Multitaper estimates of phase-amplitude coupling

Abstract

Phase-amplitude coupling (PAC) is the association of the amplitude of a high-frequency oscillation with the phase of a low-frequency oscillation. In neuroscience, this relationship provides a mechanism by which neural activity might be coordinated between distant regions. The dangers and pitfalls of assessing PAC with commonly used statistical measures have been well-documented. The limitations of these measures include: (1) response to non-oscillatory, high-frequency, broad-band activity, (2) response to high-frequency components of the low-frequency oscillation, (3) adhoc selection of analysis frequency-intervals, and (4) reliance upon data shuffling to assess statistical significance.Objective.To address issues (1)-(4) by introducing a nonparametric multitaper estimator of PAC.Approach.In this work, a multitaper PAC estimator is proposed that addresses these issues. Specifically, issue (1) is addressed by replacing the analytic signal envelope estimator computed using the Hilbert transform with a multitaper estimator that down-weights non-sinusoidal activity using a classical, multitaper super-resolution technique. Issue (2) is addressed by replacing coherence between the low-frequency and high-frequency components in a standard PAC estimator with multitaper partial coherence, while issue (3) is addressed with a physical argument regarding meaningful neural oscillation. Finally, asymptotic statistical assessment of the multitaper estimator is introduced to address issue (4).Main results.Multitaper estimates of PAC are introduced. Their efficacy is demonstrated in simulation and on human intracranial recordings obtained from epileptic patients.Significance.This work facilitates a more informative statistical assessment of PAC, a phenomena exhibited by many neural systems, and provides a basis upon which further nonparametric multitaper-related methods can be developed.

Keywords: cross-frequency coupling; estimation; multitaper spectral analysis; neuroscience; phase-amplitude coupling; statistics.