TDITI: A time-delay information transfer index algorithm for corticomuscular coupling

Time delay (TD) across corticomuscular coupling (CMC) is a significant index to assess the information transmission between brain and muscle during movement execution. Larger methods have been widely used to calculate the time delay by estimating phase information, but fail to account for both linear and nonlinear characteristics in the bidirectional coupled systems. For this, this study proposed a novel time-delay estimation method, defined as time-delay information transfer index (TDITI), to explore the TD characteristics between two signal deriving from one system with time-delay coupling. To verify this, we introduced two models to generate a series of simulation signal with linearly unidirectional/ bidirectional coupling or nonlinearly unidirectional/ bidirectional coupling. Simulation results manifested that the TDITI method, compared with the information transfer index (ITI) and coherence methods, can not only describe the TD in the linearly or nonlinearly unidirectional systems, but was also suitable for the bidirectional coupled systems. We also found its robustness to data length, coupling strength and signal-noise ratio. After that, we applied it to explore the TD of CMC by synchronizing the electroencephalogram (EEG) and electromyogram (EMG) signal during steady-state task. Experimental results showed that the CMC between cortex and muscle were direction-dependent, and the average delay time from EEG to EMG (∼25 ms) was shorter than that in the opposition (∼30 ms). Both simulation and experimental data expound the effectiveness of the TDITI method to describe the time delay in the unidirectional or bidirectional coupled systems, and this study extends our perspective to the mechanism of motor control.