Corticomuscular Coupling Analysis in Stroke Rehabilitation Based on Variational Mode Decomposition-Transfer Entropy

This study aims to explore alterations in corticomuscular and cortical coupling during the rehabilitation of stroke patients. We initiated the analysis by employing variational modal decomposition (VMD) on electromyography (EMG) data, followed by the application of VDM-transfer entropy (VMD-TE) to quantify the coupling strength between electroencephalogram (EEG) and EMG signals. Subsequently, we constructed the VMD-TE connection matrix and analyzed the clustering coefficient and small-world attributes within the cortico-muscular functional network (CMFN). Finally, a random forest algorithm was employed to extract features from the VMD-TE connection matrix across different rehabilitation periods. Beta waves in EEG were emerged as the key information carrier between the cortex and muscle, and the CMFN of patients with the beta frequency band has small-world characteristics. During rehabilitation, we observed a decrease in coupling between the initially affected motor cortex and muscle, accompanied by an increase in coupling between the frontal region and muscle. Our findings suggest potential neuro-remodeling in stroke patients after rehabilitation, with CFMN serving as a valuable metric for assessing cortico-muscular coupling.


I. INTRODUCTION
S TROKE is a disease that has caused mortality and dis- ability worldwide over the past 30 years [1].Substantial advances have yet to be made in neurorehabilitation methods to meet the demand for post-stroke rehabilitation.Despite advancements in understanding the causes of stroke, such as rupture of cerebral vessels and thrombosis, the mechanisms underlying functional recovery remain elusive.Therefore, it is necessary to understand the physiological process of neurological deficits and recovery to promote stroke recovery.Previous studies indicate that functional recovery after stroke involves distinct cortical regions.For example, Nudo et al. [2] showed post-stroke brain plasticity in non-human primates: recovery from neurological deficits can be achieved by reorganizing previously assumed functions of damaged tissues.Nelles et al. [3] observed increased cerebral blood flow in the sensorimotor cortex and two parietal regions using positron emission tomography to study the functional reorganization of the motor and sensory systems in hemiplegic stroke.Cramer et al. [4] used functional magnetic resonance imaging (fMRI) to study hemiplegic stroke patients and found that patients had greater activation of the same motor areas and contralateral hemisphere than normal controls.Elucidating how different brain functional areas contribute to motor recovery post-stroke is needed to ensure that repetitive and intensive activation of these functional areas can be used as an entry point for rehabilitation.
Post-stroke motor deficits are widely thought to result from diminished functional coupling between the motor cortex and muscles; however, restoration or support to replace this functional coupling can facilitate the recovery of motor abilities in stroke survivors.Electroencephalogram (EEG) and electromyography (EMG) help us explore the coupling relationship between the cerebral cortex and muscles by recording weak electrical signals generated by the cerebral cortex and muscle group contraction activities.First, cortical muscle synchronization was observed during isometric muscle contractions in healthy subjects [5], supporting the hypothesis that the motor cortex of the brain issues motion commands to muscle groups, and the sensation of muscle group contraction is fed back to the cortex through neurons.Second, a substantial spike in cortico-muscle coupling was found in the contralateral cortical regions of highly impaired stroke patients, supporting the hypothesis of functional recovery [6].Third, coherence between the cortex and muscle decreases post-stroke [7], [8], and a recent study showed that coherence between the cortex and muscle [9] could be used to assess motor recovery after stroke.Therefore, consistency between the cortex and muscle can serve as a biomarker for motor recovery [10].At present, these studies have mainly analyzed the changes in the coherence or coupling relationship between the cerebral cortex and muscles, but few have analyzed functional network.Hence, our study establishes a corticomuscular functional network (CMFN) using simultaneous EEG and EMG data to elucidate stroke rehabilitation mechanism.
Previous studies have found that functional networks systematically change with different cognitive states, which can be used for disease tracking and rehabilitation prediction.In recent years, large-scale network modeling has become commonplace, and the main methods of network modeling are Pearson's correlation coefficient, spectral coherence, phase-locking value (PLV) [11], partial directed coherence (PDC) [12], and transfer entropy (TE) [13].Although these methods have been effective in brain network exploration, their application of network models between the cortex and muscle remains relatively infrequent, and the coupling model between the cortex and muscle is still being studied.Because the Pearson correlation coefficient measures only linear correlation between two signals, the accuracy of the MI calculation is easily affected by the signal noise and length, and the PLV is sensitive to volume conduction.Therefore, the utilization of the Pearson correlation coefficient, MI, and PLV in assessing the coupling between cortex and muscle is limited.The power spectrum energy of EMG signals is much higher than that of EEG signal, the TE does not need to establish a model or nonlinear quantitative analysis but can be used to calculate the causal relationship between EEG and EMG sequential signals to evaluate the coupling relationship between the cortex and muscle.The key to studying the coupling information between the cortex and muscle at multiple temporal and spatial levels is fusing the high-frequency energy of EMG into the low-frequency energy of EEG.The empirical mode decomposition (EMD) [14] method can be used to decompose the signal into a series of instantaneous amplitudes and frequencies of the intrinsic mode function (IMF) adaptively.The signal decomposed by EMD exhibits a boundary effect and mode aliasing.In this study, variational mode decomposition (VMD) [15] was introduced into the scale analysis of the EMG signal, and the narrowband components of each central frequency were adaptively extracted.The VMD method transforms the estimation of the modes into the solution of the variational problem, constantly updates the modes and the center frequency in the frequency domain, and then transforms more modes into the time domain using the Fourier transform.In this study, EMG signals were decomposed into K IMF by VMD, and the average transfer entropy between EEG and each IMF was used as the coupling value between the cortex and muscle to establish the VMD-TE connection matrix.The effective connection matrix was obtained by filtering the connection matrix through the threshold value.
Corticomuscular functional coupling (CMFC) can be considered a potential biomarker for quantifying recovery from post-stroke movement disorders, offering insights into cortical regions involved in functional recovery.The CMFN is an intuitive representation of the functional interaction between different brain regions interact with muscles and can reflecting changes throughout stroke rehabilitation.Here, we present a preliminary study investigating the changes in CMFN and the major cortical regions involved at three rehabilitation stages in six ischemic stroke patients, providing new insights into stroke rehabilitation.

A. Participants and Experiment Design
6 right-handed patients (2 women and 4 men; age range: 39-67 years) with chronic stroke were recruited from the Affiliated Dongyang Hospital of Wenzhou Medical University.The experiment was approved by the Ethics Committee of the Affiliated Dongyang Hospital of Wenzhou Medical University.Each participant and their family members fully understood the purpose of the study and signed a consent form before the experiment began.
The experimental tracking cycle is illustrated in Figure 1a.The patients were followed up after hospitalization at the Affiliated Dongyang Hospital of Wenzhou Medical University.During hospitalization, the patients participated in various rehabilitation programs arranged by doctors.The rehabilitation training of these six patients was consistent, including limb function training, muscle strength training, acupuncture, and massage.Later, the EEG and surface EMG signals were synchronously recorded in the first, fourth, and sixth weeks after hospitalization.First, the patients did not undergo rehabilitation training before the experiment.The patients' hair was washed and exfoliated by a nurse one hour before the experiment began, followed by blow-drying.The laboratory is a quiet shielded room, and the indoor air conditioning is turned off to reduce the power frequency interference.The patient was brought to the lab by a caregiver and evaluated by a professional physician for testing.The patient sat quietly in a comfortable seat facing the screen and was instructed to follow on-screen instructions while holding the gripper (KS1109, KASUP).The specific experimental process is shown in Figure 1b.Each grip was held for 3 s, rested for 1 min, and repeated 20 times.

B. Data Recording
In the experiments, a 64-channel wireless EEG amplifier (NeuSen.W64, Neuracle, China) with a sampling frequency of 1000 Hz was used.Before the experimental data were recorded, EEG caps were correctly worn in accordance with the 10-20 system electrode placement method, and EEG cream was injected into the electrodes to reduce the electrode impedance to below 20 k so that EEG signals could be recorded in subsequent experiments.The selected motor cortex electrodes are shown in Figure 2(a), including 19 channels (AF3, AF4, F3, FZ, F4, FC3, FCZ, FC4, C3, CZ, C4, CP3, CP4, P3, PZ, P4, PO3, POZ, and PO4), which were selected from 59 channels of cortical EEG.Such electrode selection facilitates a thorough assessment of the motor cortex and ensures that the signal interference between the electrodes remains minimal.EMG recordings were collected using the Trigno TM wireless EMG (DelsysInc, Nat-ick, MA, USA) equipment with a sampling frequency of 1926 Hz.The corresponding muscle was wiped based on the human muscle diagram with alcohol and attached to the EMG electrode.The EMG signals of the first dorsal interosseous (FDI) muscle were then collected.The experimental acquisition process is shown in Figure 2(b).

C. Data Preprocessing
EEG and EMG data were captured synchronously according to the label, and a notch filter was used to remove 50 Hz power frequency interference.An EEGLAB v2019.0[16] toolbox was used to preprocess EEG data.First, the EEG signal was re-referenced to a common average reference.Second, a bandpass filter between 0.5 Hz and 45 Hz was used to filter low-frequency noise and high-frequency environmental noise.Finally, the plugin for independent component analysis [17] was used to remove physiological noise, such as the interference of the electrooculogram and EMG.After the noise reduction pretreatment, the EEG data were bandpass filtered at 1-38 Hz with a third-order double-pass Butterworth filter, and the sampling frequency was reduced to 500 Hz.The EMG was denoised using the wavelet soft-threshold method.Then, the EMG data were bandpass filtered at 5-125 Hz, and the sampling frequency was reduced to 500 Hz.VMD is an adaptive and non-recursive method of variational mode decomposition.According to VMD, the number of modal decompositions and the length of the sequence can be determined adaptively.In the process of searching and solving, the optimal center frequency and limited bandwidth of each mode can be adaptively matched, and the intrinsic mode components in the frequency domain can be effectively separated.Finally, the optimal solution of the variational mode decomposition, in other words, the effective decomposition components of the given signal, are obtained.

D. Variational Mode Decomposition
First, the variational problem is constructed, and the corresponding constraint variational expression is min where K is the number of modes to be decomposed, {u k } represents the number of k mode components after decomposition, {w k } represents the number of k center frequencies after decomposition, and δ(t) is the Dirac function.After calculation, it was found that when K ≥ 5, the increase of coupling value between EEG and EMG is not significant, so the K is set to 5.After decomposition, the center frequencies of the five modes decomposed in this study are 19 Hz, 41 Hz, 61 Hz, 86 Hz, and 111 Hz.The Lagrange multiplication operator λ is introduced to transform the constrained variational problem into an unconstrained variational problem, and the augmented Lagrange Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
expression is ( where α is the quadratic penalty factor.The alternating direction multiplier (ADMM) iterative algorithm set, Parseval/ Plancherel, and Fourier isometric transform were used to optimize each modal component and center frequency, and the saddle point of the augmented Lagrange function was searched for alternate optimization iteration, as shown in the following function: where γ is noise tolerance.

E. Transfer Entropy
A variational modal decomposition transfer entropy model was constructed and applied to the coupling analysis of EEG and EMG signals to quantitatively study the synchronous coupling characteristics of nonlinear EEG and EMG between different time-frequency scales.
The transfer entropy is a nonparametric statistic used to measure the coupling correlation between two random processes.The transfer entropy from one process (time series X) to another process (time series Y) indicates that the amount of information transferred between them is determined by knowing the past value of X and the future value of Y.
After VMD calculations, we can obtain multiband EMG signals and full-band EEG signals.Then, combined with the transfer entropy method, we can calculate the transfer entropy between the EEG and EMG at different time-frequency scales.
First, the time series of the EEG-related frequency band is denoted as y(t) using bandpass filtering.
Second, information on EMG at different scales was extracted using VMD, and the time series of relevant time scales was obtained as x k (t) The average transfer entropy between y and {x k } was taken as the transfer entropy coupling value between the EEG and EMG.The specific calculation process is as follows.
where p(x k n+1 , x k n , y n ) is the transition probability.

F. Graph Analysis
The connection matrix was constructed by calculating the VMD-TE value between the cortex and the muscle.Then, the threshold value was set to top 15% connection strength to filter the connection matrix to construct an N×N binary graph cortico-muscular functional coupling network (N = 20, 19 EEG electrodes, and 1 EMG electrode).
The clustering coefficient Cc (i) is defined as where Ei represents edge and Ki represents degree.
For the entire network, the value of the clustering coefficient (C)is equal to the average of each node, C c (i): The global efficiency (Eglobal) is the average reciprocal of the shortest path length between all node pairs.
where Li,j is the length of the path between nodes.The small-world coefficient (σ ) is defined as If σ > 1, CMFN has small-world characteristics.

G. Random Forest Feature Selection
Random forest [18] is a feature-selection method that measures the weight of a feature.The weight of features is determined through the following steps: (i) Select the corresponding out-of-bag data, which are not used in the establishment of the decision tree, to calculate the test error rate for each decision tree, denoted as error1.(ii) Introduce random noise to the out-of-bag data, and calculate the test error rate again, denoted as error2.(iii) Calculate the weight of the feature using the following formula: where Q represents the feature weight, and M is the number of decision trees.After determining the features weights, the steps for feature selection are as follows: (i) Calculate the weight of each feature and rank them in descending order.(ii) Select several features with larger weights in proportion to form a new feature set.(iii) Repeat the process using the new feature set.(iv) Select the feature set that consistently yields the lowest test error across all stages.

H. Statistical Analysis
The Shapiro-Wilk test was first used to assess the normality of the data distribution.Then, repeated analysis of variance (rANOVA) was used for statistical analysis, corrected for multiple comparisons with Bonferroni's correction [12].The confidence interval was set at 95%, and the significance of the statistical analysis was set at p < 0.05.

A. VMD-TE Connection Matrix
We analyzed EEG and EMG data recorded in six patients during the first, fourth, and sixth weeks after hospitalization.In this study, the data collected in the first week were recorded as the initial period (IP), the data collected in the fourth week were recorded as the middle period (MP), and the data collected in the sixth week were recorded as the late period (LP).The pretreated EEG was divided into three bands (theta: 4-8 Hz, alpha: 8-13 Hz, beta: 13-30 Hz).Then, the K of VMD-TE was set to 5, and the VMD-TE values of cortex-to-cortex (EEG→EEG), cortex-tomuscle (EEG→EMG), and muscle-to-cortex (EMG→EEG) were calculated.The VMD-TE connection matrix was averaged at each stage of patient (Figure 3).The value of VMD-TE between the EEG signals in the theta and alpha bands are much smaller than that in the beta bands, indicating that beta waves are the main carriers of information transmission between the cortex and muscle during grip (Figure 3. (a)).The EEG→EMG and EMG→EEG values of VMD-TE were similar, indicating that the transmission between the cortex and muscle was bidirectional.The cortex sends a command signal to the muscle, and the muscle sends a completion signal to the cortex.We observed an interesting rule when comparing the mean value of VMD-TE in the IP, MP, and LP of the patients.The mean values of VMD-TE in EEG→EMG and EMG→EEG showed a slightly increasing trend in the beta band (P < 0.001), which may indicate that the connections between the cortex and muscles were strengthened or reshaped in the motor areas of the cortex after rehabilitation.

B. CFMN Characteristics
In this study, we used the value of the first 15% of the network connection strength as the threshold value to filter the VMD-TE connection matrix.Such threshold selection would not make the sparsity of the CFMN filtered by different connection matrices different, and it can ensure that the current CFMN is neither an over-dense network nor an over-sparse network.Figure 4 shows the clustering coefficients of the CMFN in IP, MP, and LP.The values of C in the theta and alpha bands were smaller than those in the beta band.More interestingly, there was a significant difference in the value of C between the theta (IP&MP: P < 0.001; MP&LP: P < 0.001; IP&LP: P < 0.001) and alpha (IP&MP: P = 0.156; MP&LP: P < 0.001; IP&LP: P = 0.025) bands, whereas there was a significant difference between IP and MP (P < 0.001), Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.MP and LP (P < 0.001) in the beta band, but there was no statistical significance between IP and LP.This indicates that beta waves in the EEG during grip action are the main carriers of signal transmission between the cortex and the muscle.The C of MP in the beta band was larger than that of IP and LP, and there was no statistical significance between IP and LP, which may indicate that more cortical regions were activated in the rehabilitation process of patients and were involved in the connection between the cortex and muscle.The absence of statistical significance between IP and LP may indicate that patients underwent neural remodeling after rehabilitation.We compared the mean E global values of the three periods (Figure 5).We observed that E global of the theta and alpha bands was relatively small; however, E global of the beta band was larger.Furthermore, the E global of the beta band in MP is larger than that in IP, and the E global of the beta band in LP is larger than that in MP.These results indicate that information integration and generation efficiency between the brain and trunk muscles improved after rehabilitation training in stroke patients.In addition, it can be concluded that beta waves in EEG are the main information carriers between the brain and muscle when subjects perform experimental actions.
Scholars exploring the functional network ofthe brain have proven that the functional network of the brain has the property of a small world.In our study, we attempted to confirm that CMFN also has small-world properties.To better calculate the small-world attribute, we constructed 200 random networks with the same number of nodes and edges and calculated the average values of C and L of the random networks.The mean CMFN σ is shown in Figure 6.It is evident that CFMN of IP, MP lacks small-world attribute in theta and alpha bands, but has a small-world attribute in the beta band.LP has smallworld attribute in both alpha and beta bands.Notably, IP had the smallest small-world attribute in the beta band, followed by MP and LP.This also supports the previous conclusion that the beta wave of EEG is the carrier of information transmission between the cortex and muscle, and may indicate that the connection between the cortex and muscle gets closer during the patient's rehabilitation, indicating the reshaping of the cortex.

C. Regional Differences
In the above experiments, it was shown that the beta wave of the EEG is the carrier of information transmission between the Here, we connected VMD-TE connectivity matrix composition samples and set labels for them, in which IP was labeled 1, MP was labeled 2, and LP was labeled 3.Then, the IP and MP, IP and LP, and MP and LP were successively extracted using the random forest feature extraction algorithm for the first 15 features (Figure 7), characterizing the differences in the coupling between the cortex and muscle between each stage of the rehabilitation process.Figure 8 shows the extracted features and coupling value trend of IP versus MP, IP versus LP, and MP versus LP before these eigenvalues.We observed that these differences were mainly concentrated in the left cerebral cortex and muscle groups, indicating that the contralateral brain region is involved in human movement.Simultaneously, we observed that the coupling values of the extracted features before IP and MP, IP and LP were mainly increased in AF3, which may indicate cortical remodeling during rehabilitation, primarily from the motor area (C3) to the prefrontal area (AF3, F3).

IV. DISCUSSION
In this study, we constructed a CMFN using the EEG and EMG data.To solve the problem of EEG energy dealing with the low-frequency band while EMG energy dealing with the high-frequency band, the EMG signal is decomposed by VMD.The CMFN was constructed by calculating the  VMD-TE values between EEG and EMG.The CFMN helps analyze the coupling changes between the cortex and muscle and the corresponding cortical regions during the rehabilitation of stroke patients.Our research showed that EEG beta waves are the main carriers of information transmission between the cortex and muscle.Many previous studies have shown that during isometric contraction of muscles, the oscillatory activity of 15-30Hz in the primary motor cortex of the brain is consistent or phase-locked with that of the contralateral limb muscles.For example, Kilner et al. [19] showed that all subjects exhibited significant continuity between the cortex and muscle at 15 -30 Hz when controlling the manipulator lever of a robot.The mean value of the VMD-TE in the theta band of EEG→EMG and EMG→EEG was relatively small (Figure 3), which may indicate that the theta wave in the EEG is not a transmission medium between the cortex and muscle.This may also be related to the fact that the theta wave component in the EEG is less when patients perform experimental movements.The small-world properties of CMFN in the MP and LP beta bands were similar in stroke patients, which may be related to the consistency of experimental actions.Bassett and Bullmore, in their study on small-world networks, showed a close relationship exists between small-world topology and dynamic complexity [20].Small-world networks have high global efficiency, high local efficiency, and low-cost fault tolerance.C can be regarded as a measure of the local efficiency of information transmission.This indicates that when the CMFN has high C and smallworld properties, the global and local efficiency of information transfer between nodes is relatively high.This study ignores the reaction time of each subject in each experiment; therefore, the more complex the completed action, the higher the information transmission efficiency.Therefore, when the same movement is completed, the information integration efficiency between the brain and muscle should be close to each other, and the small-world attribute of CMFN in the MP beta band is close to LP, indicating that stroke patients may gradually recover the connection between the brain and muscle after a period of rehabilitation training.However, the small-world attribute of CMFN in the IP beta band is lower than that of MP and LP, which may be related to the impaired functional coupling between the brain and trunk muscles during IP stroke.Meanwhile, other muscles may also be involved in the completion of experimental actions, or the completion of actions may not be sufficient.
This study explored the changes in CMFC in stroke patients during rehabilitation based on the VMD-TE connectivity matrix in the beta band.CMFC changes in functional areas (C3) were mainly distributed in the movement, frontal area (AF3, F3), occipital area (PO3, POz, and PO4) and related muscle (FDI).Pins and Ffytche [21] found that the occipital lobe was related to consciousness after 100 ms, whereas the parietal lobe, frontal lobe, auditory, and motor regions were related to consciousness after 260 ms, indicating that the early activity of the occipital lobe was related to perception.The reason for the concentrated features in the occipital lobe area is related to the fact that stroke patients need to complete relevant experimental actions according to the reminder on the screen during the experiment, during which they receive a lot of visual stimulation.The coupling characteristics between the three periods are mainly concentrated in the left hemisphere and related muscles, which indicates that the contralateral cortex area mainly controls the trunk muscles after rehabilitation treatment, and the ipsilateral cortex area is not activated.This result contrasts with the findings of Luft et al. [22].In their study of lesion area alterations and cortex activation in chronic stroke survivors, they found activity in the contralateral motor areas, ipsilateral cerebellum, and bilateral mesial subcutaneous stroke, whereas the activation of the posterior central cortex is related to motor function, which may be related to the difference in the experimental subjects of the study.They primarily studied the changes in paralyzed and nonparalyzed chronic stroke patients, whereas this study examined the changes in stroke patients before and after rehabilitation treatment.The change in IP→MP CMFC showed that the coupling strength between the motor function area and the frontal lobe area became stronger, whereas the coupling strength between the motor function area and FDI became smaller.These CMFC changes may be related to the activation of nearby functional areas in response to motor skill deficiencies in stroke patients during rehabilitation.Zemke et al. [23] also expressed this view of cortical activation in their experimental study, pointing out that when subjects had similar EMG results, fully recovered stroke patients had increased contralateral sensory cortex activation compared to partially recovered stroke patients (2.7fold).In addition, Schaechter et al. [24] showed enhanced activation in the contralateral cortical regions in stroke patients with good motor recovery.For the IP→LP period, the main change in CMFC was that the coupling strength between the motor functional area and other functional areas became weaker, whereas the coupling strength between the frontal lobe area and other functional areas became stronger.However, during the MP→LP period, the changes in CMFC were not included in the motor functional area, only showing that the coupling strength between the frontal lobe area and other functional areas became stronger.These results indicate that the frontal lobe area replaces the original motor function area after rehabilitation treatment in stroke patients, thus supporting the view of neural remodeling.Bernhardi et al. [25] defined "neuroplasticity" as the ability of the nervous system to self-regulate its function and structure in response to experience and injury.Plasticity is a response to a changing environment, aging, or pathological damage.The findings in this section are consistent with those of Green [26], who showed in their study that recovery after a stroke lasting 3 -4 weeks is due to plasticity, the reorganization of the brain in which functions previously performed by the ischemic area are performed by other ipsilateral or contralateral brain regions.
The above results indicate that the CMFN established in this study can be used to explore the rehabilitation mechanism of stroke and provide new insights into the rehabilitation of stroke.However, due to the limited number of participants, the results need to be confirmed in future studies involving larger cohorts.

V. CONCLUSION
In this study, we used a functional network called the CMFN.We applied VMD-TE to determine the functional coupling between the cortex and muscle to explore the rehabilitation mechanisms after stroke.We also found that the small-world property of the CMFN could be used to assess stroke recovery.The results show that the information flow between the cerebral cortex and muscles is bidirectional, and the beta waves in the EEG are the main carriers of information interaction between the brain and muscles.Furthermore, our results suggest that after rehabilitation, the stroke patients gradually activated functional areas near the damaged cortex, and neuro remodeling occurred.

Fig. 1 .
Fig. 1.Experimental design.(a) The experimental tracking cycle.(b) The flow of the experimental task.

A
variational modal decomposition transfer entropy model was constructed and applied to the coupling analysis of EEG and EMG signals to quantitatively study the synchronous coupling characteristics of nonlinear EEG and EMG between different time-frequency scales.Previous studies have shown that the effective frequency band of the EMG signal includes a low-frequency band and high-frequency band, whereas the effective signal of the EEG signal is mainly in the low-frequency band.To show the information of EEG and EMG signals on different time-frequency scales, we introduced VMD into the scaling analysis of EMG signals.The problem is then transformed into the coupling of multi-band EMG signals and full-band EEG signals.

Fig. 3 .
Fig. 3. VMD-TE connection matrices in the three periods.(a) EEG->EEG: cortex to cortex; (b) EEG->EMG: cortex to muscle; (c) EMG->EEG: muscle to cortex.The values represent the difference in VMD-TE between MP and IP, LP and MP respectively.Significant differences between the two are given in bold.(IP: initial period; MP: middle period; LP: late period.)

Fig. 7 .
Fig. 7. Schematic of random forest feature selection (RFFS) process.(a) VMD-TE connection matrix.(b) Three periods with labels.(c) Random forest feature selection for IP and LP feature extraction.(d) Random forest feature selection for IP and MP feature extraction.(e) Random forest feature selection for LP and MP feature extraction.

Fig. 8 .
Fig. 8. Random forest feature selection for feature extraction.(a) The first 15 features were extracted between IP and MP and the difference of coupling values between them.(b) The first 15 features were extracted between IP and LP and the difference of coupling values between them.(c) The first 15 features were extracted between LP and MP and the difference of coupling values between them.