Upper Limb Cortical-Muscular Coupling Analysis Based on Time-Delayed Back Maximum Information Coefficient Model

In musculoskeletal systems, describing accurately the coupling direction and intensity between physiological electrical signals is crucial. The maximum information coefficient (MIC) can effectively quantify the coupling strength, especially for short time series. However, it cannot identify the direction of information transmission. This paper proposes an effective time-delayed back maximum information coefficient (TDBackMIC) analysis method by introducing a time delay parameter to measure the causal coupling. Firstly, the effectiveness of TDBackMIC is verified on simulations, and then it is applied to the analysis of functional cortical-muscular coupling and intermuscular coupling networks to explore the difference of coupling characteristics under different grip force intensities. Experimental results show that functional cortical-muscular coupling and intermuscular coupling are bidirectional. The average coupling strength of EEG
$\rightarrow $
EMG and EMG
$\rightarrow $
EEG in beta band is 0.86 ± 0.04 and 0.81 ± 0.05 at 10% maximum voluntary contraction (MVC) condition, 0.83 ± 0.05 and 0.76 ± 0.04 at 20% MVC, and 0.76 ± 0.03 and 0.73 ± 0.04 at 30% MVC. With the increase of grip strength, the strength of functional cortical-muscular coupling in beta frequency band decreases, the intermuscular coupling network exhibits enhanced connectivity, and the information exchange is closer. The results demonstrate that TDBackMIC can accurately judge the causal coupling relationship, and functional cortical-muscular coupling and intermuscular coupling network under different grip forces are different, which provides a certain theoretical basis for sports rehabilitation.