Astolfi L, Cincotti F, Mattia D, De Vico Fallani F, Tocci A, Colosimo A, Salinari S, Marciani M G, Hesse W, Witte H, Ursino M, Zavaglia M, Babiloni F
Dipartimento di Informatica e Sistemistica, Universitá La Sapienza, Roma 00185, Italy.
IEEE Trans Biomed Eng. 2008 Mar;55(3):902-13. doi: 10.1109/TBME.2007.905419.
The directed transfer function (DTF) and the partial directed coherence (PDC) are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods is based on the multivariate autoregressive modelling (MVAR) of time series, which requires the stationarity of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR) and to apply it to a set of real high resolution EEG data. This approach will allow the observation of rapidly changing influences between the cortical areas during the execution of a task. The simulation results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of signal-to-noise ratio (SNR) ad number of trials. An SNR of five and a number of trials of at least 20 provide a good accuracy in the estimation. After testing the method by the simulation study, we provide an application to the cortical estimations obtained from high resolution EEG data recorded from a group of healthy subject during a combined foot-lips movement and present the time-varying connectivity patterns resulting from the application of both DTF and PDC. Two different cortical networks were detected with the proposed methods, one constant across the task and the other evolving during the preparation of the joint movement.
定向传递函数（DTF）和偏定向相干性（PDC）是频域估计器，能够根据格兰杰因果关系的概念描述皮层区域之间的相互作用。然而，这些方法的经典估计是基于时间序列的多元自回归建模（MVAR），这要求信号具有平稳性。这样一来，信息传递的瞬态路径就仍然隐藏着。本研究的目的是测试一种时变多元方法，用于基于DTF/PDC以及自适应MVAR建模（AMVAR）来估计人类大脑皮层区域之间快速变化的连接关系，并将其应用于一组实际的高分辨率脑电图数据。这种方法将允许观察任务执行期间皮层区域之间快速变化的影响。模拟结果表明，在合理的信噪比（SNR）和试验次数的操作条件下，时变DTF和PDC能够正确估计所施加的连接模式。信噪比为5且试验次数至少为20时，估计具有良好的准确性。通过模拟研究对该方法进行测试后，我们将其应用于从一组健康受试者在足部 - 嘴唇联合运动期间记录的高分辨率脑电图数据中获得的皮层估计，并展示了应用DTF和PDC所产生的时变连接模式。使用所提出的方法检测到了两个不同的皮层网络，一个在整个任务中保持不变，另一个在联合运动准备过程中不断演变。
