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.

Corticomotor Plasticity Underlying Priming Effects of Motor Imagery on Force Performance

The neurophysiological processes underlying the priming effects of motor imagery (MI) on force performance remain poorly understood. Here, we tested whether the priming effects of embedded MI practice involved short-term changes in corticomotor connectivity. In a within-subjects counterbalanced experimental design, participants (n = 20) underwent a series of experimental sessions consisting of successive maximal isometric contractions of elbow flexor muscles. During inter-trial rest periods, we administered MI, action observation (AO), and a control passive recovery condition. We collected electromyograms (EMG) from both agonists and antagonists of the force task, in addition to electroencephalographic (EEG) brain potentials during force trials. Force output was higher during MI compared to AO and control conditions (both p < 0.01), although fatigability was similar across experimental conditions. We also found a weaker relationship between triceps brachii activation and force output during MI and AO compared to the control condition. Imaginary coherence topographies of alpha (8−12 Hz) oscillations revealed increased connectivity between EEG sensors from central scalp regions and EMG signals from agonists during MI, compared to AO and control. Present results suggest that the priming effects of MI on force performance are mediated by a more efficient cortical drive to motor units yielding reduced agonist/antagonist coactivation.

Investigation of Corticomuscular Functional Coupling during Hand Movements Using Vine Copula

Corticomuscular functional coupling reflects the neuronal communication between cortical oscillations and muscle activity. Although the motor cortex is significantly involved in complex motor tasks, there is still no detailed understanding of the cortical contribution during such tasks. In this paper, we first propose a vine copula model to describe corticomuscular functional coupling and we construct the brain muscle function network. First, we recorded surface electromyography (sEMG) and electroencephalography (EEG) signals corresponding to the hand open, hand close, wrist flexion, and wrist extension motions of 12 participants during the initial experiments. The pre-processed signals were translated into the marginal density functions of different channels through the generalized autoregressive conditional heteroscedasticity model. Subsequently, we calculated the Kendall rank correlation coefficient, and used the R-vine model to decompose the multi-dimensional marginal density function into two-dimensional copula coefficient to determine the structure of the R-vine. Finally, we used the normalized adjacency matrix to structure the corticomuscular network for each hand motion considered. Based on the adjacency matrix, we found that the Kendall rank correlation coefficient between EEG and EMG was low. Moreover, a significant difference was observed in the correlation between the C3 and EMG signals for the different hand-motion activities. We also observed two core nodes in the networks corresponding to the four activities when the vine copula model was applied. Moreover, there was a large difference in the connections of the network models corresponding to the different hand-motion activities. Therefore, we believe that our approach is sufficiently accurate in identifying and classifying motor tasks.

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.

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.

Analysis of corticomuscular connectivity during walking using vine copula

Corticomuscular connectivity plays an important role in the neural control of human motion. This study recorded electroencephalography (EEG) and surface electromyography (sEMG) signals from subjects performing specific tasks (walking on level ground and on stairs) based on metronome instructions. This study presents a novel method based on vine copula to jointly model EEG and sEMG signals. The advantage of vine copula is its applicability in the construction of dependency structures to describe the connectivity between the cortex and muscles during different movements. A corticomuscular function network was also constructed by analyzing the dependence of each channel sample. The successfully constructed network shows information transmission between different divisions of the cortex, between muscles, and between the cortex and muscles when the body performs lower limb movements. Additionally, it highlights the potential of the vine copula concept used in this study, indicating that significant changes in the corticomuscular network under lower limb movements can be quantified by effective connectivity values.

Identifying bidirectional total and non-linear information flow in functional corticomuscular coupling during a dorsiflexion task: a pilot study

Background

The key challenge to constructing functional corticomuscular coupling (FCMC) is to accurately identify the direction and strength of the information flow between scalp electroencephalography (EEG) and surface electromyography (SEMG). Traditional TE and TDMI methods have difficulty in identifying the information interaction for short time series as they tend to rely on long and stable data, so we propose a time-delayed maximal information coefficient (TDMIC) method. With this method, we aim to investigate the directional specificity of bidirectional total and nonlinear information flow on FCMC, and to explore the neural mechanisms underlying motor dysfunction in stroke patients.

Methods

We introduced a time-delayed parameter in the maximal information coefficient to capture the direction of information interaction between two time series. We employed the linear and non-linear system model based on short data to verify the validity of our algorithm. We then used the TDMIC method to study the characteristics of total and nonlinear information flow in FCMC during a dorsiflexion task for healthy controls and stroke patients.

Results

The simulation results showed that the TDMIC method can better detect the direction of information interaction compared with TE and TDMI methods. For healthy controls, the beta band (14–30 Hz) had higher information flow in FCMC than the gamma band (31–45 Hz). Furthermore, the beta-band total and nonlinear information flow in the descending direction (EEG to EMG) was significantly higher than that in the ascending direction (EMG to EEG), whereas in the gamma band the ascending direction had significantly higher information flow than the descending direction. Additionally, we found that the strong bidirectional information flow mainly acted on Cz, C3, CP3, P3 and CPz. Compared to controls, both the beta-and gamma-band bidirectional total and nonlinear information flows of the stroke group were significantly weaker. There is no significant difference in the direction of beta- and gamma-band information flow in stroke group.

Conclusions

The proposed method could effectively identify the information interaction between short time series. According to our experiment, the beta band mainly passes downward motor control information while the gamma band features upward sensory feedback information delivery. Our observation demonstrate that the center and contralateral sensorimotor cortex play a major role in lower limb motor control. The study further demonstrates that brain damage caused by stroke disrupts the bidirectional information interaction between cortex and effector muscles in the sensorimotor system, leading to motor dysfunction.

EEG based functional connectivity analysis of human pain empathy towards humans and robots

Humans can show emotional reactions toward humanoid robots, such as empathy. Previous neuroimaging studies have indicated that neural responses of empathy for others' pain are modulated by an early automatic emotional sharing and a late controlled cognitive evaluation process. Recent studies about pain empathy for robots found humans present similar empathy process towards humanoid robots under painful stimuli as well as to humans. However, the whole-brain functional connectivity and the spatial dynamics of neural activities underlying empathic processes are still unknown. In the present study, the functional connectivity was investigated for ERPs recorded from 18 healthy adults who were presented with pictures of human hand and robot hand under painful and non-painful situations. Functional brain networks for both early and late empathy responses were constructed and a new parameter, empathy index (EI), was proposed to represent the empathy ability of humans quantitatively. We found that the mutual dependences between early ERP components was significantly decreased, but for the late components, there were no significant changes. The mutual dependences for human hand stimuli were larger than to robot hand stimuli for early components, but not for late components. The connectivity weights for early components were larger than late components. EI value shows significant difference between painful and non-painful stimuli, indicating it is a good indicator to represent the empathy of humans. This study enriches our understanding of the neurological mechanisms implicated in human empathy, and provides evidence of functional connectivity for both early and late responses of pain empathy towards humans and robots.

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.

Predicting Improved Daily Use of the More Affected Arm Poststroke Following Constraint-Induced Movement Therapy

BACKGROUND

Constraint-induced movement therapy (CI therapy) produces, on average, large and clinically meaningful improvements in the daily use of a more affected upper extremity in individuals with hemiparesis. However, individual responses vary widely.

OBJECTIVE

The study objective was to investigate the extent to which individual characteristics before treatment predict improved use of the more affected arm following CI therapy.

DESIGN

This study was a retrospective analysis of 47 people who had chronic (> 6 months) mild to moderate upper extremity hemiparesis and were consecutively enrolled in 2 CI therapy randomized controlled trials.

METHODS

An enhanced probabilistic neural network model predicted whether individuals showed a low, medium, or high response to CI therapy, as measured with the Motor Activity Log, on the basis of the following baseline assessments: Wolf Motor Function Test, Semmes-Weinstein Monofilament Test of touch threshold, Motor Activity Log, and Montreal Cognitive Assessment. Then, a neural dynamic classification algorithm was applied to improve prognostic accuracy using the most accurate combination obtained in the previous step.

RESULTS

Motor ability and tactile sense predicted improvement in arm use for daily activities following intensive upper extremity rehabilitation with an accuracy of nearly 100%. Complex patterns of interaction among these predictors were observed.

LIMITATIONS

The fact that this study was a retrospective analysis with a moderate sample size was a limitation.

CONCLUSIONS

Advanced machine learning/classification algorithms produce more accurate personalized predictions of rehabilitation outcomes than commonly used general linear models.

A Method for Suppressing Electrical Stimulation Artifacts from Electromyography

When surface electromyography (EMG) signal is used in a real-time functional electrical stimulation (FES) system for feedback control, the artifact from electrical stimulation is a key challenge for EMG signal processing. To address this challenge, this study proposes a novel method to suppress stimulation artifacts in the EMG-driven closed-loop FES system. The proposed method is inspired by an experimental study that compares artifacts generated by electrical stimulations with different current intensities. It is found that (1) spikes of stimulation artifacts are susceptible to the current intensity and (2) tailing components are similar under different current intensities. Based on these observations, the proposed method combines the blanking and template subtracting strategies for suppressing stimulation artifact. The length of blanking window for suppressing the stimulation spike is adaptively determined by a spike detection algorithm and the first-order derivative analysis of signal. An autoregressive model is used to estimate the tailing part of stimulation artifact, which is an adaptive template for subtracting the artifact. The proposed method is evaluated on both semi-synthetic and experimental datasets. Verified on the semi-synthetic dataset, the proposed method achieves better performance than the classic blanking method. Validated on the experimental dataset, the proposed method substantially decreases the power of stimulation artifact in the EMG. These results indicate that the proposed method can effectively suppress the stimulation artifact while retains the useful EMG signal for an EMG-driven FES system.

Corticomuscular Coherence for Upper Arm Flexor and Extensor Muscles During Isometric Exercise and Cyclically Isokinetic Movement

Cortical-muscular functional coupling reflects the interaction between the cerebral cortex and the muscle activities. Corticomuscular coherence (CMC) has been extensively revealed in sustained contractions of various upper- and lower-limb muscles during static and dynamic force outputs. However, it is not well-understood that the CMC modulation mechanisms, i.e., the relation between a cerebral hemisphere and dynamic motor controlling limbs at constant speeds, such as isokinetic movement. In this paper, we explore the CMC between upper arm flexors/extensors movement and motor cortex during isometric exercise and cyclically isokinetic movement. We also provide further insights of frequency-shift and the neural pathway mechanisms in isokinetic movement by evaluating the coherence between motor cortex and agonistic or antagonistic muscles. This study is the first to investigate the relationship between cortical-muscular functional connections in elbow flexion-extension movement with constant speeds. The result shows that gamma-range coherence for isokinetic movement is greatly increased compared with isometric exercise, and significant CMC is observed in the entire flexion-extension stage regardless the nature of muscles contraction, although dominant synchronization of cortical oscillation and muscular activity resonated in sustained contraction stage principally. Besides, the CMC for extensors and flexors are explicitly consistent in contraction stage during cyclically isokinetic elbow movement. It is concluded that cortical-muscular coherence can be dynamically modulated as well as selective by cognitive demands of the body, and the time-varying mechanisms of the synchronous motor oscillation exist in healthy individuals during dynamic movement.

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.

Causal Shannon-Fisher Characterization of Motor/Imagery Movements in EEG

The electroencephalogram (EEG) is an electrophysiological monitoring method that allows us to glimpse the electrical activity of the brain. Neural oscillations patterns are perhaps the best salient feature of EEG as they are rhythmic activities of the brain that can be generated by interactions across neurons. Large-scale oscillations can be measured by EEG as the different oscillation patterns reflected within the different frequency bands, and can provide us with new insights into brain functions. In order to understand how information about the rhythmic activity of the brain during visuomotor/imagined cognitive tasks is encoded in the brain we precisely quantify the different features of the oscillatory patterns considering the Shannon–Fisher plane H×F. This allows us to distinguish the dynamics of rhythmic activities of the brain showing that the Beta band facilitate information transmission during visuomotor/imagined tasks.

Differential Effects of Simulated Cortical Network Lesions on Synchrony and EEG Complexity

Brain function has been proposed to arise as a result of the coordinated activity between distributed brain areas. An important issue in the study of brain activity is the characterization of the synchrony among these areas and the resulting complexity of the system. However, the variety of ways to define and, hence, measure brain synchrony and complexity has sometimes led to inconsistent results. Here, we study the relationship between synchrony and commonly used complexity estimators of electroencephalogram (EEG) activity and we explore how simulated lesions in anatomically based cortical networks would affect key functional measures of activity. We explored this question using different types of neural network lesions while the brain dynamics was modeled with a time-delayed set of 66 Kuramoto oscillators. Each oscillator modeled a region of the cortex (node), and the connectivity and spatial location between different areas informed the creation of a network structure (edges). Each type of lesion consisted on successive lesions of nodes or edges during the simulation of the neural dynamics. For each type of lesion, we measured the synchrony among oscillators and three complexity estimators (Higuchi's Fractal Dimension, Sample Entropy and Lempel-Ziv Complexity) of the simulated EEGs. We found a general negative correlation between EEG complexity metrics and synchrony but Sample Entropy and Lempel-Ziv showed a positive correlation with synchrony when the edges of the network were deleted. This suggests an intricate relationship between synchrony of the system and its estimated complexity. Hence, complexity seems to depend on the multiple states of interaction between the oscillators of the system. Our results can contribute to the interpretation of the functional meaning of EEG complexity.

On neuromechanical approaches for the study of biological and robotic grasp and manipulation

Biological and robotic grasp and manipulation are undeniably similar at the level of mechanical task performance. However, their underlying fundamental biological vs. engineering mechanisms are, by definition, dramatically different and can even be antithetical. Even our approach to each is diametrically opposite: inductive science for the study of biological systems vs. engineering synthesis for the design and construction of robotic systems. The past 20 years have seen several conceptual advances in both fields and the quest to unify them. Chief among them is the reluctant recognition that their underlying fundamental mechanisms may actually share limited common ground, while exhibiting many fundamental differences. This recognition is particularly liberating because it allows us to resolve and move beyond multiple paradoxes and contradictions that arose from the initial reasonable assumption of a large common ground. Here, we begin by introducing the perspective of neuromechanics, which emphasizes that real-world behavior emerges from the intimate interactions among the physical structure of the system, the mechanical requirements of a task, the feasible neural control actions to produce it, and the ability of the neuromuscular system to adapt through interactions with the environment. This allows us to articulate a succinct overview of a few salient conceptual paradoxes and contradictions regarding under-determined vs. over-determined mechanics, under- vs. over-actuated control, prescribed vs. emergent function, learning vs. implementation vs. adaptation, prescriptive vs. descriptive synergies, and optimal vs. habitual performance. We conclude by presenting open questions and suggesting directions for future research. We hope this frank and open-minded assessment of the state-of-the-art will encourage and guide these communities to continue to interact and make progress in these important areas at the interface of neuromechanics, neuroscience, rehabilitation and robotics.

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.

Dynamic Causal Modeling of the Cortical Responses to Wrist Perturbations

Mechanical perturbations applied to the wrist joint typically evoke a stereotypical sequence of cortical and muscle responses. The early cortical responses (<100 ms) are thought be involved in the "rapid" transcortical reaction to the perturbation while the late cortical responses (>100 ms) are related to the "slow" transcortical reaction. Although previous studies indicated that both responses involve the primary motor cortex, it remains unclear if both responses are engaged by the same effective connectivity in the cortical network. To answer this question, we investigated the effective connectivity cortical network after a "ramp-and-hold" mechanical perturbation, in both the early (<100 ms) and late (>100 ms) periods, using dynamic causal modeling. Ramp-and-hold perturbations were applied to the wrist joint while the subject maintained an isometric wrist flexion. Cortical activity was recorded using a 128-channel electroencephalogram (EEG). We investigated how the perturbation modulated the effective connectivity for the early and late periods. Bayesian model comparisons suggested that different effective connectivity networks are engaged in these two periods. For the early period, we found that only a few cortico-cortical connections were modulated, while more complicated connectivity was identified in the cortical network during the late period with multiple modulated cortico-cortical connections. The limited early cortical network likely allows for a rapid muscle response without involving high-level cognitive processes, while the complexity of the late network may facilitate coordinated responses.

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.