What do neural travelling waves tell us about information flow?

In many behavioral conditions, neural activity manifests itself within and across brain regions as traveling waves, revealing the importance of analyzing spatiotemporal dynamics in electrophysiological data. Most methods detect traveling waves by measuring spatial phase gradients, i.e., monotonic and ordered phase changes through space. It is unclear, however, how these traveling waves relate to the causal directionality of information flow. Here, we analyze systems of coupled nodes with an external input to one node. We demonstrate that the phase ordering in traveling waves does not always correspond to the direction of effective information flow. We show that discrepancies can emerge in the case of systems with delays and inhibitory influences. As a methodological solution, we show that Granger causality analysis can, in linear systems, recover the directionality of the information flow. We propose a new measure called DIFF, the Directional Information Flow Field. DIFF is constructed by analyzing directed causal influences in space and time between neighbours, yielding a vector field. As a proof of principle, we show that, in a 2D field where a connected network is perturbed by an external input, the Divergence of DIFF can identify the spatial source of the perturbations. We propose that causal inference methods provide complementary information to phase-based traveling wave methods in analyzing system dynamics and information flow.