Velocities of hippocampal traveling waves are proportional to their coherence frequency

Cortical traveling waves, defined by their spatial, temporal, and frequency characteristics, provide key insights into active brain regions, timing, frequency, and the direction of activity propagation. Emerging evidence suggests that the directionality and spatiotemporal extent of these waves encode cognitive processes. However, the relationship between frequency and this encoding mechanism remains unclear. We investigate the hypothesis that coherence frequency determines wave propagation velocity. By employing both bivariate linear and multivariate nonlinear coherence analyses, we demonstrate that coherence frequency encodes propagation velocity. Unlike linear analyses, which may overestimate velocities due to bidirectional flow when assessing multiple pair coherences, our nonlinear approach-calculating propagation along four-node pathways-treats pathways as holistic units with net unidirectional flow, making it more appropriate for calculating wave velocities. We extracted pairwise coherence and four-node pathways from local field potentials recorded via intracranial electrodes positioned along the hippocampal longitudinal axis in patients with drug-resistant epilepsy. Our findings reveal that average coherence values and contact pair distances calculated by the multivariate analysis are more consistent across frequencies compared to pairwise coherence. The average coherence values are higher, and the average pair distances and wave velocities are lower in the multivariate analysis than in the pairwise approach. Propagation velocities along the hippocampus at low frequencies (<~35 Hz) exhibit a linear dependence on frequency in the alpha and beta bands, with a steeper slope in the gamma band, indicating distinct mechanisms for velocity-frequency dependence across oscillation bands. While observed within the hippocampus, these findings suggest that the relationship between frequency and wave velocity may extend to other cortical areas. Our nonlinear multivariate analysis appears better suited than pairwise coherence for investigating brain network dynamics. Further research is needed to elucidate the role of conduction velocity in brain function.