Transfer Spectral Entropy and Application to Functional Corticomuscular Coupling

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 also restrained the “false coupling.” In addition, the results also revealed that the TSE method was sensitive to coupling strength but not to the 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. In addition, the 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.