Empirical analysis of phase-amplitude coupling approaches.

Analysis of the coupling between the phases and amplitudes of oscillations within the same continuously sampled signal has provided interesting insights into the physiology of memory and other brain process, and, more recently, the pathophysiology of parkinsonism and other movement disorders. Technical aspects of the analysis have a significant impact on the results. We present an empirical exploration of a variety of analysis design choices that need to be considered when measuring phase-amplitude coupling (PAC). We studied three alternative filtering approaches to the commonly used Kullback-Leibler distance-based method of PAC analysis, including one method that uses wavelets, one that uses constant filter settings, and one in which filtering of the data is optimized for individual frequency bands. Additionally, we introduce a time-dependent PAC analysis technique that takes advantage of the inherent temporality of wavelets. We examined how the duration of the sampled data, the stability of oscillations, or the presence of artifacts affect the value of the "modulation index", a commonly used parameter describing the degree of PAC. We also studied the computational costs associated with calculating modulation indices by the three techniques. We found that wavelet-based PAC performs better with similar or less computational cost than the two other methods while also allowing to examine temporal changes of PAC. We also show that the reliability of PAC measurements strongly depends on the duration and stability of PAC, and the presence (or absence) of artifacts. The best parameters to be used for PAC analyses of long samples of data may differ, depending on data characteristics and analysis objectives. Prior to settling on a specific PAC analysis approach for a given set of data, it may be useful to conduct an initial analysis of the time-dependence of PAC using our time-resolved PAC analysis.