Statistically Reliable and Fast Direct Estimation of Phase-Amplitude Cross-Frequency Coupling

Abstract

There is growing interest in phase-amplitude cross-frequency coupling (PAC), which is widely observed in human and animal brain recordings. The choice of the estimation method is vital while extracting accurate PAC parameters from data. Two desired properties of PAC estimators are reliability and computational efficiency. This study offers a methodology called normalized direct PAC (ndPAC) for the rapid and statistically reliable estimation of PAC strength. A plain confidence limit formula, depending solely on data length and confidence level, is derived. Confidence level derivation is validated numerically. It is shown through simulations that ndPAC exhibits high specificity and sensitivity performances. The suggested methodology is also demonstrated on monkey electrocorticogram recorded during a visual task.

Parkinsonian Rest Tremor Is Associated With Modulations of Subthalamic High‐Frequency Oscillations

“…As a complementary approach for studying LFP power modulation within the tremor cycle, we computed phase‐amplitude coupling (PAC) between the phase of the tremor envelope and the amplitude of HFOs. PAC at individual tremor frequency was quantified by the normalized direct PAC estimator . Preferred phases can be readily derived from this measure.…”

“…PAC at individual tremor frequency was quantified by the normalized direct PAC estimator. 33 Preferred phases can be readily derived from this measure. For each STN, epoch-specific PAC spectra were combined by computing a weighted average.…”

“…However, reliable electrophysiological markers of tremor remain to be identified. Recent studies have demonstrated a number of group-level power changes related to tremor, such as an increase at individual tremor frequency, a decrease in the beta band, and an increase in the low gamma band (31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45). [22][23][24][25][26] The consistency of these effects has not been compared so far, although consistency across patients is a major prerequisite for potential markers of tremor.…”

Assessment of cross-frequency coupling with confidence using generalized linear models

“…Although powerful, such surrogate approaches are computationally expensive. A recent approach to determine an analytic procedure assessing the significance of CFC was presented in (Ozkurt, 2012). Second, many existing measures accurately detect only monophasic relationships (i.e., the phase-amplitude probability density has at most one peak (Penny et al, 2008; Özkurt and Schnitzler, 2011)), although entropy-based measures try to overcome this (Canolty et al, 2006b; Tort et al, 2010b).…”

Tensorpac : an open-source Python toolbox for tensor-based Phase-Amplitude Coupling measurement in electrophysiological brain signals

“…In order to quantify PAC, a number of methodologies and implementations have been proposed [35][36][37][38][39][40][41][42][43][44] and compared [43,44]. Until now, there is still no gold standard on which method is the best alternative, even though the Kullback-Leibler Distance [44] is probably the most widely adopted due to its noise tolerance and amplitude independence.…”