Radboud University Nijmegen, Donders Institute for Brain, Cognition and Behavior, Nijmegen, The Netherlands; Swammerdam Institute for Life Sciences, Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands; Yale University, School of Medicine, Department of Neurobiology, New Haven, CT, USA.
Swammerdam Institute for Life Sciences, Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands.
Neuroimage. 2015 Mar;108:301-18. doi: 10.1016/j.neuroimage.2014.12.017. Epub 2014 Dec 13.
Granger-causality metrics have become increasingly popular tools to identify directed interactions between brain areas. However, it is known that additive noise can strongly affect Granger-causality metrics, which can lead to spurious conclusions about neuronal interactions. To solve this problem, previous studies have proposed the detection of Granger-causal directionality, i.e. the dominant Granger-causal flow, using either the slope of the coherency (Phase Slope Index; PSI), or by comparing Granger-causality values between original and time-reversed signals (reversed Granger testing). We show that for ensembles of vector autoregressive (VAR) models encompassing bidirectionally coupled sources, these alternative methods do not correctly measure Granger-causal directionality for a substantial fraction of VAR models, even in the absence of noise. We then demonstrate that uncorrelated noise has fundamentally different effects on directed connectivity metrics than linearly mixed noise, where the latter may result as a consequence of electric volume conduction. Uncorrelated noise only weakly affects the detection of Granger-causal directionality, whereas linearly mixed noise causes a large fraction of false positives for standard Granger-causality metrics and PSI, but not for reversed Granger testing. We further show that we can reliably identify cases where linearly mixed noise causes a large fraction of false positives by examining the magnitude of the instantaneous influence coefficient in a structural VAR model. By rejecting cases with strong instantaneous influence, we obtain an improved detection of Granger-causal flow between neuronal sources in the presence of additive noise. These techniques are applicable to real data, which we demonstrate using actual area V1 and area V4 LFP data, recorded from the awake monkey performing a visual attention task.
Granger 因果度量已成为识别大脑区域之间有向相互作用的流行工具。然而，已知加性噪声会强烈影响 Granger 因果度量，从而导致关于神经元相互作用的虚假结论。为了解决这个问题，先前的研究提出了使用相干斜率（相位斜率指数；PSI）或通过比较原始和时间反转信号之间的 Granger 因果值（反转 Granger 测试）来检测 Granger 因果方向性，即主导的 Granger 因果流。我们表明，对于包含双向耦合源的向量自回归（VAR）模型的集合，这些替代方法即使在没有噪声的情况下，对于相当一部分 VAR 模型也不能正确测量 Granger 因果方向性。然后，我们证明不相关噪声对定向连接度量的影响与线性混合噪声根本不同，后者可能是由于电容积传导的结果。不相关噪声仅对 Granger 因果方向性的检测产生微弱影响，而线性混合噪声会导致标准 Granger 因果度量和 PSI 的大量假阳性，但对反转 Granger 测试则不会。我们进一步表明，我们可以通过检查结构 VAR 模型中的瞬时影响系数的大小，可靠地识别出线性混合噪声导致大量假阳性的情况。通过拒绝具有强瞬时影响的情况，我们在存在加性噪声的情况下获得了对神经元源之间 Granger 因果流的改进检测。这些技术适用于实际数据，我们使用在执行视觉注意力任务的清醒猴子中记录的实际 V1 和 V4 LFP 数据来证明这一点。
