Keywords: 
• 脑肌电耦合 /
• 变分模态分解 /
• 传递熵 /
• 时频尺度

Abstract: The functional corticomuscular coupling (FCMC) is defined as the interaction, coherence and time synchronism between cerebral cortex and muscle tissue, which could be revealed by the synchronization analyses of electroencephalo-gram (EEG) and electromyogram (EMG) firing in a target muscle. The FCMC analysis is an effective method to describe the information transfer and interaction in neuromuscular pathways. Forthermore, the multiscaled coherence analyses of EEG and EMG signals recorded simultaneously could describe the multiple spatial and temporal functional connection characteristics of FCMC, which could be helpful for understanding the multiple spatial and temporal coupling mechanism of neuromuscular system. In this paper, based on the adaptively decomposing signal into frequency band characteristis of variational mode decomposition (VMD) and the quantitatively detecting the directed exchange of information between two systems of transfer entropy (TE), a new method—variational mode decomposition-transfer entropy (VMD-TE) is proposed. The VMD-TE method could quantitatively analyze the nonlinear functional connection characteristic on mul-tiple time-frequency scales between EEG over brain scalp and surface EMG signals from flexor digitorum surerficialis, which are recorded simultaneously during grip task with steady-state force output.
In this paper, application of VMD-TE method consists of two steps. Firstly, the EEG and EMG signals are adap-tively decomposed into multi intrinsic mode functions based on variational mode decomposition method, respectively, to describe the information on different time-frequency scales. Then the transfer entropies between the different time-frequency scales of EEG and EMG are calculated to describe the nonlinear corticomuscular coupling characteristic in different pathways (EEG→EMG and EMG→EEG), to show the functional coupling strength (namely VMD-TE values). finally, the maximum VMD-TE values between the different time-frequency scales of EEG and EMG signals among the eight subjects are selected, to describe the discrepancies of FCMC interaction strength between all time-frequency scales. The results show that functional corticomuscular coupling is significant in both descending (EEG→EMG) and ascend-ing (EMG→EEG) directions in the beta-band (15–35 Hz) in the static force output stage. Meanwhile, the interaction strength between EEG signal and the gamma band (50–72 Hz) of EMG signal in descending direction is higher than in ascending direction. Our study confirms that the beta oscillations of EEG travel bidirectionally between sensorimotor cortex and contralateral muscles in sensorimotor loop system, and the oscillation of beta-band of EMG signal is consid-ered to be driven from cortex pyramidal tract and cortex and likely to reflect the information transmission from muscle to the sensorimotor cortex. The beta-band corticomuscular coupling reveals the information transmission between the muscles and sensorimotor cortex. Additionally, the corticomuscular coupling strength discrepancy varies on different time-frequency scales between EEG and EMG signals. The results show that the VMD-TE can quantitatively estimate the nonlinear time-frequency interconnection and functional corticomuscular coupling between sensorimotor cortex and muscle.