Functional corticomuscular coupling (FCMC) with different rhythmic oscillations plays different roles in neural communication and interaction between the central nervous system and the peripheral system. Larger methods, such as coherence and Granger causality (GC), have been used to describe the frequency band characteristics in the frequency domain, but they fail to account for the inherent complexity. Considering that the transfer entropy (TE) method as an information theory has advantages in complexity and direction, we extended it and proposed a novel method named transfer spectral entropy (TSE) to explore the local frequency band characteristics between two coupling signals. To verify this, we introduced a Henon model and a neural mass model to generate the simulation signals. We then applied the proposed method to explore the FCMC by analyzing the correlation between the EEG and EMG signals during steady-state force output. Simulation results showed that the TSE method, compared with the GC method, not only described the information interaction in the local frequency band, but it also restrained the “false coupling”. Additionally, the results also revealed that the TSE method was sensitive to coupling strength but not to data length. Further analysis of the experimental data showed that beta1 (15–25 Hz) and beta2 (25–35 Hz) bands were prominent in the FCMC for both EEG to EMG and EMG to EEG directions. Additionally, statistical analysis of the significant area indicated that the coupling in the EEG to EMG direction was higher at the beta1 and beta2 bands than that in the EMG to EEG direction, and the coupling in the EMG to EEG direction was higher at the gamma1 band (35–45 Hz) than that in the opposition. The FCMC results complementarily refined the previous studies that mainly focused on the beta band (15–35 Hz). The simulation and experimental data expound the effectiveness of the TSE model to describe the information interaction in the local frequency band between two time series, and this study extends the relative studies on FCMC.

A core issue in motor control is how the central nervous system generates and selects the muscle activation patterns necessary to achieve a variety of behaviors and movements. Extensive studies have verified that it is the foundation to induce a complex movement by the modular combinations of several muscles with a synergetic relationship. However, a few studies focus on the synergetic similarity and dissimilarity among different types of movements, especially for the upper extremity movements. In this study, we introduced the non-negative matrix factorization (NMF) method to explore the muscle activation patterns and synergy structure under 6 types of movements, involving the hand open (HO), hand close (HC), wrist flexion (WF), wrist extension (WE), supination (SU), and pronation (PR). For this, we enrolled 10 healthy subjects to record the electromyography signal for NMF calculation. The results showed a highly modular similarity of the muscle synergy among subjects under the same movement. Furthermore, Spearman’s correlation analysis indicated significant similarities among HO-WE, HO-SU, and WE-SU (p< 0.001). Additionally, we also found shared synergy and special synergy in activation patterns among different movements. This study confirmed the theory of modular structure in the central nervous system, which yields a stable synergetic pattern under the same movement. Our findings on muscle synergy will be of great significance to motor control and even to clinical assessment techniques.

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.

The central nervous system (CNS) controls the limb movement by modulating multiple skeletal muscles with synergistic modules and neural oscillations with different frequencies between the activated muscles. Several researchers have found intermuscular coherence existing within the synergistic muscle pairs, and pointed out that the intermuscular synchronization existed when functional forces were generated. However, few studies involved the time-varying characteristics of the intermuscular coherence in each synergy module though all activated muscles keep in a dynamic and varying process. Therefore, this study aims to explore the time-varying coherence amongst synergistic muscles during movements based on the combination of the non-negative matrix factorization (NMF) method and the time-frequency coherence (TFC) method. We applied these methods into the electromyogram (EMG) signals recorded from eight muscles involved in the sequence of the wrist movements [wrist flexion (WF), wrist flexion transmission to wrist extension (MC) and wrist extension (WE)] in 12 healthy people. The results showed three synergistic flexor pairs (FCR-PL, FCR-FDS, and PL-FDS) in the WF stage and three extensor pairs (ECU-ECR, ECU-B, and ECR-B) in both MC and WE stages. Further analysis showed intermuscular coherence between each pairwise synergistic muscles. The intermuscular coherence between the flexor muscle pairs was mainly observed in the beta band (15–35 Hz) during the WF stage, and that amongst the extensor muscle pairs was also observed in the beta band during the WE stage. However, the intermuscular coherence between the extensor muscle pairs mainly on gamma band during the MC stage. Additionally, compared to the flexor muscle pairs, the intermuscular coherence of the extensor muscle pairs were lower in the WF stage, and higher in both MC and WE stages. These results demonstrated the time-varying mechanisms of the synergistic modulation and synchronous oscillation in motor-control system. This study contributes to expanded researches for motor control.