Note

Click here to download the full example code

# Compute all-to-all connectivity in sensor space¶

Computes the Phase Lag Index (PLI) between all gradiometers and shows the connectivity in 3D using the helmet geometry. The left visual stimulation data are used which produces strong connectvitiy in the right occipital sensors.

```
# Author: Martin Luessi <mluessi@nmr.mgh.harvard.edu>
#
# License: BSD (3-clause)
import numpy as np
from scipy import linalg
import mne
from mne import io
from mne.connectivity import spectral_connectivity
from mne.datasets import sample
print(__doc__)
```

Out:

```
```

Set parameters

```
data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
event_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'
# Setup for reading the raw data
raw = io.read_raw_fif(raw_fname)
events = mne.read_events(event_fname)
# Add a bad channel
raw.info['bads'] += ['MEG 2443']
# Pick MEG gradiometers
picks = mne.pick_types(raw.info, meg='grad', eeg=False, stim=False, eog=True,
exclude='bads')
# Create epochs for the visual condition
event_id, tmin, tmax = 3, -0.2, 1.5 # need a long enough epoch for 5 cycles
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks,
baseline=(None, 0), reject=dict(grad=4000e-13, eog=150e-6))
# Compute connectivity for band containing the evoked response.
# We exclude the baseline period
fmin, fmax = 3., 9.
sfreq = raw.info['sfreq'] # the sampling frequency
tmin = 0.0 # exclude the baseline period
con, freqs, times, n_epochs, n_tapers = spectral_connectivity(
epochs, method='pli', mode='multitaper', sfreq=sfreq, fmin=fmin, fmax=fmax,
faverage=True, tmin=tmin, mt_adaptive=False, n_jobs=1)
# the epochs contain an EOG channel, which we remove now
ch_names = epochs.ch_names
idx = [ch_names.index(name) for name in ch_names if name.startswith('MEG')]
con = con[idx][:, idx]
# con is a 3D array where the last dimension is size one since we averaged
# over frequencies in a single band. Here we make it 2D
con = con[:, :, 0]
# Now, visualize the connectivity in 3D
from mayavi import mlab # noqa
mlab.figure(size=(600, 600), bgcolor=(0.5, 0.5, 0.5))
# Plot the sensor locations
sens_loc = [raw.info['chs'][picks[i]]['loc'][:3] for i in idx]
sens_loc = np.array(sens_loc)
pts = mlab.points3d(sens_loc[:, 0], sens_loc[:, 1], sens_loc[:, 2],
color=(1, 1, 1), opacity=1, scale_factor=0.005)
# Get the strongest connections
n_con = 20 # show up to 20 connections
min_dist = 0.05 # exclude sensors that are less than 5cm apart
threshold = np.sort(con, axis=None)[-n_con]
ii, jj = np.where(con >= threshold)
# Remove close connections
con_nodes = list()
con_val = list()
for i, j in zip(ii, jj):
if linalg.norm(sens_loc[i] - sens_loc[j]) > min_dist:
con_nodes.append((i, j))
con_val.append(con[i, j])
con_val = np.array(con_val)
# Show the connections as tubes between sensors
vmax = np.max(con_val)
vmin = np.min(con_val)
for val, nodes in zip(con_val, con_nodes):
x1, y1, z1 = sens_loc[nodes[0]]
x2, y2, z2 = sens_loc[nodes[1]]
points = mlab.plot3d([x1, x2], [y1, y2], [z1, z2], [val, val],
vmin=vmin, vmax=vmax, tube_radius=0.001,
colormap='RdBu')
points.module_manager.scalar_lut_manager.reverse_lut = True
mlab.scalarbar(points, title='Phase Lag Index (PLI)', nb_labels=4)
# Add the sensor names for the connections shown
nodes_shown = list(set([n[0] for n in con_nodes] +
[n[1] for n in con_nodes]))
for node in nodes_shown:
x, y, z = sens_loc[node]
mlab.text3d(x, y, z, raw.ch_names[picks[node]], scale=0.005,
color=(0, 0, 0))
view = (-88.7, 40.8, 0.76, np.array([-3.9e-4, -8.5e-3, -1e-2]))
mlab.view(*view)
```

Out:

```
Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_filt-0-40_raw.fif...
Read a total of 4 projection items:
PCA-v1 (1 x 102) idle
PCA-v2 (1 x 102) idle
PCA-v3 (1 x 102) idle
Average EEG reference (1 x 60) idle
Range : 6450 ... 48149 = 42.956 ... 320.665 secs
Ready.
Current compensation grade : 0
73 matching events found
Applying baseline correction (mode: mean)
Not setting metadata
4 projection items activated
Connectivity computation...
only using indices for lower-triangular matrix
computing connectivity for 20706 connections
using t=0.000s..1.698s for estimation (256 points)
frequencies: 3.5Hz..8.8Hz (10 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: PLI
computing connectivity for epoch 1
computing connectivity for epoch 2
computing connectivity for epoch 3
computing connectivity for epoch 4
computing connectivity for epoch 5
computing connectivity for epoch 6
computing connectivity for epoch 7
computing connectivity for epoch 8
computing connectivity for epoch 9
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 10
computing connectivity for epoch 11
computing connectivity for epoch 12
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 13
computing connectivity for epoch 14
computing connectivity for epoch 15
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 16
computing connectivity for epoch 17
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 18
computing connectivity for epoch 19
computing connectivity for epoch 20
computing connectivity for epoch 21
computing connectivity for epoch 22
computing connectivity for epoch 23
computing connectivity for epoch 24
computing connectivity for epoch 25
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 26
computing connectivity for epoch 27
computing connectivity for epoch 28
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 29
computing connectivity for epoch 30
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 31
computing connectivity for epoch 32
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 33
computing connectivity for epoch 34
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 35
computing connectivity for epoch 36
computing connectivity for epoch 37
computing connectivity for epoch 38
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 39
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 40
computing connectivity for epoch 41
computing connectivity for epoch 42
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
computing connectivity for epoch 43
computing connectivity for epoch 44
computing connectivity for epoch 45
computing connectivity for epoch 46
computing connectivity for epoch 47
computing connectivity for epoch 48
computing connectivity for epoch 49
assembling connectivity matrix (filling the upper triangular region of the matrix)
[Connectivity computation done]
```

**Total running time of the script:** ( 0 minutes 5.734 seconds)

**Estimated memory usage:** 8 MB