Addressing Pitfalls in Phase-Amplitude Coupling Analysis with an Extended Modulation Index Toolbox.

Phase-amplitude coupling (PAC) is proposed to play an essential role in coordinating the processing of information on local and global scales. In recent years, the methods able to reveal trustworthy PAC has gained considerable interest. However, the intrinsic features of some signals can lead to the identification of spurious or waveform-dependent coupling. This prompted us to develop an easily accessible tool that could be used to differentiate spurious from authentic PAC. Here, we propose a new tool for more reliable detection of PAC named the Extended Modulation Index (eMI) based on the classical Modulation Index measure of coupling. eMI is suitable both for continuous and epoched data and allows estimation of the statistical significance of each pair of frequencies for phase and for amplitude in the whole comodulogram in the framework of extreme value statistics. We compared eMI with the reference PAC measures-direct PAC estimator (a modification of Mean Vector Length) and standard Modulation Index. All three methods were tested using computer-simulated data and actual local field potential recordings from freely moving rats. All methods exhibited similar properties in terms of sensitivity and specificity of PAC detection. eMI proved to be more selective in the dimension of frequency for phase. One of the novelty's offered by eMI is a heuristic algorithm for classification of PAC as Reliable or Ambiguous. It relies on analysis of the relation between the spectral properties of the signal and the detected coupling. Moreover, eMI generates visualizations that support further evaluation of the coupling properties. It also introduces the concept of the polar phase-histogram to study phase relations of coupled slow and fast oscillations. We discuss the extent to which eMI addresses the known problems of interpreting PAC. The Matlab