The role of dipole orientations in distributed source localization

When performing source localization in a distributed manner (MNE/dSPM/sLORETA/eLORETA), the source space is defined as a grid of dipoles that spans a large portion of the cortex. These dipoles have both a position and an orientation. In this tutorial, we will look at the various options available to restrict the orientation of the dipoles and the impact on the resulting source estimate.

Loading data

Load everything we need to perform source localization on the sample dataset.

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

data_path = sample.data_path()
evokeds = mne.read_evokeds(data_path + '/MEG/sample/sample_audvis-ave.fif')
left_auditory = evokeds[0].apply_baseline()
fwd = mne.read_forward_solution(
    data_path + '/MEG/sample/sample_audvis-meg-eeg-oct-6-fwd.fif')
mne.convert_forward_solution(fwd, surf_ori=True, copy=False)
noise_cov = mne.read_cov(data_path + '/MEG/sample/sample_audvis-cov.fif')
subjects_dir = data_path + '/subjects'

The source space

Let’s start by examining the source space as constructed by the mne.setup_source_space() function. Dipoles are placed along fixed intervals on the cortex, determined by the spacing parameter. The source space does not define the orientation for these dipoles.

lh = fwd['src'][0]  # Visualize the left hemisphere
verts = lh['rr']  # The vertices of the source space
tris = lh['tris']  # Groups of three vertices that form triangles
dip_pos = lh['rr'][lh['vertno']]  # The position of the dipoles
white = (1.0, 1.0, 1.0)  # RGB values for a white color
gray = (0.5, 0.5, 0.5)  # RGB values for a gray color
red = (1.0, 0.0, 0.0)  # RGB valued for a red color

mlab.figure(size=(600, 400), bgcolor=white)

# Plot the cortex
mlab.triangular_mesh(verts[:, 0], verts[:, 1], verts[:, 2], tris, color=gray)

# Mark the position of the dipoles with small red dots
mlab.points3d(dip_pos[:, 0], dip_pos[:, 1], dip_pos[:, 2], color=red,
              scale_factor=1E-3)

mlab.view(azimuth=180, distance=0.25)
../_images/sphx_glr_plot_dipole_orientations_001.png

Fixed dipole orientations

While the source space defines the position of the dipoles, the inverse operator defines the possible orientations of them. One of the options is to assign a fixed orientation. Since the neural currents from which MEG and EEG signals originate flows mostly perpendicular to the cortex [1], restricting the orientation of the dipoles accordingly places a useful restriction on the source estimate.

By specifying fixed=True when calling mne.minimum_norm.make_inverse_operator(), the dipole orientations are fixed to be orthogonal to the surface of the cortex, pointing outwards. Let’s visualize this:

mlab.figure(size=(600, 400), bgcolor=white)

# Plot the cortex
mlab.triangular_mesh(verts[:, 0], verts[:, 1], verts[:, 2], tris, color=gray)

# Show the dipoles as arrows pointing along the surface normal
normals = lh['nn'][lh['vertno']]
mlab.quiver3d(dip_pos[:, 0], dip_pos[:, 1], dip_pos[:, 2],
              normals[:, 0], normals[:, 1], normals[:, 2],
              color=red, scale_factor=1E-3)

mlab.view(azimuth=180, distance=0.1)
../_images/sphx_glr_plot_dipole_orientations_002.png

Restricting the dipole orientations in this manner leads to the following source estimate for the sample data:

# Compute the source estimate for the 'left - auditory' condition in the sample
# dataset.
inv = make_inverse_operator(left_auditory.info, fwd, noise_cov, fixed=True)
stc = apply_inverse(left_auditory, inv, pick_ori=None)

# Visualize it at the moment of peak activity.
_, time_max = stc.get_peak(hemi='lh')
brain = stc.plot(surface='white', subjects_dir=subjects_dir,
                 initial_time=time_max, time_unit='s', size=(600, 400))
../_images/sphx_glr_plot_dipole_orientations_003.png

The direction of the estimated current is now restricted to two directions: inward and outward. In the plot, blue areas indicate current flowing inwards and red areas indicate current flowing outwards. Given the curvature of the cortex, groups of dipoles tend to point in the same direction: the direction of the electromagnetic field picked up by the sensors.

Loose dipole orientations

Forcing the source dipoles to be strictly orthogonal to the cortex makes the source estimate sensitive to the spacing of the dipoles along the cortex, since the curvature of the cortex changes within each ~10 square mm patch. Furthermore, misalignment of the MEG/EEG and MRI coordinate frames is more critical when the source dipole orientations are strictly constrained [2]. To lift the restriction on the orientation of the dipoles, the inverse operator has the ability to place not one, but three dipoles at each location defined by the source space. These three dipoles are placed orthogonally to form a Cartesian coordinate system. Let’s visualize this:

mlab.figure(size=(600, 400), bgcolor=white)

# Define some more colors
green = (0.0, 1.0, 0.0)
blue = (0.0, 0.0, 1.0)

# Plot the cortex
mlab.triangular_mesh(verts[:, 0], verts[:, 1], verts[:, 2], tris, color=gray)

# Make an inverse operator with loose dipole orientations
inv = make_inverse_operator(left_auditory.info, fwd, noise_cov, fixed=False,
                            loose=1.0)

# Show the three dipoles defined at each location in the source space
dip_dir = inv['source_nn'].reshape(-1, 3, 3)
dip_dir = dip_dir[:len(dip_pos)]  # Only select left hemisphere
for ori, color in zip((0, 1, 2), (red, green, blue)):
    mlab.quiver3d(dip_pos[:, 0], dip_pos[:, 1], dip_pos[:, 2],
                  dip_dir[:, ori, 0], dip_dir[:, ori, 1], dip_dir[:, ori, 2],
                  color=color, scale_factor=1E-3)

mlab.view(azimuth=180, distance=0.1)
../_images/sphx_glr_plot_dipole_orientations_004.png

When computing the source estimate, the activity at each of the three dipoles is collapsed into the XYZ components of a single vector, which leads to the following source estimate for the sample data:

# Compute the source estimate, indicate that we want a vector solution
stc = apply_inverse(left_auditory, inv, pick_ori='vector')

# Visualize it at the moment of peak activity.
_, time_max = stc.magnitude().get_peak(hemi='lh')
brain = stc.plot(subjects_dir=subjects_dir, initial_time=time_max,
                 time_unit='s', size=(600, 400), overlay_alpha=0)
../_images/sphx_glr_plot_dipole_orientations_005.png

Limiting orientations, but not fixing them

Often, the best results will be obtained by allowing the dipoles to have somewhat free orientation, but not stray too far from a orientation that is perpendicular to the cortex. The loose parameter of the mne.minimum_norm.make_inverse_operator() allows you to specify a value between 0 (fixed) and 1 (unrestricted or “free”) to indicate the amount the orientation is allowed to deviate from the surface normal.

# Set loose to 0.2, the default value
inv = make_inverse_operator(left_auditory.info, fwd, noise_cov, fixed=False,
                            loose=0.2)
stc = apply_inverse(left_auditory, inv, pick_ori='vector')

# Visualize it at the moment of peak activity.
_, time_max = stc.magnitude().get_peak(hemi='lh')
brain = stc.plot(subjects_dir=subjects_dir, initial_time=time_max,
                 time_unit='s', size=(600, 400), overlay_alpha=0)
../_images/sphx_glr_plot_dipole_orientations_006.png

Discarding dipole orientation information

Often, further analysis of the data does not need information about the orientation of the dipoles, but rather their magnitudes. The pick_ori parameter of the mne.minimum_norm.apply_inverse() function allows you to specify whether to return the full vector solution ('vector') or rather the magnitude of the vectors (None, the default) or only the activity in the direction perpendicular to the cortex ('normal').

# Only retain vector magnitudes
stc = apply_inverse(left_auditory, inv, pick_ori=None)

# Visualize it at the moment of peak activity.
_, time_max = stc.get_peak(hemi='lh')
brain = stc.plot(surface='white', subjects_dir=subjects_dir,
                 initial_time=time_max, time_unit='s', size=(600, 400))
../_images/sphx_glr_plot_dipole_orientations_007.png

References

[1]Hämäläinen, M. S., Hari, R., Ilmoniemi, R. J., Knuutila, J., & Lounasmaa, O. V. “Magnetoencephalography - theory, instrumentation, and applications to noninvasive studies of the working human brain”, Reviews of Modern Physics, 1993. https://doi.org/10.1103/RevModPhys.65.413
[2]Lin, F. H., Belliveau, J. W., Dale, A. M., & Hämäläinen, M. S. (2006). Distributed current estimates using cortical orientation constraints. Human Brain Mapping, 27(1), 1–13. http://doi.org/10.1002/hbm.20155

Total running time of the script: ( 0 minutes 40.702 seconds)

Estimated memory usage: 281 MB

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