Amplitude amplitude coupling

The measurement of amplitude 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

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 AAC

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

selected_funcs is ‘aac_connectivity_mod’

- Selected Function: aac_connectivity_mod__mod

- Sample Frequency: aac_connectivity_mod__sfreq: 250 Hz

- Frequency Bands:

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

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

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

We calculate AAC for a 250 Hz single channel for theta amplitude to gamma amplitude.

fea1 = Feature(data = data, sfreq=250, selected_funcs=['aac_connectivity'],
                       funcs_params={
                                     "aac_connectivity__sfreq": 250,
                                     "aac_connectivity__band": np.array([[4, 8], [30, 45]]),
                                     "aac_connectivity__mode": 'self'
                                     } )

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

data.shape: 2 epcoh X 5 channels X 1 aac_value

Different signals AACs

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

selected_funcs is ‘pac_connectivity_mod’

- Selected Function: aac_connectivity_mod__mod

- Sample Frequency: aac_connectivity_mod__sfreq: 250 Hz

- Frequency Bands:

- AAC Phase Band: [4, 8] (Theta) seed - AAC Amplitude Band: [30, 45] (Gamma) target

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

We calculate AAC for a 250 Hz multi-channel for theta amplitude to gamma amplitude.

data = np.random.rand(2, 5, 1000)
fea1 = Feature(data = data, sfreq=250, selected_funcs=['aac_connectivity'],
                       funcs_params={
                                     "aac_connectivity__sfreq": 250,
                                     "aac_connectivity__band": np.array([[4, 8], [30, 45]]),
                                     "aac_connectivity__mode": 'non-self'
                                     } )

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

data.shape: 2 epcoh X 5 channels X 5 n_channels

Visualization of AAC

sns.heatmap(fea1.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(fea1.features[0], [f'Chan {i+1}' for i in range(n_channels)],
                         title = f'AAC connectivity', colormap = "hot",  colorbar_size = 0.35, colorbar_pos = (0, 0.5), ax=ax)

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