Properties and efficacy of a novel method for assessing phase to amplitude cross-frequency coupling
Recent studies indicate that coupling between low‑ and high‑frequency (e.g. theta and gamma) brain rhythms provides valuable information on cognitive processing in humans. The purpose of this study was to examine the properties and efficacy of a novel method of assessment of phase to amplitude cross‑frequency coupling. The proposed method is based on analysis of time‑frequency representation of signals aligned to a given phase in the low‑frequency band. Low frequen‑ cy wave is obtained with Matching Pursuit algorithm by selecting waveforms of interest. The time‑frequency representation of a signal’s energy density is derived from the continuous wavelet transform, and normal‑ ized at each frequency relative to its average value in the baseline period. Next, the representation is thresh‑ olded at values obtained from surrogate data. The re‑ sulting maps are used to compute comodulograms. The effects presented in the comodulograms are vali‑ dated with extreme values statistics. The method was tested on synthetic signals. The first signal represents proper phase to amplitude cross‑frequency coupling. It consists of a low‑frequency sine (in the range of theta rhythm frequencies) with superimposed spin‑ dles of high‑frequency (from the gamma band range) and white noise. The second and third signals display epiphenomenal cross‑frequency coupling, which orig‑ inates from their time course. We found that the pro‑ posed method is robust for high noise levels, which suggests that it has sufficient sensitivity to detect the theta‑gamma coupling as measured by high quality EEG or ECoG. Nonetheless, it is not immune to epiphenom‑ enal cross‑frequency coupling, which warns us against drawing conclusions from positive output.