Investigating the Brain Causal and Instantaneous Relations Using Information Theory

Exploring the causal (delayed) brain relations is an important topic in the Neuroscience. The traditional estimators of brain causal (delayed) relations are mainly model-based and put restrictive assumptions on the brain dynamics. In the recent years, some nonparametric measures have been introduced to solve this problem. Among them, the most important one is Transfer Entropy (TE) which is based on the information theory and Conditional Mutual Information concept. However, in the presence of significant instantaneous relations that are observed extensively in the brain functional datasets, TE may estimate the causal (delayed) relations inaccurately. In this paper, two information theoretic based measures called Instantaneous Interaction (II) and Modified Transfer entropy (MTE) are introduced to estimate the instantaneous and causal (delayed) brain relations, respectively. MTE is used instead of TE whenever II is significant. These measures are evaluated on 3 simulated models and eyes-closed resting state EEG data. The simulation results show high ability of II to estimate the linear and nonlinear instantaneous relations. Also, based on the simulation results MTE outperforms TE to estimate causal (delayed) relations in presence of significant instantaneous relations (significant II). For the real EEG data, II detects a significant instantaneous relation between Posterior and Frontal EEG channels. Also MTE detects the information flow from Posterior EEG channels to Frontal ones more significantly than TE does. So in presence of significant instantaneous relations in the real EEG data, MTE outperforms TE.