[论文解读] Coherence and phase synchronization: generalization to pairs of multivariate time series, and removal of zero-lag contributions

Roberto D. Pascual‐Marqui|ArXiv.org|Jun 12, 2007

Neural dynamics and brain function参考文献 15被引用 59

一句话总结

本文将相干性和相位同步性推广至多变量时间序列对，解决了EEG/MEG神经影像中连通性估计的挑战。提出的方法可消除由于空间分辨率较低而引起的虚假零滞后贡献，从而更准确地从非侵入性记录中推断真实的神经连通性。

ABSTRACT

Coherence and phase synchronization between time series corresponding to different spatial locations are usually interpreted as indicators of the connectivity between locations. In neurophysiology, time series of electric neuronal activity are essential for studying brain interconnectivity. Such signals can either be invasively measured from depth electrodes, or computed from very high time resolution, non-invasive, extracranial recordings of scalp electric potential differences (EEG: electroencephalogram) and magnetic fields (MEG: magnetoencephalogram) by means of a tomography such as sLORETA (standardized low resolution brain electromagnetic tomography). There are two problems in this case. First, in the usual situation of unknown cortical geometry, the estimated signal at each brain location is a vector with three components (i.e. a current density vector), which means that coherence and phase synchronization must be generalized to pairs of multivariate time series. Second, the inherent low spatial resolution of the EEG/MEG tomography introduces artificially high zero-lag coherence and phase synchronization. In this report, solutions to both problems are presented. Two additional generalizations are briefly mentioned: (1) conditional coherence and phase synchronization; and (2) non-stationary time-frequency analysis. Finally, a non-parametric randomization method for connectivity significance testing is outlined. The new connectivity measures proposed here can be applied to pairs of univariate EEG/MEG signals, as is traditional in the published literature. However, these calculations cannot be interpreted as connectivity, since it is in general incorrect to associate an extracranial electrode or sensor to the underlying cortex.

研究动机与目标

• 解决传统相干性和相位同步方法在应用于EEG/MEG源的多变量时间序列时的局限性。
• 解决EEG/MEG源定位技术空间分辨率较低导致的虚假高零滞后相干性问题。
• 通过滤除非同步的零滞后贡献，实现对脑功能连通性的更准确推断。
• 将连通性度量推广至每个脑区的向量值信号，以反映源空间中的三组分电流密度。
• 提供一种非参数化随机化方法，用于检验连通性估计的统计显著性。

提出的方法

• 通过将形式化推广至每个空间位置的向量值信号，将双变量相干性和相位同步性推广至多变量时间序列。
• 定义考虑两个多变量时间序列之间完整互谱矩阵的多变量相干性和相位同步度量。
• 采用频域方法将相干性分解为零滞后和非零滞后分量。
• 应用减法方法从总相干性中去除零滞后贡献，仅保留非零滞后、可能具有意义的连通性。
• 使用非参数化随机化程序评估剩余非零滞后连通性值的统计显著性。
• 简要概述条件相干性和时频分析在非平稳信号中的扩展。

实验结果

研究问题

• RQ1 如何在神经影像中对多变量时间序列对有意义地推广相干性和相位同步性？
• RQ2 EEG/MEG源重建中的低空间分辨率效应在多大程度上人为地放大了零滞后相干性？
• RQ3 去除零滞后贡献是否能提高脑网络中推断功能连通性的准确性？
• RQ4 多变量信号结构（例如三组分电流密度）对相干性估计有何影响？
• RQ5 如何在不依赖参数假设的情况下评估连通性估计的统计显著性？

主要发现

• 所提出的多变量相干性和相位同步度量成功地将标准双变量方法推广至向量值信号，使对源空间位置脑活动的分析成为可能。
• 由于EEG/MEG源定位中固有的空间模糊性，特别是标准低分辨率脑汤图法中，零滞后相干性贡献被显著放大。
• 去除零滞后分量可更准确地反映真实的功能连通性，因为它仅隔离了频率锁定的、非同时发生的相互作用。
• 非参数化随机化方法提供了一种稳健的、无需分布假设的连通性估计显著性检验方法。
• 该方法框架与现有EEG/MEG分析流程兼容，可应用于单变量和多变量信号。
• 条件相干性和时频扩展是可行的，并为分析复杂非平稳神经动力学提供了额外工具。