Evaluation of different measures of functional connectivity using a neural mass model

Reconstruction of phase-amplitude dynamics from signals of a network of oscillators

We present a novel method of reconstructing the phase-amplitude dynamics directly from signals of a network of oscillators to estimate the coupling between its nodes. For this purpose, we use the recent advances in the field of phase-amplitude reduction of oscillatory systems, which allow the representation of an uncoupled oscillatory system as a phase-amplitude oscillator in a unique form using transformations (parameterizations) related to the eigenfunctions of the Koopman operator. By combining the parameterization method and the Fourier-Laplace averaging method for finding the eigenfunctions of the Koopman operator, we developed a method of assessing the transformation functions from the signals of the interacting oscillatory systems. The resulting reconstructed dynamical system is a network of phase-amplitude oscillators with the interactions between them represented as coupling functions in phase and amplitude coordinates.

On the speech envelope in the cortical tracking of speech

The synchronization between the speech envelope and neural activity in auditory regions, referred to as cortical tracking of speech (CTS), plays a key role in speech processing. The method selected for extracting the envelope is a crucial step in CTS measurement, and the absence of a consensus on best practices among the various methods can influence analysis outcomes and interpretation. Here, we systematically compare five standard envelope extraction methods the absolute value of Hilbert transform (absHilbert), gammatone filterbanks, heuristic approach, Bark scale, and vocalic energy), analyzing their impact on the CTS. We present performance metrics for each method based on the recording of brain activity from participants listening to speech in clear and noisy conditions, utilizing intracranial EEG, MEG and EEG data. As expected, we observed significant CTS in temporal brain regions below 10 Hz across all datasets, regardless of the extraction methods. In general, the gammatone filterbanks approach consistently demonstrated superior performance compared to other methods. Results from our study can guide scientists in the field to make informed decisions about the optimal analysis to extract the CTS, contributing to advancing the understanding of the neuronal mechanisms implicated in CTS.

A linearized modeling framework for the frequency selectivity in neurons postsynaptic to vibration receptors

Vibration is an indispensable part of the tactile perception, which is encoded to oscillatory synaptic currents by receptors and transferred to neurons in the brain. The A2 and B1 neurons in the drosophila brain postsynaptic to the vibration receptors exhibit selective preferences for oscillatory synaptic currents with different frequencies, which is caused by the specific voltage-gated Na+ and K+ currents that both oppose the variations in membrane potential. To understand the peculiar role of the Na+ and K+ currents in shaping the filtering property of A2 and B1 neurons, we develop a linearized modeling framework that allows to systematically change the activation properties of these ionic channels. A data-driven conductance-based biophysical model is used to reproduce the frequency filtering of oscillatory synaptic inputs. Then, this data-driven model is linearized at the resting potential and its frequency response is calculated based on the transfer function, which is described by the magnitude-frequency curve. When we regulate the activation properties of the Na+ and K+ channels by changing the biophysical parameters, the dominant pole of the transfer function is found to be highly correlated with the fluctuation of the active current, which represents the strength of suppression of slow voltage variation. Meanwhile, the dominant pole also shapes the magnitude-frequency curve and further qualitatively determines the filtering property of the model. The transfer function provides a parsimonious description of how the biophysical parameters in Na+ and K+ channels change the inhibition of slow variations in membrane potential by Na+ and K+ currents, and further illustrates the relationship between the filtering properties and the activation properties of Na+ and K+ channels. This computational framework with the data-driven conductance-based biophysical model and its linearized model contributes to understanding the transmission and filtering of vibration stimulus in the tactile system.

Complexity decline of hippocampal CA1 circuit model due to cholinergic deficiency associated with Alzheimer's disease

A hallmark of Alzheimer's disease (AD) is cholinergic system dysfunction, directly affecting the hippocampal neurons. Previous experiments have demonstrated that reduced complexity is one significant effect of AD on electroencephalography (EEG). Motivated by these, this study explores reduced EEG complexity of cholinergic deficiency in AD by neurocomputation. We first construct a new hippocampal CA1 circuit model with cholinergic action. M-current I M and calcium-activated potassium current I AHP are newly introduced in the model to describe cholinergic input from the medial septum. Then, by enhancing I M and I AHP to mimic cholinergic deficiency, how cholinergic deficiency influences the model complexity is investigated by sample entropy (SampEn) and approximate entropy (ApEn). Numerical results show a more severe cholinergic deficit with lower model complexity. Furthermore, we conclude that the decline of SampEn and ApEn is due to the greatly diminished excitability of model neurons. These suggest that decreased neuronal excitability due to cholinergic impairment may contribute to reduced EEG complexity in AD. Subsequently, statistical analysis between simulated AD patients and normal control (NC) groups demonstrates that SampEn and auto-mutual-information (AMI) decrease rates significantly differ. Compared to NC, AD patients have a lower SampEn and a less negative AMI decline rate. These imply a low rate of new-generation information in AD brains with cholinergic deficits. Interestingly, the statistical correlation between SampEn and AMI is analyzed, and they have a large negative Pearson correlation coefficient. Thus, AMI reduction rates may be a complementary tool for complex analysis. Our modeling and complex analysis are expected to provide a deeper understanding of the reduced EEG complexity resulting from cholinergic deficiency.

Imitating and exploring the human brain's resting and task-performing states via brain computing: scaling and architecture

A computational human brain model with the voxel-wise assimilation method was established based on individual structural and functional imaging data. We found that the more similar the brain model is to the biological counterpart in both scale and architecture, the more similarity was found between the assimilated model and the biological brain both in resting states and during tasks by quantitative metrics. The hypothesis that resting state activity reflects internal body states was validated by the interoceptive circuit's capability to enhance the similarity between the simulation model and the biological brain. We identified that the removal of connections from the primary visual cortex (V1) to downstream visual pathways significantly decreased the similarity at the hippocampus between the model and its biological counterpart, despite a slight influence on the whole brain. In conclusion, the model and methodology present a solid quantitative framework for a digital twin brain for discovering the relationship between brain architecture and functions, and for digitally trying and testing diverse cognitive, medical and lesioning approaches that would otherwise be unfeasible in real subjects.

How representative are air transport functional complex networks? A quantitative validation

Functional networks have emerged as powerful instruments to characterize the propagation of information in complex systems, with applications ranging from neuroscience to climate and air transport. In spite of their success, reliable methods for validating the resulting structures are still missing, forcing the community to resort to expert knowledge or simplified models of the system's dynamics. We here propose the use of a real-world problem, involving the reconstruction of the structure of flights in the US air transport system from the activity of individual airports, as a way to explore the limits of such an approach. While the true connectivity is known and is, therefore, possible to provide a quantitative benchmark, this problem presents challenges commonly found in other fields, including the presence of non-stationarities and observational noise, and the limitedness of available time series. We explore the impact of elements like the specific functional metric employed, the way of detrending the time series, or the size of the reconstructed system and discuss how the conclusions here drawn could have implications for similar analyses in neuroscience.

Personalized modeling of Alzheimer's disease progression estimates neurodegeneration severity from EEG recordings

INTRODUCTION

Early identification of Alzheimer's disease (AD) is necessary for a timely onset of therapeutic care. However, cortical structural alterations associated with AD are difficult to discern.

METHODS

We developed a cortical model of AD-related neurodegeneration accounting for slowing of local dynamics and global connectivity degradation. In a monocentric study we collected electroencephalography (EEG) recordings at rest from participants in healthy (HC, n = 17), subjective cognitive decline (SCD, n = 58), and mild cognitive impairment (MCI, n = 44) conditions. For each patient, we estimated neurodegeneration model parameters based on individual EEG recordings.

RESULTS

Our model outperformed standard EEG analysis not only in discriminating between HC and MCI conditions (F1 score 0.95 vs 0.75) but also in identifying SCD patients with biological hallmarks of AD in the cerebrospinal fluid (recall 0.87 vs 0.50).

DISCUSSION

Personalized models could (1) support classification of MCI, (2) assess the presence of AD pathology, and (3) estimate the risk of cognitive decline progression, based only on economical and non-invasive EEG recordings.

Highlights

Personalized cortical model estimating structural alterations from EEG recordings.Discrimination of Mild Cognitive Impairment (MCI) and Healthy (HC) subjects (95%)Prediction of biological markers of Alzheimer's in Subjective Decline (SCD) Subjects (87%)Transition correctly predicted for 3/3 subjects that converted from SCD to MCI after 1y.

Analysis of corticomuscular-cortical functional network based on time-delayed maximal information spectral coefficient

Objective. The study of brain networks has become an influential tool for investigating post-stroke brain function. However, studies on the dynamics of cortical networks associated with muscle activity are limited. This is crucial for elucidating the altered coordination patterns in the post-stroke motor control system.Approach. In this study, we introduced the time-delayed maximal information spectral coefficient (TDMISC) method to assess the local frequency band characteristics (alpha, beta, and gamma bands) of functional corticomuscular coupling (FCMC) and cortico-cortical network parameters. We validated the effectiveness of TDMISC using a unidirectionally coupled Hénon maps model and a neural mass model.Main result. A grip task with 25% of maximum voluntary contraction was designed, and simulation results demonstrated that TDMISC accurately characterizes signals' local frequency band and directional properties. In the gamma band, the affected side showed significantly strong FCMC in the ascending direction. However, in the beta band, the affected side exhibited significantly weak FCMC in all directions. For the cortico-cortical network parameters, the affected side showed a lower clustering coefficient than the unaffected side in all frequency bands. Additionally, the affected side exhibited a longer shortest path length than the unaffected side in all frequency bands. In all frequency bands, the unaffected motor cortex in the stroke group exerted inhibitory effects on the affected motor cortex, the parietal associative areas, and the somatosensory cortices.Significance. These results provide meaningful insights into neural mechanisms underlying motor dysfunction.

From correlation to communication: Disentangling hidden factors from functional connectivity changes

While correlations in the BOLD fMRI signal are widely used to capture functional connectivity (FC) and its changes across contexts, its interpretation is often ambiguous. The entanglement of multiple factors including local coupling of two neighbors and nonlocal inputs from the rest of the network (affecting one or both regions) limits the scope of the conclusions that can be drawn from correlation measures alone. Here we present a method of estimating the contribution of nonlocal network input to FC changes across different contexts. To disentangle the effect of task-induced coupling change from the network input change, we propose a new metric, "communication change," utilizing BOLD signal correlation and variance. With a combination of simulation and empirical analysis, we demonstrate that (1) input from the rest of the network accounts for a moderate but significant amount of task-induced FC change and (2) the proposed "communication change" is a promising candidate for tracking the local coupling in task context-induced change. Additionally, when compared to FC change across three different tasks, communication change can better discriminate specific task types. Taken together, this novel index of local coupling may have many applications in improving our understanding of local and widespread interactions across large-scale functional networks.

Alterations in EEG functional connectivity in individuals with depression: A systematic review

The brain works as an organised, network-like structure of functionally interconnected regions. Disruptions to interconnectivity in certain networks have been linked to symptoms of depression and impairments in cognition. Electroencephalography (EEG) is a low-burden tool by which differences in functional connectivity (FC) can be assessed. This systematic review aims to provide a synthesis of evidence relating to EEG FC in depression. A comprehensive electronic literature search for terms relating to depression, EEG, and FC was conducted on studies published before the end of November 2021, according to PRISMA guidelines. Studies comparing EEG measures of FC of individuals with depression to that of healthy control groups were included. Data was extracted by two independent reviewers, and the quality of EEG FC methods was assessed. Fifty-two studies assessing EEG FC in depression were identified: 36 assessed resting-state FC, and 16 assessed task-related or other (i.e., sleep) FC. Somewhat consistent findings in resting-state studies suggest for no differences between depression and control groups in EEG FC in the delta and gamma frequencies. However, while most resting-state studies noted a difference in alpha, theta, and beta, no clear conclusions could be drawn about the direction of the difference, due to considerable inconsistencies between study design and methodology. This was also true for task-related and other EEG FC. More robust research is needed to understand the true differences in EEG FC in depression. Given that the FC between brain regions drives behaviour, cognition, and emotion, characterising how FC differs in depression is essential for understanding the aetiology of depression.

Global excitability and network structure in the human brain

We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us to establish relationships between the global excitability of such networks and global structural network quantities for connectomes of two different sizes for a number of individual subjects. We compare the qualitative behavior of such correlations between biological networks and shuffled networks, the latter generated by shuffling the pairwise connectivities of the former while preserving their distribution. Our results point towards a remarkable propensity of the brain to achieve a trade-off between low network wiring cost and strong functionality, and highlight the unique capacity of brain network topologies to exhibit a strong transition from an inactive state to a globally excited one.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass model, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen-Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

Selection of the Minimum Number of EEG Sensors to Guarantee Biometric Identification of Individuals

Biometric identification uses person recognition techniques based on the extraction of some of their physical or biological properties, which make it possible to characterize and differentiate one person from another and provide irreplaceable and critical information that is suitable for application in security systems. The extraction of information from the electrical biosignal of the human brain has received a great deal of attention in recent years. Analysis of EEG signals has been widely used over the last century in medicine and as a basis for brain-machine interfaces (BMIs). In addition, the application of EEG signals for biometric recognition has recently been demonstrated. In this context, EEG-based biometric systems are often considered in two different applications: identification (one-to-many classification) and authentication (one-to-one or true/false classification). In this article, we establish a methodology for selecting and reducing the minimum number of EEG sensors necessary to carry out effective biometric identification of individuals. Two methodologies were applied, one based on principal component analysis and the other on the Wilcoxon signed-rank test in order to reduce the number of electrodes. This allowed us to identify, according to the methodology used, the areas of the cerebral cortex that would allow selection of the minimum number of electrodes necessary for the identification of individuals. The methodologies were applied to two databases, one with 13 people with self-collected recordings using low-cost EEG equipment, EMOTIV EPOC+, and another publicly available database with recordings from 109 people provided by the PhysioNet BCI.

Oscillatory neurofeedback networks and poststroke rehabilitative potential in severely impaired stroke patients

Motor restoration after severe stroke is often limited. However, some of the severely impaired stroke patients may still have a rehabilitative potential. Biomarkers that identify these patients are sparse. Eighteen severely impaired chronic stroke patients with a lack of volitional finger extension participated in an EEG study. During sixty-six trials of kinesthetic motor imagery, a brain-machine interface turned event-related beta-band desynchronization of the ipsilesional sensorimotor cortex into opening of the paralyzed hand by a robotic orthosis. A subgroup of eight patients participated in a subsequent four-week rehabilitation training. Changes of the movement extent were captured with sensors which objectively quantified even discrete improvements of wrist movement. Albeit with the same motor impairment level, patients could be differentiated into two groups, i.e., with and without task-related increase of bilateral cortico-cortical phase synchronization between frontal/premotor and parietal areas. This fronto-parietal integration (FPI) was associated with a significantly higher volitional beta modulation range in the ipsilesional sensorimotor cortex. Following the four-week training, patients with FPI showed significantly higher improvement in wrist movement than those without FPI. Moreover, only the former group improved significantly in the upper extremity Fugl-Meyer-Assessment score. Neurofeedback-related long-range oscillatory coherence may differentiate severely impaired stroke patients with regard to their rehabilitative potential, a finding that needs to be confirmed in larger patient cohorts.

A systematic data-driven approach to analyze sensor-level EEG connectivity: Identifying robust phase-synchronized network components using surface Laplacian with spectral-spatial PCA

Although conventional averaging across predefined frequency bands reduces the complexity of EEG functional connectivity (FC), it obscures the identification of resting-state brain networks (RSN) and impedes accurate estimation of FC reliability. Extending prior work, we combined scalp current source density (CSD; spherical spline surface Laplacian) and spectral-spatial PCA to identify FC components. Phase-based FC was estimated via debiased-weighted phase-locking index from CSD-transformed resting EEGs (71 sensors, 8 min, eyes open/closed, 35 healthy adults, 1-week retest). Spectral PCA extracted six robust alpha and theta components (86.6% variance). Subsequent spatial PCA for each spectral component revealed seven robust regionally focused (posterior, central, and frontal) and long-range (posterior-anterior) alpha components (peaks at 8, 10, and 13 Hz) and a midfrontal theta (6 Hz) component, accounting for 37.0% of FC variance. These spatial FC components were consistent with well-known networks (e.g., default mode, visual, and sensorimotor), and four were sensitive to eyes open/closed conditions. Most FC components had good-to-excellent internal consistency (odd/even epochs, eyes open/closed) and test-retest reliability (ICCs ≥ .8). Moreover, the FC component structure was generally present in subsamples (session × odd/even epoch, or smaller subgroups [n = 7-10]), as indicated by high similarity of component loadings across PCA solutions. Apart from systematically reducing FC dimensionality, our approach avoids arbitrary thresholds and allows quantification of meaningful and reliable network components that may prove to be of high relevance for basic and clinical research applications.

Cross-validated Adaboost Classification of Emotion Regulation Strategies Identified by Spectral Coherence in Resting-State

In the present study, quantitative relations between Cognitive Emotion Regulation strategies (CERs) and EEG synchronization levels have been investigated for the first time. For this purpose, spectral coherence (COH), phase locking value and mutual information have been applied to short segments of 62-channel resting state eyes-opened EEG data collected from healthy adults who use contrasting emotion regulation strategies (frequently and rarely use of rumination&distraction, frequently and rarely use of suppression&reappraisal). In tests, the individuals are grouped depending on their self-responses to both emotion regulation questionnaire (ERQ) and cognitive ERQ. Experimental data are downloaded from publicly available data-base, LEMON. Regarding EEG electrode pairs that placed on right and left cortical regions, inter-hemispheric dependency measures are computed for non-overlapped short segments of 2 sec at 2 min duration trials. In addition to full-band EEG analysis, dependency metrics are also obtained for both alpha and beta sub-bands. The contrasting groups are discriminated from each other with respect to the corresponding features using cross-validated adaboost classifiers. High classification accuracies (CA) of 99.44% and 98.33% have been obtained through instant classification driven by full-band COH estimations. Considering regional features that provide the high CA, CERs are found to be highly relevant with associative memory functions and cognition. The new findings may indicate the close relation between neuroplasticity and cognitive skills.

Cognitive Outcome Prediction in Infants With Neonatal Hypoxic-Ischemic Encephalopathy Based on Functional Connectivity and Complexity of the Electroencephalography Signal

Impaired neurodevelopmental outcome, in particular cognitive impairment, after neonatal hypoxic-ischemic encephalopathy is a major concern for parents, clinicians, and society. This study aims to investigate the potential benefits of using advanced quantitative electroencephalography analysis (qEEG) for early prediction of cognitive outcomes, assessed here at 2 years of age. EEG data were recorded within the first week after birth from a cohort of twenty infants with neonatal hypoxic-ischemic encephalopathy (HIE). A proposed regression framework was based on two different sets of features, namely graph-theoretical features derived from the weighted phase-lag index (WPLI) and entropies metrics represented by sample entropy (SampEn), permutation entropy (PEn), and spectral entropy (SpEn). Both sets of features were calculated within the noise-assisted multivariate empirical mode decomposition (NA-MEMD) domain. Correlation analysis showed a significant association in the delta band between the proposed features, graph attributes (radius, transitivity, global efficiency, and characteristic path length) and entropy features (Pen and SpEn) from the neonatal EEG data and the cognitive development at age two years. These features were used to train and test the tree ensemble (boosted and bagged) regression models. The highest prediction performance was reached to 14.27 root mean square error (RMSE), 12.07 mean absolute error (MAE), and 0.45 R-squared using the entropy features with a boosted tree regression model. Thus, the results demonstrate that the proposed qEEG features show the state of brain function at an early stage; hence, they could serve as predictive biomarkers of later cognitive impairment, which could facilitate identifying those who might benefit from early targeted intervention.

Reorganization of Brain Functional Connectivity Network and Vision Restoration Following Combined tACS-tDCS Treatment After Occipital Stroke

Objective: Non-invasive brain stimulation (NIBS) is already known to improve visual field functions in patients with optic nerve damage and partially restores the organization of brain functional connectivity networks (FCNs). However, because little is known if NIBS is effective also following brain damage, we now studied the correlation between visual field recovery and FCN reorganization in patients with stroke of the central visual pathway.

Method: In a controlled, exploratory trial, 24 patients with hemianopia were randomly assigned to one of three brain stimulation groups: transcranial direct current stimulation (tDCS)/transcranial alternating current stimulation (tACS) (ACDC); sham tDCS/tACS (AC); sham tDCS/sham tACS (Sham), which were compared to age-matched controls (n = 24). Resting-state electroencephalogram (EEG) was collected at baseline, after 10 days stimulation and at 2 months follow-up. EEG recordings were analyzed for FCN measures using graph theory parameters, and FCN small worldness of the network and long pairwise coherence parameter alterations were then correlated with visual field performance.

Result: ACDC enhanced alpha-band FCN strength in the superior occipital lobe of the lesioned hemisphere at follow-up. A negative correlation (r = −0.80) was found between the intact visual field size and characteristic path length (CPL) after ACDC with a trend of decreased alpha-band centrality of the intact middle occipital cortex. ACDC also significantly decreased delta band coherence between the lesion and the intact occipital lobe, and coherence was enhanced between occipital and temporal lobe of the intact hemisphere in the low beta band. Responders showed significantly higher strength in the low alpha band at follow-up in the intact lingual and calcarine cortex and in the superior occipital region of the lesioned hemisphere.

Conclusion: While ACDC decreases delta band coherence between intact and damaged occipital brain areas indicating inhibition of low-frequency neural oscillations, ACDC increases FCN connectivity between the occipital and temporal lobe in the intact hemisphere. When taken together with the lower global clustering coefficient in responders, these findings suggest that FCN reorganization (here induced by NIBS) is adaptive in stroke. It leads to greater efficiency of neural processing, where the FCN requires fewer connections for visual processing.

Comparison of undirected frequency-domain connectivity measures for cerebro-peripheral analysis

Analyses of cerebro-peripheral connectivity aim to quantify ongoing coupling between brain activity (measured by MEG/EEG) and peripheral signals such as muscle activity, continuous speech, or physiological rhythms (such as pupil dilation or respiration). Due to the distinct rhythmicity of these signals, undirected connectivity is typically assessed in the frequency domain. This leaves the investigator with two critical choices, namely a) the appropriate measure for spectral estimation (i.e., the transformation into the frequency domain) and b) the actual connectivity measure. As there is no consensus regarding best practice, a wide variety of methods has been applied. Here we systematically compare combinations of six standard spectral estimation methods (comprising fast Fourier and continuous wavelet transformation, bandpass filtering, and short-time Fourier transformation) and six connectivity measures (phase-locking value, Gaussian-Copula mutual information, Rayleigh test, weighted pairwise phase consistency, magnitude squared coherence, and entropy). We provide performance measures of each combination for simulated data (with precise control over true connectivity), a single-subject set of real MEG data, and a full group analysis of real MEG data. Our results show that, overall, WPPC and GCMI tend to outperform other connectivity measures, while entropy was the only measure sensitive to bimodal deviations from a uniform phase distribution. For group analysis, choosing the appropriate spectral estimation method appears to be more critical than the connectivity measure. We discuss practical implications (sampling rate, SNR, computation time, and data length) and aim to provide recommendations tailored to particular research questions.

A model of metabolic supply-demand mismatch leading to secondary brain injury

Secondary brain injury (SBI) is defined as new or worsening injury to the brain after an initial neurologic insult, such as hemorrhage, trauma, ischemic stroke, or infection. It is a common and potentially preventable complication following many types of primary brain injury (PBI). However, mechanistic details about how PBI leads to additional brain injury and evolves into SBI are poorly characterized. In this work, we propose a mechanistic model for the metabolic supply demand mismatch hypothesis (MSDMH) of SBI. Our model, based on the Hodgkin-Huxley model, supplemented with additional dynamics for extracellular potassium, oxygen concentration, and excitotoxity, provides a high-level unified explanation for why patients with acute brain injury frequently develop SBI. We investigate how decreased oxygen, increased extracellular potassium, excitotoxicity, and seizures can induce SBI and suggest three underlying paths for how events following PBI may lead to SBI. The proposed model also helps explain several important empirical observations, including the common association of acute brain injury with seizures, the association of seizures with tissue hypoxia and so on. In contrast to current practices which assume that ischemia plays the predominant role in SBI, our model suggests that metabolic crisis involved in SBI can also be nonischemic. Our findings offer a more comprehensive understanding of the complex interrelationship among potassium, oxygen, excitotoxicity, seizures, and SBI.NEW & NOTEWORTHY We present a novel mechanistic model for the metabolic supply demand mismatch hypothesis (MSDMH), which attempts to explain why patients with acute brain injury frequently develop seizure activity and secondary brain injury (SBI). Specifically, we investigate how decreased oxygen, increased extracellular potassium, excitotoxicity, seizures, all common sequalae of primary brain injury (PBI), can induce SBI and suggest three underlying paths for how events following PBI may lead to SBI.

EEG Synchronization-Parameters in Patients With Subcortical Arteriosclerotic Encephalopathy and Gait Disorder

PURPOSE

Subcortical arteriosclerotic encephalopathy (SAE) is characterized by extensive white matter lesions in the MRI. Clinical symptoms are cognitive impairment, ranging from mild deficits to vascular dementia, impaired executive functioning, and gait disorders. In the EEG of SAE patients with vascular dementia, the lower frequencies are increased. However, it is unclear whether EEG changes also exist in SAE patients with gait disorders but without vascular dementia.

METHODS

The authors analyzed the EEGs of 50 nondemented patients with SAE and gait disorders and 50 healthy controls applying pointwise transinformation as a measure of synchronization.

RESULTS

Hundred seconds of waking EEG that appeared unaltered in visual analysis were sufficient to prove changes in synchronization. The authors found a decrease in the mean level of synchronization, combined with an elongation of synchronization time in all examined brain areas. These effects correlated slightly with the extent of subcortical lesions.

CONCLUSIONS

Changes in EEG synchronization in patients with SAE and gait disorders seem to occur independently of cognitive function. The causal relationship of the changes in EEG synchronization and gait disorders remains to be clarified. The results of this study might point to a decrease in coupling efficiency in these patients, with the increase in synchronization duration as a possible compensatory mechanism. Because a time-efficient signal transmission particularly during gait execution is crucial, reduced efficiency might contribute to an impairment of postural stabilization. The study results might indicate a neuronal network for planning and execution of motor activity and particularly gait, extending from the frontal over the central to the parietal cortex.

Infant functional networks are modulated by state of consciousness and circadian rhythm

Functional connectivity networks are valuable tools for studying development, cognition, and disease in the infant brain. In adults, such networks are modulated by the state of consciousness and the circadian rhythm; however, it is unknown if infant brain networks exhibit similar variation, given the unique temporal properties of infant sleep and circadian patterning. To address this, we analyzed functional connectivity networks calculated from long-term EEG recordings (average duration 20.8 hr) from 19 healthy infants. Networks were subject specific, as intersubject correlations between weighted adjacency matrices were low. However, within individual subjects, both sleep and wake networks were stable over time, with stronger functional connectivity during sleep than wakefulness. Principal component analysis revealed the presence of two dominant networks; visual sleep scoring confirmed that these corresponded to sleep and wakefulness. Lastly, we found that network strength, degree, clustering coefficient, and path length significantly varied with time of day, when measured in either wakefulness or sleep at the group level. Together, these results suggest that modulation of healthy functional networks occurs over ∼24 hr and is robust and repeatable. Accounting for such temporal periodicities may improve the physiological interpretation and use of functional connectivity analysis to investigate brain function in health and disease.

The Relationship between Oscillations in Brain Regions and Functional Connectivity: A Critical Analysis with the Aid of Neural Mass Models

Propagation of brain rhythms among cortical regions is a relevant aspect of cognitive neuroscience, which is often investigated using functional connectivity (FC) estimation techniques. The aim of this work is to assess the relationship between rhythm propagation, FC and brain functioning using data generated from neural mass models of connected Regions of Interest (ROIs). We simulated networks of four interconnected ROIs, each with a different intrinsic rhythm (in θ, α, β and γ ranges). Connectivity was estimated using eight estimators and the relationship between structural connectivity and FC was assessed as a function of the connectivity strength and of the inputs to the ROIs. Results show that the Granger estimation provides the best accuracy, with a good capacity to evaluate the connectivity strength. However, the estimated values strongly depend on the input to the ROIs and hence on nonlinear phenomena. When a population works in the linear region, its capacity to transmit a rhythm increases drastically. Conversely, when it saturates, oscillatory activity becomes strongly affected by rhythms incoming from other regions. Changes in functional connectivity do not always reflect a physical change in the synapses. A unique connectivity network can propagate rhythms in very different ways depending on the specific working conditions.

In your phase: neural phase synchronisation underlies visual imagery of faces

Mental imagery is the process through which we retrieve and recombine information from our memory to elicit the subjective impression of “seeing with the mind’s eye”. In the social domain, we imagine other individuals while recalling our encounters with them or modelling alternative social interactions in future. Many studies using imaging and neurophysiological techniques have shown several similarities in brain activity between visual imagery and visual perception, and have identified frontoparietal, occipital and temporal neural components of visual imagery. However, the neural connectivity between these regions during visual imagery of socially relevant stimuli has not been studied. Here we used electroencephalography to investigate neural connectivity and its dynamics between frontal, parietal, occipital and temporal electrodes during visual imagery of faces. We found that voluntary visual imagery of faces is associated with long-range phase synchronisation in the gamma frequency range between frontoparietal electrode pairs and between occipitoparietal electrode pairs. In contrast, no effect of imagery was observed in the connectivity between occipitotemporal electrode pairs. Gamma range synchronisation between occipitoparietal electrode pairs predicted subjective ratings of the contour definition of imagined faces. Furthermore, we found that visual imagery of faces is associated with an increase of short-range frontal synchronisation in the theta frequency range, which temporally preceded the long-range increase in the gamma synchronisation. We speculate that the local frontal synchrony in the theta frequency range might be associated with an effortful top-down mnemonic reactivation of faces. In contrast, the long-range connectivity in the gamma frequency range along the fronto-parieto-occipital axis might be related to the endogenous binding and subjective clarity of facial visual features.

Measuring the Coupling Direction between Neural Oscillations with Weighted Symbolic Transfer Entropy

Neural oscillations reflect rhythmic fluctuations in the synchronization of neuronal populations and play a significant role in neural processing. To further understand the dynamic interactions between different regions in the brain, it is necessary to estimate the coupling direction between neural oscillations. Here, we developed a novel method, termed weighted symbolic transfer entropy (WSTE), that combines symbolic transfer entropy (STE) and weighted probability distribution to measure the directionality between two neuronal populations. The traditional STE ignores the degree of difference between the amplitude values of a time series. In our proposed WSTE method, this information is picked up by utilizing a weighted probability distribution. The simulation analysis shows that the WSTE method can effectively estimate the coupling direction between two neural oscillations. In comparison with STE, the new method is more sensitive to the coupling strength and is more robust against noise. When applied to epileptic electrocorticography data, a significant coupling direction from the anterior nucleus of thalamus (ANT) to the seizure onset zone (SOZ) was detected during seizures. Considering the superiorities of the WSTE method, it is greatly advantageous to measure the coupling direction between neural oscillations and consequently characterize the information flow between different brain regions.

Revisiting correlation-based functional connectivity and its relationship with structural connectivity

Patterns of brain structural connectivity (SC) and functional connectivity (FC) are known to be related. In SC-FC comparisons, FC has classically been evaluated from correlations between functional time series, and more recently from partial correlations or their unnormalized version encoded in the precision matrix. The latter FC metrics yield more meaningful comparisons to SC because they capture ‘direct’ statistical dependencies, that is, discarding the effects of mediators, but their use has been limited because of estimation issues. With the rise of high-quality and large neuroimaging datasets, we revisit the relevance of different FC metrics in the context of SC-FC comparisons. Using data from 100 unrelated Human Connectome Project subjects, we first explore the amount of functional data required to reliably estimate various FC metrics. We find that precision-based FC yields a better match to SC than correlation-based FC when using 5 minutes of functional data or more. Finally, using a linear model linking SC and FC, we show that the SC-FC match can be used to further interrogate various aspects of brain structure and function such as the timescales of functional dynamics in different resting-state networks or the intensity of anatomical self-connections.

Differentiation of pain levels by deploying various EEG synchronization features and dynamic ensemble selection mechanism

OBJECTIVE

The target of this study is measuring the pain intensity in an objective manner by analysing the electroencephalogram (EEG) signals. Although this problem has attracted researchers' attention, increasing the resolution of this measurement, by increasing the number of pain states, significantly decreases the accuracy of pain level classification problem.

APPROACH

To overcome this drawback, we adopt state-of-the-art synchronization schemes to measure the linear, nonlinear and generalized synchronization between different EEG channels. 32 subjects executed the Cold Pressor Task (CPT) and experienced five defined levels of pain while recording their EEGs. Due to high number of synchronization features from 34 channels, the most discriminative features were selected using greedy overall relevancy (GOR) method. The selected features are applied to a dynamic ensemble selection system.

MAIN RESULTS

Our experiment provides 85.6% accuracy over the five classes, which significantly outperforms the results of past research. Moreover, we observe that the selected features belong to the channels placed over the ridge of cortex, the area responsible for processing somatic sensation arisen from nociceptive temperature. As expected, we noted that continuing the painful stimulus for minutes engaged regions beyond the sensorimotor cortex, e.g., the prefrontal cortex.

SIGNIFICANCE

We conclude that the amount of synchronization between scalp EEG channels is an informative tool in revealing the pain sensation.

Comparison of Phase Synchronization Measures for Identifying Stimulus-Induced Functional Connectivity in Human Magnetoencephalographic and Simulated Data

Phase synchronization measures are widely used for investigating inter-regional functional connectivity (FC) of brain oscillations, but which phase synchronization measure should be chosen for a given experiment remains unclear. Using neuromagnetic brain signals recorded from healthy participants during somatosensory stimuli, we compared the performance of four phase synchronization measures, imaginary part of phase-locking value, imaginary part of coherency (ImCoh), phase lag index and weighted phase lag index (wPLI), for detecting stimulus-induced FCs between the contralateral primary and ipsilateral secondary somatosensory cortices. The analyses revealed that ImCoh exhibited the best performance for detecting stimulus-induced FCs, followed by the wPLI. We found that amplitude weighting, which is related to computing both ImCoh and wPLI, effectively attenuated the influence of noise contamination. A simulation study modeling noise-contaminated periodograms replicated these findings. The present results suggest that the amplitude-dependent measures, ImCoh followed by wPLI, may have the advantage in detecting stimulus-induced FCs.

A Brain Network Constructed on an L1-Norm Regression Model Is More Sensitive in Detecting Small World Network Changes in Early AD

Most previous imaging studies have used traditional Pearson correlation analysis to construct brain networks. This approach fails to adequately and completely account for the interaction between adjacent brain regions. In this study, we used the L1-norm linear regression model to test the small-world attributes of the brain networks of three groups of patients, namely, those with mild cognitive impairment (MCI), Alzheimer's disease (AD), and healthy controls (HCs); we attempted to identify the method that may detect minor differences in MCI and AD patients. Twenty-four AD patients, 33 MCI patients, and 27 HC elderly subjects were subjected to functional MRI (fMRI). We applied traditional Pearson correlation and the L1-norm to construct the brain networks and then tested the small-world attributes by calculating the following parameters: clustering coefficient (Cp), path length (Lp), global efficiency (Eg), and local efficiency (Eloc). As expected, L1 could detect slight changes, mainly in MCI patients expressing higher Cp and Eloc; however, no statistical differences were found between MCI patients and HCs in terms of Cp, Lp, Eg, and Eloc, using Pearson correlation. Compared with HCs, AD patients expressed a lower Cp, Eloc, and Lp and an increased Eg using both connectivity metrics. The statistical differences between the groups indicated the brain networks constructed by the L1-norm were more sensitive to detect slight small-world network changes in early stages of AD.

Transfer Entropy as a Measure of Brain Connectivity: A Critical Analysis With the Help of Neural Mass Models

Objective: Assessing brain connectivity from electrophysiological signals is of great relevance in neuroscience, but results are still debated and depend crucially on how connectivity is defined and on mathematical instruments utilized. Aim of this work is to assess the capacity of bivariate Transfer Entropy (TE) to evaluate connectivity, using data generated from simple neural mass models of connected Regions of Interest (ROIs). Approach: Signals simulating mean field potentials were generated assuming two, three or four ROIs, connected via excitatory or by-synaptic inhibitory links. We investigated whether the presence of a statistically significant connection can be detected and if connection strength can be quantified. Main Results: Results suggest that TE can reliably estimate the strength of connectivity if neural populations work in their linear regions, and if the epoch lengths are longer than 10 s. In case of multivariate networks, some spurious connections can emerge (i.e., a statistically significant TE even in the absence of a true connection); however, quite a good correlation between TE and synaptic strength is still preserved. Moreover, TE appears more robust for distal regions (longer delays) compared with proximal regions (smaller delays): an approximate a priori knowledge on this delay can improve the procedure. Finally, non-linear phenomena affect the assessment of connectivity, since they may significantly reduce TE estimation: information transmission between two ROIs may be weak, due to non-linear phenomena, even if a strong causal connection is present. Significance: Changes in functional connectivity during different tasks or brain conditions, might not always reflect a true change in the connecting network, but rather a change in information transmission. A limitation of the work is the use of bivariate TE. In perspective, the use of multivariate TE can improve estimation and reduce some of the problems encountered in the present study.

Comparing different EEG connectivity methods in young males with ASD

Although EEG connectivity data are often used to build models of the association between overt behavioural signs of Autism Spectrum Disorder (ASD) and underlying brain connectivity indices, use of a large number of possible connectivity methods across studies has produced a fairly inconsistent set of results regarding this association. To explore the level of agreement between results from five commonly-used EEG connectivity models (i.e., Coherence, Weighted Phased Lag Index- Debiased, Phase Locking Value, Phase Slope Index, Granger Causality), a sample of 41 young males with ASD provided EEG data under eyes-opened and eyes-closed conditions. There were relatively few statistically significant and/or meaningful correlations between the results obtained from the five connectivity methods, arguing for a re-estimation of the methodology used in such studies so that specific connectivity methods may be matched to particular research questions regarding the links between neural connectivity and overt behaviour within this population.

Organizing principles of whole-brain functional connectivity in zebrafish larvae

Network science has begun to reveal the fundamental principles by which large-scale brain networks are organized, including geometric constraints, a balance between segregative and integrative features, and functionally flexible brain areas. However, it remains unknown whether whole-brain networks imaged at the cellular level are organized according to similar principles. Here, we analyze whole-brain functional networks reconstructed from calcium imaging data recorded in larval zebrafish. Our analyses reveal that functional connections are distance-dependent and that networks exhibit hierarchical modular structure and hubs that span module boundaries. We go on to show that spontaneous network structure places constraints on stimulus-evoked reconfigurations of connections and that networks are highly consistent across individuals. Our analyses reveal basic organizing principles of whole-brain functional brain networks at the mesoscale. Our overarching methodological framework provides a blueprint for studying correlated activity at the cellular level using a low-dimensional network representation. Our work forms a conceptual bridge between macro- and mesoscale network neuroscience and opens myriad paths for future studies to investigate network structure of nervous systems at the cellular level.

EEG Functional Connectivity is a Weak Predictor of Causal Brain Interactions

In recent years there has been an explosion of research evaluating resting-state brain functional connectivity (FC) using different modalities. However, the relationship between such measures of FC and the underlying causal brain interactions has not been well characterized. To further characterize this relationship, we assessed the relationship between electroencephalography (EEG) resting state FC and propagation of transcranial magnetic stimulation (TMS) evoked potentials (TEPs) at the sensor and source level in healthy participants. TMS was applied to six different cortical regions in ten healthy individuals (9 male; 1 female), and effects on brain activity were measured using simultaneous EEG. Pre-stimulus FC was assessed using five different FC measures (Pearson's correlation, mutual information, weighted phase lag index, coherence and phase locking value). Propagation of the TEPs was quantified as the root mean square (RMS) of the TEP voltage and current source density (CSD) at the sensor and source level, respectively. The relationship between pre-stimulus FC and the spatial distribution of TEP activity was determined using a generalized linear model (GLM) analysis. On the group level, all FC measures correlated significantly with TEP activity over the early (15-75 ms) and full range (15-400 ms) of the TEP at the sensor and source level. However, the predictive value of all FC measures is quite limited, accounting for less than 10% of the variance of TEP activity, and varies substantially across participants and stimulation sites. Taken together, these results suggest that EEG functional connectivity studies in sensor and source space should be interpreted with caution.

Advancing functional connectivity research from association to causation

Cognition and behavior emerge from brain network interactions, such that investigating causal interactions should be central to the study of brain function. Approaches that characterize statistical associations among neural time series-functional connectivity (FC) methods-are likely a good starting point for estimating brain network interactions. Yet only a subset of FC methods ('effective connectivity') is explicitly designed to infer causal interactions from statistical associations. Here we incorporate best practices from diverse areas of FC research to illustrate how FC methods can be refined to improve inferences about neural mechanisms, with properties of causal neural interactions as a common ontology to facilitate cumulative progress across FC approaches. We further demonstrate how the most common FC measures (correlation and coherence) reduce the set of likely causal models, facilitating causal inferences despite major limitations. Alternative FC measures are suggested to immediately start improving causal inferences beyond these common FC measures.

How Sensitive Are Conventional MEG Functional Connectivity Metrics With Sliding Windows to Detect Genuine Fluctuations in Dynamic Functional Connectivity?

Despite advances in the field of dynamic connectivity, fixed sliding window approaches for the detection of fluctuations in functional connectivity are still widely used. The use of conventional connectivity metrics in conjunction with a fixed sliding window comes with the arbitrariness of the chosen window lengths. In this paper we use multivariate autoregressive and neural mass models with a priori defined ground truths to systematically analyze the sensitivity of conventional metrics in combination with different window lengths to detect genuine fluctuations in connectivity for various underlying state durations. Metrics of interest are the coherence, imaginary coherence, phase lag index, phase locking value and the amplitude envelope correlation. We performed analysis for two nodes and at the network level. We demonstrate that these metrics show indeed higher variability for genuine temporal fluctuations in connectivity compared to a static connectivity state superimposed by noise. Overall, the error of the connectivity estimates themselves decreases for longer state durations (order of seconds), while correlations of the connectivity fluctuations with the ground truth was higher for longer state durations. In general, metrics, in combination with a sliding window, perform poorly for very short state durations. Increasing the SNR of the system only leads to a moderate improvement. In addition, at the network level, only longer window widths were sufficient to detect plausible resting state networks that matched the underlying ground truth, especially for the phase locking value, amplitude envelope correlation and coherence. The length of these longer window widths did not necessarily correspond to the underlying state durations. For short window widths resting state network connectivity patterns could not be retrieved. We conclude that fixed sliding window approaches for connectivity can detect modulations of connectivity, but mostly if the underlying dynamics operate on moderate to slow timescales. In practice, this can be a drawback, as state durations can vary significantly in empirical data.

EEG functional connectivity metrics wPLI and wSMI account for distinct types of brain functional interactions

The weighted Phase Lag Index (wPLI) and the weighted Symbolic Mutual Information (wSMI) represent two robust and widely used methods for MEG/EEG functional connectivity estimation. Interestingly, both methods have been shown to detect relative alterations of brain functional connectivity in conditions associated with changes in the level of consciousness, such as following severe brain injury or under anaesthesia. Despite these promising findings, it was unclear whether wPLI and wSMI may account for distinct or similar types of functional interactions. Using simulated high-density (hd-)EEG data, we demonstrate that, while wPLI has high sensitivity for couplings presenting a mixture of linear and nonlinear interdependencies, only wSMI can detect purely nonlinear interaction dynamics. Moreover, we evaluated the potential impact of these differences on real experimental data by computing wPLI and wSMI connectivity in hd-EEG recordings of 12 healthy adults during wakefulness and deep (N3-)sleep, characterised by different levels of consciousness. In line with the simulation-based findings, this analysis revealed that both methods have different sensitivity for changes in brain connectivity across the two vigilance states. Our results indicate that the conjoint use of wPLI and wSMI may represent a powerful tool to study the functional bases of consciousness in physiological and pathological conditions.

Evaluation of connectivity estimates using spiking neuronal network models

The flow of information between different regions of the cortex is fundamental for brain function. Researchers use causality detection techniques, such as Granger causality, to infer connectivity among brain areas from time series. Generalized partial directed coherence (GPDC) is a frequency domain linear method based on vector autoregressive model, which has been applied in electroencephalography, local field potential, and blood oxygenation level-dependent signals. Despite its widespread usage, previous attempts to validate GPDC use oversimplified simulated data, which do not reflect the nonlinearities and network couplings present in biological signals. In this work, we evaluated the GPDC performance when applied to simulated LFP signals, i.e., generated from networks of spiking neuronal models. We created three models, each containing five interacting networks, and evaluated whether the GPDC method could accurately detect network couplings. When using a stronger coupling, we showed that GPDC correctly detects all existing connections from simulated LFP signals in the three models, without false positives. Varying the coupling strength between networks, by changing the number of connections or synaptic strengths, and adding noise in the times series, altered the receiver operating characteristic (ROC) curve, ranging from perfect to chance level retrieval. We also showed that GPDC values correlated with coupling strength, indicating that GPDC values can provide useful information regarding coupling strength. These results reinforce that GPDC can be used to detect causality relationships over neural signals.

Reconstruction of effective connectivity in the case of asymmetric phase distributions

BACKGROUND

The interaction of different brain regions is supported by transient synchronization between neural oscillations at different frequencies. Different measures based on synchronization theory are used to assess the strength of the interactions from experimental data. One method of estimating the effective connectivity between brain regions, within the framework of the theory of weakly coupled phase oscillators, was implemented in Dynamic Causal Modelling (DCM) for phase coupling (Penny et al., 2009). However, the results of such an approach strongly depend on the observables used to reconstruct the equations (Kralemann et al., 2008). In particular, an asymmetric distribution of the observables could result in a false estimation of the effective connectivity between the network nodes.

NEW METHOD

In this work we built a new modelling part into DCM for phase coupling, and extended it with a distortion function that accommodates departures from purely sinusoidal oscillations.

RESULTS

By analysing numerically generated data sets with an asymmetric phase distribution, we demonstrated that the extended DCM for phase coupling with the additional modelling component, correctly estimates the coupling functions.

COMPARISON WITH EXISTING METHODS

The new method allows for different intrinsic frequencies among coupled neuronal populations and provides results that do not depend on the distribution of the observables.

CONCLUSIONS

The proposed method can be used to analyse effective connectivity between brain regions within and between different frequency bands, to characterize m:n phase coupling, and to unravel underlying mechanisms of the transient synchronization.

Estimating coupling strength between multivariate neural series with multivariate permutation conditional mutual information

Recently, coupling between groups of neurons or different brain regions has been widely studied to provide insights into underlying mechanisms of brain functions. To comprehensively understand the effect of such coupling, it is necessary to accurately extract the coupling strength information among multivariate neural signals from the whole brain. This study proposed a new method named multivariate permutation conditional mutual information (MPCMI) to quantitatively estimate the coupling strength of multivariate neural signals (MNS). The performance of the MPCMI method was validated on the simulated MNS generated by multi-channel neural mass model (MNMM). The coupling strength feature of simulated MNS extracted by MPCMI showed better performance compared with standard methods, such as permutation conditional mutual information (PCMI), multivariate Granger causality (MVGC), and Granger causality analysis (GCA). Furthermore, the MPCMI was applied to estimate the coupling strengths of two-channel resting-state electroencephalographic (rsEEG) signals from different brain regions of 19 patients with amnestic mild cognitive impairment (aMCI) with type 2 diabetes mellitus (T2DM) and 20 normal control (NC) with T2DM in Alpha1 and Alpha2 frequency bands. Empirical results showed that the MPCMI could effectively extract the coupling strength features that were significantly different between the aMCI and the NC. Hence, the proposed MPCMI method could be an effective estimate of coupling strengths of MNS, and might be a viable biomarker for clinical applications.

Frequency-based brain networks: From a multiplex framework to a full multilayer description

We explore how to study dynamical interactions between brain regions by using functional multilayer networks whose layers represent different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as (i) a multilayer network, in which all brain regions can interact with each other at different frequency bands; and as (ii) a multiplex network, in which interactions between different frequency bands are allowed only within each brain region and not between them. We study the second-smallest eigenvalue λ 2 of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as λ 2 has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases. We show that the heterogeneity of interlayer edge weights and, especially, the fraction of missing edges crucially modify the value of λ 2, and we illustrate our results with both synthetic network models and real data obtained from resting-state magnetoencephalography. Our work highlights the differences between using a multiplex approach and a full multilayer approach when studying frequency-based multilayer brain networks.

Optimization of relative parameters in transfer entropy estimation and application to corticomuscular coupling in humans

BACKGROUND

As a non-modeled information theoretical measure, the transfer entropy (TE) could be applied to quantitatively analyze the linear and nonlinear coupling characteristics between two observations. However, the parameters selection of TE (the parameters used in state space reconstruction and estimating Shannon entropy) has a serious influence on the accuracy of its results.

NEW METHOD

In this study, the hybrid particle swarm optimization (HPSO) was applied to improve the accuracy of TE by optimizing its parameters. In HPSO, the TE calculation and significant analysis were integrated into the fitness function, and the optimal parameters group within the parameter space could be automatically found through an iteration process.

RESULTS

The TE results computed under the parameters optimized by HPSO (HPSO-TE), was assessed with a numerical non-linear model, the neural mass model and the recorded electroencephalogram (EEG) and electromyogram (EMG) signals. Compared with TE, HPSO-TE could reduce the 'false positive' in non-linear model, and 'spurious coupling', i.e. two nonzero TEs for unidirectionally coupled systems, especially when coupling strength was weak. The robustness against noise and long time-delay was improved. Moreover, the experimental data analysis showed HPSO-TE revealed the dominant direction (EEG → EMG) in corticomuscular coupling, and had higher values than TE which showed the same dominant direction.

COMPARISON WITH EXISTING METHOD

The implication of HPSO improved the accuracy of TE in estimating the coupling strength and direction.

CONCLUSIONS

The efficiency of TE could be improved by HPSO for estimating coupling relationships, especially for weakly coupled, strong noisy and long time-delay series.

Role of Dimensionality in Predicting the Spontaneous Behavior of the Brain Using the Classical Ising Model and the Ising Model Implemented on a Structural Connectome

There is accumulating evidence that spontaneous fluctuations of the brain are sustained by a structural architecture of axonal fiber bundles. Various models have been used to investigate this structure–function relationship. In this work, we implemented the Ising model using the number of fibers between each pair of brain regions as input. The output of the Ising model simulations on a structural connectome was then compared with empirical functional connectivity data. A simpler two-dimensional classical Ising model was used as the baseline model for comparison purpose. Thermodynamic properties, such as the magnetic susceptibility and the specific heat, illustrated a phase transition from an ordered phase to a disordered phase at the critical temperature. Despite the differences between the two models, the lattice Ising model and the Ising model implemented on a structural connectome (the generalized Ising model) exhibited similar patterns of global properties. To study the behavior of the generalized Ising model around criticality, calculation of the dimensionality and critical exponents was performed for the first time, by introducing a new concept of distance based on structural connectivity. Same value inside the fitting error was found for the dimensionality in both models suggesting similar behavior of the models around criticality.

Simulating laminar neuroimaging data for a visual delayed match-to-sample task

Invasive electrophysiological and neuroanatomical studies in nonhuman mammalian experimental preparations have helped elucidate the lamina (layer) dependence of neural computations and interregional connections. Noninvasive functional neuroimaging can, in principle, resolve cortical laminae (layers), and thus provide insight into human neural computations and interregional connections. However human neuroimaging data are noisy and difficult to interpret; biologically realistic simulations can aid experimental interpretation by relating the neuroimaging data to simulated neural activity. We illustrate the potential of laminar neuroimaging by upgrading an existing large-scale, multiregion neural model that simulates a visual delayed match-to-sample (DMS) task. The new laminar-based neural unit incorporates spiny stellate, pyramidal, and inhibitory neural populations which are divided among supragranular, granular, and infragranular laminae (layers). We simulated neural activity which is translated into local field potential-like data used to simulate conventional and laminar fMRI activity. We implemented the laminar connectivity schemes proposed by Felleman and Van Essen (Cerebral Cortex, 1991) for interregional connections. The hemodynamic model that we employ is a modified version of one due to Heinzle et al. (Neuroimage, 2016) that incorporates the effects of draining veins. We show that the laminar version of the model replicates the findings of the existing model. The laminar model shows the finer structure in fMRI activity and functional connectivity. Laminar differences in the magnitude of neural activities are a prominent finding; these are also visible in the simulated fMRI. We illustrate differences between task and control conditions in the fMRI signal, and demonstrate differences in interregional laminar functional connectivity that reflect the underlying connectivity scheme. These results indicate that multi-layer computational models can aid in interpreting layer-specific fMRI, and suggest that increased use of laminar fMRI could provide unique and fundamental insights to human neuroscience.

Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model

Despite their biological plausibility, neural network models with asymmetric weights are rarely solved analytically, and closed-form solutions are available only in some limiting cases or in some mean-field approximations. We found exact analytical solutions of an asymmetric spin model of neural networks with arbitrary size without resorting to any approximation, and we comprehensively studied its dynamical and statistical properties. The network had discrete time evolution equations and binary firing rates, and it could be driven by noise with any distribution. We found analytical expressions of the conditional and stationary joint probability distributions of the membrane potentials and the firing rates. By manipulating the conditional probability distribution of the firing rates, we extend to stochastic networks the associating learning rule previously introduced by Personnaz and coworkers. The new learning rule allowed the safe storage, under the presence of noise, of point and cyclic attractors, with useful implications for content-addressable memories. Furthermore, we studied the bifurcation structure of the network dynamics in the zero-noise limit. We analytically derived examples of the codimension 1 and codimension 2 bifurcation diagrams of the network, which describe how the neuronal dynamics changes with the external stimuli. This showed that the network may undergo transitions among multistable regimes, oscillatory behavior elicited by asymmetric synaptic connections, and various forms of spontaneous symmetry breaking. We also calculated analytically groupwise correlations of neural activity in the network in the stationary regime. This revealed neuronal regimes where, statistically, the membrane potentials and the firing rates are either synchronous or asynchronous. Our results are valid for networks with any number of neurons, although our equations can be realistically solved only for small networks. For completeness, we also derived the network equations in the thermodynamic limit of infinite network size and we analytically studied their local bifurcations. All the analytical results were extensively validated by numerical simulations.

Multiple Kernel Learning Model for Relating Structural and Functional Connectivity in the Brain

A challenging problem in cognitive neuroscience is to relate the structural connectivity (SC) to the functional connectivity (FC) to better understand how large-scale network dynamics underlying human cognition emerges from the relatively fixed SC architecture. Recent modeling attempts point to the possibility of a single diffusion kernel giving a good estimate of the FC. We highlight the shortcomings of the single-diffusion-kernel model (SDK) and propose a multi-scale diffusion scheme. Our multi-scale model is formulated as a reaction-diffusion system giving rise to spatio-temporal patterns on a fixed topology. We hypothesize the presence of inter-regional co-activations (latent parameters) that combine diffusion kernels at multiple scales to characterize how FC could arise from SC. We formulated a multiple kernel learning (MKL) scheme to estimate the latent parameters from training data. Our model is analytically tractable and complex enough to capture the details of the underlying biological phenomena. The parameters learned by the MKL model lead to highly accurate predictions of subject-specific FCs from test datasets at a rate of 71%, surpassing the performance of the existing linear and non-linear models. We provide an example of how these latent parameters could be used to characterize age-specific reorganization in the brain structure and function.

The Effects of rTMS Combined with Motor Training on Functional Connectivity in Alpha Frequency Band

It has recently been reported that repetitive transcranial magnetic stimulation combined with motor training (rTMS-MT) could improve motor function in post-stroke patients. However, the effects of rTMS-MT on cortical function using functional connectivity and graph theoretical analysis remain unclear. Ten healthy subjects were recruited to receive rTMS immediately before application of MT. Low frequency rTMS was delivered to the dominant hemisphere and non-dominant hand performed MT over 14 days. The reaction time of Nine-Hole Peg Test and electroencephalography (EEG) in resting condition with eyes closed were recorded before and after rTMS-MT. Functional connectivity was assessed by phase synchronization index (PSI), and subsequently thresholded to construct undirected graphs in alpha frequency band (8–13 Hz). We found a significant decrease in reaction time after rTMS-MT. The functional connectivity between the parietal and frontal cortex, and the graph theory statistics of node degree and efficiency in the parietal cortex increased. Besides the functional connectivity between premotor and frontal cortex, the degree and efficiency of premotor cortex showed opposite results. In addition, the number of connections significantly increased within inter-hemispheres and inter-regions. In conclusion, this study could be helpful in our understanding of how rTMS-MT modulates brain activity. The methods and results in this study could be taken as reference in future studies of the effects of rTMS-MT in stroke patients.