Event-Related Phase Amplitude Coupling

Event-Related Phase-Amplitude Coupling (ERPAC) do not measure PAC across time cycle but instead, across trials (just as proposed JP. Lachaux with the PLV/PLS) or with the Inter-Trial Coherence (ITC). Measuring across trials enable to have a real-time estimation of PAC.

In this example, we generate a signal that have a 10hz phase <->100 hz amplitude coupling first followed by a random noise.

import numpy as np

from tensorpac import EventRelatedPac
from tensorpac.signals import pac_signals_wavelet

import matplotlib.pyplot as plt

Generate a synthetic signal

in order to illustrate how the ERPAC does works, we are going to concatenate two signals. A first one with an alpha <-> gamma coupling during one second and then a second one which is going to be a one second random noise

# First signal consisting of a one second 10 <-> 100hz coupling
n_epochs = 300
n_times = 1000
sf = 1000.
x1, tvec = pac_signals_wavelet(f_pha=10, f_amp=100, n_epochs=n_epochs, noise=2,
                               n_times=n_times, sf=sf)

# Second signal : one second of random noise
x2 = np.random.rand(n_epochs, 1000)

# now, concatenate the two signals across the time axis
x = np.concatenate((x1, x2), axis=1)
time = np.arange(x.shape[1]) / sf

Define an ERPAC object and extract the phase and the amplitude

use tensorpac.EventRelatedPac.filter method to extract phases and amplitudes

# define an ERPAC object
p = EventRelatedPac(f_pha=[9, 11], f_amp='hres')

# extract phases and amplitudes
pha = p.filter(sf, x, ftype='phase', n_jobs=1)
amp = p.filter(sf, x, ftype='amplitude', n_jobs=1)

Compute the ERPAC using the two implemented methods and plot it

# implemented ERPAC methods
methods = ['circular', 'gc']

plt.figure(figsize=(14, 8))
for n_m, m in enumerate(methods):
    # compute the erpac
    erpac = p.fit(pha, amp, method=m, smooth=100, n_jobs=-1).squeeze()

    # plot
    plt.subplot(len(methods), 1, n_m + 1)
    p.pacplot(erpac, time, p.yvec, xlabel='Time (second)' * n_m,
              cmap='Spectral_r', ylabel='Amplitude frequency', title=p.method,
              cblabel='ERPAC', vmin=0., rmaxis=True)
    plt.axvline(1., linestyle='--', color='w', linewidth=2)

plt.tight_layout()
p.show()