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.
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.