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

Brain connectivity characterizes interactions between different regions of a brain network during resting-state or performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), one formal approach to investigating connectivity is through an information-theoretic causal measure called transfer entropy (TE). To enhance the functionality of TE in brain signal analysis, we propose a novel methodology that captures 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 band-specific oscillation of one channel to another band-specific oscillation of another channel. The main advantage of our proposed approach is that it formulates TE in a novel way to perform inference on band-specific oscillations while maintaining robustness to the inherent problems associated with filtering. In addition, an advantage of STE is that it allows adjustments for multiple comparisons to control false positive rates. Another novel contribution is a simple yet efficient method for estimating STE using vine copula theory. This method can produce an exact zero estimate of STE (which is the boundary point of the parameter space) without the need for bias adjustments. With the vine copula representation, a null copula model, which exhibits zero STE, is defined, thus enabling straightforward significance testing through standard resampling. Lastly, we demonstrate the advantage of the proposed STE measure through numerical experiments and provide interesting and novel findings on the analysis of EEG data in a visual-memory experiment.