Source localization with MNE/dSPM/sLORETA/eLORETA

The aim of this tutorial is to teach you how to compute and apply a linear inverse method such as MNE/dSPM/sLORETA/eLORETA on evoked/raw/epochs data.

# sphinx_gallery_thumbnail_number = 10

import numpy as np
import matplotlib.pyplot as plt

import mne
from mne.datasets import sample
from mne.minimum_norm import make_inverse_operator, apply_inverse

Process MEG data

data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'

raw = mne.io.read_raw_fif(raw_fname)  # already has an average reference
events = mne.find_events(raw, stim_channel='STI 014')

event_id = dict(aud_l=1)  # event trigger and conditions
tmin = -0.2  # start of each epoch (200ms before the trigger)
tmax = 0.5  # end of each epoch (500ms after the trigger)
raw.info['bads'] = ['MEG 2443', 'EEG 053']
baseline = (None, 0)  # means from the first instant to t = 0
reject = dict(grad=4000e-13, mag=4e-12, eog=150e-6)

epochs = mne.Epochs(raw, events, event_id, tmin, tmax, proj=True,
                    picks=('meg', 'eog'), baseline=baseline, reject=reject)

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
319 events found
Event IDs: [ 1  2  3  4  5 32]
72 matching events found
Applying baseline correction (mode: mean)
Not setting metadata
Created an SSP operator (subspace dimension = 3)
4 projection items activated

Compute regularized noise covariance

For more details see Computing a covariance matrix.

noise_cov = mne.compute_covariance(
    epochs, tmax=0., method=['shrunk', 'empirical'], rank=None, verbose=True)

fig_cov, fig_spectra = mne.viz.plot_cov(noise_cov, raw.info)
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_001.png
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_002.png

Out:

Loading data for 72 events and 106 original time points ...
    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']
    Rejecting  epoch based on MAG : ['MEG 1711']
    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']
    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']
    Rejecting  epoch based on EOG : ['EOG 061']
17 bad epochs dropped
Computing data rank from raw with rank=None
    Using tolerance 2.8e-09 (2.2e-16 eps * 305 dim * 4.2e+04  max singular value)
    Estimated rank (mag + grad): 302
    MEG: rank 302 computed from 305 data channels with 3 projectors
    Created an SSP operator (subspace dimension = 3)
    Setting small MEG eigenvalues to zero (without PCA)
Reducing data rank from 305 -> 302
Estimating covariance using SHRUNK
Done.
Estimating covariance using EMPIRICAL
Done.
Using cross-validation to select the best estimator.
Number of samples used : 1705
log-likelihood on unseen data (descending order):
   shrunk: -1468.447
   empirical: -1574.608
selecting best estimator: shrunk
[done]

Compute the evoked response

Let’s just use MEG channels for simplicity.

evoked = epochs.average().pick('meg')
evoked.plot(time_unit='s')
evoked.plot_topomap(times=np.linspace(0.05, 0.15, 5), ch_type='mag',
                    time_unit='s')

# Show whitening
evoked.plot_white(noise_cov, time_unit='s')

del epochs  # to save memory
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_003.png
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_004.png
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_005.png

Out:

Computing data rank from covariance with rank=None
    Using tolerance 1.6e-13 (2.2e-16 eps * 203 dim * 3.5  max singular value)
    Estimated rank (grad): 203
    GRAD: rank 203 computed from 203 data channels with 0 projectors
Computing data rank from covariance with rank=None
    Using tolerance 2.2e-14 (2.2e-16 eps * 102 dim * 0.98  max singular value)
    Estimated rank (mag): 99
    MAG: rank 99 computed from 102 data channels with 3 projectors
    Created an SSP operator (subspace dimension = 3)
Computing data rank from covariance with rank={'grad': 203, 'mag': 99, 'meg': 302}
    Setting small MEG eigenvalues to zero (without PCA)
    Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)

Inverse modeling: MNE/dSPM on evoked and raw data

# Read the forward solution and compute the inverse operator
fname_fwd = data_path + '/MEG/sample/sample_audvis-meg-oct-6-fwd.fif'
fwd = mne.read_forward_solution(fname_fwd)

# make an MEG inverse operator
info = evoked.info
inverse_operator = make_inverse_operator(info, fwd, noise_cov,
                                         loose=0.2, depth=0.8)
del fwd

# You can write it to disk with::
#
#     >>> from mne.minimum_norm import write_inverse_operator
#     >>> write_inverse_operator('sample_audvis-meg-oct-6-inv.fif',
#                                inverse_operator)

Out:

Reading forward solution from /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis-meg-oct-6-fwd.fif...
    Reading a source space...
    Computing patch statistics...
    Patch information added...
    Distance information added...
    [done]
    Reading a source space...
    Computing patch statistics...
    Patch information added...
    Distance information added...
    [done]
    2 source spaces read
    Desired named matrix (kind = 3523) not available
    Read MEG forward solution (7498 sources, 306 channels, free orientations)
    Source spaces transformed to the forward solution coordinate frame
Converting forward solution to surface orientation
    Average patch normals will be employed in the rotation to the local surface coordinates....
    Converting to surface-based source orientations...
    [done]
info["bads"] and noise_cov["bads"] do not match, excluding bad channels from both
Computing inverse operator with 305 channels.
    305 out of 306 channels remain after picking
Selected 305 channels
Creating the depth weighting matrix...
    203 planar channels
    limit = 7265/7498 = 10.037795
    scale = 2.52065e-08 exp = 0.8
Applying loose dipole orientations. Loose value of 0.2.
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 3)
Computing data rank from covariance with rank=None
    Using tolerance 2.9e-13 (2.2e-16 eps * 305 dim * 4.3  max singular value)
    Estimated rank (mag + grad): 302
    MEG: rank 302 computed from 305 data channels with 3 projectors
    Setting small MEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing SVD of whitened and weighted lead field matrix.
    largest singular value = 4.68021
    scaling factor to adjust the trace = 9.16714e+18

Compute inverse solution

method = "dSPM"
snr = 3.
lambda2 = 1. / snr ** 2
stc, residual = apply_inverse(evoked, inverse_operator, lambda2,
                              method=method, pick_ori=None,
                              return_residual=True, verbose=True)

Out:

Preparing the inverse operator for use...
    Scaled noise and source covariance from nave = 1 to nave = 55
    Created the regularized inverter
    Created an SSP operator (subspace dimension = 3)
    Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
    Computing noise-normalization factors (dSPM)...
[done]
Applying inverse operator to "aud_l"...
    Picked 305 channels from the data
    Computing inverse...
    Eigenleads need to be weighted ...
    Computing residual...
    Explained  65.3% variance
    Combining the current components...
    dSPM...
[done]

Visualization

View activation time-series

plt.figure()
plt.plot(1e3 * stc.times, stc.data[::100, :].T)
plt.xlabel('time (ms)')
plt.ylabel('%s value' % method)
plt.show()
../../_images/sphx_glr_plot_mne_dspm_source_localization_006.png

Examine the original data and the residual after fitting:

fig, axes = plt.subplots(2, 1)
evoked.plot(axes=axes)
for ax in axes:
    ax.texts = []
    for line in ax.lines:
        line.set_color('#98df81')
residual.plot(axes=axes)
../../_images/sphx_glr_plot_mne_dspm_source_localization_007.png

Here we use peak getter to move visualization to the time point of the peak and draw a marker at the maximum peak vertex.

vertno_max, time_max = stc.get_peak(hemi='rh')

subjects_dir = data_path + '/subjects'
surfer_kwargs = dict(
    hemi='rh', subjects_dir=subjects_dir,
    clim=dict(kind='value', lims=[8, 12, 15]), views='lateral',
    initial_time=time_max, time_unit='s', size=(800, 800), smoothing_steps=5)
brain = stc.plot(**surfer_kwargs)
brain.add_foci(vertno_max, coords_as_verts=True, hemi='rh', color='blue',
               scale_factor=0.6, alpha=0.5)
brain.add_text(0.1, 0.9, 'dSPM (plus location of maximal activation)', 'title',
               font_size=14)
../../_images/sphx_glr_plot_mne_dspm_source_localization_008.png

Morph data to average brain

# setup source morph
morph = mne.compute_source_morph(
    src=inverse_operator['src'], subject_from=stc.subject,
    subject_to='fsaverage', spacing=5,  # to ico-5
    subjects_dir=subjects_dir)
# morph data
stc_fsaverage = morph.apply(stc)

brain = stc_fsaverage.plot(**surfer_kwargs)
brain.add_text(0.1, 0.9, 'Morphed to fsaverage', 'title', font_size=20)
del stc_fsaverage
../../_images/sphx_glr_plot_mne_dspm_source_localization_009.png

Dipole orientations

The pick_ori parameter of the mne.minimum_norm.apply_inverse() function controls the orientation of the dipoles. One useful setting is pick_ori='vector', which will return an estimate that does not only contain the source power at each dipole, but also the orientation of the dipoles.

stc_vec = apply_inverse(evoked, inverse_operator, lambda2,
                        method=method, pick_ori='vector')
brain = stc_vec.plot(**surfer_kwargs)
brain.add_text(0.1, 0.9, 'Vector solution', 'title', font_size=20)
del stc_vec
../../_images/sphx_glr_plot_mne_dspm_source_localization_010.png

Out:

Preparing the inverse operator for use...
    Scaled noise and source covariance from nave = 1 to nave = 55
    Created the regularized inverter
    Created an SSP operator (subspace dimension = 3)
    Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
    Computing noise-normalization factors (dSPM)...
[done]
Applying inverse operator to "aud_l"...
    Picked 305 channels from the data
    Computing inverse...
    Eigenleads need to be weighted ...
    Computing residual...
    Explained  65.3% variance
    dSPM...
[done]

Note that there is a relationship between the orientation of the dipoles and the surface of the cortex. For this reason, we do not use an inflated cortical surface for visualization, but the original surface used to define the source space.

For more information about dipole orientations, see The role of dipole orientations in distributed source localization.

Now let’s look at each solver:

for mi, (method, lims) in enumerate((('dSPM', [8, 12, 15]),
                                     ('sLORETA', [3, 5, 7]),
                                     ('eLORETA', [0.75, 1.25, 1.75]),)):
    surfer_kwargs['clim']['lims'] = lims
    stc = apply_inverse(evoked, inverse_operator, lambda2,
                        method=method, pick_ori=None)
    brain = stc.plot(figure=mi, **surfer_kwargs)
    brain.add_text(0.1, 0.9, method, 'title', font_size=20)
    del stc
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_011.png
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_012.png
  • ../../_images/sphx_glr_plot_mne_dspm_source_localization_013.png

Out:

Preparing the inverse operator for use...
    Scaled noise and source covariance from nave = 1 to nave = 55
    Created the regularized inverter
    Created an SSP operator (subspace dimension = 3)
    Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
    Computing noise-normalization factors (dSPM)...
[done]
Applying inverse operator to "aud_l"...
    Picked 305 channels from the data
    Computing inverse...
    Eigenleads need to be weighted ...
    Computing residual...
    Explained  65.3% variance
    Combining the current components...
    dSPM...
[done]
Preparing the inverse operator for use...
    Scaled noise and source covariance from nave = 1 to nave = 55
    Created the regularized inverter
    Created an SSP operator (subspace dimension = 3)
    Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
    Computing noise-normalization factors (sLORETA)...
[done]
Applying inverse operator to "aud_l"...
    Picked 305 channels from the data
    Computing inverse...
    Eigenleads need to be weighted ...
    Computing residual...
    Explained  65.3% variance
    Combining the current components...
    sLORETA...
[done]
Preparing the inverse operator for use...
    Scaled noise and source covariance from nave = 1 to nave = 55
    Created the regularized inverter
    Created an SSP operator (subspace dimension = 3)
    Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
    Computing noise-normalization factors (eLORETA)...
        Using uniform orientation weights
        Fitting up to 20 iterations (this make take a while)...
        Converged on iteration 10 (3.9e-07 < 1e-06)
        Assembling eLORETA kernel and modifying inverse
[done]
Applying inverse operator to "aud_l"...
    Picked 305 channels from the data
    Computing inverse...
    Eigenleads need to be weighted ...
    Computing residual...
    Explained -4640316421171626115072.0% variance
    Combining the current components...
[done]

Total running time of the script: ( 1 minutes 3.034 seconds)

Estimated memory usage: 114 MB

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