connectivity

The measurement of functional connectivity is a very commonly used and effective function. Below, I will provide a detailed explanation of the call parameters of functional connectivity functions, as shown in source code 1, and give appropriate examples.

Import related packages

import warnings
warnings.filterwarnings('ignore')
from scuteegfe import Feature
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import mne
from mne.datasets import eegbci
from mne import Epochs, pick_types, events_from_annotations
from mne.channels import make_standard_montage
from mne.io import concatenate_raws, read_raw_edf
from nilearn import plotting
import matplotlib.cm as cm
from mne_connectivity.viz import plot_connectivity_circle

get motor image data

def get_data_example_motor_image():
    tmin, tmax = -1., 4.
    event_id = dict(hands=2, feet=3)
    subject = 1
    runs = [6, 10, 14]  # motor imagery: hands vs feet
    raw_fnames = eegbci.load_data(subject, runs)
    raw = concatenate_raws([read_raw_edf(f, preload=True) for f in raw_fnames])
    eegbci.standardize(raw)  # set channel names
    montage = make_standard_montage('standard_1005')
    raw.set_montage(montage)

    # Apply band-pass filter
    raw.filter(7., 30., fir_design='firwin', skip_by_annotation='edge')

    events, _ = events_from_annotations(raw, event_id=dict(T1=2, T2=3))

    picks = pick_types(raw.info, meg=False, eeg=True, stim=False, eog=False,
                       exclude='bads')

    # Read epochs (train will be done only between 1 and 2s)
    # Testing will be done with a running classifier
    epochs = Epochs(raw, events, event_id, tmin, tmax, proj=True, picks=picks,
                    baseline=None, preload=True)
    epochs_train = epochs.copy().crop(tmin=1., tmax=2.)
    labels = epochs.events[:, -1] - 2
    data = epochs.get_data()
    print(data.shape)
    return data, labels

data, _ = get_data_example_motor_image()
# 7-channel data are used.
data = data[:,:7,:]

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: 45 epcoh X 7 channels X 801 samples

Connectivity Function

The function used to measure functional connection calls is correlation_matrix.

Available Options for the Parameter kind:

• covariance: Measures the covariance between signals.

• correlation: Measures the Pearson correlation coefficient between signals.

• partial correlation: Measures the partial correlation, accounting for the influence of other signals.

• tangent: Computes the tangent connectivity measure. For usage, see Varoquaux et al [1].

• precision: Measures the precision of the connectivity.

• coh: Coherence.

• cohy: Coherency.

• imcoh: Imaginary part of Coherency.

• cacoh: Canonical Coherency (CaCoh).

• mic: Maximised Imaginary part of Coherency (MIC).

• mim: Multivariate Interaction Measure (MIM).

• plv: Phase-Locking Value (PLV).

• ciplv: Corrected Imaginary PLV (ciPLV).

• ppc: Pairwise Phase Consistency (PPC).

• pli: Phase Lag Index (PLI).

• pli2_unbiased: Unbiased estimator of squared PLI.

• dpli: Directed PLI (DPLI).

• wpli: Weighted PLI (WPLI).

• wpli2_debiased: Debiased estimator of squared WPLI.

• gc: State-space Granger Causality (GC).

• gc_tr: State-space GC on time-reversed signals.

• pec: power envolope correlation on time-reversed signals.

Reference

[1]

Gael Varoquaux, Flore Baronnet, Andreas Kleinschmidt, Pierre Fillard, and Bertrand Thirion. Detection of brain functional-connectivity difference in post-stroke patients using group-level covariance modeling. In Tianzi Jiang, Nassir Navab, Josien P. W. Pluim, and Max A. Viergever, editors, Medical Image Computing and Computer-Assisted Intervention - MICCAI 2010, Lecture Notes in Computer Science, 200–208. Berlin, Heidelberg, 2010. Springer. doi:10/cn2h9c.

pec: power envolope correlation

fea = Feature(data, sfreq=160, selected_funcs=['correlation_matrix'],
              funcs_params={"correlation_matrix__sfreq":160,"correlation_matrix__kind":"pec"})

C:\software\Anaconda\envs\py3.9\lib\site-packages\scuteegfe\mne_features_wrapper\feature_wrapper.py:63: UserWarning: 提案的函数sfreq需要再以参数的形式传入
  warnings.warn("提案的函数sfreq需要再以参数的形式传入", UserWarning)

print(fea.features.shape)
n_epoch,n_channel,n_channel = fea.features.shape
print(f"feature shape: {n_epcoh} epcoh X {n_channels} channels X {n_channels} channels")
fig, ax = plt.subplots(figsize=(8, 8),  facecolor="Black", subplot_kw=dict(polar=True))
plot_connectivity_circle(fea.features[0], [f'Chan {i+1}' for i in range(n_channels)],
                         title=f'pec function connectivity of motor image',
                    colormap="hot",  colorbar_size=0.35, colorbar_pos=(0, 0.5), ax=ax)

(45, 7, 7)
feature shape: 45 epcoh X 7 channels X 7 channels

(<Figure size 800x800 with 2 Axes>,
 <PolarAxes: title={'center': 'pec function connectivity of motor image'}>)

coh: Coherence.

fea = Feature(data, sfreq=160, selected_funcs=['correlation_matrix'],
              funcs_params={"correlation_matrix__sfreq":160,"correlation_matrix__kind":"coh"})

C:\software\Anaconda\envs\py3.9\lib\site-packages\scuteegfe\mne_features_wrapper\feature_wrapper.py:63: UserWarning: 提案的函数sfreq需要再以参数的形式传入
  warnings.warn("提案的函数sfreq需要再以参数的形式传入", UserWarning)

print(fea.features.shape)
n_epoch,n_channel,n_channel = fea.features.shape
print(f"feature shape: {n_epcoh} epcoh X {n_channels} channels X {n_channels} channels")
fig, ax = plt.subplots(figsize=(8, 8),  facecolor="Black", subplot_kw=dict(polar=True))
plot_connectivity_circle(fea.features[0], [f'Chan {i+1}' for i in range(n_channels)],
                         title=f'coh function connectivity of motor image',
                    colormap="hot",  colorbar_size=0.35, colorbar_pos=(0, 0.5), ax=ax)

(45, 7, 7)
feature shape: 45 epcoh X 7 channels X 7 channels

(<Figure size 800x800 with 2 Axes>,
 <PolarAxes: title={'center': 'coh function connectivity of motor image'}>)

covariance: Covariance.

meature covariance for alpha frequency band.

fea2 = Feature(data, sfreq=160, selected_funcs=['correlation_matrix'],
               funcs_params={"correlation_matrix__sfreq":160,"correlation_matrix__kind":"covariance",
                             "correlation_matrix__filter_bank":[8,12]})

print(fea2.features.shape)
n_epoch,n_channel,n_channel = fea2.features.shape
print(f"feature shape: {n_epcoh} epcoh X {n_channels} channels X {n_channels} channels")
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'covariance function connectivity of motor image',
                    colormap="hot",  colorbar_size=0.35, colorbar_pos=(0, 0.5), ax=ax)

Setting up band-pass filter from 8 - 12 Hz

FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal bandpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 8.00
- Lower transition bandwidth: 2.00 Hz (-6 dB cutoff frequency: 7.00 Hz)
- Upper passband edge: 12.00 Hz
- Upper transition bandwidth: 3.00 Hz (-6 dB cutoff frequency: 13.50 Hz)
- Filter length: 265 samples (1.656 s)

(45, 7, 7)
feature shape: 45 epcoh X 7 channels X 7 channels

[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s
[Parallel(n_jobs=1)]: Done   2 out of   2 | elapsed:    0.0s remaining:    0.0s
[Parallel(n_jobs=1)]: Done   3 out of   3 | elapsed:    0.0s remaining:    0.0s
[Parallel(n_jobs=1)]: Done   4 out of   4 | elapsed:    0.0s remaining:    0.0s
[Parallel(n_jobs=1)]: Done   7 out of   7 | elapsed:    0.0s finished

(<Figure size 800x800 with 2 Axes>,
 <PolarAxes: title={'center': 'covariance function connectivity of motor image'}>)