Source alignment and coordinate frames

The aim of this tutorial is to show how to visually assess that the data are well aligned in space for computing the forward solution, and understand the different coordinate frames involved in this process.

Let’s start out by loading some data.

import os.path as op

import numpy as np

import mne
from mne.datasets import sample

print(__doc__)

data_path = sample.data_path()
subjects_dir = op.join(data_path, 'subjects')
raw_fname = op.join(data_path, 'MEG', 'sample', 'sample_audvis_raw.fif')
trans_fname = op.join(data_path, 'MEG', 'sample',
                      'sample_audvis_raw-trans.fif')
raw = mne.io.read_raw_fif(raw_fname)
trans = mne.read_trans(trans_fname)
src = mne.read_source_spaces(op.join(subjects_dir, 'sample', 'bem',
                                     'sample-oct-6-src.fif'))

Out:

Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_raw.fif...
    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
    Range : 25800 ... 192599 =     42.956 ...   320.670 secs
Ready.
Current compensation grade : 0
    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

Understanding coordinate frames

For M/EEG source imaging, there are three coordinate frames (further explained in the next section) that we must bring into alignment using two 3D transformation matrices that define how to rotate and translate points in one coordinate frame to their equivalent locations in another.

mne.viz.plot_alignment() is a very useful function for inspecting these transformations, and the resulting alignment of EEG sensors, MEG sensors, brain sources, and conductor models. If the subjects_dir and subject parameters are provided, the function automatically looks for the Freesurfer MRI surfaces to show from the subject’s folder.

We can use the show_axes argument to see the various coordinate frames given our transformation matrices. These are shown by axis arrows for each coordinate frame:

• shortest arrow is (R)ight/X

• medium is forward/(A)nterior/Y

• longest is up/(S)uperior/Z

i.e., a RAS coordinate system in each case. We can also set the coord_frame argument to choose which coordinate frame the camera should initially be aligned with.

Let’s take a look:

fig = mne.viz.plot_alignment(raw.info, trans=trans, subject='sample',
                             subjects_dir=subjects_dir, surfaces='head-dense',
                             show_axes=True, dig=True, eeg=[], meg='sensors',
                             coord_frame='meg')
mne.viz.set_3d_view(fig, 45, 90, distance=0.6, focalpoint=(0., 0., 0.))
print('Distance from head origin to MEG origin: %0.1f mm'
      % (1000 * np.linalg.norm(raw.info['dev_head_t']['trans'][:3, 3])))
print('Distance from head origin to MRI origin: %0.1f mm'
      % (1000 * np.linalg.norm(trans['trans'][:3, 3])))
dists = mne.dig_mri_distances(raw.info, trans, 'sample',
                              subjects_dir=subjects_dir)
print('Distance from %s digitized points to head surface: %0.1f mm'
      % (len(dists), 1000 * np.mean(dists)))

Out:

Using lh.seghead for head surface.
Distance from head origin to MEG origin: 65.0 mm
Distance from head origin to MRI origin: 29.9 mm
Using surface from /home/circleci/mne_data/MNE-sample-data/subjects/sample/bem/sample-head.fif.
Distance from 72 digitized points to head surface: 1.7 mm

Coordinate frame definitions

1. Neuromag/Elekta/MEGIN head coordinate frame (“head”, pink axes)

   The head coordinate frame is defined through the coordinates of anatomical landmarks on the subject’s head: Usually the Nasion (NAS), and the left and right preauricular points (LPA and RPA). Different MEG manufacturers may have different definitions of the coordinate head frame. A good overview can be seen in the FieldTrip FAQ on coordinate systems.

   For Neuromag/Elekta/MEGIN, the head coordinate frame is defined by the intersection of

   1. the line between the LPA (red sphere) and RPA (purple sphere), and

   2. the line perpendicular to this LPA-RPA line one that goes through the Nasion (green sphere).

   The axes are oriented as X origin→RPA, Y origin→NAS, Z origin→upward (orthogonal to X and Y).

   Note

   The required 3D coordinates for defining the head coordinate frame (NAS, LPA, RPA) are measured at a stage separate from the MEG data recording. There exist numerous devices to perform such measurements, usually called “digitizers”. For example, see the devices by the company Polhemus.

2. MEG device coordinate frame (“meg”, blue axes)

   The MEG device coordinate frame is defined by the respective MEG manufacturers. All MEG data is acquired with respect to this coordinate frame. To account for the anatomy and position of the subject’s head, we use so-called head position indicator (HPI) coils. The HPI coils are placed at known locations on the scalp of the subject and emit high-frequency magnetic fields used to coregister the head coordinate frame with the device coordinate frame.

   From the Neuromag/Elekta/MEGIN user manual:

   The origin of the device coordinate system is located at the center of the posterior spherical section of the helmet with X axis going from left to right and Y axis pointing front. The Z axis is, again normal to the plane with positive direction up.

   Note

   The HPI coils are shown as magenta spheres. Coregistration happens at the beginning of the recording and the data is stored in raw.info['dev_head_t'].

3. MRI coordinate frame (“mri”, gray axes)

   Defined by Freesurfer, the MRI (surface RAS) origin is at the center of a 256×256×256 1mm anisotropic volume (may not be in the center of the head).

   Note

   We typically align the MRI coordinate frame to the head coordinate frame through a rotation and translation matrix, that we refer to in MNE as trans.

A bad example

Let’s try using trans=None, which (incorrectly!) equates the MRI and head coordinate frames.

mne.viz.plot_alignment(raw.info, trans=None, subject='sample', src=src,
                       subjects_dir=subjects_dir, dig=True,
                       surfaces=['head-dense', 'white'], coord_frame='meg')

Out:

Using lh.seghead for head surface.
Getting helmet for system 306m

It is quite clear that the MRI surfaces (head, brain) are not well aligned to the head digitization points (dots).

A good example

Here is the same plot, this time with the trans properly defined (using a precomputed matrix).

mne.viz.plot_alignment(raw.info, trans=trans, subject='sample',
                       src=src, subjects_dir=subjects_dir, dig=True,
                       surfaces=['head-dense', 'white'], coord_frame='meg')

Out:

Using lh.seghead for head surface.
Getting helmet for system 306m

Defining the head↔MRI trans using the GUI

You can try creating the head↔MRI transform yourself using mne.gui.coregistration().

• First you must load the digitization data from the raw file (Head Shape Source). The MRI data is already loaded if you provide the subject and subjects_dir. Toggle Always Show Head Points to see the digitization points.

• To set the landmarks, toggle Edit radio button in MRI Fiducials.

• Set the landmarks by clicking the radio button (LPA, Nasion, RPA) and then clicking the corresponding point in the image.

• After doing this for all the landmarks, toggle Lock radio button. You can omit outlier points, so that they don’t interfere with the finetuning.

  Note

  You can save the fiducials to a file and pass mri_fiducials=True to plot them in mne.viz.plot_alignment(). The fiducials are saved to the subject’s bem folder by default.

• Click Fit Head Shape. This will align the digitization points to the head surface. Sometimes the fitting algorithm doesn’t find the correct alignment immediately. You can try first fitting using LPA/RPA or fiducials and then align according to the digitization. You can also finetune manually with the controls on the right side of the panel.

• Click Save As... (lower right corner of the panel), set the filename and read it with mne.read_trans().

For more information, see step by step instructions in these slides. Uncomment the following line to align the data yourself.

# mne.gui.coregistration(subject='sample', subjects_dir=subjects_dir)

Alignment without MRI

The surface alignments above are possible if you have the surfaces available from Freesurfer. mne.viz.plot_alignment() automatically searches for the correct surfaces from the provided subjects_dir. Another option is to use a spherical conductor model. It is passed through bem parameter.

sphere = mne.make_sphere_model(info=raw.info, r0='auto', head_radius='auto')
src = mne.setup_volume_source_space(sphere=sphere, pos=10.)
mne.viz.plot_alignment(
    raw.info, eeg='projected', bem=sphere, src=src, dig=True,
    surfaces=['brain', 'outer_skin'], coord_frame='meg', show_axes=True)

Out:

Fitted sphere radius:         91.0 mm
Origin head coordinates:      -4.1 16.0 51.7 mm
Origin device coordinates:    1.4 17.8 -10.3 mm

Equiv. model fitting -> RV = 0.0034856 %
mu1 = 0.944754    lambda1 = 0.137089
mu2 = 0.667504    lambda2 = 0.683819
mu3 = -0.26966    lambda3 = -0.0105378
Set up EEG sphere model with scalp radius    91.0 mm

Sphere                : origin at (-4.1 16.0 51.7) mm
              radius  : 81.9 mm
grid                  : 10.0 mm
mindist               : 5.0 mm

Setting up the sphere...
Surface CM = (  -4.1   16.0   51.7) mm
Surface fits inside a sphere with radius   81.9 mm
Surface extent:
    x =  -86.0 ...   77.8 mm
    y =  -65.9 ...   97.9 mm
    z =  -30.2 ...  133.7 mm
Grid extent:
    x =  -90.0 ...   80.0 mm
    y =  -70.0 ...  100.0 mm
    z =  -40.0 ...  140.0 mm
6156 sources before omitting any.
2300 sources after omitting infeasible sources not within 0.0 - 81.9 mm.
1904 sources remaining after excluding the sources outside the surface and less than    5.0 mm inside.
Adjusting the neighborhood info.
Getting helmet for system 306m
    Triangle neighbors and vertex normals...

It is also possible to use mne.gui.coregistration() to warp a subject (usually fsaverage) to subject digitization data, see these slides.

Estimated memory usage: 9 MB