Granger Causality Based Directional Phase-Amplitude Coupling Measure

Phase-amplitude coupling (PAC), which quantifies the coupling between the amplitude of a fast oscillation and the phase of a slow oscillation, is reported as a possible mechanism that controls the flow of information in the brain. Although there is ample evidence suggesting that neural interactions are directional, conventional PAC measures mostly quantify the cross-frequency coupling, failing to provide information on the direction of interactions. In this paper, we introduce a Granger causality (GC) based approach to estimate the direction of PAC. This approach infers the directionality of cross-frequency coupling by computing GC between the instantaneous phase and amplitude components extracted from the signal through a complex time-frequency (t-f) distribution, known as the Reduced Interference Distribution (RID)-Rihaczek. The method is evaluated on both simulated and real electroencephalogram (EEG) signals. The results demonstrate that the proposed GC based directional PAC measure can infer the direction of neural interactions across frequency bands.