An important challenge in the study of functional corticomuscular coupling (FCMC) is an accurate capture of the coupling relationship between the cerebral cortex and the effector muscle. The coherence method is a linear analysis method, which has certain limitations in further revealing the nonlinear coupling between neural signals. Although mutual information (MI) and transfer entropy (TE) based on information theory can capture both linear and nonlinear correlations, the equitability of these algorithms is ignored and the nonlinear components of the correlation cannot be separated. The maximal information coefficient (MIC) is a suitable method to measure the coupling between neurophysiological signals. This study extends the MIC to the time–frequency domain, named time–frequency maximal information coefficient (TFMIC), to explore the FCMC in a specific frequency band. The effectiveness, equitability, and robustness of the algorithm on the simulation data was verified and compared with coherence, TE- and MI- based methods. Simulation results showed that the TFMIC could accurately detect the coupling for different functional relationships at low noise levels. The dorsiflexion experimental results revealed that the beta-band (14–30 Hz) significant coupling was observed at channels Cz, C4, FC4, and FCz. Additionally, the results showed that the coupling was higher in the alpha-band (8–13 Hz) and beta-band (14–30 Hz) than in the gamma-band (31–45 Hz). This might be related to a transition between sensorimotor states. Specifically, the nonlinear component of FCMC was also observed at channels Cz, C4, FC4, and FCz. This study expanded the research on nonlinear coupling components in FCMC.

中文翻译：

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时频最大信息系数法及其在功能性皮层耦合中的应用

在功能性皮层神经系统耦合（FCMC）研究中的一个重要挑战是准确捕捉大脑皮层与效应肌之间的耦合关系。相干方法是一种线性分析方法，在进一步揭示神经信号之间的非线性耦合方面有一定的局限性。尽管基于信息论的互信息（MI）和传递熵（TE）可以捕获线性和非线性相关性，但是这些算法的等效性被忽略，并且相关性的非线性成分无法分离。最大信息系数（MIC）是测量神经生理信号之间耦合的合适方法。这项研究将MIC扩展到时频域，称为时频最大信息系数（TFMIC），探索特定频段的FCMC。验证了算法在仿真数据上的有效性，公平性和鲁棒性，并与基于一致性，基于TE和MI的方法进行了比较。仿真结果表明，TFMIC可以在低噪声水平下准确检测不同功能关系的耦合。背屈实验结果表明，在通道Cz，C4，FC4和FCz处观察到了β波段（14-30 Hz）的显着耦合。此外，结果表明，在α波段（8–13 Hz）和β波段（14–30 Hz）中的耦合比在γ波段（31–45 Hz）中更高。这可能与感觉运动状态之间的转换有关。具体而言，在通道Cz，C4，FC4和FCz上也观察到了FCMC的非线性分量。