Measuring Information Transfer Between Nodes in a Brain Network through Spectral Transfer Entropy

Abstract

Brain connectivity reflects how different regions of the brain interact during performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), this may be explored via Granger causality (GC) which tests if knowledge of the past values of a channel improves predictions on future values of another channel. However, the common approach to investigating GC is the vector autoregressive (VAR) model which is limited only to linear lead-lag relations. An alternative information-theoretic causal measure, transfer entropy (TE), becomes more appropriate since it does not impose any distributional assumption on the variables and covers any form of relationship (beyond linear) between them. To improve utility of TE in brain signal analysis, we propose a novel methodology to capture cross-channel information transfer in the frequency domain. Specifically, we introduce a new measure, the spectral transfer entropy (STE), to quantify the magnitude and direction of information flow from a certain frequency-band oscillation of a channel to an oscillation of another channel. In contrast with previous works on TE in the frequency domain, we differentiate our work by considering the magnitude of filtered series (frequency band-specific), instead of using the spectral representation (frequency-specific) of a series. The main advantage of our proposed approach is that it allows adjustments for multiple comparisons to control family-wise error rate (FWER). One novel contribution is a simple yet efficient estimation method based on vine copula theory that enables estimates to capture zero (boundary point) without the need for bias adjustments. We showcase the advantage of our proposed measure through some numerical experiments and provide interesting and novel findings on the analysis of EEG recordings linked to a visual task.