Temporal kernel CCA and its application in multimodal neuronal data analysis

Canonical Response Parameterization: Quantifying the structure of responses to single-pulse intracranial electrical brain stimulation

Single-pulse electrical stimulation in the nervous system, often called cortico-cortical evoked potential (CCEP) measurement, is an important technique to understand how brain regions interact with one another. Voltages are measured from implanted electrodes in one brain area while stimulating another with brief current impulses separated by several seconds. Historically, researchers have tried to understand the significance of evoked voltage polyphasic deflections by visual inspection, but no general-purpose tool has emerged to understand their shapes or describe them mathematically. We describe and illustrate a new technique to parameterize brain stimulation data, where voltage response traces are projected into one another using a semi-normalized dot product. The length of timepoints from stimulation included in the dot product is varied to obtain a temporal profile of structural significance, and the peak of the profile uniquely identifies the duration of the response. Using linear kernel PCA, a canonical response shape is obtained over this duration, and then single-trial traces are parameterized as a projection of this canonical shape with a residual term. Such parameterization allows for dissimilar trace shapes from different brain areas to be directly compared by quantifying cross-projection magnitudes, response duration, canonical shape projection amplitudes, signal-to-noise ratios, explained variance, and statistical significance. Artifactual trials are automatically identified by outliers in sub-distributions of cross-projection magnitude, and rejected. This technique, which we call "Canonical Response Parameterization" (CRP) dramatically simplifies the study of CCEP shapes, and may also be applied in a wide range of other settings involving event-triggered data.

Age-dependent neurovascular coupling characteristics in children and adults during general anesthesia

General anesthesia is an indispensable procedure in clinical practice. Anesthetic drugs induce dramatic changes in neuronal activity and cerebral metabolism. However, the age-related changes in neurophysiology and hemodynamics during general anesthesia remain unclear. Therefore, the objective of this study was to explore the neurovascular coupling between neurophysiology and hemodynamics in children and adults during general anesthesia. We analyzed frontal electroencephalogram (EEG) and functional near-infrared spectroscopy (fNIRS) signals recorded from children (6-12 years old, n = 17) and adults (18-60 years old, n = 25) during propofol-induced and sevoflurane-maintained general anesthesia. The neurovascular coupling was evaluated in wakefulness, maintenance of a surgical state of anesthesia (MOSSA), and recovery by using correlation, coherence and Granger-causality (GC) between the EEG indices [EEG power in different bands and permutation entropy (PE)], and hemodynamic responses the oxyhemoglobin (Δ[HbO]) and deoxy-hemoglobin (Δ[Hb]) from fNIRS in the frequency band in 0.01-0.1 Hz. The PE and Δ[Hb] performed well in distinguishing the anesthesia state (p > 0.001). The correlation between PE and Δ[Hb] was higher than those of other indices in the two age groups. The coherence significantly increased during MOSSA (p < 0.05) compared with wakefulness, and the coherences between theta, alpha and gamma, and hemodynamic activities of children are significantly stronger than that of adults' bands. The GC from neuronal activities to hemodynamic responses decreased during MOSSA, and can better distinguish anesthesia state in adults. Propofol-induced and sevoflurane-maintained combination exhibited age-dependent neuronal activities, hemodynamics, and neurovascular coupling, which suggests the need for separate rules for children's and adults' brain states monitoring during general anesthesia.

Visualizing advances in the future of primate neuroscience research

Future neuroscience and biomedical projects involving non-human primates (NHPs) remain essential in our endeavors to understand the complexities and functioning of the mammalian central nervous system. In so doing, the NHP neuroscience researcher must be allowed to incorporate state-of-the-art technologies, including the use of novel viral vectors, gene therapy and transgenic approaches to answer continuing and emerging research questions that can only be addressed in NHP research models. This perspective piece captures these emerging technologies and some specific research questions they can address. At the same time, we highlight some current caveats to global NHP research and collaborations including the lack of common ethical and regulatory frameworks for NHP research, the limitations involving animal transportation and exports, and the ongoing influence of activist groups opposed to NHP research.

Extracting electrophysiological correlates of functional magnetic resonance imaging data using the canonical polyadic decomposition

The relation between electrophysiology and BOLD-fMRI requires further elucidation. One approach for studying this relation is to find time-frequency features from electrophysiology that explain the variance of BOLD time-series. Convolution of these features with a canonical hemodynamic response function (HRF) is often required to model neurovascular coupling mechanisms and thus account for time shifts between electrophysiological and BOLD-fMRI data. We propose a framework for extracting the spatial distribution of these time-frequency features while also estimating more flexible, region-specific HRFs. The core component of this method is the decomposition of a tensor containing impulse response functions using the Canonical Polyadic Decomposition. The outputs of this decomposition provide insight into the relation between electrophysiology and BOLD-fMRI and can be used to construct estimates of BOLD time-series. We demonstrated the performance of this method on simulated data while also examining the effects of simulated measurement noise and physiological confounds. Afterwards, we validated our method on publicly available task-based and resting-state EEG-fMRI data. We adjusted our method to accommodate the multisubject nature of these datasets, enabling the investigation of inter-subject variability with regards to EEG-to-BOLD neurovascular coupling mechanisms. We thus also demonstrate how EEG features for modelling the BOLD signal differ across subjects.

Modulation transfer functions for audiovisual speech

Temporal synchrony between facial motion and acoustic modulations is a hallmark feature of audiovisual speech. The moving face and mouth during natural speech is known to be correlated with low-frequency acoustic envelope fluctuations (below 10 Hz), but the precise rates at which envelope information is synchronized with motion in different parts of the face are less clear. Here, we used regularized canonical correlation analysis (rCCA) to learn speech envelope filters whose outputs correlate with motion in different parts of the speakers face. We leveraged recent advances in video-based 3D facial landmark estimation allowing us to examine statistical envelope-face correlations across a large number of speakers (∼4000). Specifically, rCCA was used to learn modulation transfer functions (MTFs) for the speech envelope that significantly predict correlation with facial motion across different speakers. The AV analysis revealed bandpass speech envelope filters at distinct temporal scales. A first set of MTFs showed peaks around 3-4 Hz and were correlated with mouth movements. A second set of MTFs captured envelope fluctuations in the 1-2 Hz range correlated with more global face and head motion. These two distinctive timescales emerged only as a property of natural AV speech statistics across many speakers. A similar analysis of fewer speakers performing a controlled speech task highlighted only the well-known temporal modulations around 4 Hz correlated with orofacial motion. The different bandpass ranges of AV correlation align notably with the average rates at which syllables (3-4 Hz) and phrases (1-2 Hz) are produced in natural speech. Whereas periodicities at the syllable rate are evident in the envelope spectrum of the speech signal itself, slower 1-2 Hz regularities thus only become prominent when considering crossmodal signal statistics. This may indicate a motor origin of temporal regularities at the timescales of syllables and phrases in natural speech.

Basis profile curve identification to understand electrical stimulation effects in human brain networks

Brain networks can be explored by delivering brief pulses of electrical current in one area while measuring voltage responses in other areas. We propose a convergent paradigm to study brain dynamics, focusing on a single brain site to observe the average effect of stimulating each of many other brain sites. Viewed in this manner, visually-apparent motifs in the temporal response shape emerge from adjacent stimulation sites. This work constructs and illustrates a data-driven approach to determine characteristic spatiotemporal structure in these response shapes, summarized by a set of unique "basis profile curves" (BPCs). Each BPC may be mapped back to underlying anatomy in a natural way, quantifying projection strength from each stimulation site using simple metrics. Our technique is demonstrated for an array of implanted brain surface electrodes in a human patient. This framework enables straightforward interpretation of single-pulse brain stimulation data, and can be applied generically to explore the diverse milieu of interactions that comprise the connectome.

The integration of social and neural synchrony: a case for ecologically valid research using MEG neuroimaging

The recent decade has seen a shift from artificial and environmentally deprived experiments in neuroscience to real-life studies on multiple brains in interaction, coordination and synchrony. In these new interpersonal synchrony experiments, there has been a growing trend to employ naturalistic social interactions to evaluate mechanisms underlying synchronous neuronal communication. Here, we emphasize the importance of integrating the assessment of neural synchrony with measurement of nonverbal behavioral synchrony as expressed in various social contexts: relaxed social interactions, planning a joint pleasurable activity, conflict discussion, invocation of trauma, or support giving and assess the integration of neural and behavioral synchrony across developmental stages and psychopathological conditions. We also showcase the advantages of magnetoencephalography neuroimaging as a promising tool for studying interactive neural synchrony and consider the challenge of ecological validity at the expense of experimental rigor. We review recent evidence of rhythmic information flow between brains in interaction and conclude with addressing state-of-the-art developments that may contribute to advance research on brain-to-brain coordination to the next level.

Randomized sketches for kernel CCA

Kernel canonical correlation analysis (KCCA) is a popular tool as a nonlinear extension of canonical correlation analysis. Consistency and optimal convergence rate have been established in the literature. However, the time complexity of KCCA scales as O(n³) and is thus prohibitive when n is large. We propose an m-dimensional randomized sketches approach for KCCA with m<<n, based on the recent work on randomized sketches for kernel ridge regression (KRR). Technically we establish our theoretical results relying on an interesting connection between KCCA and KRR by utilizing a novel "duality tracking" device that alternates between the infinite-dimensional operator-theory-based view of KCCA and the finite-dimensional kernel-matrix-based view.

Machine Learning for Molecular Simulation

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.

Improved physiological noise regression in fNIRS: A multimodal extension of the General Linear Model using temporally embedded Canonical Correlation Analysis

For the robust estimation of evoked brain activity from functional Near-Infrared Spectroscopy (fNIRS) signals, it is crucial to reduce nuisance signals from systemic physiology and motion. The current best practice incorporates short-separation (SS) fNIRS measurements as regressors in a General Linear Model (GLM). However, several challenging signal characteristics such as non-instantaneous and non-constant coupling are not yet addressed by this approach and additional auxiliary signals are not optimally exploited. We have recently introduced a new methodological framework for the unsupervised multivariate analysis of fNIRS signals using Blind Source Separation (BSS) methods. Building onto the framework, in this manuscript we show how to incorporate the advantages of regularized temporally embedded Canonical Correlation Analysis (tCCA) into the supervised GLM. This approach allows flexible integration of any number of auxiliary modalities and signals. We provide guidance for the selection of optimal parameters and auxiliary signals for the proposed GLM extension. Its performance in the recovery of evoked HRFs is then evaluated using both simulated ground truth data and real experimental data and compared with the GLM with short-separation regression. Our results show that the GLM with tCCA significantly improves upon the current best practice, yielding significantly better results across all applied metrics: Correlation (HbO max. +45%), Root Mean Squared Error (HbO max. −55%), F-Score (HbO up to 3.25-fold) and p-value as well as power spectral density of the noise floor. The proposed method can be incorporated into the GLM in an easily applicable way that flexibly combines any available auxiliary signals into optimal nuisance regressors. This work has potential significance both for conventional neuroscientific fNIRS experiments as well as for emerging applications of fNIRS in everyday environments, medicine and BCI, where high Contrast to Noise Ratio is of importance for single trial analysis.

Canonical maximization of coherence: A novel tool for investigation of neuronal interactions between two datasets

Synchronization between oscillatory signals is considered to be one of the main mechanisms through which neuronal populations interact with each other. It is conventionally studied with mass-bivariate measures utilizing either sensor-to-sensor or voxel-to-voxel signals. However, none of these approaches aims at maximizing synchronization, especially when two multichannel datasets are present. Examples include cortico-muscular coherence (CMC), cortico-subcortical interactions or hyperscanning (where electroencephalographic EEG/magnetoencephalographic MEG activity is recorded simultaneously from two or more subjects). For all of these cases, a method which could find two spatial projections maximizing the strength of synchronization would be desirable. Here we present such method for the maximization of coherence between two sets of EEG/MEG/EMG (electromyographic)/LFP (local field potential) recordings. We refer to it as canonical Coherence (caCOH). caCOH maximizes the absolute value of the coherence between the two multivariate spaces in the frequency domain. This allows very fast optimization for many frequency bins. Apart from presenting details of the caCOH algorithm, we test its efficacy with simulations using realistic head modelling and focus on the application of caCOH to the detection of cortico-muscular coherence. For this, we used diverse multichannel EEG and EMG recordings and demonstrate the ability of caCOH to extract complex patterns of CMC distributed across spatial and frequency domains. Finally, we indicate other scenarios where caCOH can be used for the extraction of neuronal interactions.

Multimodal Neuroimaging: Basic Concepts and Classification of Neuropsychiatric Diseases

Neuroimaging techniques are widely used in neuroscience to visualize neural activity, to improve our understanding of brain mechanisms, and to identify biomarkers-especially for psychiatric diseases; however, each neuroimaging technique has several limitations. These limitations led to the development of multimodal neuroimaging (MN), which combines data obtained from multiple neuroimaging techniques, such as electroencephalography, functional magnetic resonance imaging, and yields more detailed information about brain dynamics. There are several types of MN, including visual inspection, data integration, and data fusion. This literature review aimed to provide a brief summary and basic information about MN techniques (data fusion approaches in particular) and classification approaches. Data fusion approaches are generally categorized as asymmetric and symmetric. The present review focused exclusively on studies based on symmetric data fusion methods (data-driven methods), such as independent component analysis and principal component analysis. Machine learning techniques have recently been introduced for use in identifying diseases and biomarkers of disease. The machine learning technique most widely used by neuroscientists is classification-especially support vector machine classification. Several studies differentiated patients with psychiatric diseases and healthy controls with using combined datasets. The common conclusion among these studies is that the prediction of diseases increases when combining data via MN techniques; however, there remain a few challenges associated with MN, such as sample size. Perhaps in the future N-way fusion can be used to combine multiple neuroimaging techniques or nonimaging predictors (eg, cognitive ability) to overcome the limitations of MN.

Elucidating relations between fMRI, ECoG, and EEG through a common natural stimulus

Human brain mapping relies heavily on fMRI, ECoG and EEG, which capture different physiological signals. Relationships between these signals have been established in the context of specific tasks or during resting state, often using spatially confined concurrent recordings in animals. But it is not certain whether these correlations generalize to other contexts relevant for human cognitive neuroscience. Here, we address the case of complex naturalistic stimuli and ask two basic questions. First, how reliable are the responses evoked by a naturalistic audio-visual stimulus in each of these imaging methods, and second, how similar are stimulus-related responses across methods? To this end, we investigated a wide range of brain regions and frequency bands. We presented the same movie clip twice to three different cohorts of subjects (NEEG = 45, NfMRI = 11, NECoG = 5) and assessed stimulus-driven correlations across viewings and between imaging methods, thereby ruling out task-irrelevant confounds. All three imaging methods had similar repeat-reliability across viewings when fMRI and EEG data were averaged across subjects, highlighting the potential to achieve large signal-to-noise ratio by leveraging large sample sizes. The fMRI signal correlated positively with high-frequency ECoG power across multiple task-related cortical structures but positively with low-frequency EEG and ECoG power. In contrast to previous studies, these correlations were as strong for low-frequency as for high frequency ECoG. We also observed links between fMRI and infra-slow EEG voltage fluctuations. These results extend previous findings to the case of natural stimulus processing.

Detecting multivariate cross-correlation between brain regions

The problem of identifying functional connectivity from multiple time series data recorded in each of two or more brain areas arises in many neuroscientific investigations. For a single stationary time series in each of two brain areas statistical tools such as cross-correlation and Granger causality may be applied. On the other hand, to examine multivariate interactions at a single time point, canonical correlation, which finds the linear combinations of signals that maximize the correlation, may be used. We report here a new method that produces interpretations much like these standard techniques and, in addition, 1) extends the idea of canonical correlation to 3-way arrays (with dimensionality number of signals by number of time points by number of trials), 2) allows for nonstationarity, 3) also allows for nonlinearity, 4) scales well as the number of signals increases, and 5) captures predictive relationships, as is done with Granger causality. We demonstrate the effectiveness of the method through simulation studies and illustrate by analyzing local field potentials recorded from a behaving primate. NEW & NOTEWORTHY Multiple signals recorded from each of multiple brain regions may contain information about cross-region interactions. This article provides a method for visualizing the complicated interdependencies contained in these signals and assessing them statistically. The method combines signals optimally but allows the resulting measure of dependence to change, both within and between regions, as the responses evolve dynamically across time. We demonstrate the effectiveness of the method through numerical simulations and by uncovering a novel connectivity pattern between hippocampus and prefrontal cortex during a declarative memory task.

3D spatially-adaptive canonical correlation analysis: Local and global methods

Local spatially-adaptive canonical correlation analysis (local CCA) with spatial constraints has been introduced to fMRI multivariate analysis for improved modeling of activation patterns. However, current algorithms require complicated spatial constraints that have only been applied to 2D local neighborhoods because the computational time would be exponentially increased if the same method is applied to 3D spatial neighborhoods. In this study, an efficient and accurate line search sequential quadratic programming (SQP) algorithm has been developed to efficiently solve the 3D local CCA problem with spatial constraints. In addition, a spatially-adaptive kernel CCA (KCCA) method is proposed to increase accuracy of fMRI activation maps. With oriented 3D spatial filters anisotropic shapes can be estimated during the KCCA analysis of fMRI time courses. These filters are orientation-adaptive leading to rotational invariance to better match arbitrary oriented fMRI activation patterns, resulting in improved sensitivity of activation detection while significantly reducing spatial blurring artifacts. The kernel method in its basic form does not require any spatial constraints and analyzes the whole-brain fMRI time series to construct an activation map. Finally, we have developed a penalized kernel CCA model that involves spatial low-pass filter constraints to increase the specificity of the method. The kernel CCA methods are compared with the standard univariate method and with two different local CCA methods that were solved by the SQP algorithm. Results show that SQP is the most efficient algorithm to solve the local constrained CCA problem, and the proposed kernel CCA methods outperformed univariate and local CCA methods in detecting activations for both simulated and real fMRI episodic memory data.

A Wearable EEG-HEG-HRV Multimodal System With Simultaneous Monitoring of tES for Mental Health Management

A multimodal mental management system in the shape of the wearable headband and earplugs is proposed to monitor electroencephalography (EEG), hemoencephalography (HEG) and heart rate variability (HRV) for accurate mental health monitoring. It enables simultaneous transcranial electrical stimulation (tES) together with real-time monitoring. The total weight of the proposed system is less than 200 g. The multi-loop low-noise amplifier (MLLNA) achieves over 130 dB CMRR for EEG sensing and the capacitive correlated-double sampling transimpedance amplifier (CCTIA) has low-noise characteristics for HEG and HRV sensing. Measured three-physiology domains such as neural, vascular and autonomic domain signals are combined with canonical correlation analysis (CCA) and temporal kernel canonical correlation analysis (tkCCA) algorithm to find the neural-vascular-autonomic coupling. It supports highly accurate classification with the 19% maximum improvement with multimodal monitoring. For the multi-channel stimulation functionality, after-effects maximization monitoring and sympathetic nerve disorder monitoring, the stimulator is designed as reconfigurable. The 3.37 × 2.25 mm(2) chip has 2-channel EEG sensor front-end, 2-channel NIRS sensor front-end, NIRS current driver to drive dual-wavelength VCSEL and 6-b DAC current source for tES mode. It dissipates 24 mW with 2 mA stimulation current and 5 mA NIRS driver current.

Multi-Variate EEG Analysis as a Novel Tool to Examine Brain Responses to Naturalistic Music Stimuli

Note onsets in music are acoustic landmarks providing auditory cues that underlie the perception of more complex phenomena such as beat, rhythm, and meter. For naturalistic ongoing sounds a detailed view on the neural representation of onset structure is hard to obtain, since, typically, stimulus-related EEG signatures are derived by averaging a high number of identical stimulus presentations. Here, we propose a novel multivariate regression-based method extracting onset-related brain responses from the ongoing EEG. We analyse EEG recordings of nine subjects who passively listened to stimuli from various sound categories encompassing simple tone sequences, full-length romantic piano pieces and natural (non-music) soundscapes. The regression approach reduces the 61-channel EEG to one time course optimally reflecting note onsets. The neural signatures derived by this procedure indeed resemble canonical onset-related ERPs, such as the N1-P2 complex. This EEG projection was then utilized to determine the Cortico-Acoustic Correlation (CACor), a measure of synchronization between EEG signal and stimulus. We demonstrate that a significant CACor (i) can be detected in an individual listener's EEG of a single presentation of a full-length complex naturalistic music stimulus, and (ii) it co-varies with the stimuli's average magnitudes of sharpness, spectral centroid, and rhythmic complexity. In particular, the subset of stimuli eliciting a strong CACor also produces strongly coordinated tension ratings obtained from an independent listener group in a separate behavioral experiment. Thus musical features that lead to a marked physiological reflection of tone onsets also contribute to perceived tension in music.

A multimodal stress monitoring system with canonical correlation analysis

The multimodal stress monitoring headband is proposed for mobile stress management system. It is composed of headband and earplugs. Electroencephalography (EEG), hemoencephalography (HEG) and heart-rate variability (HRV) can be achieved simultaneously in the proposed system for user status estimation. With canonical correlation analysis (CCA) and temporal-kernel CCA (tkCCA) algorithm, those different signals can be combined for maximum correlation. Thanks to the proposed combination algorithm, the accuracy of the proposed system increased up to 19 percentage points than unimodal monitoring system in n-back task.

Characterizing nonlinear relationships in functional imaging data using eigenspace maximal information canonical correlation analysis (emiCCA)

Many important problems in the analysis of neuroimages can be formulated as discovering the relationship between two sets of variables, a task for which linear techniques such as canonical correlation analysis (CCA) have been commonly used. However, to further explore potential nonlinear processes that might co-exist with linear ones in brain function, a more flexible method is required. Here, we propose a new unsupervised and data-driven method, termed the eigenspace maximal information canonical correlation analysis (emiCCA), which is capable of automatically capturing the linear and/or nonlinear relationships between various data sets. A simulation confirmed the superior performance of emiCCA in comparison with linear CCA and kernel CCA (a nonlinear version of CCA). An emiCCA framework for functional magnetic resonance imaging (fMRI) data processing was designed and applied to data from a real motor execution fMRI experiment. This analysis uncovered one linear (in primary motor cortex) and a few nonlinear networks (e.g., in the supplementary motor area, bilateral insula, and cerebellum). This suggests that these various task-related brain areas are part of networks that also contribute to the execution of movements of the hand. These results suggest that emiCCA is a promising technique for exploring various data.

ECoG high gamma activity reveals distinct cortical representations of lyrics passages, harmonic and timbre-related changes in a rock song

Listening to music moves our minds and moods, stirring interest in its neural underpinnings. A multitude of compositional features drives the appeal of natural music. How such original music, where a composer's opus is not manipulated for experimental purposes, engages a listener's brain has not been studied until recently. Here, we report an in-depth analysis of two electrocorticographic (ECoG) data sets obtained over the left hemisphere in ten patients during presentation of either a rock song or a read-out narrative. First, the time courses of five acoustic features (intensity, presence/absence of vocals with lyrics, spectral centroid, harmonic change, and pulse clarity) were extracted from the audio tracks and found to be correlated with each other to varying degrees. In a second step, we uncovered the specific impact of each musical feature on ECoG high-gamma power (70-170 Hz) by calculating partial correlations to remove the influence of the other four features. In the music condition, the onset and offset of vocal lyrics in ongoing instrumental music was consistently identified within the group as the dominant driver for ECoG high-gamma power changes over temporal auditory areas, while concurrently subject-individual activation spots were identified for sound intensity, timbral, and harmonic features. The distinct cortical activations to vocal speech-related content embedded in instrumental music directly demonstrate that song integrated in instrumental music represents a distinct dimension in complex music. In contrast, in the speech condition, the full sound envelope was reflected in the high gamma response rather than the onset or offset of the vocal lyrics. This demonstrates how the contributions of stimulus features that modulate the brain response differ across the two examples of a full-length natural stimulus, which suggests a context-dependent feature selection in the processing of complex auditory stimuli.

Finding brain oscillations with power dependencies in neuroimaging data

Phase synchronization among neuronal oscillations within the same frequency band has been hypothesized to be a major mechanism for communication between different brain areas. On the other hand, cross-frequency communications are more flexible allowing interactions between oscillations with different frequencies. Among such cross-frequency interactions amplitude-to-amplitude interactions are of a special interest as they show how the strength of spatial synchronization in different neuronal populations relates to each other during a given task. While, previously, amplitude-to-amplitude correlations were studied primarily on the sensor level, we present a source separation approach using spatial filters which maximize the correlation between the envelopes of brain oscillations recorded with electro-/magnetoencephalography (EEG/MEG) or intracranial multichannel recordings. Our approach, which is called canonical source power correlation analysis (cSPoC), is thereby capable of extracting genuine brain oscillations solely based on their assumed coupling behavior even when the signal-to-noise ratio of the signals is low. In addition to using cSPoC for the analysis of cross-frequency interactions in the same subject, we show that it can also be utilized for studying amplitude dynamics of neuronal oscillations across subjects. We assess the performance of cSPoC in simulations as well as in three distinctively different analysis scenarios of real EEG data, each involving several subjects. In the simulations, cSPoC outperforms unsupervised state-of-the-art approaches. In the analysis of real EEG recordings, we demonstrate excellent unsupervised discovery of meaningful power-to-power couplings, within as well as across subjects and frequency bands.

Parallel independent component analysis using an optimized neurovascular coupling for concurrent EEG-fMRI sources

The complexity of the human brain and the limitation of any one imaging approach motivates the need for multimodal measurements to better understand cerebral processing. A very natural goal is to integrate electrophysiological and hemodynamic activity. Among them, concurrent EEG-fMRI studies have shown great promise for understanding intrinsic brain properties yet analyzing such data presents a significant methodological challenge. Here, we propose a multivariate parallel ICA decomposition incorporating dynamic neurovascular coupling for concurrent EEG-fMRI recordings. The goal of our algorithm is to fuse multimodal EEG-fMRI information and detect/interpret the relationship between electrophysiological and hemodynamic sources via a temporal neurovascular connection enhancement. We analyze the performance of the algorithm on a valid simulation based on real EEG and fMRI components (sources) from our previous works and a neurovascular coupling built from an extended 'balloon model'. The results from our simulations yield an accurate source tracking and linkage for concurrent EEG-fMRI, and provide a novel and efficient way to combine EEG and hemodynamic responses.

Intracortical recordings and fMRI: an attempt to study operational modules and networks simultaneously

The brain can be envisaged as a complex adaptive system. It is characterized by a very high structural complexity and by massive connectivity, both of which change and evolve in response to experience. Information related to sensors and effectors is processed in both a parallel and a hierarchical fashion; the connectivity between different hierarchical levels is bidirectional, and its effectiveness is continuously controlled by specific associational and neuromodulatory centers. When questions are addressed at the level of a distributed, large-scale whole system such as that underlying perception and cognition, it is not clear what should be considered as an elementary operational unit because the behavior of integral, aggregate systems is always emergent and most often remains unpredicted by the behaviors of single cells. To localize and comprehend the neural mechanisms underlying our perceptual or cognitive capacities, concurrent studies of microcircuits, of local and long-range interconnectivity between small assemblies, and of the synergistic activity of larger neuronal populations are called for. In other words, multimodal methodologies that include invasive neuroscientific methods as well as global neuroimaging techniques are required, such as the various functional aspects of magnetic resonance imaging. These facts were the driving force behind the decision to begin animal-MRI in my lab. The wonderful idea of the editors of NeuroImage to publish a Special Issue commemorating 20years of functional fMRI provides me with the opportunity of sharing not only our first moments of frustration with the readers, but also our successful results.

Phase Coupling Estimation from Multivariate Phase Statistics

Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems and are compelling models of neural systems. However, these formulations usually deal with the forward problem: simulating a system from known coupling parameters. Here we provide a solution to the inverse problem: determining the coupling parameters from measurements. Starting from the dynamic equations of a system of symmetrically coupled phase oscillators, given by a nonlinear Langevin equation, we derive the corresponding equilibrium distribution. This formulation leads us to the maximum entropy distribution that captures pairwise phase relationships. To solve the inverse problem for this distribution, we derive a closed-form solution for estimating the phase coupling parameters from observed phase statistics. Through simulations, we show that the algorithm performs well in high dimensions (d = 100) and in cases with limited data (as few as 100 samples per dimension). In addition, we derive a regularized solution to the estimation and show that the resulting procedure improves performance when only a limited amount of data is available. Because the distribution serves as the unique maximum entropy solution for pairwise phase statistics, phase coupling estimation can be broadly applied in any situation where phase measurements are made. Under the physical interpretation, the model may be used for inferring coupling relationships within cortical networks.