brain2brain – first example on real data

I proudly present: the first working example! It is demonstrated, how to use DIPY in order to move your volumetric grid space obtained from a LCMV beamformer computed in MNE-Python.

The procedure is as follows:

  •  compute the results we want to morph
  •  select reference spaces (in our case the subject’s individual T1 and “fsaverage”, which comes with mne or FreeSurfer). Note that we only use the “brain”, excluding skull and other surrounding parts. A brain only image can be obtained from the FreeSurfer segmentation.
  •  morph subject brain to average brain
  •  apply the resulting transform to the volumetric grid obtained from the lcmv beamformer

The following Python packages should be installed beforehand: mne, dipy, nibabel, nilearn. This should work easily using pip:

pip install mne dipy nibabel nilearn

After that is done we will use an existing example of MNE-Python to obtain the the individual result we want to morph. The full example, can be found here.

But first let’s import some packages:

import numpy as np

import mne
from mne.datasets import sample
from mne.beamformer import make_lcmv, apply_lcmv

from dipy.align.imwarp import SymmetricDiffeomorphicRegistration
from dipy.align.metrics import CCMetric
from dipy.align.reslice import reslice
from dipy.align.transforms import (TranslationTransform3D,
                                   RigidTransform3D,
                                   AffineTransform3D)
from dipy.align.imaffine import (transform_centers_of_mass,
                                 MutualInformationMetric,
                                 AffineRegistration)
import nibabel as nib

from nilearn.plotting import plot_anat
from nilearn.image import index_img, resample_img

Next we compute a slightly modified version of the example provided by MNE-Python:

# Setup paths
data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_raw.fif'
event_fname = data_path + '/MEG/sample/sample_audvis_raw-eve.fif'
fname_fwd = data_path + '/MEG/sample/sample_audvis-meg-vol-7-fwd.fif'

# Get epochs
event_id, tmin, tmax = [1, 2], -0.2, 0.5

# Setup for reading the raw data
raw = mne.io.read_raw_fif(raw_fname, preload=True)
raw.info['bads'] = ['MEG 2443', 'EEG 053']  # 2 bad channels
events = mne.read_events(event_fname)

# Set up pick list: gradiometers and magnetometers, excluding bad channels
picks = mne.pick_types(raw.info, meg=True, eeg=False, stim=True, eog=True,
                       exclude='bads')

# Pick the channels of interest
raw.pick_channels([raw.ch_names[pick] for pick in picks])

# Re-normalize our empty-room projectors, so they are fine after subselection
raw.info.normalize_proj()
# Read epochs
proj = False  # already applied
epochs = mne.Epochs(raw, events, event_id, tmin, tmax,
                    baseline=(None, 0), preload=True, proj=proj,
                    reject=dict(grad=4000e-13, mag=4e-12, eog=150e-6))
evoked = epochs.average()

# Read regularized noise covariance and compute regularized data covariance
noise_cov = mne.compute_covariance(epochs, tmin=tmin, tmax=0, method='shrunk')
data_cov = mne.compute_covariance(epochs, tmin=0.04, tmax=0.15,
                                  method='shrunk')
###############################################################################
# Read forward model
forward = mne.read_forward_solution(fname_fwd)

# Compute weights of free orientation (vector) beamformer with weight
# normalization (neural activity index, NAI). Providing a noise covariance
# matrix enables whitening of the data and forward solution. Source orientation
# is optimized by setting pick_ori to 'max-power'.
# weight_norm can also be set to 'unit-noise-gain'. Source orientation can also
# be 'normal' (but only when using a surface-based source space) or None,
# which computes a vector beamfomer. Note, however, that not all combinations
# of orientation selection and weight normalization are implemented yet.
filters = make_lcmv(evoked.info, forward, data_cov, reg=0.05,
                    noise_cov=noise_cov, pick_ori='max-power',
                    weight_norm='nai')

# Apply this spatial filter to the evoked data.
stc = apply_lcmv(evoked, filters, max_ori_out='signed')

# take absolute values for plotting
stc.data[:, :] = np.abs(stc.data)

# Save result in stc files
stc.save('lcmv-vol')

# select time window (tmin, tmax)
stc.crop(0.0, 0.0)

# Save result in a 4D nifti file
mne.save_stc_as_volume('lcmv_inverse.nii.gz', stc,
                       forward['src'], mri_resolution=True)

Note, that we set “mri_resolution” to “true”. This helps us later on in morphing the grid, since the (non-linear) transform will be estimated based on the anatomical MRI(s).

Next, we will prepare our data for the morph. This includes loading the respective volumes, defining a new voxel size (note, that because this is an example, a voxel size was chosen towards optimizing performance, rather than resolution), and normalizing our two reference T1s. Furthermore we will define the number of iterations used for each optimizations step (explained below). In order to keep things comprehensible, we will from now on call the fsaverage T1 image Static, because it is the volume we want to move to. The subject’s T1 in turn will be called Moving, since it will be moved towards Static:

# isometric voxel size of 3 mm - reconsider for real data
voxel_size = (3., 3., 3.)

# number of iterations for each optimisation level
niter_affine = [100, 100, 10]
niter_sdr = [5, 5, 3]

# load lcmv inverse
img_vol = nib.load('lcmv_inverse.nii.gz')

# reslice lcmv inverse
img_vol_res, img_vol_res_affine = reslice(img_vol.get_data(), img_vol.affine,
                                          img_vol.header.get_zooms()[:3],
                                          voxel_size)
img_vol = nib.Nifti1Image(img_vol_res, img_vol_res_affine)

img_vol_first = index_img(img_vol, 0)  # for plotting

# select first time volume and output ndarray
img = img_vol.dataobj[:, :, :, 0]

# load subject brain (Moving)
t1_fname = data_path + '/subjects/sample/mri/brain.mgz'
t1_m_img = nib.load(t1_fname)

# reslice Moving
t1_m_img_res, t1_m_img_res_affine = reslice(t1_m_img.get_data(),
                                            t1_m_img.affine,
                                            t1_m_img.header.get_zooms()[:3],
                                            voxel_size)
t1_m_img = nib.Nifti1Image(t1_m_img_res, t1_m_img_res_affine)

# get Moving to world transform
t1_m_grid2world = t1_m_img.affine

# output Moving as ndarray
t1_m = t1_m_img.dataobj[:, :, :]

# normalize values
t1_m = t1_m.astype('float') / t1_m.max()

# load fsaverage brain (Static)
t1_fname = data_path + '/subjects/fsaverage/mri/brain.mgz'
t1_s_img = nib.load(t1_fname)

# reslice Static
t1_s_img_res, t1_s_img_res_affine = reslice(t1_s_img.get_data(),
                                            t1_s_img.affine,
                                            t1_s_img.header.get_zooms()[:3],
                                            voxel_size)
t1_s_img = nib.Nifti1Image(t1_s_img_res, t1_s_img_res_affine)

# get Static to world transform
t1_s_grid2world = t1_s_img.affine

# output Static as ndarray
t1_s = t1_s_img.dataobj[:, :, :]

# normalize values
t1_s = t1_s.astype('float') / t1_s.max()

Now we can compute the transform. First we will use an affine transformation, to get both images pre-aligned as good as possible. Based on that result, the non-linear transform will follow.

Step 1 – affine transform:

# compute center of mass
c_of_mass = transform_centers_of_mass(t1_s, t1_s_grid2world,
                                      t1_m, t1_m_grid2world)

nbins = 32

# prepare affine registration
affreg = AffineRegistration(metric=MutualInformationMetric(nbins, None),
                            level_iters=niter_affine,
                            sigmas=[3.0, 1.0, 0.0],
                            factors=[4, 2, 1])

# translation
translation = affreg.optimize(t1_s, t1_m, TranslationTransform3D(), None,
                              t1_s_grid2world, t1_m_grid2world,
                              starting_affine=c_of_mass.affine)

# rigid body transform (translation + rotation)
rigid = affreg.optimize(t1_s, t1_m, RigidTransform3D(), None,
                        t1_s_grid2world, t1_m_grid2world,
                        starting_affine=translation.affine)

# affine transform (translation + rotation + scaling)
affine = affreg.optimize(t1_s, t1_m, AffineTransform3D(), None,
                         t1_s_grid2world, t1_m_grid2world,
                         starting_affine=rigid.affine)

# apply affine transformation
t1_m_affine = affine.transform(t1_m)

We shift the center of mass of Moving to Static. Afterwards, we compute a rigid body transform, that is preserving the distance between each set of points. Hence the object will be rotated, translated and reflected to match Static even better. In a third step, we will finally compute a full affine transform, that additionally includes scaling ans shearing.

We use the mutual information as an optimization metric as common in the field (Mattes et al., 2003).

Our two brains should overlap quite nicely by now. However, we still have the problem of “individuality”. Even though our brains overlap very well by now, structural differences across different individuals are still not accounted.

Step 2 – non-linear transform:

# set up Symmetric Diffeomorphic Registration (metric, iterations per level)
sdr = SymmetricDiffeomorphicRegistration(CCMetric(3), niter_sdr)

# compute mapping
mapping = sdr.optimize(t1_s, t1_m_affine)

# morph img data
img_sdr_affine = mapping.transform(affine.transform(img))

The result is a displacement map, telling exactly which voxel in Moving corresponds to which voxel in Static and how Moving has to be moved to match Static. We will use the cross-correlation optimization metric as described in Avants et al. (2009).

Step 3 – plotting, saving, happiness:

# make transformed ndarray a nifti
img_vol_sdr_affine = nib.Nifti1Image(img_sdr_affine, affine=t1_s_grid2world)

# save morphed grid
nib.save(img_vol_sdr_affine, 'lcmv_inverse_fsavg.nii.gz')

# plot result
imgs = [img_vol_first, img_vol_first,
        nib.load('lcmv_inverse_fsavg.nii.gz')]

t1_imgs = [t1_m_img, t1_s_img, t1_s_img]

titles = ['subject brain', 'fsaverage brian',
          'fsaverage brian\nmorphed source']

saveas = ['lcmv_subject.png', 'lcmv_fsaverage.png',
          'lcmv_fsaverage_morphed.png']

for img, t1_img, title, fname in zip(imgs, t1_imgs, titles,
                                     saveas):
    display = plot_anat(t1_img, display_mode='x',
                        title=title)
    display.add_overlay(img)
    display.savefig(fname)
    display.close()

The result of the above code will vary slightly. In the example 3 PNG files will be saved in order to visualize the transform. For reasons of eye candy I transformed the results into GIF images:

Here you see how the subject’s anatomical T1 and the result of the source analysis overlap nicely:

Subject’s brain with LCMV beamformer result as an overlay

When overlaying the FreeSurfer average brain with the very same overlay, then we see that it does not fit. The spaces are off. The same would happen, if we tried to apply the result-space of subject A to the brain of subject B. Hence in order to make results comparable, they must fit a common space (in this case fsaverage):

fsaverage brain with LCMV beamformer result as an overlay

After estimating the volumetric morph based on the anatomical scans, we can now transform our beamformer results to the same space. By applying first the affine transform and afterwards the non-linear transform, we shift our individual results into a common space (fsaverage):

fsaverage brain with morphed LCMV beamformer result as an overlay

If we would do this for a set of subjects, we could compute any statistics as usual. Because anatomical (/ functional) areas overlap now between subjects.

What’s next?

The next step would be to provide this example as an official example as part of the MNE-Python documentation.

Afterwards it’s time to go into the API that the will make the workflow accessible from higher order functions. Thereby it could be linked directly to the existing surface morph, such that the user experiences no difference in the actual handling of the function. The magic will be done “under the hood”.

Alright! Have fun trying it out and stay tuned 😉

Grid-ings,

Tommy

References

Avants, B. B., Epstein, C. L., Grossman, M., & Gee, J. C. (2009). Symmetric Diffeomorphic Image Registration with Cross- Correlation: Evaluating Automated Labeling of Elderly and Neurodegenerative Brain, 12(1), 26-41.

Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K., & Eubank, W. (2003). PET-CT image registration in the chest using free-form deformations. IEEE transactions on medical imaging, 22(1), 120-128.

Source Code:

https://github.com/TommyClausner/GSoC2018MNE/blob/master/example2_brain2avg.py

First moment of success!!

Hey together!

The digging for existing functions and implementations regarding the non-linear volumetric morph, might turn out shorter than expected.

The basic functionality has already been implemented in DIPY, which is using the Symmetric Normalization (SyN) algorithm proposed by Avants et al. (2009).

Based on the provided example I tested the algorithm on two T1 weighted anatomical MRIs. Furthermore I tested how well the algorithm performs on arbitrarily distributed cubes in a larger otherwise empty cuboid. The volume that was needed to be morphed was (in this case) created by randomly shifting each cube’s location of the initial random volume slightly.

And here are the results:

Example morph for two different anatomical MRIs
Example morph for arbitrarily distributed cubes in a larger cuboid

While the red color indicates the moving volume, the green color represents the static. Hence the more areas are yellow the better (higher overlap). Each frame of the respective GIF represents a slice through the corresponding volume.

For both simulations it turns out, that the amount of overlap after morphing the “moving” volume towards the “static” volume increased. Hence a (non-linear) transformation to morph image landmarks towards each other was achieved.

Structural differences in my testing examples were quite significant (human head vs. random cubes), however the algorithm performed well in both scenarios.

I think that’s quite a good starter!

Let’s see what else is out there!

Cheers,

Tommy

 

References:

Avants, B. B., Epstein, C. L., Grossman, M., & Gee, J. C. (2009). Symmetric Diffeomorphic Image Registration with Cross- Correlation: Evaluating Automated Labeling of Elderly and Neurodegenerative Brain, 12(1), 26-41.

Source Code:

https://github.com/TommyClausner/GSoC2018MNE/blob/master/example1_dipyTest.py

import GoogleSummerOfCode as GSoC

Hi everyone!

Summer is on it’s way and the Google Summer Of Code is by no means an exception!

I’m very happy that my project with Python Software Foundation and MNE Python got accepted!

The project is titled: mne.set_volumeAverage(True) – preparing Group level analyses for volumetric data

So what’s it all about?

MNE Python is a Open Source software package for Python, providing tools for the analysis of (electrophysiological) brain data. Those tools include functions for neural source reconstructions of MEG/EEG data. In a nutshell, the goal is to infer sources of brain activity given electrophysiological brain data, recorded at multiple locations around the head. One approach to solve this so called inverse problem is the beamforming approach: The anatomical brain is partialized into a volumetric grid and by “scanning” through all the grid points while trying to maximize the explanation of the recorded data, grid points can be identified as relevant generators for a certain set of brain data. Furthermore time resolved (LCMV beamformer) or frequency resolved (DICS beamformer) data for those “virtual channels” can be obtained.

Due to anatomical differences across subjects, grid points might expose different relations. Or in other words: not two brains are alike. Imagine lining up all facial features of two faces. Even though they share almost always the same features it is also almost always impossible to align all features at the same time.

In order to compute group level statistics on volumetric brain data we are facing the same problem. It is hence necessary to transform individual “brain grids” into a common grid space, where functional (and anatomical) similar regions are represented at similar voxel locations in the volumetric grid.

This is were my project becomes relevant:
As a result of the proposed project I would like to see a set of functions, that allow for (non-) linear warping of volumetric grids and creating pseudo-individual MR images, based on subjects head shape. If time allows the respective visualization would be a “nice to have” as well.

Source code produced throughout the project, will be provided via GitHub.

All right! Let’s get started!

Stay tuned for any updates on the grid side of life!

Cheers,

Tommy