Time-Frequency-Domain Copula-Based Granger Causality and Application to Corticomuscular Coupling in Stroke

Abstract

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.