How MNE uses FreeSurfer’s outputs

This tutorial explains how MRI coordinate frames are handled in MNE-Python, and how MNE-Python integrates with FreeSurfer for handling MRI data and source space data in general.

As usual we’ll start by importing the necessary packages; for this tutorial that includes nibabel to handle loading the MRI images (MNE-Python also uses nibabel under the hood). We’ll also use a special Matplotlib function for adding outlines to text, so that text is readable on top of an MRI image.

import os

import numpy as np
import nibabel
import matplotlib.pyplot as plt
import matplotlib.patheffects as path_effects

import mne
from mne.transforms import apply_trans
from mne.io.constants import FIFF

MRI coordinate frames

Let’s start out by looking at the sample subject MRI. Following standard FreeSurfer convention, we look at T1.mgz, which gets created from the original MRI sample/mri/orig/001.mgz when you run the FreeSurfer command recon-all. Here we use nibabel to load the T1 image, and the resulting object’s orthoview() method to view it.

plot background freesurfer mne

Notice that the axes in the orthoview() figure are labeled L-R, S-I, and P-A. These reflect the standard RAS (right-anterior-superior) coordinate system that is widely used in MRI imaging. If you are unfamiliar with RAS coordinates, see the excellent nibabel tutorial Coordinate systems and affines.

Nibabel already takes care of some coordinate frame transformations under the hood, so let’s do it manually so we understand what is happening. First let’s get our data as a 3D array and note that it’s already a standard size:

Out:

(256, 256, 256)

These data are voxel intensity values. Here they are unsigned integers in the range 0-255, though in general they can be floating point values. A value data[i, j, k] at a given index triplet (i, j, k) corresponds to some real-world physical location (x, y, z) in space. To get its physical location, first we have to choose what coordinate frame we’re going to use.

For example, we could choose a geographical coordinate frame, with origin is at the center of the earth, Z axis through the north pole, X axis through the prime meridian (zero degrees longitude), and Y axis orthogonal to these forming a right-handed coordinate system. This would not be a very useful choice for defining the physical locations of the voxels during the MRI acquisition for analysis, but you could nonetheless figure out the transformation that related the (i, j, k) to this coordinate frame.

Instead, each scanner defines a more practical, native coordinate system that it uses during acquisition, usually related to the physical orientation of the scanner itself and/or the subject within it. During acquisition the relationship between the voxel indices (i, j, k) and the physical location (x, y, z) in the scanner’s native coordinate frame is saved in the image’s affine transformation.

We can use nibabel to examine this transformation, keeping in mind that it processes everything in units of millimeters, unlike MNE where things are always in SI units (meters).

This allows us to take an arbitrary voxel or slice of data and know where it is in the scanner’s native physical space (x, y, z) (in mm) by applying the affine transformation to the voxel coordinates.

print(t1.affine)
vox = np.array([122, 119, 102])
xyz_ras = apply_trans(t1.affine, vox)
print('Our voxel has real-world coordinates {}, {}, {} (mm)'
      .format(*np.round(xyz_ras, 3)))

Out:

[[-1.00000000e+00  1.15484021e-07 -1.91852465e-07  1.22726395e+02]
 [ 8.56816911e-08  1.57160827e-08  1.00000000e+00 -1.18960930e+02]
 [ 1.49011647e-08 -1.00000000e+00  6.40284092e-09  1.00712036e+02]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]
Our voxel has real-world coordinates 0.726, -16.961, -18.288 (mm)

If you have a point (x, y, z) in scanner-native RAS space and you want the corresponding voxel number, you can get it using the inverse of the affine. This involves some rounding, so it’s possible to end up off by one voxel if you’re not careful:

ras_coords_mm = np.array([1, -17, -18])
inv_affine = np.linalg.inv(t1.affine)
i_, j_, k_ = np.round(apply_trans(inv_affine, ras_coords_mm)).astype(int)
print('Our real-world coordinates correspond to voxel ({}, {}, {})'
      .format(i_, j_, k_))

Out:

Our real-world coordinates correspond to voxel (122, 119, 102)

Let’s write a short function to visualize where our voxel lies in an image, and annotate it in RAS space (rounded to the nearest millimeter):

def imshow_mri(data, img, vox, xyz, suptitle):
    """Show an MRI slice with a voxel annotated."""
    i, j, k = vox
    fig, ax = plt.subplots(1, figsize=(6, 6))
    codes = nibabel.orientations.aff2axcodes(img.affine)
    # Figure out the title based on the code of this axis
    ori_slice = dict(P='Coronal', A='Coronal',
                     I='Axial', S='Axial',
                     L='Sagittal', R='Saggital')
    ori_names = dict(P='posterior', A='anterior',
                     I='inferior', S='superior',
                     L='left', R='right')
    title = ori_slice[codes[0]]
    ax.imshow(data[i], vmin=10, vmax=120, cmap='gray', origin='lower')
    ax.axvline(k, color='y')
    ax.axhline(j, color='y')
    for kind, coords in xyz.items():
        annotation = ('{}: {}, {}, {} mm'
                      .format(kind, *np.round(coords).astype(int)))
        text = ax.text(k, j, annotation, va='baseline', ha='right',
                       color=(1, 1, 0.7))
        text.set_path_effects([
            path_effects.Stroke(linewidth=2, foreground='black'),
            path_effects.Normal()])
    # reorient view so that RAS is always rightward and upward
    x_order = -1 if codes[2] in 'LIP' else 1
    y_order = -1 if codes[1] in 'LIP' else 1
    ax.set(xlim=[0, data.shape[2] - 1][::x_order],
           ylim=[0, data.shape[1] - 1][::y_order],
           xlabel=f'k ({ori_names[codes[2]]}+)',
           ylabel=f'j ({ori_names[codes[1]]}+)',
           title=f'{title} view: i={i} ({ori_names[codes[0]]}+)')
    fig.suptitle(suptitle)
    fig.subplots_adjust(0.1, 0.1, 0.95, 0.85)
    return fig


imshow_mri(data, t1, vox, {'Scanner RAS': xyz_ras}, 'MRI slice')
MRI slice, Sagittal view: i=122 (left+)

Notice that the axis scales (i, j, and k) are still in voxels (ranging from 0-255); it’s only the annotation text that we’ve translated into real-world RAS in millimeters.

“MRI coordinates” in MNE-Python: FreeSurfer surface RAS

While nibabel uses scanner RAS (x, y, z) coordinates, FreeSurfer uses a slightly different coordinate frame: MRI surface RAS. The transform from voxels to the FreeSurfer MRI surface RAS coordinate frame is known in the FreeSurfer documentation as Torig, and in nibabel as vox2ras_tkr. This transformation sets the center of its coordinate frame in the middle of the conformed volume dimensions (N / 2.) with the axes oriented along the axes of the volume itself. For more information, see MEG/EEG and MRI coordinate systems.

Since MNE-Python uses FreeSurfer extensively for surface computations (e.g., white matter, inner/outer skull meshes), internally MNE-Python uses the Freeurfer surface RAS coordinate system (not the nibabel scanner RAS system) for as many computations as possible, such as all source space and BEM mesh vertex definitions.

Whenever you see “MRI coordinates” or “MRI coords” in MNE-Python’s documentation, you should assume that we are talking about the “FreeSurfer MRI surface RAS” coordinate frame!

We can do similar computations as before to convert the given voxel indices into FreeSurfer MRI coordinates (i.e., what we call “MRI coordinates” or “surface RAS” everywhere else in MNE), just like we did above to convert voxel indices to scanner RAS:

Torig = t1.header.get_vox2ras_tkr()
print(t1.affine)
print(Torig)
xyz_mri = apply_trans(Torig, vox)
imshow_mri(data, t1, vox, dict(MRI=xyz_mri), 'MRI slice')
MRI slice, Sagittal view: i=122 (left+)

Out:

[[-1.00000000e+00  1.15484021e-07 -1.91852465e-07  1.22726395e+02]
 [ 8.56816911e-08  1.57160827e-08  1.00000000e+00 -1.18960930e+02]
 [ 1.49011647e-08 -1.00000000e+00  6.40284092e-09  1.00712036e+02]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]
[[  -1.    0.    0.  128.]
 [   0.    0.    1. -128.]
 [   0.   -1.    0.  128.]
 [   0.    0.    0.    1.]]

Knowing these relationships and being mindful about transformations, we can get from a point in any given space to any other space. Let’s start out by plotting the Nasion on a saggital MRI slice:

fiducials = mne.coreg.get_mni_fiducials(subject, subjects_dir=subjects_dir)
nasion_mri = [d for d in fiducials if d['ident'] == FIFF.FIFFV_POINT_NASION][0]
print(nasion_mri)  # note it's in Freesurfer MRI coords

Out:

<DigPoint |     Nasion : (2.6, 99.8, 40.8) mm      : MRI (surface RAS) frame>

When we print the nasion, it displays as a DigPoint and shows its coordinates in millimeters, but beware that the underlying data is actually stored in meters, so before transforming and plotting we’ll convert to millimeters:

nasion_mri = nasion_mri['r'] * 1000  # meters → millimeters
nasion_vox = np.round(
    apply_trans(np.linalg.inv(Torig), nasion_mri)).astype(int)
imshow_mri(data, t1, nasion_vox, dict(MRI=nasion_mri),
           'Nasion estimated from MRI transform')
Nasion estimated from MRI transform, Sagittal view: i=125 (left+)

We can also take the digitization point from the MEG data, which is in the “head” coordinate frame.

Let’s look at the nasion in the head coordinate frame:

info = mne.io.read_info(
    os.path.join(data_path, 'MEG', 'sample', 'sample_audvis_raw.fif'))
nasion_head = [d for d in info['dig'] if
               d['kind'] == FIFF.FIFFV_POINT_CARDINAL and
               d['ident'] == FIFF.FIFFV_POINT_NASION][0]
print(nasion_head)  # note it's in "head" coordinates

Out:

    Read a total of 3 projection items:
        PCA-v1 (1 x 102)  idle
        PCA-v2 (1 x 102)  idle
        PCA-v3 (1 x 102)  idle
<DigPoint |     Nasion : (0.0, 102.6, 0.0) mm      : head frame>

Notice that in “head” coordinate frame the nasion has values of 0 for the x and z directions (which makes sense given that the nasion is used to define the y axis in that system). To convert from head coordinate frame to voxels, we first apply the head → MRI (surface RAS) transform from a trans file (typically created with the MNE-Python coregistration GUI), then convert meters → millimeters, and finally apply the inverse of Torig to get to voxels.

Under the hood, functions like mne.setup_source_space(), mne.setup_volume_source_space(), and mne.compute_source_morph() make extensive use of these coordinate frames.

trans = mne.read_trans(
    os.path.join(data_path, 'MEG', 'sample', 'sample_audvis_raw-trans.fif'))

# first we transform from head to MRI, and *then* convert to millimeters
nasion_dig_mri = apply_trans(trans, nasion_head['r']) * 1000

# ...then we can use Torig to convert MRI to voxels:
nasion_dig_vox = np.round(
    apply_trans(np.linalg.inv(Torig), nasion_dig_mri)).astype(int)
imshow_mri(data, t1, nasion_dig_vox, dict(MRI=nasion_dig_mri),
           'Nasion transformed from digitization')
Nasion transformed from digitization, Sagittal view: i=125 (left+)

Using FreeSurfer’s surface reconstructions

An important part of what FreeSurfer does is provide cortical surface reconstructions. For example, let’s load and view the white surface of the brain. This is a 3D mesh defined by a set of vertices (conventionally called rr) with shape (n_vertices, 3) and a set of triangles (tris) with shape (n_tris, 3) defining which vertices in rr form each triangular facet of the mesh.

fname = os.path.join(subjects_dir, subject, 'surf', 'rh.white')
rr_mm, tris = mne.read_surface(fname)
print(f'rr_mm.shape == {rr_mm.shape}')
print(f'tris.shape == {tris.shape}')
print(f'rr_mm.max() = {rr_mm.max()}')  # just to show that we are in mm

Out:

rr_mm.shape == (156866, 3)
tris.shape == (313728, 3)
rr_mm.max() = 97.80481719970703

Let’s actually plot it:

renderer = mne.viz.backends.renderer.create_3d_figure(
    size=(600, 600), bgcolor='w', scene=False)
gray = (0.5, 0.5, 0.5)
renderer.mesh(*rr_mm.T, triangles=tris, color=gray)
view_kwargs = dict(elevation=90, azimuth=0)
mne.viz.set_3d_view(
    figure=renderer.figure, distance=350, focalpoint=(0., 0., 40.),
    **view_kwargs)
renderer.show()
plot background freesurfer mne

We can also plot the mesh on top of an MRI slice. The mesh surfaces are defined in millimeters in the MRI (FreeSurfer surface RAS) coordinate frame, so we can convert them to voxels by applying the inverse of the Torig transform:

rr_vox = apply_trans(np.linalg.inv(Torig), rr_mm)
fig = imshow_mri(data, t1, vox, {'Scanner RAS': xyz_ras}, 'MRI slice')
# Based on how imshow_mri works, the "X" here is the last dim of the MRI vol,
# the "Y" is the middle dim, and the "Z" is the first dim, so now that our
# points are in the correct coordinate frame, we need to ask matplotlib to
# do a tricontour slice like:
fig.axes[0].tricontour(rr_vox[:, 2], rr_vox[:, 1], tris, rr_vox[:, 0],
                       levels=[vox[0]], colors='r', linewidths=1.0,
                       zorder=1)
MRI slice, Sagittal view: i=122 (left+)

This is the method used by mne.viz.plot_bem() to show the BEM surfaces.

Cortical alignment (spherical)

A critical function provided by FreeSurfer is spherical surface alignment of cortical surfaces, maximizing sulcal-gyral alignment. FreeSurfer first expands the cortical surface to a sphere, then aligns it optimally with fsaverage. Because the vertex ordering is preserved when expanding to a sphere, a given vertex in the source (sample) mesh can be mapped easily to the same location in the destination (fsaverage) mesh, and vice-versa.

renderer_kwargs = dict(bgcolor='w', smooth_shading=False)
renderer = mne.viz.backends.renderer.create_3d_figure(
    size=(800, 400), scene=False, **renderer_kwargs)
curvs = [
    (mne.surface.read_curvature(os.path.join(
        subjects_dir, subj, 'surf', 'rh.curv'),
        binary=False) > 0).astype(float)
    for subj in ('sample', 'fsaverage') for _ in range(2)]
fnames = [os.path.join(subjects_dir, subj, 'surf', surf)
          for subj in ('sample', 'fsaverage')
          for surf in ('rh.white', 'rh.sphere')]
y_shifts = [-450, -150, 450, 150]
z_shifts = [-40, 0, -30, 0]
for name, y_shift, z_shift, curv in zip(fnames, y_shifts, z_shifts, curvs):
    this_rr, this_tri = mne.read_surface(name)
    this_rr += [0, y_shift, z_shift]
    renderer.mesh(*this_rr.T, triangles=this_tri, color=None, scalars=curv,
                  colormap='copper_r', vmin=-0.2, vmax=1.2)
zero = [0., 0., 0.]
width = 50.
y = np.sort(y_shifts)
y = (y[1:] + y[:-1]) / 2. - width / 2.
renderer.quiver3d(zero, y, zero,
                  zero, [1] * 3, zero, 'k', width, 'arrow')
view_kwargs['focalpoint'] = (0., 0., 0.)
mne.viz.set_3d_view(figure=renderer.figure, distance=1000, **view_kwargs)
renderer.show()
plot background freesurfer mne

Let’s look a bit more closely at the spherical alignment by overlaying the two spherical meshes as wireframes and zooming way in (the purple points are separated by about 1 mm):

cyan = '#66CCEE'
purple = '#AA3377'
renderer = mne.viz.backends.renderer.create_3d_figure(
    size=(800, 800), scene=False, **renderer_kwargs)
fnames = [os.path.join(subjects_dir, subj, 'surf', 'rh.sphere')
          for subj in ('sample', 'fsaverage')]
colors = [cyan, purple]
for name, color in zip(fnames, colors):
    this_rr, this_tri = mne.read_surface(name)
    renderer.mesh(*this_rr.T, triangles=this_tri, color=color,
                  representation='wireframe')
mne.viz.set_3d_view(figure=renderer.figure, distance=20, **view_kwargs)
renderer.show()
plot background freesurfer mne

You can see that the fsaverage (purple) mesh is uniformly spaced, and the mesh for subject “sample” (in cyan) has been deformed along the spherical surface by FreeSurfer. This deformation is designed to optimize the sulcal-gyral alignment.

Surface decimation

These surfaces have a lot of vertices, and in general we only need to use a subset of these vertices for creating source spaces. A uniform sampling can easily be achieved by subsampling in the spherical space. To do this, we use a recursively subdivided icosahedron or octahedron. For example, let’s load a standard oct-6 source space, and at the same zoom level as before visualize how it subsampled the dense mesh:

src = mne.read_source_spaces(os.path.join(subjects_dir, 'sample', 'bem',
                                          'sample-oct-6-src.fif'))
print(src)

blue = '#4477AA'
renderer = mne.viz.backends.renderer.create_3d_figure(
    size=(800, 800), scene=False, **renderer_kwargs)
rr_sph, _ = mne.read_surface(fnames[0])
for tris, color in [(src[1]['tris'], cyan), (src[1]['use_tris'], blue)]:
    renderer.mesh(*rr_sph.T, triangles=tris, color=color,
                  representation='wireframe')
mne.viz.set_3d_view(figure=renderer.figure, distance=20, **view_kwargs)
renderer.show()
plot background freesurfer mne

Out:

    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
<SourceSpaces: [<surface (lh), n_vertices=155407, n_used=4098>, <surface (rh), n_vertices=156866, n_used=4098>] MRI (surface RAS) coords, subject 'sample', ~27.3 MB>

We can also then look at how these two meshes compare by plotting the original, high-density mesh as well as our decimated mesh white surfaces.

renderer = mne.viz.backends.renderer.create_3d_figure(
    size=(800, 400), scene=False, **renderer_kwargs)
y_shifts = [-125, 125]
tris = [src[1]['tris'], src[1]['use_tris']]
for y_shift, tris in zip(y_shifts, tris):
    this_rr = src[1]['rr'] * 1000. + [0, y_shift, -40]
    renderer.mesh(*this_rr.T, triangles=tris, color=None, scalars=curvs[0],
                  colormap='copper_r', vmin=-0.2, vmax=1.2)
renderer.quiver3d([0], [-width / 2.], [0], [0], [1], [0], 'k', width, 'arrow')
mne.viz.set_3d_view(figure=renderer.figure, distance=400, **view_kwargs)
renderer.show()
plot background freesurfer mne

Warning

Some source space vertices can be removed during forward computation. See Head model and forward computation for more information.

Total running time of the script: ( 0 minutes 34.673 seconds)

Estimated memory usage: 19 MB

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