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Phase-amplitude coupling (PAC) estimates the statistical dependence between the phase of a low-frequency component and the amplitude of a high-frequency component of local field potentials (LFP). To date PAC has been mainly applied to one signal. In this work, we introduce a new application of PAC to two LFPs and suggest that it can be used to infer the direction and strength of rhythmic neural transmission between distinct brain networks. This hypothesis is based on the accumulating evidence that transmembrane currents related to action potentials contribute a broad-band component to LFP in the high-gamma band, and PAC calculated between the amplitude of high-gamma (>60 Hz) in one LFP and the phase of a low-frequency oscillation (e.g., theta) in another would therefore relate the output (spiking) of one area to the input (somatic/dendritic postsynaptic potentials) of the other. We tested the hypothesis on theta-band long range communications between hippocampus and prefrontal cortex (PFC) and theta-band short range communications between dentate gyrus (DG) and the Ammon’s horn (CA1) within the hippocampus. The ground truth was provided by the known anatomical connections predicting hippocampus → PFC and DG → CA1, i.e., theta transmission is unidirectional in both cases: from hippocampus to PFC and from DG to CA1 along the tri-synaptic pathway within hippocampus. We found that (1) hippocampal high-gamma amplitude was significantly coupled to PFC theta phase, but not vice versa; (2) similarly, DG high-gamma amplitude was significantly coupled to CA1 theta phase, but not vice versa, and (3) the DG high-gamma-CA1 theta PAC was significantly correlated with DG → CA1 Granger causality, a well-established analytical measure of directional neural transmission. These results support the hypothesis that inter-regional PAC (ir-PAC) can be used to relate the output of a rhythmic “driver” network (i.e., high gamma) to the input of a rhythmic “receiver” network (i.e., theta) and thereby establish the direction and strength of rhythmic neural transmission.

Inferring the direction of rhythmic neural transmission via inter-regional phase-amplitude coupling (ir-PAC)