Measuring Phase-Amplitude Coupling Between Neuronal Oscillations of Different Frequencies

Abstract

Neuronal oscillations of different frequencies can interact in several ways. There has been particular interest in the modulation of the amplitude of high-frequency oscillations by the phase of low-frequency oscillations, since recent evidence suggests a functional role for this type of cross-frequency coupling (CFC). Phase-amplitude coupling has been reported in continuous electrophysiological signals obtained from the brain at both local and macroscopic levels. In the present work, we present a new measure for assessing phase-amplitude CFC. This measure is defined as an adaptation of the Kullback-Leibler distance-a function that is used to infer the distance between two distributions-and calculates how much an empirical amplitude distribution-like function over phase bins deviates from the uniform distribution. We show that a CFC measure defined this way is well suited for assessing the intensity of phase-amplitude coupling. We also review seven other CFC measures; we show that, by some performance benchmarks, our measure is especially attractive for this task. We also discuss some technical aspects related to the measure, such as the length of the epochs used for these analyses and the utility of surrogate control analyses. Finally, we apply the measure and a related CFC tool to actual hippocampal recordings obtained from freely moving rats and show, for the first time, that the CA3 and CA1 regions present different CFC characteristics.

Vagus Nerve Stimulation Applied with a Rapid Cycle Has More Profound Influence on Hippocampal Electrophysiology Than a Standard Cycle

“…PAC between theta and gamma oscillations has been described previously in different hippocampal regions of the rat [16,23,24]. This study shows for the first time a reduced PAC between theta and gamma oscillations during rapid-cycle Fig.…”

“…VNS was associated with a general reduction in broadband 2-100 Hz hippocampal power, which was most prominent in the theta frequency band (4-12 Hz) and gamma frequency ranges (>30 Hz), while little change was observed in an intermediate [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] Hz band (Fig. 3a, b).…”

“…On consecutive days, rapid cycle recording sessions were performed using VNS intensities ramped up in daily 25 μA increments from 0 to 250 μA (day 1-11), in daily increments of 50 μA from 300 μA to 500 μA (day [12][13][14][15][16], and up to 1000 μA in a final recording session (day 17). In this experiment, only hippocampal EEG was acquired.…”

“…Note that for plot (b), the direction of the y-axis has been reversed according to the methods of Tort et al [16]. The MI reflects the modulation of the amplitude of faster oscillations by the phase of slower oscillations, and has previously been used to characterize coupling of theta and gamma frequencies in the hippocampal region [16,23,24]. To calculate the MI, hippocampal EEG was band pass filtered to isolate the frequencies of interest (see below).…”

“…Theta-gamma PAC has been described both in human and rodent hippocampus [16,17], and is thought to be the mechanism by which the activity of local hippocampal neurons or small neuronal assemblies (represented by gamma frequency power) is controlled by field potential changes of larger areas (represented by theta frequency phase) [15]. PAC is hypothesized to support memory encoding and retrieval [17,18].…”