Rotman Research Institute, Baycrest Centre, Toronto, Ontario, Canada.
PLoS One. 2013;8(1):e53588. doi: 10.1371/journal.pone.0053588. Epub 2013 Jan 21.
Linear and non-linear techniques for inferring causal relations between the brain signals representing the underlying neuronal systems have become a powerful tool to extract the connectivity patterns in the brain. Typically these tools employ the idea of Granger causality, which is ultimately based on the temporal precedence between the signals. At the same time, phase synchronization between coupled neural ensembles is considered a mechanism implemented in the brain to integrate relevant neuronal ensembles to perform a cognitive or perceptual task. Phase synchronization can be studied by analyzing the effects of phase-locking between the brain signals. However, we should expect that there is no one-to-one mapping between the observed phase lag and the time precedence as specified by physically interacting systems. Specifically, phase lag observed between two signals may interfere with inferring causal relations. This could be of critical importance for the coupled non-linear oscillating systems, with possible time delays in coupling, when classical linear cross-spectrum strategies for solving phase ambiguity are not efficient. To demonstrate this, we used a prototypical model of coupled non-linear systems, and compared three typical pipelines of inferring Granger causality, as established in the literature. Specifically, we compared the performance of the spectral and information-theoretic Granger pipelines as well as standard Granger causality in their relations to the observed phase differences for frequencies at which the signals become synchronized to each other. We found that an information-theoretic approach, which takes into account different time lags between the past of one signal and the future of another signal, was the most robust to phase effects.
线性和非线性技术已成为从代表潜在神经元系统的大脑信号中提取大脑连接模式的有力工具,用于推断大脑信号之间的因果关系。这些工具通常采用格兰杰因果关系的思想,而格兰杰因果关系最终基于信号之间的时间优先关系。同时,耦合神经集合之间的相位同步被认为是大脑中用于整合相关神经元集合以执行认知或感知任务的一种机制。可以通过分析大脑信号之间的锁相效应来研究相位同步。然而,我们应该预期,观察到的相移与物理相互作用系统指定的时间优先顺序之间没有一一对应的映射关系。具体来说,两个信号之间观察到的相移可能会干扰因果关系的推断。对于具有耦合非线性振荡系统和可能的耦合延迟的情况,这可能至关重要,因为经典的线性互谱策略无法有效地解决相位模糊问题。为了证明这一点,我们使用了耦合非线性系统的原型模型,并比较了文献中建立的三种典型的推断格兰杰因果关系的方法。具体来说,我们比较了谱和信息论格兰杰因果关系的性能以及标准格兰杰因果关系,以了解它们与信号相互同步时频率的观察相位差之间的关系。我们发现,考虑到一个信号的过去和另一个信号的未来之间的不同时间延迟的信息论方法对相位效应最稳健。