Defining the filter parameters for phase-amplitude coupling from a bispectral point of view

Two measures of cross-frequency coupling are phase-amplitude coupling (PAC) and bicoherence. The estimation of PAC with meaningful bandwidth for the high-frequency amplitude is crucial in order to avoid misinterpretations. While recommendations on the bandwidth of PAC's amplitude component exist, there is no consensus yet. Theoretical relationships between PAC and bicoherence can provide insights on how to set PAC's filters.

To illustrate this, PAC estimated from simulated and empirical data are compared to the bispectrum. We used simulations replicated from earlier studies and empirical data from human electro-encephalography and rat local field potentials. PAC's amplitude component was estimated using a filter bandwidth with a ratio of (1) 2:1, (2) 1:1, or (3) 0.5:1 relative to the phase frequency.

For both simulated and empirical data, PAC was smeared over a broad frequency range and not present when the estimates comprised a 2:1- and 0.5:1-ratio, respectively. In contrast, the 1:1-ratio accurately avoids smearing and results in clear signals of cross-frequency coupling. Bicoherence estimates were found to be essentially identical to PAC calculated with the recommended frequency setting.

Earlier recommendations on filter settings of PAC lead to estimates which are smeared in the frequency domain, which makes it difficult to identify cross-frequency coupling of neural processes operating in narrow frequency bands.

We conclude that smearing of PAC estimates can be avoided with a different choice of filter settings by theoretically relating PAC to bicoherence.