The corticomuscular coupling (CMC) characterization between the motor cortex and muscles during motion control is a valid biomarker of motor system function after stroke, which can improve clinical decision-making. However, traditional CMC analysis is mainly based on the coherence method that can’t determine the coupling direction, whereas Granger Causality (GC) is limited in identifying linear cause–effect relationship. In this paper, a time-frequency domain copula-based GC (copula-GC) method is proposed to assess CMC characteristic. The 32-channel electroencephalogram (EEG) signals over brain scalp and electromyography (EMG) signals from upper limb were recorded during controlling and maintaining steady-state force output for five stroke patients and five healthy controls. Then, the time-frequency copula-GC analysis was applied to evaluate the CMC strength in both directions. Experimental results show that the CMC strength of descending direction is greater than that of ascending direction in the time domain for healthy controls. With the increase of grip strength, the bi-directional CMC strength has an increasing trend. Meanwhile, the bi-directional CMC strength of right hand is larger than that of left hand. In addition, the bi-directional CMC strength of stroke patients is lower than that of healthy controls. In the frequency domain, the strongest CMC is observed at the beta frequency band. Additionally, the CMC strength of descending direction is slightly larger than that of ascending direction in healthy controls, while the CMC strength of descending direction is lower than that of ascending direction in stroke patients. We suggest that the proposed time-frequency domain analysis approach based on copula-GC can effectively detect complex functional coupling between cortical oscillations and muscle activities, and provide a potential quantitative analysis measure for motion control and rehabilitation evaluation.

中文翻译：

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基于时频域 Copula 的 Granger 因果关系及其在脑卒中皮质肌肉耦合中的应用

运动控制期间运动皮层和肌肉之间的皮质肌肉耦合 (CMC) 表征是卒中后运动系统功能的有效生物标志物，可改善临床决策。然而，传统的CMC分析主要基于不能确定耦合方向的相干方法，而格兰杰因果关系（GC）在识别线性因果关系方面受到限制。本文提出了一种基于时频域copula的GC（copula-GC）方法来评估CMC特性。在控制和维持五名中风患者和五名健康对照者的稳态力输出期间，记录了脑头皮上的 32 通道脑电图 (EEG) 信号和上肢的肌电图 (EMG) 信号。然后，应用时频copula-GC分析来评估两个方向的CMC强度。实验结果表明，对于健康对照组，下降方向的CMC强度在时域上大于上升方向的强度。随着握力的增加，双向CMC强度有增加的趋势。同时，右手的双向CMC强度大于左手。此外，脑卒中患者的双向 CMC 强度低于健康对照组。在频域中，最强的 CMC 在 β 频段被观察到。此外，健康对照组下降方向的 CMC 强度略大于上升方向，而脑卒中患者下行方向的CMC强度低于上行方向的CMC强度。我们建议提出的基于 copula-GC 的时频域分析方法可以有效地检测皮质振荡和肌肉活动之间的复杂功能耦合，并为运动控制和康复评估提供潜在的定量分析手段。