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). 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=.8, 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=(60, 140, 5, 1))

# method for correcting p-values for multiple comparisons
mcp = 'bonferroni'
# extract phases and amplitudes
erpac = p.filterfit(sf, x, method='circular', mcp=mcp).squeeze()
# get the p-values and squeeze unused dimensions
pvalues = p.pvalues.squeeze()
# set to nan everywhere it's not significant
erpac[pvalues > .05] = np.nan

vmin, vmax = np.nanmin(erpac), np.nanmax(erpac)

p.pacplot(erpac, time, p.yvec, xlabel='Time (second)',
          cmap='Spectral_r', ylabel='Amplitude frequency', title=p.method,
          cblabel='ERPAC', rmaxis=True, vmin=vmin, vmax=vmax)
plt.axvline(1., linestyle='--', color='k', linewidth=2)

p.show()