Note

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# Compute source level time-frequency timecourses using a DICS beamformer#

In this example, a Dynamic Imaging of Coherent Sources (DICS) [1] beamformer is used to transform sensor-level time-frequency objects to the source level. We will look at the event-related synchronization (ERS) of beta band activity in the somato dataset.

```
# Authors: Marijn van Vliet <w.m.vanvliet@gmail.com>
# Alex Rockhill <aprockhill@mailbox.org>
#
# License: BSD-3-Clause
import numpy as np
import mne
from mne.datasets import somato
from mne.time_frequency import tfr_morlet, csd_tfr
from mne.beamformer import make_dics, apply_dics_tfr_epochs
print(__doc__)
```

Organize the data that we will use for this example.

```
data_path = somato.data_path()
subject = "01"
task = "somato"
raw_fname = data_path / f"sub-{subject}" / "meg" / f"sub-{subject}_task-{task}_meg.fif"
fname_fwd = (
data_path / "derivatives" / f"sub-{subject}" / f"sub-{subject}_task-{task}-fwd.fif"
)
subjects_dir = data_path / "derivatives" / "freesurfer" / "subjects"
```

First, we load the data and compute for each epoch the time-frequency decomposition in sensor space.

```
# Load raw data and make epochs.
raw = mne.io.read_raw_fif(raw_fname)
events = mne.find_events(raw)
epochs = mne.Epochs(
raw,
events,
event_id=1,
tmin=-1,
tmax=2.5,
reject=dict(
grad=5000e-13, # unit: T / m (gradiometers)
mag=5e-12, # unit: T (magnetometers)
eog=250e-6, # unit: V (EOG channels)
),
preload=True,
)
epochs = epochs[:10] # just for speed of execution for the tutorial
# We are mostly interested in the beta band since it has been shown to be
# active for somatosensory stimulation
freqs = np.linspace(13, 31, 5)
# Use Morlet wavelets to compute sensor-level time-frequency (TFR)
# decomposition for each epoch. We must pass ``output='complex'`` if we wish to
# use this TFR later with a DICS beamformer. We also pass ``average=False`` to
# compute the TFR for each individual epoch.
epochs_tfr = tfr_morlet(
epochs, freqs, n_cycles=5, return_itc=False, output="complex", average=False
)
# crop either side to use a buffer to remove edge artifact
epochs_tfr.crop(tmin=-0.5, tmax=2)
```

```
Opening raw data file /home/circleci/mne_data/MNE-somato-data/sub-01/meg/sub-01_task-somato_meg.fif...
Range : 237600 ... 506999 = 791.189 ... 1688.266 secs
Ready.
111 events found
Event IDs: [1]
Not setting metadata
111 matching events found
Setting baseline interval to [-0.9989760657919393, 0.0] s
Applying baseline correction (mode: mean)
0 projection items activated
Loading data for 111 events and 1052 original time points ...
Rejecting epoch based on MAG : ['MEG 0121']
Rejecting epoch based on MAG : ['MEG 0121']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 0211', 'MEG 1331', 'MEG 2211', 'MEG 2241', 'MEG 2521']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 1641', 'MEG 1831', 'MEG 1921', 'MEG 1941', 'MEG 2241']
Rejecting epoch based on MAG : ['MEG 1831']
Rejecting epoch based on MAG : ['MEG 1611']
Rejecting epoch based on MAG : ['MEG 0211', 'MEG 0441', 'MEG 1631']
Rejecting epoch based on MAG : ['MEG 1611']
Rejecting epoch based on MAG : ['MEG 1611', 'MEG 1641']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 1611', 'MEG 1641']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 1611', 'MEG 1631', 'MEG 1641', 'MEG 1941']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0231']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 1411']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0211', 'MEG 0231', 'MEG 0341', 'MEG 1621', 'MEG 1811', 'MEG 2211']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0211', 'MEG 1521', 'MEG 1611', 'MEG 1641', 'MEG 1721', 'MEG 1941']
Rejecting epoch based on MAG : ['MEG 0121']
Rejecting epoch based on MAG : ['MEG 0211']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0211']
Rejecting epoch based on MAG : ['MEG 0121']
Rejecting epoch based on MAG : ['MEG 0341']
Rejecting epoch based on MAG : ['MEG 1911', 'MEG 1921', 'MEG 1931', 'MEG 1941', 'MEG 2111', 'MEG 2121']
Rejecting epoch based on MAG : ['MEG 0121']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 2021', 'MEG 2241']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0211', 'MEG 0341']
Rejecting epoch based on MAG : ['MEG 1341', 'MEG 1611']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0341']
Rejecting epoch based on MAG : ['MEG 0121']
Rejecting epoch based on MAG : ['MEG 1611', 'MEG 1641', 'MEG 1831', 'MEG 1911', 'MEG 1941', 'MEG 2011']
Rejecting epoch based on MAG : ['MEG 0211']
Rejecting epoch based on MAG : ['MEG 1641']
Rejecting epoch based on MAG : ['MEG 0211', 'MEG 0221', 'MEG 0231', 'MEG 0241', 'MEG 0341', 'MEG 0441', 'MEG 1611', 'MEG 1621', 'MEG 1641', 'MEG 1731', 'MEG 1911', 'MEG 1921', 'MEG 1941', 'MEG 2041', 'MEG 2241']
Rejecting epoch based on MAG : ['MEG 0731', 'MEG 1141', 'MEG 2211', 'MEG 2241']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0211', 'MEG 0241', 'MEG 1521', 'MEG 1611', 'MEG 1621', 'MEG 1641', 'MEG 1721']
Rejecting epoch based on MAG : ['MEG 1611']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 0211', 'MEG 0221', 'MEG 0231']
Rejecting epoch based on MAG : ['MEG 0211']
Rejecting epoch based on MAG : ['MEG 1331', 'MEG 1641', 'MEG 2211', 'MEG 2241']
Rejecting epoch based on MAG : ['MEG 0231']
Rejecting epoch based on MAG : ['MEG 1641']
Rejecting epoch based on MAG : ['MEG 0121']
Rejecting epoch based on MAG : ['MEG 1131']
Rejecting epoch based on MAG : ['MEG 0211', 'MEG 0341']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0131', 'MEG 0211', 'MEG 0341', 'MEG 1611', 'MEG 1621', 'MEG 1641']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 0211', 'MEG 0341']
Rejecting epoch based on MAG : ['MEG 0121', 'MEG 1611']
53 bad epochs dropped
[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 306 out of 306 | elapsed: 1.5s finished
Not setting metadata
```

Now, we build a DICS beamformer and project the sensor-level TFR to the source level.

```
# Compute the Cross-Spectral Density (CSD) matrix for the sensor-level TFRs.
# We are interested in increases in power relative to the baseline period, so
# we will make a separate CSD for just that period as well.
csd = csd_tfr(epochs_tfr, tmin=-0.5, tmax=2)
baseline_csd = csd_tfr(epochs_tfr, tmin=-0.5, tmax=-0.1)
# use the CSDs and the forward model to build the DICS beamformer
fwd = mne.read_forward_solution(fname_fwd)
# compute scalar DICS beamfomer
filters = make_dics(
epochs.info,
fwd,
csd,
noise_csd=baseline_csd,
pick_ori="max-power",
reduce_rank=True,
real_filter=True,
)
# project the TFR for each epoch to source space
epochs_stcs = apply_dics_tfr_epochs(epochs_tfr, filters, return_generator=True)
# average across frequencies and epochs
data = np.zeros((fwd["nsource"], epochs_tfr.times.size))
for epoch_stcs in epochs_stcs:
for stc in epoch_stcs:
data += (stc.data * np.conj(stc.data)).real
stc.data = data / len(epochs) / len(freqs)
# apply a baseline correction
stc.apply_baseline((-0.5, -0.1))
```

```
Reading forward solution from /home/circleci/mne_data/MNE-somato-data/derivatives/sub-01/sub-01_task-somato-fwd.fif...
Reading a source space...
[done]
Reading a source space...
[done]
2 source spaces read
Desired named matrix (kind = 3523) not available
Read MEG forward solution (8155 sources, 306 channels, free orientations)
Source spaces transformed to the forward solution coordinate frame
Identifying common channels ...
Dropped the following channels:
['STI 014', 'STI 004', 'STI 001', 'EOG 061', 'STI 006', 'STI 005', 'STI 016', 'STI 015', 'STI 003', 'STI 002']
Identifying common channels ...
Computing inverse operator with 306 channels.
306 out of 306 channels remain after picking
Selected 306 channels
Creating the depth weighting matrix...
Whitening the forward solution.
Computing rank from covariance with rank=None
Using tolerance 2.8e-14 (2.2e-16 eps * 306 dim * 0.4 max singular value)
Estimated rank (mag + grad): 64
MEG: rank 64 computed from 306 data channels with 0 projectors
Setting small MEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing rank from covariance with rank=None
Using tolerance 2.8e-14 (2.2e-16 eps * 306 dim * 0.4 max singular value)
Estimated rank (mag + grad): 64
MEG: rank 64 computed from 306 data channels with 0 projectors
Computing rank from covariance with rank=None
Using tolerance 8.1e-14 (2.2e-16 eps * 306 dim * 1.2 max singular value)
Estimated rank (mag + grad): 64
MEG: rank 64 computed from 306 data channels with 0 projectors
Computing rank from covariance with rank=None
Using tolerance 3.8e-14 (2.2e-16 eps * 306 dim * 0.56 max singular value)
Estimated rank (mag + grad): 64
MEG: rank 64 computed from 306 data channels with 0 projectors
Computing rank from covariance with rank=None
Using tolerance 1.7e-14 (2.2e-16 eps * 306 dim * 0.26 max singular value)
Estimated rank (mag + grad): 64
MEG: rank 64 computed from 306 data channels with 0 projectors
Computing rank from covariance with rank=None
Using tolerance 9.3e-15 (2.2e-16 eps * 306 dim * 0.14 max singular value)
Estimated rank (mag + grad): 64
MEG: rank 64 computed from 306 data channels with 0 projectors
Computing rank from covariance with rank=None
Using tolerance 5e-15 (2.2e-16 eps * 306 dim * 0.074 max singular value)
Estimated rank (mag + grad): 64
MEG: rank 64 computed from 306 data channels with 0 projectors
Computing DICS spatial filters...
computing DICS spatial filter at 13.0 Hz (1/5)
Computing beamformer filters for 8155 sources
Filter computation complete
computing DICS spatial filter at 17.5 Hz (2/5)
Computing beamformer filters for 8155 sources
Filter computation complete
computing DICS spatial filter at 22.0 Hz (3/5)
Computing beamformer filters for 8155 sources
Filter computation complete
computing DICS spatial filter at 26.5 Hz (4/5)
Computing beamformer filters for 8155 sources
Filter computation complete
computing DICS spatial filter at 31.0 Hz (5/5)
Computing beamformer filters for 8155 sources
Filter computation complete
Processing epoch : 1
Processing epoch : 2
Processing epoch : 3
Processing epoch : 4
Processing epoch : 5
Processing epoch : 6
Processing epoch : 7
Processing epoch : 8
Processing epoch : 9
Processing epoch : 10
[done]
Applying baseline correction (mode: mean)
```

Letâ€™s visualize the source time course estimate. We can see the expected activation of the two gyri bordering the central sulcus, the primary somatosensory and motor cortices (S1 and M1).

```
fmax = 4500
brain = stc.plot(
subjects_dir=subjects_dir,
hemi="both",
views="dorsal",
initial_time=0.55,
brain_kwargs=dict(show=False),
add_data_kwargs=dict(
fmin=fmax / 10,
fmid=fmax / 2,
fmax=fmax,
scale_factor=0.0001,
colorbar_kwargs=dict(label_font_size=10),
),
)
# You can save a movie like the one on our documentation website with:
# brain.save_movie(tmin=0.55, tmax=1.5, interpolation='linear',
# time_viewer=True)
```