What do neural travelling waves tell us about information flow?

In many behavioral conditions, neural activity propagates within and across brain regions as traveling waves, revealing the importance of analyzing spatiotemporal dynamics in electrophysiological data. Most methods quantify such propagation by measuring spatial phase gradients, i.e., monotonic and ordered phase changes through space. Here, we demonstrate that the phase ordering in travelling waves is insufficient to determine the effective flow of information unambiguously. We demonstrate that, in some specific cases, the phase gradient indicates information propagation in the opposite direction than indicated by methods for causal inference. Using autoregressive modeling, we further show that such a discrepancy between the effective waves and the apparent waves measured via phase-based methods can, for example, be predicted by the sign of the projection from the lower to the higher nodes in the hierarchy. Together with an input signal in the lowest node, inhibitory bottom-up connections produce apparent waves propagating in the opposite, top-down direction. As a methodological solution, we show that Granger causality analysis can recover the information flow and its underlying causal structure, which can be used to disambiguate the “effective” flow.