Direct Interaction on Specific Frequency Bands in Functional Corticomuscular Coupling

Multiscale Canonical Coherence for Functional Corticomuscular Coupling Analysis

Functional corticomuscular coupling (FCMC) probes multi-level information communication in the sensorimotor system. The canonical Coherence (caCOH) method has been leveraged to measure the FCMC between two multivariate signals within the single scale. In this paper, we propose the concept of multiscale canonical Coherence (MS-caCOH) to disentangle complex multi-layer information and extract coupling features in multivariate spaces from multiple scales. Then, we verified the reliability and effectiveness of MS-caCOH on two types of data sets, i.e., a synthetic multivariate data set and a real-world multivariate data set. Our simulation results showed that compared with caCOH, MS-caCOH enhanced coupling detection and achieved lower pattern recovery errors at multiple frequency scales. Further analysis on experimental data demonstrated that the proposed MS-caCOH method could also capture detailed multiscale spatial-frequency characteristics. This study leverages the multiscale analysis framework and multivariate method to give a new insight into corticomuscular coupling analysis.

Multiscale information interaction at local frequency band in functional corticomuscular coupling

The multiscale information interaction between the cortex and the corresponding muscles is of great significance for understanding the functional corticomuscular coupling (FCMC) in the sensory-motor systems. Though the multiscale transfer entropy (MSTE) method can effectively detect the multiscale characteristics between two signals, it lacks in describing the local frequency-band characteristics. Therefore, to quantify the multiscale interaction at local-frequency bands between the cortex and the muscles, we proposed a novel method, named bivariate empirical mode decomposition-MSTE (BMSTE), by combining the bivariate empirical mode decomposition (BEMD) with MSTE. To verify this, we introduced two simulation models and then applied it to explore the FCMC by analyzing the EEG over brain scalp and surface EMG signals from the effector muscles during steady-state force output. The simulation results showed that the BMSTE method could describe the multiscale time-frequency characteristics compared with the MSTE method, and was sensitive to the coupling strength but not to the data length. The experiment results showed that the coupling at beta1 (15-25 Hz), beta2 (25-35 Hz) and gamma (35-60 Hz) bands in the descending direction was higher than that in the opposition, and at beta2 band was higher than that at beta1 band. Furthermore, there were significant differences at the low scales in beta1 band, almost all scales in beta2 band, and high scales in gamma band. These results suggest the effectiveness of the BMSTE method in describing the interaction between two signals at different time-frequency scales, and further provide a novel approach to understand the motor control.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09895-y.

Upper Limb Cortical-Muscular Coupling Analysis Based on Time-Delayed Back Maximum Information Coefficient Model

In musculoskeletal systems, describing accurately the coupling direction and intensity between physiological electrical signals is crucial. The maximum information coefficient (MIC) can effectively quantify the coupling strength, especially for short time series. However, it cannot identify the direction of information transmission. This paper proposes an effective time-delayed back maximum information coefficient (TDBackMIC) analysis method by introducing a time delay parameter to measure the causal coupling. Firstly, the effectiveness of TDBackMIC is verified on simulations, and then it is applied to the analysis of functional cortical-muscular coupling and intermuscular coupling networks to explore the difference of coupling characteristics under different grip force intensities. Experimental results show that functional cortical-muscular coupling and intermuscular coupling are bidirectional. The average coupling strength of EEG → EMG and EMG → EEG in beta band is 0.86 ± 0.04 and 0.81 ± 0.05 at 10% maximum voluntary contraction (MVC) condition, 0.83 ± 0.05 and 0.76 ± 0.04 at 20% MVC, and 0.76 ± 0.03 and 0.73 ± 0.04 at 30% MVC. With the increase of grip strength, the strength of functional cortical-muscular coupling in beta frequency band decreases, the intermuscular coupling network exhibits enhanced connectivity, and the information exchange is closer. The results demonstrate that TDBackMIC can accurately judge the causal coupling relationship, and functional cortical-muscular coupling and intermuscular coupling network under different grip forces are different, which provides a certain theoretical basis for sports rehabilitation.

The Characteristics of Electroencephalogram Signatures in Minimally Conscious State Patients Induced by General Anesthesia

OBJECTIVE

General anesthesia (GA) is necessary for surgery, even for patients in a minimally conscious state (MCS). The characteristics of the electroencephalogram (EEG) signatures of the MCS patients under GA are still unclear.

METHODS

The EEG during GA were recorded from 10 MCS patients undergoing spinal cord stimulation surgery. The power spectrum, phase-amplitude coupling (PAC), the diversity of connectivity, and the functional network were investigated. Long term recovery was assessed by the Coma Recovery Scale-Revised at one year after the surgery, and the characteristics of the patients with good or bad prognosis status were compared.

RESULTS

For the four MCS patients with good prognostic recovery, slow oscillation (0.1-1 Hz) and the alpha band (8-12 Hz) in the frontal areas increased during the maintenance of a surgical state of anesthesia (MOSSA), and "peak-max" and "trough-max" patterns emerged in frontal and parietal areas. During MOSSA, the six MCS patients with bad prognosis demonstrated: increased modulation index, reduced diversity of connectivity (from mean±SD of 0.877 ± 0.003 to 0.776 ± 0.003, p < 0.001), reduced function connectivity significantly in theta band (from mean±SD of 1.032 ± 0.043 to 0.589 ± 0.036, p < 0.001, in prefrontal-frontal; and from mean±SD of 0.989 ± 0.043 to 0.684 ± 0.036, p < 0.001, in frontal-parietal) and reduced local and global efficiency of the network in delta band.

CONCLUSIONS

A bad prognosis in MCS patients is associated with signs of impaired thalamocortical and cortico-cortical connectivity - as indicated by inability to produce inter-frequency coupling and phase synchronization. These indices may have a role in predicting the long-term recovery of MCS patients.

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

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

TV-NARX and Coiflets WPT based time-frequency Granger causality with application to corticomuscular coupling in hand-grasping

The study of the synchronous characteristics and functional connections between the functional cortex and muscles of hand-grasping movements is important in basic research, clinical disease diagnosis and rehabilitation evaluation. The electroencephalogram (EEG) and electromyographic signal (EMG) signals of 15 healthy participants were used to analyze the corticomuscular coupling under grasping movements by holding three different objects, namely, card, ball, and cup by using the time-frequency Granger causality method based on time-varying nonlinear autoregressive with exogenous input (TV-NARX) model and Coiflets wavelet packet transform. The results show that there is a bidirectional coupling between cortex and muscles under grasping movement, and it is mainly reflected in the beta and gamma frequency bands, in which there is a statistically significant difference (p < 0.05) among the different grasping actions during the movement execution period in the beta frequency band, and a statistically significant difference (p < 0.1) among the different grasping actions during the movement preparation period in the gamma frequency band. The results show that the proposed method can effectively characterize the EEG-EMG synchronization features and functional connections in different frequency bands during the movement preparation and execution phases in the time-frequency domain, and reveal the neural control mechanism of sensorimotor system to control the hand-grasping function achievement by regulating the intensity of neuronal synchronization oscillations.

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.

Directed Information Flow Analysis Reveals Muscle Fatigue-Related Changes in Muscle Networks and Corticomuscular Coupling

As a common neurophysiological phenomenon, voluntary muscle fatigue is accompanied by changes in both the central nervous system and peripheral muscles. Considering the effectiveness of the muscle network and the functional corticomuscular coupling (FCMC) in analyzing motor function, muscle fatigue can be analyzed by quantitating the intermuscular coupling and corticomuscular coupling. However, existing coherence-based research on muscle fatigue are limited by the inability of the coherence algorithm to identify the coupling direction, which cannot further reveal the underlying neural mechanism of muscle fatigue. To address this problem, we applied the time-delayed maximal information coefficient (TDMIC) method to quantitate the directional informational interaction in the muscle network and FCMC during a right-hand stabilized grip task. Eight healthy subjects were recruited to the present study. For the muscle networks, the beta-band information flow increased significantly due to muscle fatigue, and the information flow between the synergist muscles were stronger than that between the synergist and antagonist muscles. The information flow in the muscle network mainly flows to flexor digitorum superficialis (FDS), flexor carpi ulnar (FCU), and brachioradialis (BR). For the FCMC, muscle fatigue caused a significant decrease in the beta- and gamma-band bidirectional information flow. Further analysis revealed that the beta-band information flow was significantly stronger in the descending direction [electroencephalogram (EEG) to surface electromyography (sEMG)] than that in the ascending direction (sEMG to EEG) during pre-fatigue tasks. After muscle fatigue, the beta-band information flow in the ascending direction was significantly stronger than that in the descending direction. The present study demonstrates the influence of muscle fatigue on information flow in muscle networks and FCMC. We proposes that beta-band intermuscular and corticomuscular informational interaction plays an adjusting role in autonomous movement completion under muscle fatigue. Directed information flow analysis can be used as an effective method to explore the neural mechanism of muscle fatigue on the macroscopic scale.

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.

Propofol Anesthesia Decreased the Efficiency of Long-Range Cortical Interaction in Humans

OBJECTIVE

Phase-amplitude coupling (PAC) has recently been used to illuminate cross-frequency coordination in neurophysiological activity of electroencephalogram. However, the PAC at a meso-scale (electrocorticogram, ECoG) and PAC between different areas have still not been fully clarified.

METHODS

In this study, we analyzed ECoG data recorded from surgical patients (n = 9) with pharmaco-resistant epilepsy during the surgical treatment. The modulogram and a genuine modulation index, based on a Kullback-Leibler distance and permutation test method, were developed and used to measure the slow oscillation (SO) (0.15-1 Hz)-α (8-13 Hz) PAC of within-lead and cross-lead during transitions from states of wakefulness to unconsciousness during propofol induced general anesthesia.

RESULTS

In within-lead SO-α PAC, the modulation index increased in the unconscious state (p < 0.05, Tukey's test), the percentages of genuine modulation indices also increased in the unconscious state (p < 0.001 in the frontal area and p < 0.01 in the parietal area), and distinct PAC patterns emerged more often. In cross-lead SO-α PAC, there are fewer PAC patterns compared to within-lead, and the percentages of genuine modulation indices decreased significantly (p < 0.001).

CONCLUSION

The increased modulation index of within-lead and cross-lead SO-α PAC is associated with a reduction of information integration and the efficiency of long distance synchronization. These findings demonstrate that the propofol causes the neuronal populations to enter a 'busy' state in a local scale, which prevents the information integration in long-range areas.

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.

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.

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.

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.