

In [ ]:

    
%matplotlib inline

Head model and forward computation

The aim of this tutorial is to be a getting started for forward computation.

For more extensive details and presentation of the general concepts for forward modeling, see ch_forward.



In [ ]:

    
import os.path as op
import mne
from mne.datasets import sample
data_path = sample.data_path()

# the raw file containing the channel location + types
raw_fname = data_path + '/MEG/sample/sample_audvis_raw.fif'
# The paths to Freesurfer reconstructions
subjects_dir = data_path + '/subjects'
subject = 'sample'

Computing the forward operator

To compute a forward operator we need:

a -trans.fif file that contains the coregistration info.
a source space
the :term:BEM surfaces

Compute and visualize BEM surfaces

The :term:BEM surfaces are the triangulations of the interfaces between different tissues needed for forward computation. These surfaces are for example the inner skull surface, the outer skull surface and the outer skin surface, a.k.a. scalp surface.

Computing the BEM surfaces requires FreeSurfer and makes use of the command-line tools mne watershed_bem or mne flash_bem, or the related functions :func:mne.bem.make_watershed_bem or :func:mne.bem.make_flash_bem.

Here we'll assume it's already computed. It takes a few minutes per subject.

For EEG we use 3 layers (inner skull, outer skull, and skin) while for MEG 1 layer (inner skull) is enough.

Let's look at these surfaces. The function :func:mne.viz.plot_bem assumes that you have the bem folder of your subject's FreeSurfer reconstruction, containing the necessary surface files.



In [ ]:

    
mne.viz.plot_bem(subject=subject, subjects_dir=subjects_dir,
                 brain_surfaces='white', orientation='coronal')

Visualizing the coregistration

The coregistration is the operation that allows to position the head and the sensors in a common coordinate system. In the MNE software the transformation to align the head and the sensors in stored in a so-called trans file. It is a FIF file that ends with -trans.fif. It can be obtained with :func:mne.gui.coregistration (or its convenient command line equivalent mne coreg), or mrilab if you're using a Neuromag system.

Here we assume the coregistration is done, so we just visually check the alignment with the following code.



In [ ]:

    
# The transformation file obtained by coregistration
trans = data_path + '/MEG/sample/sample_audvis_raw-trans.fif'

info = mne.io.read_info(raw_fname)
# Here we look at the dense head, which isn't used for BEM computations but
# is useful for coregistration.
mne.viz.plot_alignment(info, trans, subject=subject, dig=True,
                       meg=['helmet', 'sensors'], subjects_dir=subjects_dir,
                       surfaces='head-dense')

Compute Source Space

The source space defines the position and orientation of the candidate source locations. There are two types of source spaces:

surface-based source space when the candidates are confined to a surface.
volumetric or discrete source space when the candidates are discrete, arbitrarily located source points bounded by the surface.

Surface-based source space is computed using :func:mne.setup_source_space, while volumetric source space is computed using :func:mne.setup_volume_source_space.

We will now compute a surface-based source space with an 'oct6' resolution. See setting_up_source_space for details on source space definition and spacing parameter.



In [ ]:

    
src = mne.setup_source_space(subject, spacing='oct6', add_dist='patch',
                             subjects_dir=subjects_dir)
print(src)

The surface based source space src contains two parts, one for the left hemisphere (4098 locations) and one for the right hemisphere (4098 locations). Sources can be visualized on top of the BEM surfaces in purple.



In [ ]:

    
mne.viz.plot_bem(subject=subject, subjects_dir=subjects_dir,
                 brain_surfaces='white', src=src, orientation='coronal')

To compute a volume based source space defined with a grid of candidate dipoles inside a sphere of radius 90mm centered at (0.0, 0.0, 40.0) mm you can use the following code. Obviously here, the sphere is not perfect. It is not restricted to the brain and it can miss some parts of the cortex.



In [ ]:

    
sphere = (0.0, 0.0, 0.04, 0.09)
vol_src = mne.setup_volume_source_space(subject, subjects_dir=subjects_dir,
                                        sphere=sphere, sphere_units='m')
print(vol_src)

mne.viz.plot_bem(subject=subject, subjects_dir=subjects_dir,
                 brain_surfaces='white', src=vol_src, orientation='coronal')

To compute a volume based source space defined with a grid of candidate dipoles inside the brain (requires the :term:BEM surfaces) you can use the following.



In [ ]:

    
surface = op.join(subjects_dir, subject, 'bem', 'inner_skull.surf')
vol_src = mne.setup_volume_source_space(subject, subjects_dir=subjects_dir,
                                        surface=surface)
print(vol_src)

mne.viz.plot_bem(subject=subject, subjects_dir=subjects_dir,
                 brain_surfaces='white', src=vol_src, orientation='coronal')

Note

Some sources may appear to be outside the BEM inner skull contour. This is because the ``slices`` are decimated for plotting here. Each slice in the figure actually represents several MRI slices, but only the MRI voxels and BEM boundaries for a single (midpoint of the given slice range) slice are shown, whereas the source space points plotted on that midpoint slice consist of all points for which that slice (out of all slices shown) was the closest.

Now let's see how to view all sources in 3D.



In [ ]:

    
fig = mne.viz.plot_alignment(subject=subject, subjects_dir=subjects_dir,
                             surfaces='white', coord_frame='head',
                             src=src)
mne.viz.set_3d_view(fig, azimuth=173.78, elevation=101.75,
                    distance=0.30, focalpoint=(-0.03, -0.01, 0.03))

Compute forward solution

We can now compute the forward solution. To reduce computation we'll just compute a single layer BEM (just inner skull) that can then be used for MEG (not EEG). We specify if we want a one-layer or a three-layer BEM using the conductivity parameter. The BEM solution requires a BEM model which describes the geometry of the head the conductivities of the different tissues.



In [ ]:

    
conductivity = (0.3,)  # for single layer
# conductivity = (0.3, 0.006, 0.3)  # for three layers
model = mne.make_bem_model(subject='sample', ico=4,
                           conductivity=conductivity,
                           subjects_dir=subjects_dir)
bem = mne.make_bem_solution(model)

Note that the :term:BEM does not involve any use of the trans file. The BEM only depends on the head geometry and conductivities. It is therefore independent from the MEG data and the head position.

Let's now compute the forward operator, commonly referred to as the gain or leadfield matrix. See :func:mne.make_forward_solution for details on the meaning of each parameter.



In [ ]:

    
fwd = mne.make_forward_solution(raw_fname, trans=trans, src=src, bem=bem,
                                meg=True, eeg=False, mindist=5.0, n_jobs=2)
print(fwd)

Warning

Forward computation can remove vertices that are too close to (or outside) the inner skull surface. For example, here we have gone from 8096 to 7498 vertices in use. For many functions, such as :func:`mne.compute_source_morph`, it is important to pass ``fwd['src']`` or ``inv['src']`` so that this removal is adequately accounted for.



In [ ]:

    
print(f'Before: {src}')
print(f'After:  {fwd["src"]}')

We can explore the content of fwd to access the numpy array that contains the gain matrix.



In [ ]:

    
leadfield = fwd['sol']['data']
print("Leadfield size : %d sensors x %d dipoles" % leadfield.shape)

To extract the numpy array containing the forward operator corresponding to the source space fwd['src'] with cortical orientation constraint we can use the following:



In [ ]:

    
fwd_fixed = mne.convert_forward_solution(fwd, surf_ori=True, force_fixed=True,
                                         use_cps=True)
leadfield = fwd_fixed['sol']['data']
print("Leadfield size : %d sensors x %d dipoles" % leadfield.shape)

This is equivalent to the following code that explicitly applies the forward operator to a source estimate composed of the identity operator (which we omit here because it uses a lot of memory)::

>>> import numpy as np
>>> n_dipoles = leadfield.shape[1]
>>> vertices = [src_hemi['vertno'] for src_hemi in fwd_fixed['src']]
>>> stc = mne.SourceEstimate(1e-9 * np.eye(n_dipoles), vertices)
>>> leadfield = mne.apply_forward(fwd_fixed, stc, info).data / 1e-9

To save to disk a forward solution you can use :func:mne.write_forward_solution and to read it back from disk :func:mne.read_forward_solution. Don't forget that FIF files containing forward solution should end with :file:-fwd.fif.

To get a fixed-orientation forward solution, use :func:mne.convert_forward_solution to convert the free-orientation solution to (surface-oriented) fixed orientation.

Exercise

By looking at sphx_glr_auto_examples_forward_plot_forward_sensitivity_maps.py plot the sensitivity maps for EEG and compare it with the MEG, can you justify the claims that:

MEG is not sensitive to radial sources
EEG is more sensitive to deep sources

How will the MEG sensitivity maps and histograms change if you use a free instead if a fixed/surface oriented orientation?

Try this changing the mode parameter in :func:mne.sensitivity_map accordingly. Why don't we see any dipoles on the gyri?