Topology, Cross-Frequency, and Same-Frequency Band Interactions Shape the Generation of Phase-Amplitude Coupling in a Neural Mass Model of a Cortical Column

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Objective.Phase-amplitude coupling (PAC), the coupling of the amplitude of a faster brain rhythm to the phase of a slower brain rhythm, plays a significant role in brain activity and has been implicated in various neurological disorders. For example, in Parkinson's disease, PAC between the beta (13-30 Hz) and gamma (30-100 Hz) rhythms in the motor cortex is exaggerated, while in Alzheimer's disease, PAC between the theta (4-8 Hz) and gamma rhythms is diminished. Modulating PAC (i.e. reducing or enhancing PAC) using brain stimulation could therefore open new therapeutic avenues. However, while it has been previously reported that phase-locked stimulation can increase PAC, it is unclear what the optimal stimulation strategy to modulate PAC might be. Here, we provide a theoretical framework to narrow down the experimental optimisation of stimulation aimed at modulating PAC, which would otherwise rely on trial and error.Approach.We make analytical predictions using a Stuart-Landau model, and confirm these predictions in a more realistic model of coupled neural populations.Main results.Our framework specifies the critical Fourier coefficients of the stimulation waveform which should be tuned to optimally modulate PAC. Depending on the characteristics of the amplitude response curve of the fast population, these components may include the slow frequency, the fast frequency, combinations of these, as well as their harmonics. We also show that the optimal balance of energy between these Fourier components depends on the relative strength of the endogenous slow and fast rhythms, and that the alignment of fast components with the fast rhythm should change throughout the slow cycle. Furthermore, we identify the conditions requiring to phase-lock stimulation to the fast and/or slow rhythms.Significance.Together, our theoretical framework lays the foundation for guiding the development of innovative and more effective brain stimulation aimed at modulating PAC for therapeutic benefit.

CiftiStorm pipeline: facilitating reproducible EEG/MEG source connectomics

We present CiftiStorm, an electrophysiological source imaging (ESI) pipeline incorporating recently developed methods to improve forward and inverse solutions. The CiftiStorm pipeline produces Human Connectome Project (HCP) and megconnectome-compliant outputs from dataset inputs with varying degrees of spatial resolution. The input data can range from low-sensor-density electroencephalogram (EEG) or magnetoencephalogram (MEG) recordings without structural magnetic resonance imaging (sMRI) to high-density EEG/MEG recordings with an HCP multimodal sMRI compliant protocol. CiftiStorm introduces a numerical quality control of the lead field and geometrical corrections to the head and source models for forward modeling. For the inverse modeling, we present a Bayesian estimation of the cross-spectrum of sources based on multiple priors. We facilitate ESI in the T1w/FSAverage32k high-resolution space obtained from individual sMRI. We validate this feature by comparing CiftiStorm outputs for EEG and MRI data from the Cuban Human Brain Mapping Project (CHBMP) acquired with technologies a decade before the HCP MEG and MRI standardized dataset.

The diagnostic performance of machine learning based on resting-state functional magnetic resonance imaging data for major depressive disorders: a systematic review and meta-analysis

Objective

Machine learning (ML) has been widely used to detect and evaluate major depressive disorder (MDD) using neuroimaging data, i.e., resting-state functional magnetic resonance imaging (rs-fMRI). However, the diagnostic efficiency is unknown. The aim of the study is to conduct an updated meta-analysis to evaluate the diagnostic performance of ML based on rs-fMRI data for MDD.

Methods

English databases were searched for relevant studies. The Quality Assessment of Diagnostic Accuracy Studies (QUADAS-2) was used to assess the methodological quality of the included studies. A random-effects meta-analytic model was implemented to investigate the diagnostic efficiency, including sensitivity, specificity, diagnostic odds ratio (DOR), and area under the curve (AUC). Regression meta-analysis and subgroup analysis were performed to investigate the cause of heterogeneity.

Results

Thirty-one studies were included in this meta-analysis. The pooled sensitivity, specificity, DOR, and AUC with 95% confidence intervals were 0.80 (0.75, 0.83), 0.83 (0.74, 0.82), 14.00 (9, 22.00), and 0.86 (0.83, 0.89), respectively. Substantial heterogeneity was observed among the studies included. The meta-regression showed that the leave-one-out cross-validation (loocv) (sensitivity: p < 0.01, specificity: p < 0.001), graph theory (sensitivity: p < 0.05, specificity: p < 0.01), n > 100 (sensitivity: p < 0.001, specificity: p < 0.001), simens equipment (sensitivity: p < 0.01, specificity: p < 0.001), 3.0T field strength (Sensitivity: p < 0.001, specificity: p = 0.04), and Beck Depression Inventory (BDI) (sensitivity: p = 0.04, specificity: p = 0.06) might be the sources of heterogeneity. Furthermore, the subgroup analysis showed that the sample size (n > 100: sensitivity: 0.71, specificity: 0.72, n < 100: sensitivity: 0.81, specificity: 0.79), the different levels of disease evaluated by the Hamilton Depression Rating Scale (HDRS/HAMD) (mild vs. moderate vs. severe: sensitivity: 0.52 vs. 0.86 vs. 0.89, specificity: 0.62 vs. 0.78 vs. 0.82, respectively), the depression scales in patients with comparable levels of severity. (BDI vs. HDRS/HAMD: sensitivity: 0.86 vs. 0.87, specificity: 0.78 vs. 0.80, respectively), and the features (graph vs. functional connectivity: sensitivity: 0.84 vs. 0.86, specificity: 0.76 vs. 0.78, respectively) selected might be the causes of heterogeneity.

Conclusion

ML showed high accuracy for the automatic diagnosis of MDD. Future studies are warranted to promote the potential use of these classification algorithms in clinical settings.

Temporospatial Nestedness in Consciousness: An Updated Perspective on the Temporospatial Theory of Consciousness

Time and space are fundamental elements that permeate the fabric of nature, and their significance in relation to neural activity and consciousness remains a compelling yet unexplored area of research. The Temporospatial Theory of Consciousness (TTC) provides a framework that links time, space, neural activity, and consciousness, shedding light on the intricate relationships among these dimensions. In this review, I revisit the fundamental concepts and mechanisms proposed by the TTC, with a particular focus on the central concept of temporospatial nestedness. I propose an extension of temporospatial nestedness by incorporating the nested relationship between the temporal circuit and functional geometry of the brain. To further unravel the complexities of temporospatial nestedness, future research directions should emphasize the characterization of functional geometry and the temporal circuit across multiple spatial and temporal scales. Investigating the links between these scales will yield a more comprehensive understanding of how spatial organization and temporal dynamics contribute to conscious states. This integrative approach holds the potential to uncover novel insights into the neural basis of consciousness and reshape our understanding of the world-brain dynamic.

A physical neural mass model framework for the analysis of oscillatory generators from laminar electrophysiological recordings

Cortical function emerges from the interactions of multi-scale networks that may be studied at a high level using neural mass models (NMM) that represent the mean activity of large numbers of neurons. Here, we provide first a new framework called laminar NMM, or LaNMM for short, where we combine conduction physics with NMMs to simulate electrophysiological measurements. Then, we employ this framework to infer the location of oscillatory generators from laminar-resolved data collected from the prefrontal cortex in the macaque monkey. We define a minimal model capable of generating coupled slow and fast oscillations, and we optimize LaNMM-specific parameters to fit multi-contact recordings. We rank the candidate models using an optimization function that evaluates the match between the functional connectivity (FC) of the model and data, where FC is defined by the covariance between bipolar voltage measurements at different cortical depths. The family of best solutions reproduces the FC of the observed electrophysiology by selecting locations of pyramidal cells and their synapses that result in the generation of fast activity at superficial layers and slow activity across most depths, in line with recent literature proposals. In closing, we discuss how this hybrid modeling framework can be more generally used to infer cortical circuitry.

Phase-Amplitude Coupling Brain Networks in Children with Attention-Deficit/Hyperactivity Disorder

In cognitive neuroscience, there is an increasing interest in identifying and understanding the synchronization of distinct neural oscillations with different frequencies that might support dynamic communication within the brain. This study explored the cross-frequency phase-amplitude coupling brain network characteristics of resting-state electroencephalograms between 30 children with attention-deficit/hyperactivity disorder (ADHD) and 30 age-matched typically developing children. Compared with control group, children with ADHD show increased coupling intensity and altered distribution patterns of dominant paired channels, especially in the δ-γ_H, θ-γ_H, α-γ_H, β_L-γ_H, and β_H-γ_H coupling networks. Regarding graph theory properties, the characteristic path length, the mean clustering coefficient, the global efficiency, and the mean local efficiency significant difference in many cross-frequency coupling networks, especially in the δ-γ_H, θ-γ_H, α-γ_H, β_L-γ_H, and β_H-γ_H coupling networks. The area under the receiver operating characteristic curve (AUC) in low-frequency coupling with a high-gamma frequency was larger than that in coupling with low-gamma frequency (AUC values of δ-γ_L, θ-γ_L, α-γ_L, β_L-γ_L, β_H-γ_L, δ-γ_H, θ-γ_H, α-γ_H, β_L-γ_H, and β_H-γ_H were 0.794, 0.722, 0.666, 0.570, 0.881, 0.992, 0.998, 0.998, 0.989, and 0.974, respectively). These findings demonstrate altered coupling intensity and disrupted topological organization of coupling networks, support the altered brain network theory in children with ADHD. The coupling intensity and graph theory properties of low-frequency coupling with high-gamma frequency were promising resting-state electroencephalogram biomarkers of ADHD in children.

Structure-function models of temporal, spatial, and spectral characteristics of non-invasive whole brain functional imaging

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.

Working Memory and Transcranial-Alternating Current Stimulation-State of the Art: Findings, Missing, and Challenges

Working memory (WM) is a cognitive process that involves maintaining and manipulating information for a short period of time. WM is central to many cognitive processes and declines rapidly with age. Deficits in WM are seen in older adults and in patients with dementia, schizophrenia, major depression, mild cognitive impairment, Alzheimer's disease, etc. The frontal, parietal, and occipital cortices are significantly involved in WM processing and all brain oscillations are implicated in tackling WM tasks, particularly theta and gamma bands. The theta/gamma neural code hypothesis assumes that retained memory items are recorded via theta-nested gamma cycles. Neuronal oscillations can be manipulated by sensory, invasive- and non-invasive brain stimulations. Transcranial alternating-current stimulation (tACS) and repetitive transcranial magnetic stimulation (rTMS) are frequency-tuned non-invasive brain stimulation (NIBS) techniques that have been used to entrain endogenous oscillations in a frequency-specific manner. Compared to rTMS, tACS demonstrates superior cost, tolerability, portability, and safety profile, making it an attractive potential tool for improving cognitive performance. Although cognitive research with tACS is still in its infancy compared to rTMS, a number of studies have shown a promising WM enhancement effect, especially in the elderly and patients with cognitive deficits. This review focuses on the various methods and outcomes of tACS on WM in healthy and unhealthy human adults and highlights the established findings, unknowns, challenges, and perspectives important for translating laboratory tACS into realistic clinical settings. This will allow researchers to identify gaps in the literature and develop frequency-tuned tACS protocols with promising safety and efficacy outcomes. Therefore, research efforts in this direction should help to consider frequency-tuned tACS as a non-pharmacological tool of cognitive rehabilitation in physiological aging and patients with cognitive deficits.

Working Memory and Cross-Frequency Coupling of Neuronal Oscillations

Working memory (WM) is the active retention and processing of information over a few seconds and is considered an essential component of cognitive function. The reduced WM capacity is a common feature in many diseases, such as schizophrenia, attention deficit hyperactivity disorder (ADHD), mild cognitive impairment (MCI), and Alzheimer's disease (AD). The theta-gamma neural code is an essential component of memory representations in the multi-item WM. A large body of studies have examined the association between cross-frequency coupling (CFC) across the cerebral cortices and WM performance; electrophysiological data together with the behavioral results showed the associations between CFC and WM performance. The oscillatory entrainment (sensory, non-invasive electrical/magnetic, and invasive electrical) remains the key method to investigate the causal relationship between CFC and WM. The frequency-tuned non-invasive brain stimulation is a promising way to improve WM performance in healthy and non-healthy patients with cognitive impairment. The WM performance is sensitive to the phase and rhythm of externally applied stimulations. CFC-transcranial-alternating current stimulation (CFC-tACS) is a recent approach in neuroscience that could alter cognitive outcomes. The studies that investigated (1) the association between CFC and WM and (2) the brain stimulation protocols that enhanced WM through modulating CFC by the means of the non-invasive brain stimulation techniques have been included in this review. In principle, this review can guide the researchers to identify the most prominent form of CFC associated with WM processing (e.g., theta/gamma phase-amplitude coupling), and to define the previously published studies that manipulate endogenous CFC externally to improve WM. This in turn will pave the path for future studies aimed at investigating the CFC-tACS effect on WM. The CFC-tACS protocols need to be thoroughly studied before they can be considered as therapeutic tools in patients with WM deficits.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Detecting brain network communities: Considering the role of information flow and its different temporal scales

The identification of community structure in graphs continues to attract great interest in several fields. Network neuroscience is particularly concerned with this problem considering the key roles communities play in brain processes and functionality. Most methods used for community detection in brain graphs are based on the maximization of a parameter-dependent modularity function that often obscures the physical meaning and hierarchical organization of the partitions of network nodes. In this work, we present a new method able to detect communities at different scales in a natural, unrestricted way. First, to obtain an estimation of the information flow in the network we release random walkers to freely move over it. The activity of the walkers is separated into oscillatory modes by using empirical mode decomposition. After grouping nodes by their co-occurrence at each time scale, k-modes clustering returns the desired partitions. Our algorithm was first tested on benchmark graphs with favorable performance. Next, it was applied to real and simulated anatomical and/or functional connectomes in the macaque and human brains. We found a clear hierarchical repertoire of community structures in both the anatomical and the functional networks. The observed partitions range from the evident division in two hemispheres -in which all processes are managed globally- to specialized communities seemingly shaped by physical proximity and shared function. Additionally, the spatial scales of a network's community structure (characterized by a measure we term within-communities path length) appear inversely proportional to the oscillatory modes' average frequencies. The proportionality constant may constitute a network-specific propagation velocity for the information flow. Our results stimulate the research of hierarchical community organization in terms of temporal scales of information flow in the brain network.

Rodent EEG: Expanding the Spectrum of Analysis

In epilepsy research, the analysis of rodent electroencephalogram (EEG) has been performed by many laboratories with a variety of techniques. However, the acquisition and basic analysis of rodent EEG have only recently been standardized. Since a number of software platforms and increased computational power have become widely available, advanced rodent EEG analysis is now more accessible to investigators working with rodent models of epilepsy. In this review, the approach to the analysis of rodent EEG will be examined, including the evaluation of both epileptiform and background activity. Major caveats when employing these analyses, cellular and circuit-level correlates of EEG changes, and important differences between rodent and human EEG are also reviewed. The currently available techniques show great promise in gaining a deeper understanding of the complexities hidden within the EEG in rodent models of epilepsy.

Relationship between resting-state theta phase-gamma amplitude coupling and neurocognitive functioning in patients with first-episode psychosis

BACKGROUND

Although cognitive dysfunction is a core element of schizophrenia, the neurobiological underpinnings of the pathophysiology are not yet sufficiently understood. Because the resting state is crucial for cognitive functioning and electroencephalography (EEG) can reflect instantaneous neural activity, we investigated theta phase-gamma amplitude coupling (TGC) of resting-state EEG and its relationship with cognitive function in patients with first-episode psychosis (FEP) to reveal the neural correlates of cognitive dysfunction.

METHODS

A total of 59 FEP patients and 50 healthy controls (HCs) underwent resting-state, eyes-closed EEG recordings and performed the Trail Making Test Part A (TMT-A) and Part B (TMT-B) and California Verbal Learning Test (CVLT). TGC from the source signal of the resting-state EEG in default mode network (DMN)-related brain regions was compared between groups. Correlation analyses were performed between TGC and cognitive function test performance in FEP patients.

RESULTS

Mean resting-state TGC was larger for the FEP patients than for the HCs. Patients with FEP showed increased TGC in the left posterior cingulate cortex, which was correlated with better performance on the TMT-A and TMT-B and on immediate and delayed recall in the CVLT.

CONCLUSIONS

These results suggest that patients with FEP show compensatory hyperactivation of resting-state TGC in DMN-related brain regions, which may be related to the reallocation of cognitive resources to prepare for successful cognitive execution. This study not only highlights the neural underpinnings of cognitive dysfunction in FEP patients but also provides useful background to support the development of treatments for cognitive dysfunction in schizophrenia.

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.

Bifurcation structure determines different phase-amplitude coupling patterns in the activity of biologically plausible neural networks

Phase-amplitude cross frequency coupling (PAC) is a rather ubiquitous phenomenon that has been observed in a variety of physical domains; however, the mechanisms underlying the emergence of PAC and its functional significance in the context of neural processes are open issues under debate. In this work we analytically demonstrate that PAC phenomenon naturally emerges in mean-field models of biologically plausible networks, as a signature of specific bifurcation structures. The proposed analysis, based on bifurcation theory, allows the identification of the mechanisms underlying oscillatory dynamics that are essentially different in the context of PAC. Specifically, we found that two PAC classes can coexist in the complex dynamics of the analyzed networks: 1) harmonic PAC which is an epiphenomenon of the nonsinusoidal waveform shape characterized by the linear superposition of harmonically related spectral components, and 2) nonharmonic PAC associated with "true" coupled oscillatory dynamics with independent frequencies elicited by a secondary Hopf bifurcation and mechanisms involving periodic excitation/inhibition (PEI) of a network population. Importantly, these two PAC types have been experimentally observed in a variety of neural architectures confounding traditional parametric and nonparametric PAC metrics, like those based on linear filtering or the waveform shape analysis, due to the fact that these methods operate on a single one-dimensional projection of an intrinsically multidimensional system dynamics. We exploit the proposed tools to study the functional significance of the PAC phenomenon in the context of Parkinson's disease (PD). Our results show that pathological slow oscillations (e.g. β band) and nonharmonic PAC patterns emerge from dissimilar underlying mechanisms (bifurcations) and are associated to the competition of different BG-thalamocortical loops. Thus, this study provides theoretical arguments that demonstrate that nonharmonic PAC is not an epiphenomenon related to the pathological β band oscillations, thus supporting the experimental evidence about the relevance of PAC as a potential biomarker of PD.

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.

The Strength of Alpha-Beta Oscillatory Coupling Predicts Motor Timing Precision

Precise timing makes the difference between harmony and cacophony, but how the brain achieves precision during timing is unknown. In this study, human participants (7 females, 5 males) generated a time interval while being recorded with magnetoencephalography. Building on the proposal that the coupling of neural oscillations provides a temporal code for information processing in the brain, we tested whether the strength of oscillatory coupling was sensitive to self-generated temporal precision. On a per individual basis, we show the presence of alpha-beta phase-amplitude coupling whose strength was associated with the temporal precision of self-generated time intervals, not with their absolute duration. Our results provide evidence that active oscillatory coupling engages α oscillations in maintaining the precision of an endogenous temporal motor goal encoded in β power; the when of self-timed actions. We propose that oscillatory coupling indexes the variance of neuronal computations, which translates into the precision of an individual's behavioral performance.SIGNIFICANCE STATEMENT Which neural mechanisms enable precise volitional timing in the brain is unknown, yet accurate and precise timing is essential in every realm of life. In this study, we build on the hypothesis that neural oscillations, and their coupling across time scales, are essential for the coding and for the transmission of information in the brain. We show the presence of alpha-beta phase-amplitude coupling (α-β PAC) whose strength was associated with the temporal precision of self-generated time intervals, not with their absolute duration. α-β PAC indexes the temporal precision with which information is represented in an individual's brain. Our results link large-scale neuronal variability on the one hand, and individuals' timing precision, on the other.

Topological Properties of Resting-State fMRI Functional Networks Improve Machine Learning-Based Autism Classification

Automatic algorithms for disease diagnosis are being thoroughly researched for use in clinical settings. They usually rely on pre-identified biomarkers to highlight the existence of certain problems. However, finding such biomarkers for neurodevelopmental disorders such as Autism Spectrum Disorder (ASD) has challenged researchers for many years. With enough data and computational power, machine learning (ML) algorithms can be used to interpret the data and extract the best biomarkers from thousands of candidates. In this study, we used the fMRI data of 816 individuals enrolled in the Autism Brain Imaging Data Exchange (ABIDE) to introduce a new biomarker extraction pipeline for ASD that relies on the use of graph theoretical metrics of fMRI-based functional connectivity to inform a support vector machine (SVM). Furthermore, we split the dataset into 5 age groups to account for the effect of aging on functional connectivity. Our methodology achieved better results than most state-of-the-art investigations on this dataset with the best model for the >30 years age group achieving an accuracy, sensitivity, and specificity of 95, 97, and 95%, respectively. Our results suggest that measures of centrality provide the highest contribution to the classification power of the models.

Measuring transient phase-amplitude coupling using local mutual information

Here we demonstrate the suitability of a local mutual information measure for estimating the temporal dynamics of cross-frequency coupling (CFC) in brain electrophysiological signals. In CFC, concurrent activity streams in different frequency ranges interact and transiently couple. A particular form of CFC, phase-amplitude coupling (PAC), has raised interest given the growing amount of evidence of its possible role in healthy and pathological brain information processing. Although several methods have been proposed for PAC estimation, only a few have addressed the estimation of the temporal evolution of PAC, and these typically require a large number of experimental trials to return a reliable estimate. Here we explore the use of mutual information to estimate a PAC measure (MIPAC) in both continuous and event-related multi-trial data. To validate these two applications of the proposed method, we first apply it to a set of simulated phase-amplitude modulated signals and show that MIPAC can successfully recover the temporal dynamics of the simulated coupling in either continuous or multi-trial data. Finally, to explore the use of MIPAC to analyze data from human event-related paradigms, we apply it to an actual event-related human electrocorticographic (ECoG) data set that exhibits strong PAC, demonstrating that the MIPAC estimator can be used to successfully characterize amplitude-modulation dynamics in electrophysiological data.

How to Build a Functional Connectomic Biomarker for Mild Cognitive Impairment From Source Reconstructed MEG Resting-State Activity: The Combination of ROI Representation and Connectivity Estimator Matters

Our work aimed to demonstrate the combination of machine learning and graph theory for the designing of a connectomic biomarker for mild cognitive impairment (MCI) subjects using eyes-closed neuromagnetic recordings. The whole analysis based on source-reconstructed neuromagnetic activity. As ROI representation, we employed the principal component analysis (PCA) and centroid approaches. As representative bi-variate connectivity estimators for the estimation of intra and cross-frequency interactions, we adopted the phase locking value (PLV), the imaginary part (iPLV) and the correlation of the envelope (CorrEnv). Both intra and cross-frequency interactions (CFC) have been estimated with the three connectivity estimators within the seven frequency bands (intra-frequency) and in pairs (CFC), correspondingly. We demonstrated how different versions of functional connectivity graphs single-layer (SL-FCG) and multi-layer (ML-FCG) can give us a different view of the functional interactions across the brain areas. Finally, we applied machine learning techniques with main scope to build a reliable connectomic biomarker by analyzing both SL-FCG and ML-FCG in two different options: as a whole unit using a tensorial extraction algorithm and as single pair-wise coupling estimations. We concluded that edge-weighed feature selection strategy outperformed the tensorial treatment of SL-FCG and ML-FCG. The highest classification performance was obtained with the centroid ROI representation and edge-weighted analysis of the SL-FCG reaching the 98% for the CorrEnv in α1:α2 and 94% for the iPLV in α2. Classification performance based on the multi-layer participation coefficient, a multiplexity index reached 52% for iPLV and 52% for CorrEnv. Selected functional connections that build the multivariate connectomic biomarker in the edge-weighted scenario are located in default-mode, fronto-parietal, and cingulo-opercular network. Our analysis supports the notion of analyzing FCG simultaneously in intra and cross-frequency whole brain interactions with various connectivity estimators in beamformed recordings.

Design of optimal nonlinear network controllers for Alzheimer's disease

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer’s disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients’ biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks–namely, networks having low average shortest path length, high global efficiency–are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

This work aims to close the knowledge gap between theory and experiment in brain stimulation. Previous modeling approaches for stimulation have overlooked the nonlinear dynamical nature of the brain and failed to shed light on efficient mechanisms for the exogenous control of the brain. Amid the current efforts for developing personalized medicine, we introduce a framework for producing tailored stimulation signals, based on individual neuroimaging data and innovative modeling. This is the first time, to our knowledge, that brain stimulation for the most common cause of dementia, Alzheimer’s disease, is theoretically addressed. Our approach leads to the identification of potential target regions and subjects to successfully respond to brain stimulation therapies and yields various disease-reverting signals. Although focused on Alzheimer’s in this study, our methodology could be applied to other clinical conditions characterized by abnormalities in brain dynamics, like epilepsy and Parkinson’s, the treatment of which can benefit from the use of optimal control strategies.

Neural Cross-Frequency Coupling Functions

Although neural interactions are usually characterized only by their coupling strength and directionality, there is often a need to go beyond this by establishing the functional mechanisms of the interaction. We introduce the use of dynamical Bayesian inference for estimation of the coupling functions of neural oscillations in the presence of noise. By grouping the partial functional contributions, the coupling is decomposed into its functional components and its most important characteristics-strength and form-are quantified. The method is applied to characterize the δ-to-α phase-to-phase neural coupling functions from electroencephalographic (EEG) data of the human resting state, and the differences that arise when the eyes are either open (EO) or closed (EC) are evaluated. The δ-to-α phase-to-phase coupling functions were reconstructed, quantified, compared, and followed as they evolved in time. Using phase-shuffled surrogates to test for significance, we show how the strength of the direct coupling, and the similarity and variability of the coupling functions, characterize the EO and EC states for different regions of the brain. We confirm an earlier observation that the direct coupling is stronger during EC, and we show for the first time that the coupling function is significantly less variable. Given the current understanding of the effects of e.g., aging and dementia on δ-waves, as well as the effect of cognitive and emotional tasks on α-waves, one may expect that new insights into the neural mechanisms underlying certain diseases will be obtained from studies of coupling functions. In principle, any pair of coupled oscillations could be studied in the same way as those shown here.

Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models

Phase-amplitude coupling (PAC), the phenomenon where the amplitude of a high frequency oscillation is modulated by the phase of a lower frequency oscillation, is attracting an increasing interest in the neuroscience community due to its potential relevance for understanding healthy and pathological information processing in the brain. PAC is a diverse phenomenon, having been experimentally detected in at least ten combinations of rhythms: delta-theta, delta-alpha, delta-beta, delta-gamma, theta-alpha, theta-beta, theta-gamma, alpha-beta, alpha-gamma, and beta-gamma. However, a complete understanding of the biophysical mechanisms generating this diversity is lacking. Here we review computational models of PAC generation that range from detailed models of neuronal networks, where each cell is described by Hodgkin-Huxley-type equations, to neural mass models (NMMs) where only the average activities of neuronal populations are considered. We argue that NMMs are an appropriate mathematical framework (due to the small number of parameters and variables involved and the richness of the dynamics they can generate) to study the PAC phenomenon.