Functional Connectivity Estimated using the Phase Lag Index and Transfer Entropy

Over the decades, the development of various types of indexes for estimating functional connectivity has opened new avenues for revealing complex neural networks in the brain. Specifically, the phase lag index (PLI), which is defined through instantaneous phase dynamics, achieves high spatiotemporal resolution, and transfer entropy (TE), which is defined through information flow, reveals directed network characteristics. However, the relationship between the PLI and TE remains unclear. Based on this context, in this study, we hypothesize that there exists a complementary relationship between the PLI and TE to discover new aspects of functional connectivity that cannot be detected using either the PLI or TE. To validate this hypothesis, we evaluated the synchronization in a coupled Rössler model using the PLI and TE. As a result, we proved the existence of non-linear relationships between the PLI and TE. Both indexes exhibited a specific trend that demonstrated a linear relationship in the region of small TE values. However, above a specific TE value, the PLI converged to a constant value regardless of the TE value. This relationship might be utilized to reveal complex spatiotemporal functional connectivity.