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

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.

Synchronous analyses between electroencephalogram and surface electromyogram based on motor imagery and motor execution

The functional coupling of the cerebral cortex and muscle contraction indicates that electroencephalogram (EEG) and surface electromyogram (sEMG) signals are coherent. The objective of this study is to clearly describe the coupling relationship between EEG and sEMG through a variety of analysis methods. We collected the EEG and sEMG data of left- or right-hand motor imagery and motor execution from six healthy subjects and six stroke patients. To enhance the coherence coefficient between EEG and sEMG signals, the algorithm of EEG modification based on the peak position of sEMG signals is proposed. Through analyzing a variety of signal synchronization analysis methods, the most suitable coherence analysis algorithm is selected. In addition, the wavelet coherence analysis method based on time spectrum estimation was used to study the linear correlation characteristics of the frequency domain components of EEG and sEMG signals, which verified that wavelet coherence analysis can effectively describe the temporal variation characteristics of EEG-sEMG coherence. In the task of motor imagery, the significant EEG-sEMG coherence is mainly in the imagination process with the frequency distribution of the alpha and beta frequency bands; in the task of motor execution, the significant EEG-sEMG coherence mainly concentrates before and during the task with the frequency distribution of the alpha, beta, and gamma frequency bands. The results of this study may provide a theoretical basis for the cooperative working mode of neurorehabilitation training and introduce a new method for evaluating the functional state of neural rehabilitation movement.

Corticomuscular integrated representation of voluntary motor effort in robotic control for wrist-hand rehabilitation after stroke

OBJECTIVE

The central-to-peripheral voluntary motor effort (VME) in physical practice of the paretic limb is a dominant force for driving functional neuroplasticity on motor restoration post-stroke. However, current rehabilitation robots isolated the central and peripheral involvements in the control design, resulting in limited rehabilitation effectiveness. The purpose of this study was to design a corticomuscular coherence (CMC) and electromyography (EMG)-driven (CMC-EMG-driven) system with central-and-peripheral integrated representation of VME for wrist-hand rehabilitation after stroke.

APPROACH

The CMC-EMG-driven control was developed in a neuromuscular electrical stimulation (NMES)-robot system, i.e., CMC-EMG-driven NMES-robot system, to instruct and assist the wrist-hand extension and flexion in persons after stroke. A pilot single-group trial of 20 training sessions was conducted with the developed system to assess the feasibility for wrist-hand practice on the chronic strokes (n=16). The rehabilitation effectiveness was evaluated through clinical assessments, CMC, and EMG activation levels.

MAIN RESULTS

The trigger success rate and laterality index (LI) of CMC were significantly increased in wrist-hand extension across training sessions (p<0.05). After the training, significant improvements in the target wrist-hand joints and suppressed compensation from the proximal shoulder-elbow joints were observed through the clinical scores and EMG activation levels (p<0.05). The central-to-peripheral VME distribution across upper extremity (UE) muscles was also significantly improved, as revealed by the CMC values (p<0.05).

SIGNIFICANCE

Precise wrist-hand rehabilitation was achieved by the developed system, presenting suppressed cortical and muscular compensation from the contralesional hemisphere and the proximal UE, and improved distribution of the central-and-peripheral VME on UE muscles.

Pathway-specific cortico-muscular coherence in proximal-to-distal compensation during fine motor control of finger extension after stroke

Objective.Proximal-to-distal compensation is commonly observed in the upper extremity (UE) after a stroke, mainly due to the impaired fine motor control in hand joints. However, little is known about its related neural reorganization. This study investigated the pathway-specific corticomuscular interaction in proximal-to-distal UE compensation during fine motor control of finger extension post-stroke by directed corticomuscular coherence (dCMC).Approach.We recruited 14 chronic stroke participants and 11 unimpaired controls. Electroencephalogram (EEG) from the sensorimotor area was concurrently recorded with electromyography (EMG) from extensor digitorum (ED), flexor digitorum (FD), triceps brachii (TRI) and biceps brachii (BIC) muscles in both sides of the stroke participants and in the dominant (right) side of the controls during the unilateral isometric finger extension at 20% maximal voluntary contractions. The dCMC was analyzed in descending (EEG → EMG) and ascending pathways (EMG → EEG) via the directed coherence. It was also analyzed in stable (segments with higher EMG stability) and less-stable periods (segments with lower EMG stability) subdivided from the whole movement period to investigate the fine motor control. Finally, the corticomuscular conduction time was estimated by dCMC phase delay.Main results.The affected limb had significantly lower descending dCMC in distal UE (ED and FD) than BIC (P< 0.05). It showed the descending dominance (significantly higher descending dCMC than the ascending,P< 0.05) in proximal UE (BIC and TRI) rather than the distal UE as in the controls. In the less-stable period, the affected limb had significantly lower EMG stability but higher ascending dCMC (P< 0.05) in distal UE than the controls. Furthermore, significantly prolonged descending conduction time (∼38.8 ms) was found in ED in the affected limb than the unaffected (∼26.94 ms) and control limbs (∼25.74 ms) (P< 0.05).Significance.The proximal-to-distal UE compensation in fine motor control post-stroke exhibited altered descending dominance from the distal to proximal UE, increased ascending feedbacks from the distal UE for fine motor control, and prolonged descending conduction time in the agonist muscle.

Multiscale Wavelet Transfer Entropy with Application to Corticomuscular Coupling Analysis

OBJECTIVE

Functional coupling between the motor cortex and muscle activity is commonly detected and quantified by cortico-muscular coherence (CMC) or Granger causality (GC) analysis, which are applicable only to linear couplings and are not sufficiently sensitive: some healthy subjects show no significant CMC and GC, and yet have good motor skills. The objective of this work is to develop measures of functional cortico-muscular coupling that have improved sensitivity and are capable of detecting both linear and non-linear interactions.

METHODS

A multiscale wavelet transfer entropy (TE) methodology is proposed. The methodology relies on a dyadic stationary wavelet transform to decompose electroencephalogram (EEG) and electromyogram (EMG) signals into functional bands of neural oscillations. Then, it applies TE analysis based on a range of embedding delay vectors to detect and quantify intra- and cross-frequency band cortico-muscular coupling at different time scales.

RESULTS

Our experiments with neurophysiological signals substantiate the potential of the developed methodologies for detecting and quantifying information flow between EEG and EMG signals for subjects with and without significant CMC or GC, including non-linear cross-frequency interactions, and interactions across different temporal scales. The obtained results are in agreement with the underlying sensorimotor neurophysiology.

CONCLUSION

These findings suggest that the concept of multiscale wavelet TE provides a comprehensive framework for analyzing cortex-muscle interactions.

SIGNIFICANCE

The proposed methodologies will enable developing novel insights into movement control and neurophysiological processes more generally.

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.

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

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

Direct Interaction on Specific Frequency Bands in Functional Corticomuscular Coupling

OBJECTIVE

Direct interaction between the brain and muscle is significant for investigating the oscillation mechanisms in the motor control system.

METHODS

To our knowledge, the partial directed coherence (PDC) method is sufficient to reflect the direct interaction among multivariate time series in the frequency domain, but fails to eliminate the spectral overlap among frequency bands. Therefore, we expanded the PDC method and constructed a novel method, named variational-mode-decomposition-based PDC (VMDPDC), to describe the direct interaction on specific frequency bands.

RESULTS

To verify this, we made a comparison with the Granger causality (GC), PDC, and FIR-based PDC (FIRPDC) methods in two numerical models (bivariate coupling model and multivariate coupling model). After that, we applied this method to analyze the functional corticomuscular coupling (FCMC) during steady-state grip task. Simulation results showed that, compared with the GC, PDC, and FIRPDC methods, the VMDPDC method could accurately detect the direct interaction on specific frequency bands. The results on experimental data showed that the direct interaction in FCMC mainly focused on the alpha (8-15 Hz), beta (15-35 Hz), and gamma (35-60 Hz) bands. Further analysis demonstrated that the coupling strength in descending direction was significantly higher than that in the opposite direction.

CONCLUSION

Both simulation and experimental results indicated that the proposed method could effectively describe the direct interaction on specific frequency bands.

SIGNIFICANCE

This study also provides a theoretical foundation for further exploration on the mechanism of the motor control.

Effect of pulsed transcranial ultrasound stimulation at different number of tone-burst on cortico-muscular coupling

Background

Pulsed transcranial ultrasound stimulation (pTUS) can modulate the neuronal activity of motor cortex and elicit muscle contractions. Cortico-muscular coupling (CMC) can serve as a tool to identify interaction between the oscillatory activity of the motor cortex and effector muscle. This research aims to explore the neuromodulatory effect of low-intensity, pTUS with different number of tone burst to neural circuit of motor-control system by analyzing the coupling relationship between motor cortex and tail muscle in mouse. The motor cortex of mice was stimulated by pulsed transcranial ultrasound with different number of tone bursts (NTB = 100 150 200 250 300). The local field potentials (LFPs) in tail motor cortex and electromyography (EMG) in tail muscles were recorded simultaneously during pTUS. The change of integral coupling strength between cortex and muscle was evaluated by mutual information (MI). The directional information interaction between them were analyzed by transfer entropy (TE).

Results

Almost all of the MI and TE values were significantly increased by pTUS. The results of MI showed that the CMC was significantly enhanced with the increase of NTB. The TE results showed the coupling strength of CMC in descending direction (from LFPs to EMG) was significantly higher than that in ascending direction (from EMG to LFPs) after stimulation. Furthermore, compared to NTB = 100, the CMC in ascending direction were significantly enhanced when NTB = 250, 300, and CMC in descending direction were significantly enhanced when NTB = 200, 250, 300.

Conclusion

These results confirm that the CMC between motor cortex and the tail muscles in mouse could be altered by pTUS. And by increasing the NTB (i.e. sonication duration), the coupling strength within the cortico-muscular circuit could be increased, which might further influence the motor function of mice. It demonstrates that, using MI and TE method, the CMC could be used for quantitatively evaluating the effect of pTUS with different NTBs, which might provide a new insight into the effect of pTUS neuromodulation in motor cortex.