Assessment of dynamic phase amplitude coupling using matching pursuit

Neuronal transmission and communication are enabled by the interactions across multiple oscillatory frequencies. Phase amplitude coupling (PAC) quantifies these interactions during cognitive brain functions. PAC is defined as the modulation of the amplitude of the high frequency rhythm by the phase of the low frequency rhythm. Existing PAC measures are limited to quantifying the average coupling within a time window of interest. However, as PAC is dynamic, it is necessary to quantify time-varying PAC. Existing time-varying PAC approaches are based on using a sliding window approach. These approaches do not adapt to the signal dynamics, and thus the arbitrary selection of the window length substantially hampers PAC estimation.

To address the limitations of sliding window PAC estimation approaches, in this paper, we introduce a dynamic PAC measure that relies on matching pursuit (MP). This approach decomposes the signal into time and frequency localized atoms that best describe the signal. Dynamic PAC is quantified by computing the coupling between these time and frequency localized atoms. As such, the proposed approach is data-driven and tracks the change of PAC with time. We evaluate the proposed method on both synthesized and real electroencephalogram (EEG) data.

The results from synthesized data show that the proposed method detects the coupled frequencies and the time variation of the coupling correctly with high time and frequency resolution. The analysis of EEG data revealed theta-gamma and alpha-gamma PAC during response and post-response time intervals.

Compared to the existing sliding window based approach, the proposed MP based dynamic PAC measure is more effective at capturing PAC within a short time window and is more robust to noise. This is because this method quantifies the low frequency phase and high frequency amplitude components from the time and frequency localized MP atoms and, as such, can capture the signal dynamics.

We posit that the proposed MP based data-driven approach offers a more robust and possibly more sensitive method to effectively quantify and track dynamic PAC.