Direct interaction on specific frequency bands in functional corticomuscular coupling

Ping Xie, Shengcui Cheng, Yuanyuan Zhang*, Zhaojun Liu, Huan Liu, Xiaolling Chen* and Xiaoli Li

Abstract

Objective: Direct interaction between the brain and muscle is significant for investigating the oscillation mechanisms in the motor control system. Methods: To our knowledge, the partial directed coherence (PDC) method is sufficient to reflect the direct interaction among multivariate time series in the frequency domain, but fails to eliminate the spectral overlap among frequency bands. Therefore, we expanded the PDC method and constructed a novel method, named variational-mode-decomposition-based PDC (VMDPDC), to describe the direct interaction on specific frequency bands. Results: To verify this, we made a comparison with the Granger causality (GC), PDC, and FIR-based PDC (FIRPDC) methods in two numerical models (bivariate coupling model and multivariate coupling model). After that, we applied this method to analyze the functional corticomuscular coupling (FCMC) during steady-state grip task. Simulation results showed that, compared with the GC, PDC, and FIRPDC methods, the VMDPDC method could accurately detect the direct interaction on specific frequency bands. The results on experimental data showed that the direct interaction in FCMC mainly focused on the alpha (8-15 Hz), beta (15-35 Hz), and gamma (35-60 Hz) bands. Further analysis demonstrated that the coupling strength in descending direction was significantly higher than that in the opposite direction. Conclusion: Both simulation and experimental results indicated that the proposed method could effectively describe the direct interaction on specific frequency bands. Significance: This study also provides a theoretical foundation for further exploration on the mechanism of the motor control.

摘要

目的：大脑与肌肉之间的直接互动对于研究运动控制系统的振荡机制具有重要意义。方法：据我们所知，部分定向相干（PDC）方法足以反映多变量时间序列在频域中的直接相互作用，但无法消除频带间的频谱重叠。因此，我们扩展了 PDC 方法，并构建了一种新方法，命名为基于变异模式分解的 PDC（VMDPDC），以描述特定频段上的直接交互作用。结果为了验证这一点，我们在两个数值模型（二元耦合模型和多元耦合模型）中对格兰杰因果关系（GC）、PDC 和基于 FIR 的 PDC（FIRPDC）方法进行了比较。之后，我们应用该方法分析了稳态握力任务中的皮质肌肉功能耦合（FCMC）。仿真结果表明，与 GC、PDC 和 FIRPDC 方法相比，VMDPDC 方法能准确检测特定频段上的直接相互作用。实验数据结果表明，FCMC 中的直接相互作用主要集中在α（8-15 Hz）、β（15-35 Hz）和γ（35-60 Hz）频段。进一步分析表明，下降方向的耦合强度明显高于相反方向。结论模拟和实验结果都表明，所提出的方法能有效地描述特定频段上的直接相互作用。意义：这项研究也为进一步探索运动控制的机制提供了理论基础。