta, 0.5–1, 1–2, 2–3, and 3–4 Hz; theta, 4–8 Hz), and compared it between ESM responders and non-responders. ResultsWe identified 20 children with a diagnosis of DEE-SWAS who took ESM. Fifteen were ESM responders. Regarding gamma oscillations, significant differences were seen only in MI with 0.5–1 Hz slow waves in the frontal pole and occipital regions. Regarding ripples, ESM responders had significantly higher MI in coupling with all slow waves in the frontal pole region, 0.5–1, 3–4, and 4–8 Hz slow waves in the frontal region, 3–4 Hz slow waves in the parietal region, 0.5–1, 2–3, 3–4, and 4–8 Hz slow waves in the occipital region, and 3–4 Hz slow waves in the anterior-temporal region. SignificanceHigh MI in a wider area of the brain may represent the epileptic network mediated by the thalamus in DEE-SWAS and may be a predictor of ESM effectiveness.

Direct modulation index: A measure of phase amplitude coupling for neurophysiology data.

Neural communication across different spatial and temporal scales is a topic of great interest in clinical and basic science. Phase-amplitude coupling (PAC) has attracted particular interest due to its functional role in a wide range of cognitive and motor functions. Here, we introduce a novel measure termed the direct modulation index (dMI). Based on the classical modulation index, dMI provides an estimate of PAC that is (1) bound to an absolute interval between 0 and +1, (2) resistant against noise, and (3) reliable even for small amounts of data. To highlight the properties of this newly-proposed measure, we evaluated dMI by comparing it to the classical modulation index, mean vector length, and phase-locking value using simulated data. We ascertained that dMI provides a more accurate estimate of PAC than the existing methods and that is resilient to varying noise levels and signal lengths. As such, dMI permits a reliable investigation of PAC, which may reveal insights crucial to our understanding of functional brain architecture in key contexts such as behaviour and cognition. A Python toolbox that implements dMI and other measures of PAC is freely available at https://github.com/neurophysiological-analysis/FiNN.

Assessment of dynamic phase amplitude coupling using matching pursuit

BackgroundNeuronal transmission and communication are enabled by the interactions across multiple oscillatory frequencies. Phase amplitude coupling (PAC) quantifies these interactions during cognitive brain functions. PAC is defined as the modulation of the amplitude of the high frequency rhythm by the phase of the low frequency rhythm. Existing PAC measures are limited to quantifying the average coupling within a time window of interest. However, as PAC is dynamic, it is necessary to quantify time-varying PAC. Existing time-varying PAC approaches are based on using a sliding window approach. These approaches do not adapt to the signal dynamics, and thus the arbitrary selection of the window length substantially hampers PAC estimation. New methodTo address the limitations of sliding window PAC estimation approaches, in this paper, we introduce a dynamic PAC measure that relies on matching pursuit (MP). This approach decomposes the signal into time and frequency localized atoms that best describe the signal. Dynamic PAC is quantified by computing the coupling between these time and frequency localized atoms. As such, the proposed approach is data-driven and tracks the change of PAC with time. We evaluate the proposed method on both synthesized and real electroencephalogram (EEG) data. ResultsThe results from synthesized data show that the proposed method detects the coupled frequencies and the time variation of the coupling correctly with high time and frequency resolution. The analysis of EEG data revealed theta-gamma and alpha-gamma PAC during response and post-response time intervals. Comparison with existing method(s)Compared to the existing sliding window based approach, the proposed MP based dynamic PAC measure is more effective at capturing PAC within a short time window and is more robust to noise. This is because this method quantifies the low frequency phase and high frequency amplitude components from the time and frequency localized MP atoms and, as such, can capture the signal dynamics. ConclusionsWe posit that the proposed MP based data-driven approach offers a more robust and possibly more sensitive method to effectively quantify and track dynamic PAC.

Phase-amplitude coupling measures for determination of the epileptic network: A methodological comparison

• Phase Amplitude Coupling (PAC) between neuronal oscillations was computed using different measures. • Significant differences in coupling were noted between algorithms to compute PAC between gamma and lower phase-frequencies. • Computing PAC between ripples and lower-frequency oscillations showed that choice of lower phase-frequency affected PAC values.

Dynamical Analysis of Seizure in Epileptic Brain: a Dynamic Phase-Amplitude Coupling Estimation Approach.

Cross-frequency coupling in general and phase-amplitude coupling (PAC) as a particular form of it, provides an opportunity to investigate the complex interactions between neural oscillations in the human brain and neurological disorders such as epilepsy. Using PAC detection methods on temporal sliding windows, we developed a map of dynamic PAC evolution to investigate the spatiotemporal changes occurring during ictal transitions in a patient with intractable mesial temporal lobe epilepsy. The map is built by computing the modulation index between the amplitude of high frequency oscillations and the phase of lower frequency rhythms from the intracranial stereoelectroencephalography recordings during seizure. Our preliminary results show early abnormal PAC changes occurring in the preictal state prior to the occurrence of clinical or visible electrographic seizure onset, and suggest that dynamic PAC measures may serve as a potential clinical technique for analyzing seizure dynamics.Clinical Relevance-Application of a dynamic temporal PAC map as a new tool may provide novel insights into the neurophysiology of epileptic seizure activity and its spatio-temporal dynamics.

Multivariate Analysis of Bivariate Phase-Amplitude Coupling in EEG Data Using Tensor Robust PCA.

Cross-frequency coupling is emerging as a crucial mechanism that coordinates the integration of spectrally and spatially distributed neuronal oscillations. Recently, phase-amplitude coupling, a form of cross-frequency coupling, where the phase of a slow oscillation modulates the amplitude of a fast oscillation, has gained attention. Existing phase-amplitude coupling measures are mostly confined to either coupling within a region or between pairs of brain regions. Given the availability of multi-channel electroencephalography recordings, a multivariate analysis of phase amplitude coupling is needed to accurately quantify the coupling across multiple frequencies and brain regions. In the present work, we propose a tensor based approach, i.e., higher order robust principal component analysis, to identify response-evoked phase-amplitude coupling across multiple frequency bands and brain regions. Our experiments on both simulated and electroencephalography data demonstrate that the proposed multivariate phase-amplitude coupling method can capture the spatial and spectral dynamics of phase-amplitude coupling more accurately compared to existing methods. Accordingly, we posit that the proposed higher order robust principal component analysis based approach filters out the background phase-amplitude coupling activity and predominantly captures the event-related phase-amplitude coupling dynamics to provide insight into the spatially distributed brain networks across different frequency bands.

Tensorpac: An open-source Python toolbox for tensor-based phase-amplitude coupling measurement in electrophysiological brain signals.

Despite being the focus of a thriving field of research, the biological mechanisms that underlie information integration in the brain are not yet fully understood. A theory that has gained a lot of traction in recent years suggests that multi-scale integration is regulated by a hierarchy of mutually interacting neural oscillations. In particular, there is accumulating evidence that phase-amplitude coupling (PAC), a specific form of cross-frequency interaction, plays a key role in numerous cognitive processes. Current research in the field is not only hampered by the absence of a gold standard for PAC analysis, but also by the computational costs of running exhaustive computations on large and high-dimensional electrophysiological brain signals. In addition, various signal properties and analyses parameters can lead to spurious PAC. Here, we present Tensorpac, an open-source Python toolbox dedicated to PAC analysis of neurophysiological data. The advantages of Tensorpac include (1) higher computational efficiency thanks to software design that combines tensor computations and parallel computing, (2) the implementation of all most widely used PAC methods in one package, (3) the statistical analysis of PAC measures, and (4) extended PAC visualization capabilities. Tensorpac is distributed under a BSD-3-Clause license and can be launched on any operating system (Linux, OSX and Windows). It can be installed directly via pip or downloaded from Github (https://github.com/EtienneCmb/tensorpac). By making Tensorpac available, we aim to enhance the reproducibility and quality of PAC research, and provide open tools that will accelerate future method development in neuroscience.

Addressing Pitfalls in Phase-Amplitude Coupling Analysis with an Extended Modulation Index Toolbox

Phase-amplitude coupling (PAC) is proposed to play an essential role in coordinating the processing of information on local and global scales. In recent years, the methods able to reveal trustworthy PAC has gained considerable interest. However, the intrinsic features of some signals can lead to the identification of spurious or waveform-dependent coupling. This prompted us to develop an easily accessible tool that could be used to differentiate spurious from authentic PAC. Here, we propose a new tool for more reliable detection of PAC named the Extended Modulation Index (eMI) based on the classical Modulation Index measure of coupling. eMI is suitable both for continuous and epoched data and allows estimation of the statistical significance of each pair of frequencies for phase and for amplitude in the whole comodulogram in the framework of extreme value statistics. We compared eMI with the reference PAC measures—direct PAC estimator (a modification of Mean Vector Length) and standard Modulation Index. All three methods were tested using computer-simulated data and actual local field potential recordings from freely moving rats. All methods exhibited similar properties in terms of sensitivity and specificity of PAC detection. eMI proved to be more selective in the dimension of frequency for phase. One of the novelty’s offered by eMI is a heuristic algorithm for classification of PAC as Reliable or Ambiguous. It relies on analysis of the relation between the spectral properties of the signal and the detected coupling. Moreover, eMI generates visualizations that support further evaluation of the coupling properties. It also introduces the concept of the polar phase-histogram to study phase relations of coupled slow and fast oscillations. We discuss the extent to which eMI addresses the known problems of interpreting PAC. The Matlab® toolbox implementing eMI framework, and the two reference PAC estimators is freely available as EEGLAB plugin at https://github.com/GabrielaJurkiewicz/ePAC.

Comparison of Wavelet and RID-Rihaczek Based Methods for Phase-Amplitude Coupling

Oscillatory phenomena and linear/nonlinear interactions across different oscillatory frequencies are commonly seen between the elements of complex systems. One particular form of interaction that is widely encountered is the modulation of the amplitude of broadband high-frequency oscillations by the phase of low-frequency oscillations, defined as phase-amplitude coupling (PAC). Conventional methods for assessing PAC mostly rely on the Hilbert transform. Previous studies have shown that this method produces biased or spurious PAC estimates as it is highly dependent on the parameters of the bandpass filter used to extract narrowband signals from broadband signals. Recently, wavelet-based methods have been proposed to address some of these limitations. In this letter, we provide a thorough comparison between wavelet-based PAC measures and our recently introduced Reduced Interference Rihaczek (RID-Rihaczek) distribution based PAC both analytically and through simulations. The proposed method is shown to yield higher frequency resolution PAC estimates compared to wavelet-based methods.

A statistical framework to assess cross-frequency coupling while accounting for confounding analysis effects.

Cross frequency coupling (CFC) is emerging as a fundamental feature of brain activity, correlated with brain function and dysfunction. Many different types of CFC have been identified through application of numerous data analysis methods, each developed to characterize a specific CFC type. Choosing an inappropriate method weakens statistical power and introduces opportunities for confounding effects. To address this, we propose a statistical modeling framework to estimate high frequency amplitude as a function of both the low frequency amplitude and low frequency phase; the result is a measure of phase-amplitude coupling that accounts for changes in the low frequency amplitude. We show in simulations that the proposed method successfully detects CFC between the low frequency phase or amplitude and the high frequency amplitude, and outperforms an existing method in biologically-motivated examples. Applying the method to in vivo data, we illustrate examples of CFC during a seizure and in response to electrical stimuli.

Quantification of Phase-Amplitude Coupling in Neuronal Oscillations: Comparison of Phase-Locking Value, Mean Vector Length, Modulation Index, and Generalized-Linear-Modeling-Cross-Frequency-Coupling

Phase-amplitude coupling is a promising construct to study cognitive processes in electroencephalography (EEG) and magnetencephalography (MEG). Due to the novelty of the concept, various measures are used in the literature to calculate phase-amplitude coupling. Here, performance of the three most widely used phase-amplitude coupling measures – phase-locking value (PLV), mean vector length (MVL), and modulation index (MI) – and of the generalized linear modeling cross-frequency coupling (GLM-CFC) method is thoroughly compared with the help of simulated data. We combine advantages of previous reviews and use a realistic data simulation, examine moderators and provide inferential statistics for the comparison of all four indices of phase-amplitude coupling. Our analyses show that all four indices successfully differentiate coupling strength and coupling width when monophasic coupling is present. While the MVL was most sensitive to modulations in coupling strengths and width, only the MI and GLM-CFC can detect biphasic coupling. Coupling values of all four indices were influenced by moderators including data length, signal-to-noise-ratio, and sampling rate when approaching Nyquist frequencies. The MI was most robust against confounding influences of these moderators. Based on our analyses, we recommend the MI for noisy and short data epochs with unknown forms of coupling. For high quality and long data epochs with monophasic coupling and a high signal-to-noise ratio, the use of the MVL is recommended. Ideally, both indices are reported simultaneously for one data set.

Multi-timescale phase-amplitude couplings in transitions of anesthetic-induced unconsciousness

Under general anesthesia (GA), advanced analysis methods enhance the awareness of the electroencephalography (EEG) signature of transitions from consciousness to unconsciousness. For nonlinear and nonstationary signals, empirical mode decomposition (EMD) works as a dyadic filter bank to reserve local dynamical properties in decomposed components. Moreover, cross-frequency phase-amplitude coupling analysis illustrates that the coupling between the phase of low-frequency components and the amplitude of high-frequency components is correlated with the brain functions of sensory detection, working memory, consciousness, and attentional selection. To improve the functions of phase-amplitude coupling analysis, we utilized a multi-timescale approach based on EMD to assess changes in brain functions in anesthetic-induced unconsciousness using a measure of phase-amplitude coupling. Two groups of patients received two different anesthetic recipes (with or without ketamine) during the induction period of GA. Long-term (low-frequency) coupling represented a common transitional process of brain functions from consciousness to unconsciousness with a decay trend in both groups. By contrast, short-term coupling reflected a reverse trend to long-term coupling. However, the measures of short-term coupling also reflected a higher degree of coupling for the group with ketamine compared with that without ketamine. In addition, the coupling phase is a factor of interest. The phases for different combinations of coupling components showed significant changes in anesthetic-induced unconsciousness. The coupling between the delta-band phase and the theta-band amplitude changed from in-phase to out-phase coupling during the induction process from consciousness to unconsciousness. The changes in the coupling phase in EEG signals were abrupt and sensitive in anesthetic-induced unconsciousness.

Quantitative Signal Characteristics of Electrocorticography and Stereoelectroencephalography: The Effect of Contact Depth.

Patients undergoing epilepsy surgery often require invasive EEG, but few studies have examined the signal characteristics of contacts on the surface of the brain (electrocorticography, ECOG) versus depth contacts, used in stereoelectroencephalography (SEEG). As SEEG and ECOG have significant differences in complication rates, it is important to determine whether both modalities produce similar signals for analysis, to ultimately guide management of medically intractable epilepsy. Twenty-seven patients who underwent SEEG (19), ECOG (6), or both (2) were analyzed for quantitative measures of activity including spectral power and phase-amplitude coupling during approximately 1 hour of wakefulness. The position of the contacts was calculated by coregistering the postoperative computed tomography with a reconstructed preoperative MRI. Using two types of referencing schemes-local versus common average reference-the brain regions where any quantitative measure differed systematically with contact depth were established. Using even the most permissive statistical criterion, few quantitative measures were significantly correlated with contact depth in either ECOG or SEEG contacts. The factors that predicted changes in spectral power and phase-amplitude coupling with contact depth were failing to baseline correct spectral power measures, use of a local rather than common average reference, using baseline correction for phase-amplitude coupling measures, and proximity of other grey matter structures near the region where the contact was located. The signals recorded by ECOG and SEEG have very similar spectral power and phase-amplitude coupling, suggesting that both modalities are comparable from an electrodiagnostic standpoint in delineation of the epileptogenic network.

Complex Modulation Method for Measuring Cross-Frequency Coupling of Neural Oscillations.

There is growing evidence from human intracranial electrocorticography (ECoG) studies that interactions between cortical frequencies are important for sensory perception, cognition and inter-regional neuronal communication. Recent studies have focused mainly on the strength of phase-amplitude coupling in cross-frequency interactions. Here, we introduce a complex modulation method based on measures of coherence to investigate cross-frequency coupling in the neural time series. This novel approach uses complex demodulation transform and coherence measures from the transformed signals. We used this method to quantify power coupling between two cortical frequency bands: theta (47 Hz) and high gamma (70-150 Hz) in ECoG signals recorded during an auditory task. We compared complex modulation results with traditional phase-amplitude coupling measures (PAC) derived from the same ECoG dataset. Our results suggest that cross-frequency coupling may involve changes in both phase-amplitude and power relationships between frequencies, reflecting the complexity of neuronal oscillatory interactions.

The bispectrum and its relationship to phase-amplitude coupling

Most biological signals are non-Gaussian, reflecting their origins in highly nonlinear physiological systems. A versatile set of techniques for studying non-Gaussian signals relies on the spectral representations of higher moments, known as polyspectra, which describe forms of cross-frequency dependence that do not arise in time-invariant Gaussian signals. The most commonly used of these employ the bispectrum. Recently, other measures of cross-frequency dependence have drawn interest in EEG literature, in particular those which address phase-amplitude coupling (PAC). Here we demonstrate a close relationship between the bispectrum and popular measures of PAC, which we relate to smoothings of the signal bispectrum, making them fundamentally bispectral estimators. Viewed this way, however, conventional PAC measures exhibit some unfavorable qualities, including poor bias properties, lack of correct symmetry and artificial constraints on the spectral range and resolution of the estimate. Moreover, information obscured by smoothing in measures of PAC, but preserved in standard bispectral estimators, may be critical for distinguishing nested oscillations from transient signal features and other non-oscillatory causes of “spurious” PAC. We propose guidelines for gauging the nature and origin of cross-frequency coupling with bispectral statistics. Beyond clarifying the relationship between PAC and the bispectrum, the present work lays out a general framework for the interpretation of the bispectrum, which extends to other higher-order spectra. In particular, this framework holds promise for the detailed identification of signal features related to both nested oscillations and transient phenomena. We conclude with a discussion of some broader theoretical implications of this framework and highlight promising directions for future development.

Time-resolved phase-amplitude coupling in neural oscillations

Cross-frequency coupling between neural oscillations is a phenomenon observed across spatial scales in a wide range of preparations, including human non-invasive electrophysiology. Although the functional role and mechanisms involved are not entirely understood, the concept of interdependent neural oscillations drives an active field of research to comprehend the ubiquitous polyrhythmic activity of the brain, beyond empirical observations. Phase-amplitude coupling, a particular form of cross-frequency coupling between bursts of high-frequency oscillations and the phase of lower frequency rhythms, has recently received considerable attention. However, the measurement methods have relatively poor sensitivity and require long segments of experimental data. This obliterates the resolution of fast changes in coupling related to behavior, and more generally, to the non-stationary dynamics of brain electrophysiology.We propose a new measure of phase-amplitude coupling that can resolve up to one, optimally two, cycles of the underlying slow frequency component. The method also provides a measure of the coupling strength, for augmented insight into the mechanisms involved. We demonstrate the technique with synthesized data and compare its performances with existing methods. We also show that the method reveals rapid changes in coupling parameters in data from the entorhinal cortex of a free-behaving rat. The time-resolved changes revealed are compatible with behavior and complement observed modulations of oscillatory power.We anticipate that this new measure of dynamic phase-amplitude coupling will contribute to accelerate research into the dynamics of inter-dependent oscillatory components related to brain functions and dysfunctions.

Dual origins of measured phase-amplitude coupling reveal distinct neural mechanisms underlying episodic memory in the human cortex

Phase-amplitude coupling (PAC) is hypothesized to coordinate neural activity, but its role in successful memory formation in the human cortex is unknown. Measures of PAC are difficult to interpret, however. Both increases and decreases in PAC have been linked to memory encoding, and PAC may arise due to different neural mechanisms. Here, we use a waveform analysis to examine PAC in the human cortex as participants with intracranial electrodes performed a paired associates memory task. We found that successful memory formation exhibited significant decreases in left temporal lobe and prefrontal cortical PAC, and these two regions exhibited changes in PAC within different frequency bands. Two underlying neural mechanisms, nested oscillations and sharp waveforms, were responsible for the changes in these regions. Our data therefore suggest that decreases in measured cortical PAC during episodic memory reflect two distinct underlying mechanisms that are anatomically segregated in the human brain.

Encephalography Connectivity on Sources in Male Nonsmokers after Nicotine Administration during the Resting State

We present an encephalography (EEG) connectivity study where 30 healthy male nonsmokers were randomly allocated either to a nicotine group (14 subjects, 7 mg of transdermal nicotine) or to a placebo group. EEG activity was recorded in an eyes-open (EO) and eyes-closed (EC) condition before and after drug administration. This is a reanalysis of a previous dataset. Through a source reconstruction procedure, we extracted 13 time series representing 13 sources belonging to a resting-state network. Here, we conducted connectivity analysis (renormalized partial directed coherence; rPDC) on sources, focusing on the frequency range of 8.5-18.4 Hz, subdivided into 3 frequency bands (α₁, α₂, and β₁) with the hypothesis that an increase in vigilance would modulate connectivity. Furthermore, a phase-amplitude coupling (mean resultant vector length; VL) analysis, was performed investigating whether an increase of vigilance would modulate phase-amplitude coupling. In the VL analysis we estimated the coupling of the phases of 3 low frequencies (α₁, α₂, and β₁), respectively, with the amplitude of high-frequency oscillations (30-40 Hz, low γ). With rPDC we found that during the EC condition, nicotine decreased feedback connectivity (from the precentral gyrus to precuneus, angular gyrus, cuneus and superior occipital gyrus) at 10.5-12.4 Hz. The VL analysis showed nicotine-induced increases in coupling at 10.5-18.4 Hz in the precuneus, cuneus and superior occipital gyrus during the EC condition. During the EO condition, no significant results were found in connectivity or phase-amplitude coupling measures at any frequency range. In conclusion, the results suggest that nicotine potentially increases the level of vigilance in the EC condition.

Discriminating Valid from Spurious Indices of Phase-Amplitude Coupling.

Recently there has been a strong interest in cross-frequency coupling, the interaction between neuronal oscillations in different frequency bands. In particular, measures quantifying the coupling between the phase of slow oscillations and the amplitude of fast oscillations have been applied to a wide range of data recorded from animals and humans. Some of the measures applied to detect phase-amplitude coupling have been criticized for being sensitive to nonsinusoidal properties of the oscillations and thus spuriously indicate the presence of coupling. While such instances of spurious identification of coupling have been observed, in this commentary we give concrete examples illustrating cases when the identification of cross-frequency coupling can be trusted. These examples are based on control analyses and empirical observations rather than signal-processing tools. Finally, we provide concrete advice on how to determine when measures of phase-amplitude coupling can be considered trustworthy.

The Phase of Thalamic Alpha Activity Modulates Cortical Gamma-Band Activity: Evidence from Resting-State MEG Recordings

Recent findings have implicated thalamic alpha oscillations in the phasic modulation of cortical activity. However, the precise relationship between thalamic alpha oscillations and neocortical activity remains unclear. Here we show in a large sample of healthy human participants (n = 45) using spatial filtering techniques and measures of phase amplitude coupling that the amplitude of gamma-band activity in posterior medial parietal cortex is modulated by the phase of thalamic alpha oscillations during eyes-closed resting-state recordings. In addition, our findings show that gamma-band activity in visual cortex was not modulated by thalamic alpha oscillations but coupled to the phase of strong cortical alpha activity. To overcome the limitations of electromagnetic source localization we estimated conduction delays using transfer entropy and found nonspurious information transfer from thalamus to cortex. The present findings provide novel evidence for magneto-encephalography-measured phase coupling between cortical gamma-band activity and thalamic alpha oscillations, which highlight the role of phasic inhibition in the coordination of cortical activity.