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Extended Granger causality: a new tool to identify the structure of physiological networks

机译：扩展的格兰杰因果关系：识别生理网络结构的新工具

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Granger causality (GC) is a very popular tool for assessing the presence of directional interactions between two time series of a multivariate data set. In its original formulation, GC does not account for zero-lag correlations possibly existing between the observed time series. In the present study we compare the GC with a novel measure, termed extended GC (eGC), able to capture instantaneous causal relationships. We present a two-step procedure for the practical estimation of eGC based on first detecting the existence of zero-lag correlations, and then assigning them to one of the two possible causal directions using pairwise measures of non-Gaussianity. The proposed method was validated in a simulation study, showing that the estimation procedure based on the extended representation overcomes the limits of the classic computation of GC, correctly detecting the presence and direction of zero-lag interactions and providing a meaningful causal interpretation based on the eGC. Then, GC and eGC were computed on the physiological variability series of heart period (HP), mean arterial pressure (AP) and cerebral blood flow velocity (FV) in ten subjects with postural related syncope (PRS), during different epochs of an head-up tilt test protocol. We found that both measures reflect the baroreflex impairment and the loss of cerebral autoregulation during pre-syncope. Furthermore, eGC analysis suggests that fast, within-beat effects between AP and FV variability contribute substantially to the mutual regulation of these physiological variables, and may play an important role in the impairment of cerebrovascular regulation associated with PRS.
机译：Granger因果关系（GC）是一种非常流行的工具，用于评估多元数据集的两个时间序列之间是否存在方向性相互作用。在其原始公式中，GC并未考虑观察到的时间序列之间可能存在的零延迟相关性。在本研究中，我们将GC与一种称为扩展GC（eGC）的新颖措施进行了比较，该措施能够捕获瞬时因果关系。基于首先检测零滞后相关性的存在，然后使用成对的非高斯度量将它们分配给两个可能的因果方向之一，我们提出了两步过程，用于eGC的实际估算。所提方法在仿真研究中得到验证，表明基于扩展表示的估算程序克服了传统气相色谱的局限性，可以正确检测零滞后相互作用的存在和方向，并基于该模型提供有意义的因果解释。 eGC。然后，根据头部的不同时期，对十个患有姿势相关性晕厥（PRS）的受试者的心周期（HP），平均动脉压（AP）和脑血流速度（FV）的生理变异性序列进行GC和eGC计算向上倾斜测试协议。我们发现，这两种措施都反映了晕厥前的压力感受反射障碍和脑自动调节功能的丧失。此外，eGC分析表明，AP和FV变异性之间的快速，心跳内效应在很大程度上促进了这些生理变量的相互调节，并且可能在损害与PRS相关的脑血管调节中发挥重要作用。

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