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.

中文翻译：

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TDITI：一种用于皮质肌肉耦合的时滞信息传递指数算法

皮质肌肉耦合（CMC）的时间延迟（TD）是评估运动执行过程中大脑和肌肉之间信息传递的重要指标。较大的方法已广泛用于通过估计相位信息来计算时间延迟，但无法考虑双向耦合系统中的线性和非线性特性。为此，本研究提出了一种新颖的时延估计方法，定义为时延信息传输指数（TDITI），以探索来自具有时延耦合的一个系统的两个信号之间的TD特性。为了验证这一点，我们引入了两个模型来生成一系列具有线性单向/双向耦合或非线性单向/双向耦合的仿真信号。仿真结果表明，TDITI方法与信息传输指数(ITI)和相干方法相比，不仅可以描述线性或非线性单向系统中的TD，而且适用于双向耦合系统。我们还发现它对数据长度、耦合强度和信噪比的鲁棒性。之后，我们应用它通过在稳态任务期间同步脑电图（EEG）和肌电图（EMG）信号来探索 CMC 的 TD。实验结果表明，皮层和肌肉之间的 CMC 具有方向依赖性，并且从 EEG 到 EMG 的平均延迟时间（∼25 ms）比相反的延迟时间（∼30 ms）短。仿真和实验数据都阐述了 TDITI 方法描述单向或双向耦合系统时滞的有效性，本研究将我们的视角扩展到电机控制机制。