A General Approach for Quantifying Nonlinear Connectivity in the Nervous System Based on Phase Coupling

Delay estimation for cortical-muscular interaction with wavelet coherence time lag

BACKGROUND

Cortico-muscular coherence (CMC) between the cerebral cortex and muscle activity is an effective tool for studying neural communication in the motor control system. To accurately evaluate the coherence between electroencephalogram (EEG) and electromyogram (EMG) signals, it is necessary to accurately calculate the time delay between physiological signals to ensure signal synchronization.

NEW METHOD

We proposed a new delay estimation method, named wavelet coherence time lag (WCTL) and the significant increase areas (SIA) index as a measure of the specific region enhancement effect of the magnitude squared coherence (MSC) image.

RESULTS

The grip strength level had a small effect on the information transmission time from the cortex to the muscles, while the transmission time from the cortex to different muscle channels was different for the same task. A positive correlation was found between the grip strength level and the SIA index on the β band of C3-B and the α and β bands of C3-FDS.

COMPARISON WITH EXISTING METHOD

The WCTL method was found to accurately calculate the delay time even when the number of repeated segments was low in a simple motor control model, and the results were more accurate than the rate of voxels change (RVC) and CMC with time lag (CMCTL) methods.

CONCLUSIONS

The WCTL is an effective method for detecting the transmission time of information between the cortex and muscles, laying the foundation for future rehabilitation treatment for stroke patients.

Bi-sinusoidal light stimulation reveals an enhanced response power and reduced phase coherence at the visual cortex in migraine

Introduction

Migraine is associated with enhanced visual sensitivity during and outside attacks. Processing of visual information is a highly non-linear process involving complex interactions across (sub)cortical networks. In this exploratory study, we combined electroencephalography with bi-sinusoidal light stimulation to assess non-linear features of visual processing in participants with migraine.

Methods

Twenty participants with migraine (10 with aura, 10 without aura) and ten non-headache controls were measured (outside attacks). Participants received bi-sinusoidal 13 + 23 Hz red light visual stimulation. Electroencephalography spectral power and multi-spectral phase coherence were compared between groups at the driving stimulation frequencies together with multiples and combinations of these frequencies (harmonic and intermodulation frequencies) caused by non-linearities.

Results

Only at the driving frequency of 13 Hz higher spectral power was found in migraine with aura participants compared with those with migraine without aura and controls. Differences in phase coherence were present for 2nd, 4th, and 5th-order non-linearities in those with migraine (migraine with and without aura) compared with controls. Bi-sinusoidal light stimulation revealed evident non-linearities in the brain's electroencephalography response up to the 5th order with reduced phase coherence for higher order interactions in interictal participants with migraine.

Discussion

Insight into interictal non-linear visual processing may help understand brain dynamics underlying migraine attack susceptibility. Future research is needed to determine the clinical value of the results.

Multi-phase locking value: A generalized method for determining instantaneous multi-frequency phase coupling

BACKGROUND

Many physical, biological and neural systems behave as coupled oscillators, with characteristic phase coupling across different frequencies. Methods such as n : m phase locking value (where two coupling frequencies are linked as: mf ₁ = nf ₂) and bi-phase locking value have previously been proposed to quantify phase coupling between two resonant frequencies (e.g. f, 2f/3) and across three frequencies (e.g. f ₁, f ₂, f ₁ + f ₂), respectively. However, the existing phase coupling metrics have their limitations and limited applications. They cannot be used to detect or quantify phase coupling across multiple frequencies (e.g. f ₁, f ₂, f ₃, f ₄, f ₁ + f ₂ + f ₃ - f ₄), or coupling that involves non-integer multiples of the frequencies (e.g. f ₁, f ₂, 2f ₁/3 + f ₂/3).

NEW METHODS

To address the gap, this paper proposes a generalized approach, named multi-phase locking value (M-PLV), for the quantification of various types of instantaneous multi-frequency phase coupling. Different from most instantaneous phase coupling metrics that measure the simultaneous phase coupling, the proposed M-PLV method also allows the detection of delayed phase coupling and the associated time lag between coupled oscillators.

RESULTS

The M-PLV has been tested on cases where synthetic coupled signals are generated using white Gaussian signals, and a system comprised of multiple coupled Rössler oscillators, as well as a human subject dataset. Results indicate that the M-PLV can provide a reliable estimation of the time window and frequency combination where the phase coupling is significant, as well as a precise determination of time lag in the case of delayed coupling. This method has the potential to become a powerful new tool for exploring phase coupling in complex nonlinear dynamic systems.

Correlation Evaluation of Functional Corticomuscular Coupling With Abnormal Muscle Synergy After Stroke

OBJECTIVE

While neuroplasticity and functional reorganization during motor recovery can be indirectly reflected and evaluated by functional corticomuscular coupling (fCMC), little work has been published regarding the cortical origin of abnormal muscle synergy and compensatory mechanism in the separation movement of stroke patients.

METHODS

In this study, we proposed to use extended partial directed coherence (ePDC) combined with an optimal spatial filtering approach to estimate fCMC in stroke patients and healthy controls, and further established muscle synergy model (MSM) to jointly explore the modulation mechanism between cortex and muscles.

RESULTS

Compared to healthy controls, stroke patients had significantly reduced coupling strength in both descending and ascending pathway. Moreover, the MSM were abnormal with high variability and low similarity in the separation stage of stroke patients. Further exploration of the positive relationship between fCMC characteristics and MSM parameters proved the possibility of using fCMC-MSM-based correlation indicator to evaluate abnormality of the cortical related synergy movement as well as the rehabilitation level of stroke patients.

CONCLUSION

We developed a computational procedure to evaluate the correlation between fCMC and MSM in stroke patients.

SIGNIFICANCE

This article provides a quantitative evaluation metrics based on fCMC to reveal the deficits during poststroke motor restoration and a promising approach to help patients correct abnormal movement habits, paving the way for neurophysiological assessment of neuromuscular control in conjunction with clinical scores.

Disrupted cortico-peripheral interactions in motor disorders

Motor disorders may arise from neurological damage or diseases at different levels of the hierarchical motor control system and side-loops. Altered cortico-peripheral interactions might be essential characteristics indicating motor dysfunctions. By integrating cortical and peripheral responses, top-down and bottom-up cortico-peripheral coupling measures could provide new insights into the motor control and recovery process. This review first discusses the neural bases of cortico-peripheral interactions, and corticomuscular coupling and corticokinematic coupling measures are addressed. Subsequently, methodological efforts are summarized to enhance the modeling reliability of neural coupling measures, both linear and nonlinear approaches are introduced. The latest progress, limitations, and future directions are discussed. Finally, we emphasize clinical applications of cortico-peripheral interactions in different motor disorders, including stroke, neurodegenerative diseases, tremor, and other motor-related disorders. The modified interaction patterns and potential changes following rehabilitation interventions are illustrated. Altered coupling strength, modified coupling directionality, and reorganized cortico-peripheral activation patterns are pivotal attributes after motor dysfunction. More robust coupling estimation methodologies and combination with other neurophysiological modalities might more efficiently shed light on motor control and recovery mechanisms. Future studies with large sample sizes might be necessary to determine the reliabilities of cortico-peripheral interaction measures in clinical practice.

A novel delay estimation method for improving corticomuscular coherence in continuous synchronization events

OBJECTIVE

While the corticomuscular coupling between motor cortex and muscle tissue has received considerable attention, which is typically quantitative measure to evaluate neural signals synchronization in the motor control system, little work has been published regarding the effect of underlying delay of two coupled physiological signals on coherence.

METHODS

In this study, we developed a novel delay estimation method, named rate of voxels change (RVC), detecting time delay in two coupled physiological signals. Based on RVC framework, delay compensation was used to adjust magnitude squared coherence (MSC) image. To illustrate the effectiveness of the RVC method, we compared the estimated delays and the adjusted MSC results based on RVC method and corticomuscular coherence with time lag (CMCTL) method.

RESULTS

The simulation results suggested that RVC method was not only superior to the CMCTL method in estimating different time delays, but also has better optimization effect on MSC image. The experimental results further confirmed that delay estimated by the proposed RVC method was more in line with the underlying physiology (controls: 22.8 ms vs patients: 34.5 ms). Meanwhile, RVC-based delay compensation could significantly optimize the MSC of specific regions.

SIGNIFICANCE

This study proved that RVC has remarkably higher reliability in detecting time delay between coupled neurophysiological signals, and the application of RVC was an improvement on the previous studies that mainly focused on biased MSC estimation.

Short-Term Impact of Sleep Apnea/Hypopnea on the Interaction Between Various Cortical Areas

INTRODUCTION

Sleep apnea/hypopnea syndrome (SAHS) can change brain structure and function. These alterations are related to respiratory event-induced abnormal sleep, however, how brain activity changes during these events is less well understood.

METHODS

To study information content and interaction among various cortical regions, we analyzed the variations of permutation entropy (PeEn) and symbolic transfer entropy (STE) of electroencephalography (EEG) activity during respiratory events. In this study, 57 patients with moderate SAHS were enrolled, including 2804 respiratory events. The events terminated with cortical arousal were independently researched.

RESULTS

PeEn and STE were lower during apnea/hypopnea, and most of the brain interaction was higher after apnea/hypopnea termination than that before apnea in N2 stage. As indicated by STE, the respiratory events also affected the stability of information transmission mode. In N1, N2, and rapid eye movement (REM) stages, the information flow direction was posterior-to-anterior, but the anterior-to-posterior increased relatively during apnea/hypopnea. The above EEG activity trends maintained in events with cortical arousal.

CONCLUSIONS

These results may be related to the intermittent hypoxia during apnea and the cortical response. Furthermore, increased frontal information outflow, which was related to the compensatory activation of frontal neurons, may associate with cognitive function.

Multiscale Transfer Spectral Entropy for Quantifying Corticomuscular Interaction

Corticomuscular coupling reflects nonlinear interactions and multi-layer neural information transmission between the motor cortex and effector muscle in the sensorimotor system. Transfer spectral entropy (TSE) method has been used to describe corticomuscular coupling within single scale. As an extension of TSE, multiscale transfer spectral entropy (MSTSE) is proposed in this paper to depict multi-layer of neural information transfer between two coupling signals. The reliability and effectiveness of MSTSE were verified on data generated by nonlinear numerical models and those of a force tracking task. Compared with TSE, MSTSE is more robust to the embedding dimension and performs optimally in the detection of the coupling properties. Further analysis of the physiological signals showed that the MSTSE provided more detailed band characteristics than the single scale TSE measurement. MSTSE indicates significant coupling scattered in alpha, beta and low gamma bands during the force tracking task. Besides, the coupling strength in the descending direction of the beta band was significantly higher than that in the ascending direction. This study constructs multi-scale coupling information to provide a new perspective for exploring corticomuscular interaction.

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a certain amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention.

Nonlinear Modeling of Cortical Responses to Mechanical Wrist Perturbations Using the NARMAX Method

OBJECTIVE

Nonlinear modeling of cortical responses (EEG) to wrist perturbations allows for the quantification of cortical sensorimotor function in healthy and neurologically impaired individuals. A common model structure reflecting key characteristics shared across healthy individuals may provide a reference for future clinical studies investigating abnormal cortical responses associated with sensorimotor impairments. Thus, the goal of our study is to identify this common model structure and therefore to build a nonlinear dynamic model of cortical responses, using nonlinear autoregressive-moving-average model with exogenous inputs (NARMAX).

METHODS

EEG was recorded from ten participants when receiving continuous wrist perturbations. A common model structure detection method was developed for identifying a common NARMAX model structure across all participants, with individualized parameter values. The results were compared to conventional subject-specific models.

RESULTS

The proposed method achieved 93.91% variance accounted for (VAF) when implementing a one-step-ahead prediction and around 50% VAF for a k-step ahead prediction (k = 3), without a substantial drop of VAF as compare to subject-specific models. The estimated common structure suggests that the measured cortical response is a mixed outcome of the nonlinear transformation of external inputs and local neuronal interactions or inherent neuronal dynamics at the cortex.

CONCLUSION

The proposed method well determined the common characteristics across subjects in the cortical responses to wrist perturbations.

SIGNIFICANCE

It provides new insights into the human sensorimotor nervous system in response to somatosensory inputs and paves the way for future translational studies on assessments of sensorimotor impairments using our modeling approach.

Estimating multiple latencies in the auditory system from auditory steady-state responses on a single EEG channel

The latency of the auditory steady-state response (ASSR) may provide valuable information regarding the integrity of the auditory system, as it could potentially reveal the presence of multiple intracerebral sources. To estimate multiple latencies from high-order ASSRs, we propose a novel two-stage procedure that consists of a nonparametric estimation method, called apparent latency from phase coherence (ALPC), followed by a heuristic sequential forward selection algorithm (SFS). Compared with existing methods, ALPC-SFS requires few prior assumptions, and is straightforward to implement for higher-order nonlinear responses to multi-cosine sound complexes with their initial phases set to zero. It systematically evaluates the nonlinear components of the ASSRs by estimating multiple latencies, automatically identifies involved ASSR components, and reports a latency consistency index. To verify the proposed method, we performed simulations for several scenarios: two nonlinear subsystems with different or overlapping outputs. We compared the results from our method with predictions from existing, parametric methods. We also recorded the EEG from ten normal-hearing adults by bilaterally presenting superimposed tones with four frequencies that evoke a unique set of ASSRs. From these ASSRs, two major latencies were found to be stable across subjects on repeated measurement days. The two latencies are dominated by low-frequency (LF) (near 40 Hz, at around 41-52 ms) and high-frequency (HF) (> 80 Hz, at around 21-27 ms) ASSR components. The frontal-central brain region showed longer latencies on LF components, but shorter latencies on HF components, when compared with temporal-lobe regions. In conclusion, the proposed nonparametric ALPC-SFS method, applied to zero-phase, multi-cosine sound complexes is more suitable for evaluating embedded nonlinear systems underlying ASSRs than existing methods. It may therefore be a promising objective measure for hearing performance and auditory cortex (dys)function.

Slowly activating outward membrane currents generate input-output sub-harmonic cross frequency coupling in neurons

A major challenge in understanding spike-time dependent information encoding in the neural system is the non-linear firing response to inputs of the individual neurons. Hence, quantitative exploration of the putative mechanisms of this non-linear behavior is fundamental to formulating the theory of information transfer in the neural system. The objective of this simulation study was to evaluate and quantify the effect of slowly activating outward membrane current, on the non-linearity in the output of a one-compartment Hodgkin-Huxley styled neuron. To evaluate this effect, the peak conductance of the slow potassium channel (g_K-slow) was varied from 0% to 200% of its normal value in steps of 33%. Both cross- and iso-frequency coupling between the input and the output of the simulated neuron was computed using a generalized coherence measure, i.e., n:m coherence. With increasing g_K-slow, the amount of sub-harmonic cross-frequency coupling, where the output frequencies (1-8 Hz) are lower than the input frequencies (15-35 Hz), increased progressively whereas no change in iso-frequency coupling was observed. Power spectral and phase-space analysis of the neuronal membrane voltage vs. slow potassium channel activation variable showed that the interaction of the slow channel dynamics with the fast membrane voltage dynamics generates the observed sub-harmonic coupling. This study provides quantitative insights into the role of an important membrane mechanism i.e. the slowly activating outward current in generating non-linearities in the output of a neuron.

Cross-frequency and iso-frequency estimation of functional corticomuscular coupling after stroke

Functional corticomuscular coupling (FCMC) between the brain and muscles has been used for motor function assessment after stroke. Two types, iso-frequency coupling (IFC) and cross-frequency coupling (CFC), are existed in sensory-motor system for healthy people. However, in stroke, only a few studies focused on IFC between electroencephalogram (EEG) and electromyogram (EMG) signals, and no CFC studies have been found. Considering the intrinsic complexity and rhythmicity of the biological system, we first used the wavelet package transformation (WPT) to decompose the EEG and EMG signals into several subsignals with different frequency bands, and then applied transfer entropy (TE) to analyze the IFC and CFC relationship between each pair-wise subsignal. In this study, eight stroke patients and eight healthy people were enrolled. Results showed that both IFC and CFC still existed in stroke patients (EEG → EMG: 1:1, 3:2, 2:1; EMG → EEG: 1:1, 2:1, 2:3, 3:1). Compared with the stroke-unaffected side and healthy controls, the stroke-affected side yielded lower alpha, beta and gamma synchronization (IFC: beta; CFC: alpha, beta and gamma). Further analysis indicated that stroke patients yielded no significant difference of the FCMC between EEG → EMG and EMG → EEG directions. Our study indicated that alpha and beta bands were essential to concentrating and maintaining the motor capacities, and provided a new insight in understanding the propagation and function in the sensory-motor system.

Assessing Neural Connectivity and Associated Time Delays of Muscle Responses to Continuous Position Perturbations

Both linear and nonlinear electromyographic (EMG) connectivity has been reported during the expression of stretch reflexes, though it is not clear whether they are generated by the same neural pathways. To answer this question, we aim to distinguish linear and nonlinear connectivity, as well as their delays in muscle responses, resulting from continuous elbow joint perturbations. We recorded EMG from Biceps Brachii muscle when eight able-bodied participants were performing a steady elbow flexion torque while simultaneously receiving a continuous position perturbation. Using a recently developed phase coupling metric, we estimated linear and nonlinear connectivity as well as their associated delays between Biceps EMG responses and perturbations. We found that the time delay for linear connectivity (24.5 ± 5.4 ms) is in the range of short-latency stretch reflex period (< 35 ms), while that for nonlinear connectivity (53.8 ± 3.2 ms) is in the range of long-latency stretch reflex period (40-70 ms). These results suggest that the estimated linear connectivity between EMG and perturbations is very likely generated by the mono-synaptic spinal stretch reflex loop, while the nonlinear connectivity may be associated with multi-synaptic supraspinal stretch reflex loops. As such, this study provides new evidence of the nature of neural connectivity related to the stretch reflex.

Quantifying Altered Neural Connectivity of the Stretch Reflex in Chronic Hemiparetic Stroke

Post-stroke flexion synergy limits arm/hand function and is also linked to hyperactive stretch reflexes or spasticity. It is implicated in the increased role of indirect motor pathways following damage to direct corticospinal projections. We hypothesized that this maladaptive neuroplasticity also affects stretch reflexes. Specifically, multi-synaptic interactions in indirect motor pathways may increase nonlinear neural connectivity and time lag between stretch and reflex muscle response. Continuous position perturbations were applied to the elbow joint when eleven participants with stroke generated two levels of shoulder abduction (SABD) torques with their paretic arm to induce synergy-related spasticity. Likewise, the perturbations were applied to eleven control subjects while performing SABD and elbow flexion levels matching the synergy torques in stroke. We quantified linear and non-linear connectivity and the corresponding time lags between perturbations and muscle activity. Enhanced nonlinear connectivity with a prolonged time lag was found in stroke as compared to controls. Non-linear connectivity and time lag also increased with the expression of the flexion synergy, as induced by greater SABD load levels, in stroke. This study provides new evidence of changes in neural connectivity and long-latency time lag in the stretch reflex response post-stroke. The results suggest the contribution of indirect motor pathways to synergy-related spasticity.

Quantifying the Nonlinear Interaction in the Nervous System Based on Phase-Locked Amplitude Relationship

OBJECTIVE

This paper introduces the Cross-frequency Amplitude Transfer Function (CATF), a model-free method for quantifying nonlinear stimulus-response interaction based on phase-locked amplitude relationship.

METHOD

The CATF estimates the amplitude transfer from input frequencies at stimulation signal to their harmonics/intermodulation at the response signal. We first verified the performance of CATF in simulation tests with systems containing a static nonlinear function and a linear dynamic, i.e., Hammerstein and Wiener systems. We then applied the CATF to investigate the second-order nonlinear amplitude transfer in the human proprioceptive system from the periphery to the cortex.

RESULT

The simulation demonstrated that the CATF is a general method, which can well quantify nonlinear stimulus-response amplitude transfer for different orders of nonlinearity in Wiener or Hammerstein system configurations. Applied to the human proprioceptive system, we found a complicated nonlinear system behavior with substantial amplitude transfer from the periphery stimulation to cortical response signals in the alpha band. This complicated system behavior may be associated with the nonlinear behavior of the muscle spindle and the dynamic interaction in the thalamocortical radiation.

CONCLUSION

This paper provides a new tool to identify nonlinear interaction in the nervous system.

SIGNIFICANCE

The results provide novel insight of nonlinear dynamics in the human proprioceptive system.

Neurologically Motivated Coupling Functions in Models of Motor Coordination

We present an analysis of two Haken-Kelso-Bunz (HKB) oscillators coupled by a neurologically motivated function. We study the effect of time delay and weighted self-feedback and mutual feedback on the synchronization behavior of the model. We focus on identifying parameter regimes supporting experimentally observed decrease in oscillation amplitude and loss of anti-phase stability that has inspired the development of the HKB model. We show that a combination of cross-talk and nonlinearity in the coupling, along with physiologically relevant time delay, is able to quantitatively account for both drop in oscillation amplitude and loss of anti-phase stability in a frequency dependent manner. Furthermore, we demonstrate that the transition between discrete and rhythmic movements could be captured by this model. To this end, we carry out theoretical and numerical analysis of the emergence of in-phase and anti-phase oscillations.

From intermodulation components to visual perception and cognition-a review

Perception results from complex interactions among sensory and cognitive processes across hierarchical levels in the brain. Intermodulation (IM) components, used in frequency tagging neuroimaging designs, have emerged as a promising direct measure of such neural interactions. IMs have initially been used in electroencephalography (EEG) to investigate low-level visual processing. In a more recent trend, IMs in EEG and other neuroimaging methods are being used to shed light on mechanisms of mid- and high-level perceptual processes, including the involvement of cognitive functions such as attention and expectation. Here, we provide an account of various mechanisms that may give rise to IMs in neuroimaging data, and what these IMs may look like. We discuss methodologies that can be implemented for different uses of IMs and we demonstrate how IMs can provide insights into the existence, the degree and the type of neural integration mechanisms at hand. We then review a range of recent studies exploiting IMs in visual perception research, placing an emphasis on high-level vision and the influence of awareness and cognition on visual processing. We conclude by suggesting future directions that can enhance the benefits of IM-methodology in perception research.

Identification of Hidden Sources by Estimating Instantaneous Causality in High-Dimensional Biomedical Time Series

The study of connectivity patterns of a system’s variables, such as multi-channel electroencephalograms (EEG), is of utmost importance towards a better understanding of its internal evolutionary mechanisms. Here, the problem of estimating the connectivity network from multivariate time series in the presence of prominent unobserved variables is addressed. The causality measure of partial mutual information from mixed embedding (PMIME), designed to estimate direct lag-causal effects in the presence of many observed variables, is adapted to estimate also zero-lag effects, the so-called instantaneous causality. We term the proposed advanced method, PMIME0. The estimation of instantaneous causality by PMIME0 is a signature of the presence of hidden source in the observed system, as demonstrated analytically in a toy model. It is further demonstrated that the PMIME0 identifies the true instantaneous with great accuracy in a variety of high-dimensional dynamical systems. The method is applied to EEG data with epileptiform discharges (EDs), and the results imply a strong impact of unobserved confounders during the EDs. This finding comes as a possible explanation for the increased levels of causality during epileptic seizures estimated by some measures affected by the presence of a common source.

Expectation and attention increase the integration of top-down and bottom-up signals in perception through different pathways

Perception likely results from the interplay between sensory information and top-down signals. In this electroencephalography (EEG) study, we utilised the hierarchical frequency tagging (HFT) method to examine how such integration is modulated by expectation and attention. Using intermodulation (IM) components as a measure of nonlinear signal integration, we show in three different experiments that both expectation and attention enhance integration between top-down and bottom-up signals. Based on a multispectral phase coherence (MSPC) measure, we present two direct physiological measures to demonstrate the distinct yet related mechanisms of expectation and attention, which would not have been possible using other amplitude-based measures. Our results link expectation to the modulation of descending signals and to the integration of top-down and bottom-up information at lower levels of the visual hierarchy. Meanwhile, the results link attention to the modulation of ascending signals and to the integration of information at higher levels of the visual hierarchy. These results are consistent with the predictive coding account of perception.

Empirical Functional PCA for 3D Image Feature Extraction Through Fractal Sampling

Medical image classification is currently a challenging task that can be used to aid the diagnosis of different brain diseases. Thus, exploratory and discriminative analysis techniques aiming to obtain representative features from the images play a decisive role in the design of effective Computer Aided Diagnosis (CAD) systems, which is especially important in the early diagnosis of dementia. In this work, we present a technique that allows using specific time series analysis techniques with 3D images. This is achieved by sampling the image using a fractal-based method which preserves the spatial relationship among voxels. In addition, a method called Empirical functional PCA (EfPCA) is presented, which combines Empirical Mode Decomposition (EMD) with functional PCA to express an image in the space spanned by a basis of empirical functions, instead of using components computed by a predefined basis as in Fourier or Wavelet analysis. The devised technique has been used to classify images from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) and the Parkinson Progression Markers Initiative (PPMI), achieving accuracies up to 93% and 92% differential diagnosis tasks (AD versus controls and PD versus Controls, respectively). The results obtained validate the method, proving that the information retrieved by our methodology is significantly linked to the diseases.

A Novel Approach for Modeling Neural Responses to Joint Perturbations Using the NARMAX Method and a Hierarchical Neural Network

The human nervous system is an ensemble of connected neuronal networks. Modeling and system identification of the human nervous system helps us understand how the brain processes sensory input and controls responses at the systems level. This study aims to propose an advanced approach based on a hierarchical neural network and non-linear system identification method to model neural activity in the nervous system in response to an external somatosensory input. The proposed approach incorporates basic concepts of Non-linear AutoRegressive Moving Average Model with eXogenous input (NARMAX) and neural network to acknowledge non-linear closed-loop neural interactions. Different from the commonly used polynomial NARMAX method, the proposed approach replaced the polynomial non-linear terms with a hierarchical neural network. The hierarchical neural network is built based on known neuroanatomical connections and corresponding transmission delays in neural pathways. The proposed method is applied to an experimental dataset, where cortical activities from ten young able-bodied individuals are extracted from electroencephalographic signals while applying mechanical perturbations to their wrist joint. The results yielded by the proposed method were compared with those obtained by the polynomial NARMAX and Volterra methods, evaluated by the variance accounted for (VAF). Both the proposed and polynomial NARMAX methods yielded much better modeling results than the Volterra model. Furthermore, the proposed method modeled cortical responded with a mean VAF of 69.35% for a three-step ahead prediction, which is significantly better than the VAF from a polynomial NARMAX model (mean VAF 47.09%). This study provides a novel approach for precise modeling of cortical responses to sensory input. The results indicate that the incorporation of knowledge of neuroanatomical connections in building a realistic model greatly improves the performance of system identification of the human nervous system.

Principal States of Dynamic Functional Connectivity Reveal the Link Between Resting-State and Task-State Brain: An fMRI Study

Task-related reorganization of functional connectivity (FC) has been widely investigated. Under classic static FC analysis, brain networks under task and rest have been demonstrated a general similarity. However, brain activity and cognitive process are believed to be dynamic and adaptive. Since static FC inherently ignores the distinct temporal patterns between rest and task, dynamic FC may be more a suitable technique to characterize the brain’s dynamic and adaptive activities. In this study, we adopted [Formula: see text]-means clustering to investigate task-related spatiotemporal reorganization of dynamic brain networks and hypothesized that dynamic FC would be able to reveal the link between resting-state and task-state brain organization, including broadly similar spatial patterns but distinct temporal patterns. In order to test this hypothesis, this study examined the dynamic FC in default-mode network (DMN) and motor-related network (MN) using Blood-Oxygenation-Level-Dependent (BOLD)-fMRI data from 26 healthy subjects during rest (REST) and a hand closing-and-opening (HCO) task. Two principal FC states in REST and one principal FC state in HCO were identified. The first principal FC state in REST was found similar to that in HCO, which appeared to represent intrinsic network architecture and validated the broadly similar spatial patterns between REST and HCO. However, the second FC principal state in REST with much shorter “dwell time” implied the transient functional relationship between DMN and MN during REST. In addition, a more frequent shifting between two principal FC states indicated that brain network dynamically maintained a “default mode” in the motor system during REST, whereas the presence of a single principal FC state and reduced FC variability implied a more temporally stable connectivity during HCO, validating the distinct temporal patterns between REST and HCO. Our results further demonstrated that dynamic FC analysis could offer unique insights in understanding how the brain reorganizes itself during rest and task states, and the ways in which the brain adaptively responds to the cognitive requirements of tasks.

Functional Semi-Blind Source Separation Identifies Primary Motor Area Without Active Motor Execution

High time resolution techniques are crucial for investigating the brain in action. Here, we propose a method to identify a section of the upper-limb motor area representation (FS_M1) by means of electroencephalographic (EEG) signals recorded during a completely passive condition (FS_M1bySS). We delivered a galvanic stimulation to the median nerve and we applied to EEG the semi-Blind Source Separation (s-BSS) algorithm named Functional Source Separation (FSS). In order to prove that FS_M1bySS is part of FS_M1, we also collected EEG in a motor condition, i.e. during a voluntary movement task (isometric handgrip) and in a rest condition, i.e. at rest with eyes open and closed. In motor condition, we show that the cortico-muscular coherence (CMC) of FS_M1bySS does not differ from FS_ M1 CMC (0.04 for both sources). Moreover, we show that the FS_M1bySS’s ongoing whole band activity during Motor and both rest conditions displays high mutual information and time correlation with FS_M1 (above 0.900 and 0.800, respectively) whereas much smaller ones with the primary somatosensory cortex [Formula: see text] (about 0.300 and 0.500, [Formula: see text]). FS_M1bySS as a marker of the upper-limb FS_M1 representation obtainable without the execution of an active motor task is a great achievement of the FSS algorithm, relevant in most experimental, neurological and psychiatric protocols.

From Structure to Activity: Using Centrality Measures to Predict Neuronal Activity

It is clear that the topological structure of a neural network somehow determines the activity of the neurons within it. In the present work, we ask to what extent it is possible to examine the structural features of a network and learn something about its activity? Specifically, we consider how the centrality (the importance of a node in a network) of a neuron correlates with its firing rate. To investigate, we apply an array of centrality measures, including In-Degree, Closeness, Betweenness, Eigenvector, Katz, PageRank, Hyperlink-Induced Topic Search (HITS) and NeuronRank to Leaky-Integrate and Fire neural networks with different connectivity schemes. We find that Katz centrality is the best predictor of firing rate given the network structure, with almost perfect correlation in all cases studied, which include purely excitatory and excitatory–inhibitory networks, with either homogeneous connections or a small-world structure. We identify the properties of a network which will cause this correlation to hold. We argue that the reason Katz centrality correlates so highly with neuronal activity compared to other centrality measures is because it nicely captures disinhibition in neural networks. In addition, we argue that these theoretical findings are applicable to neuroscientists who apply centrality measures to functional brain networks, as well as offer a neurophysiological justification to high level cognitive models which use certain centrality measures.

Unveiling neural coupling within the sensorimotor system: directionality and nonlinearity

Neural coupling between the central nervous system and the periphery is essential for the neural control of movement. Corticomuscular coherence is a popular linear technique to assess synchronised oscillatory activity in the sensorimotor system. This oscillatory coupling originates from ascending somatosensory feedback and descending motor commands. However, corticomuscular coherence cannot separate this bidirectionality. Furthermore, the sensorimotor system is nonlinear, resulting in cross‐frequency coupling. Cross‐frequency oscillations cannot be assessed nor exploited by linear measures. Here, we emphasise the need of novel coupling measures, which provide directionality and acknowledge nonlinearity, to unveil neural coupling in the sensorimotor system. We highlight recent advances in the field and argue that assessing directionality and nonlinearity of neural coupling will break new ground in the study of the control of movement in healthy and neurologically impaired individuals.

Deep convolutional neural network for the automated detection and diagnosis of seizure using EEG signals

An encephalogram (EEG) is a commonly used ancillary test to aide in the diagnosis of epilepsy. The EEG signal contains information about the electrical activity of the brain. Traditionally, neurologists employ direct visual inspection to identify epileptiform abnormalities. This technique can be time-consuming, limited by technical artifact, provides variable results secondary to reader expertise level, and is limited in identifying abnormalities. Therefore, it is essential to develop a computer-aided diagnosis (CAD) system to automatically distinguish the class of these EEG signals using machine learning techniques. This is the first study to employ the convolutional neural network (CNN) for analysis of EEG signals. In this work, a 13-layer deep convolutional neural network (CNN) algorithm is implemented to detect normal, preictal, and seizure classes. The proposed technique achieved an accuracy, specificity, and sensitivity of 88.67%, 90.00% and 95.00%, respectively.

Modeling the Nonlinear Cortical Response in EEG Evoked by Wrist Joint Manipulation

Joint manipulation elicits a response from the sensors in the periphery which, via the spinal cord, arrives in the cortex. The average evoked cortical response recorded using electroencephalography was shown to be highly nonlinear; a linear model can only explain 10% of the variance of the evoked response, and over 80% of the response is generated by nonlinear behavior. The goal of this paper is to obtain a nonparametric nonlinear dynamic model, which can consistently explain the recorded cortical response requiring little a priori assumptions about model structure. Wrist joint manipulation was applied in ten healthy participants during which their cortical activity was recorded and modeled using a truncated Volterra series. The obtained models could explain 46% of the variance of the evoked cortical response, thereby demonstrating the relevance of nonlinear modeling. The high similarity of the obtained models across participants indicates that the models reveal common characteristics of the underlying system. The models show predominantly high-pass behavior, which suggests that velocity-related information originating from the muscle spindles governs the cortical response. In conclusion, the nonlinear modeling approach using a truncated Volterra series with regularization, provides a quantitative way of investigating the sensorimotor system, offering insight into the underlying physiology.

Dynamics of Epileptiform Discharges Induced by Transcranial Magnetic Stimulation in Genetic Generalized Epilepsy

Objective: In patients with Genetic Generalized Epilepsy (GGE), transcranial magnetic stimulation (TMS) can induce epileptiform discharges (EDs) of varying duration. We hypothesized that (a) the ED duration is determined by the dynamic states of critical network nodes (brain areas) at the early post-TMS period, and (b) brain connectivity changes before, during and after the ED, as well as within the ED. Methods: EEG recordings from two GGE patients were analyzed. For hypothesis (a), the characteristics of the brain dynamics at the early ED stage are measured with univariate and multivariate EEG measures and the dependence of the ED duration on these measures is evaluated. For hypothesis (b), effective connectivity measures are combined with network indices so as to quantify the brain network characteristics and identify changes in brain connectivity. Results: A number of measures combined with specific channels computed on the first EEG segment post-TMS correlate with the ED duration. In addition, brain connectivity is altered from pre-ED to ED and post-ED and statistically significant changes were also detected across stages within the ED. Conclusion: ED duration is not purely stochastic, but depends on the dynamics of the post-TMS brain state. The brain network dynamics is significantly altered in the course of EDs.

Decreased variability of dynamic phase synchronization in brain networks during hand movement

Dynamic functional connectivity analysis, a rapidly growing method, has been demonstrated to provide new spatiotemporal information about how brain motor network would reorganize from rest to motor tasks. Phase synchronization analysis, which has been widely applied in EEG-based FC analysis, is a promising alternative method in dynamic FC analysis. In this study, fMRI data were recorded from 28 healthy volunteers when they are resting and performing hand closing and opening (HCO) task. Dynamic FC was estimated by phase synchronization analysis. In addition, functional connectivity variability (FCV) was compared between rest and HCO to investigate the modulation induced by motor task on dynamics of motor-related FC and network. Results showed that the FCVs in network-of-interest, including default-mode network and motor network, decreased during HCO comparing with rest. Our results demonstrated that the unconstrained mental activities, which resulted in high FCV during rest, would focus on motor execution during HCO and thus led to decreased FCV during HCO.

Quantification of task-dependent cortical activation evoked by robotic continuous wrist joint manipulation in chronic hemiparetic stroke

Background

Cortical damage after stroke can drastically impair sensory and motor function of the upper limb, affecting the execution of activities of daily living and quality of life. Motor impairment after stroke has been thoroughly studied, however sensory impairment and its relation to movement control has received less attention. Integrity of the somatosensory system is essential for feedback control of human movement, and compromised integrity due to stroke has been linked to sensory impairment.

Methods

The goal of this study is to assess the integrity of the somatosensory system in individuals with chronic hemiparetic stroke with different levels of sensory impairment, through a combination of robotic joint manipulation and high-density electroencephalogram (EEG). A robotic wrist manipulator applied continuous periodic disturbances to the affected limb, providing somatosensory (proprioceptive and tactile) stimulation while challenging task execution. The integrity of the somatosensory system was evaluated during passive and active tasks, defined as ‘relaxed wrist’ and ‘maintaining 20% maximum wrist flexion’, respectively. The evoked cortical responses in the EEG were quantified using the power in the averaged responses and their signal-to-noise ratio.

Results

Thirty individuals with chronic hemiparetic stroke and ten unimpaired individuals without stroke participated in this study. Participants with stroke were classified as having severe, mild, or no sensory impairment, based on the Erasmus modification of the Nottingham Sensory Assessment. Under passive conditions, wrist manipulation resulted in contralateral cortical responses in unimpaired and chronic stroke participants with mild and no sensory impairment. In participants with severe sensory impairment the cortical responses were strongly reduced in amplitude, which related to anatomical damage. Under active conditions, participants with mild sensory impairment showed reduced responses compared to the passive condition, whereas unimpaired and chronic stroke participants without sensory impairment did not show this reduction.

Conclusions

Robotic continuous joint manipulation allows studying somatosensory cortical evoked responses during the execution of meaningful upper limb control tasks. Using such an approach it is possible to quantitatively assess the integrity of sensory pathways; in the context of movement control this provides additional information required to develop more effective neurorehabilitation therapies.

Graph Theory and Brain Connectivity in Alzheimer's Disease

This article presents a review of recent advances in neuroscience research in the specific area of brain connectivity as a potential biomarker of Alzheimer's disease with a focus on the application of graph theory. The review will begin with a brief overview of connectivity and graph theory. Then resent advances in connectivity as a biomarker for Alzheimer's disease will be presented and analyzed.

Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion

Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15–35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.

Two step transfer entropy - An estimator of delayed directional couplings between multivariate EEG time series

Quantifying delayed directional couplings between electroencephalographic (EEG) time series requires an efficient method of causal network inference. This is especially due to the limited knowledge about the underlying dynamics of the brain activity. Recent methods based on information theoretic measures such as Transfer Entropy (TE) made significant progress on this issue by providing a model-free framework for causality detection. However, TE estimation from observed data is not a trivial task, especially when the number of variables is large which is the case in a highly complex system like human brain. Here we propose a computationally efficient procedure for TE estimation based on using sets of the Most Informative Variables that effectively contribute to resolving the uncertainty of the destination. In the first step of this method, some conditioning sets are determined through a nonlinear state space reconstruction; then in the second step, optimal estimation of TE is done based on these sets. Validation of the proposed method using synthetic data and neurophysiological signals demonstrates computational efficiency in quantifying delayed directional couplings compared with the common TE analysis.

Nonlinear Connectivity in the Human Stretch Reflex Assessed by Cross-Frequency Phase Coupling

Communication between neuronal populations is facilitated by synchronization of their oscillatory activity. Although nonlinearity has been observed in the sensorimotor system, its nonlinear connectivity has not been widely investigated yet. This study investigates nonlinear connectivity during the human stretch reflex based on neuronal synchronization. Healthy participants generated isotonic wrist flexion while receiving a periodic mechanical perturbation to the wrist. Using a novel cross-frequency phase coupling metric, we estimate directional nonlinear connectivity, including time delay, from the perturbation to brain and to muscle, as well as from brain to muscle. Nonlinear phase coupling is significantly stronger from the perturbation to the muscle than to the brain, with a shorter time delay. The time delay from the perturbation to the muscle is 33 ms, similar to the reported latency of the spinal stretch reflex at the wrist. Source localization of nonlinear phase coupling from the brain to the muscle suggests activity originating from the motor cortex, although its effect on the stretch reflex is weak. As such nonlinear phase coupling between the perturbation and muscle activity is dominated by the spinal reflex loop. This study provides new evidence of nonlinear neuronal synchronization in the stretch reflex at the wrist joint with respect to spinal and transcortical loops.