Phase amplitude coupling

The measurement of phase amplitude coupling is a very commonly used and effective function. Below, I will provide a detailed explanation of the call parameters of functional phase amplitude coupling, as shown in source code, and give appropriate examples.

Import related packages

import warnings
warnings.filterwarnings('ignore')
from scuteegfe import Feature
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from mne_connectivity.viz import plot_connectivity_circle
import seaborn as sns

d:\code_cloud\new_eeg_deep\scut_eeg_dl\scut_eeg_fe\src\scuteegfe\features\any_feature.py:19: DeprecationWarning:
The `fooof` package is being deprecated and replaced by the `specparam` (spectral parameterization) package.
This version of `fooof` (1.1) is fully functional, but will not be further updated.
New projects are recommended to update to using `specparam` (see Changelog for details).
  from fooof import FOOOFGroup

data = np.random.rand(2, 5, 1000)

n_epcoh, n_channels, n_samples = data.shape
print(f"data.shape: {n_epcoh} epcoh X {n_channels} channels X {n_samples} samples")

data.shape: 2 epcoh X 5 channels X 1000 samples

Single signal PAC

We calculate phase amplitude coupling (PAC) in single channel, which means the phase modulation of a signal corresponds to the amplitude of the same signal.

selected_funcs is ‘pac_connectivity_mod’

- Selected Function: pac_connectivity_mod__mod

- Sample Frequency: pac_connectivity_mod__sfreq: 250 Hz

- Calculation Method: pac_connectivity_mod__method: ‘tort’

- Frequency Bands:

- PAC Phase Band: [4, 8] (Theta)

- PAC Amplitude Band: [30, 45] (Gamma)

- Mode: pac_connectivity_mod__mode: ‘self’ (Single signal)

We calculate PAC for a 250 Hz single channel using the ‘tort’ method for theta phase to gamma amplitude.

data = np.random.rand(2, 5, 1000)
fea1 = Feature(data = data, sfreq=250, selected_funcs = ['pac_connectivity_mod'],
               funcs_params={
                             "pac_connectivity_mod__sfreq": 250,
                             "pac_connectivity_mod__method": 'tort',
                             "pac_connectivity_mod__band": np.array([[4, 8], [30, 45]]),
                             "pac_connectivity_mod__mode": 'self'
                             } )

n_epcoh, n_channels, pac_value = fea1.features.shape
print(f"data.shape: {n_epcoh} epcoh X {n_channels} channels X {pac_value} pac_value")

[........................................] 100% | 0.07 sec | comodulogram: tort
data.shape: 2 epcoh X 5 channels X 1 pac_value

Different signals PACs

The phase and amplitude modulation between different signals is similar to a functional connection between different signals.

selected_funcs is ‘pac_connectivity_mod’

- Selected Function: pac_connectivity_mod__mod

- Sample Frequency: pac_connectivity_mod__sfreq: 250 Hz

- Calculation Method: pac_connectivity_mod__method: ‘tort’

- Frequency Bands:

- PAC Phase Band: [4, 8] (Theta)

- PAC Amplitude Band: [30, 45] (Gamma)

- Mode: pac_connectivity_mod__mode: ‘non-self’ (Different signals)

We calculate PAC for a 250 Hz multi-channel using the ‘tort’ method for theta phase to gamma amplitude.

data = np.random.rand(2, 5, 1000)
fea2 = Feature(data = data, sfreq=250, selected_funcs=['pac_connectivity_mod'],
               funcs_params={
                             "pac_connectivity_mod__sfreq": 250,
                             "pac_connectivity_mod__method": 'tort',
                             "pac_connectivity_mod__band": np.array([[4, 8], [30, 45]]),
                             "pac_connectivity_mod__mode": 'non-self'
                             } )

n_epcoh, n_channels, n_channels = fea2.features.shape
print(f"data.shape: {n_epcoh} epcoh X {n_channels} channels X {n_channels} n_channels")

[........................................] 100% | 0.07 sec | comodulogram: tort
data.shape: 2 epcoh X 5 channels X 5 n_channels

Visualization of PAC

sns.heatmap(fea2.features[0])

<Axes: >

fea2.features[k,i,j] represents that the i-th channel signal of theta phase modulate the j-th channel signal of gamma amplitude for k-th epcoh data.

fig, ax = plt.subplots(figsize=(8, 8),  facecolor="Black", subplot_kw=dict(polar=True))
plot_connectivity_circle(fea2.features[0], [f'Chan {i+1}' for i in range(n_channels)],
                         title = f'PAC connectivity', colormap = "hot",  colorbar_size = 0.35, colorbar_pos = (0, 0.5), ax=ax)

(<Figure size 800x800 with 2 Axes>,
 <PolarAxes: title={'center': 'PAC connectivity'}>)