Has been a while since the last post, however I’m now able to proudly present the pre-built of the later functionality. To achieve this parts of the script were wrapped into functions, that in turn were set up such, that they can easily be ported to become a method of an object in the final API. Furthermore the example will probably soon be available via the MNE-python documentation.

All right! Let’s get into it!

from dipy.align import imaffine, imwarp, metrics, reslice, transforms import matplotlib.pylab as plt import mne from mne.beamformer import make_lcmv, apply_lcmv from mne.datasets import sample from mne.externals.h5io import read_hdf5, write_hdf5 import nibabel as nib from nilearn.image import index_img from nilearn.plotting import plot_anat import numpy as np from os import path, makedirs print(__doc__)

The first function will compute our example data according to the existing MNE-Python example and return a volumetric source space result of the example’s peak time:

def compute_lcmv_example_data(data_path, fname=None): 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 if desired if fname is not None: stc.save('lcmv-vol') # select time window (tmin, tmax) in ms - consider changing for real data # scenario, since those values were chosen to optimize computation time stc.crop(0.087, 0.087) # Save result in a 4D nifti file img = mne.save_stc_as_volume(fname, stc, forward['src'], mri_resolution=True) return img

Next, we define our morph mapping that we want to compute. The function takes a *Moving *volume (img_m) that is morphed towards the *Static* volume (img_s). In general we compute the morph in two steps:

- we compute an affine linear transform
- we compute a non-linear transform on the pre-transformed image

The maximum number of iterations during the optimization can be set. niter_affine defines the number of optimization levels and the corresponding maximum number of iterations. The same applies to niter_sdr but for performing the Symmetric Diffeomorphic Registration.

As a result the function will return *mapping* and *affine*, being the respective non-linear and affine mapping objects.

def compute_morph_map(img_m, img_s=None, niter_affine=(100, 100, 10), niter_sdr=(5, 5, 3)): # get Static to world transform img_s_grid2world = img_s.affine # output Static as ndarray img_s = img_s.dataobj[:, :, :] # normalize values img_s = img_s.astype('float') / img_s.max() # get Moving to world transform img_m_grid2world = img_m.affine # output Moving as ndarray img_m = img_m.dataobj[:, :, :] # normalize values img_m = img_m.astype('float') / img_m.max() # compute center of mass c_of_mass = imaffine.transform_centers_of_mass(img_s, img_s_grid2world, img_m, img_m_grid2world) nbins = 32 # set up Affine Registration affreg = imaffine.AffineRegistration( metric=imaffine.MutualInformationMetric(nbins, None), level_iters=list(niter_affine), sigmas=[3.0, 1.0, 0.0], factors=[4, 2, 1]) # translation translation = affreg.optimize(img_s, img_m, transforms.TranslationTransform3D(), None, img_s_grid2world, img_m_grid2world, starting_affine=c_of_mass.affine) # rigid body transform (translation + rotation) rigid = affreg.optimize(img_s, img_m, transforms.RigidTransform3D(), None, img_s_grid2world, img_m_grid2world, starting_affine=translation.affine) # affine transform (translation + rotation + scaling) affine = affreg.optimize(img_s, img_m, transforms.AffineTransform3D(), None, img_s_grid2world, img_m_grid2world, starting_affine=rigid.affine) # apply affine transformation img_m_affine = affine.transform(img_m) # set up Symmetric Diffeomorphic Registration (metric, iterations) sdr = imwarp.SymmetricDiffeomorphicRegistration( metrics.CCMetric(3), list(niter_sdr)) # compute mapping mapping = sdr.optimize(img_s, img_m_affine) return mapping, affine

In order to make the functionality useful in a real case scenario, one might want to save and load the respective mapping data. For this reason the following two functions were implemented:

def save_mapping(fname, data, overwrite=True): out = dict() # dissolve object structure for d in data: # save type for order independent decomposition out[type(d).__name__] = d.__dict__ write_hdf5(fname + '.h5', out, overwrite=overwrite)

… saves the data, by creating a dictionary with all data types and their respective sub-structure, that is obtained in form of the internal dictionary of *mapping* or *affine*.

def load_mapping(fname): # create new instances mapping = imwarp.DiffeomorphicMap(None, []) affine = imaffine.AffineMap(None) data = read_hdf5(fname + '.h5') mapping.__dict__ = data.get(type(mapping).__name__) affine.__dict__ = data.get(type(affine).__name__) return mapping, affine

… looks up the desired data types in the loaded dictionary and recomposes *mapping* and *affine* by creating an empty instance and reassigning the loaded data.

Now we are able to create, save and load our non-linear morphs. A crucial part however is still missing, namely applying the morph to our data. This step is done by the following function:

def morph_precomputed(img, affine, mapping): # morph img data img_sdr_affine = np.zeros(img.shape) for vol in range(img.shape[3]): img_sdr_affine[:, :, :, vol] = mapping.transform( affine.transform(img.dataobj[:, :, :, vol])) return img_sdr_affine

… the function takes 4D image data and loops over the 4th dimension (normally a time series). The respective 3D volume that is left, will be morphed using the affine transform first, followed by the non-linear transform. The function will return a 4D volume in the new space.

Because we also want to visualize our data later on, we want select slices to show, that are not similar relative to the volume itself, rather than the *brain* structure that is housed by it. Hence we might want to show different slices for *Moving *and *Static* respectively. Slices are defined as cut coordinates and shifted using a transformation matrix (in this example the inverse affine transform). The function returns an array containing the morphed 3D coordinates. Note, that in order to perform a 3D transform using a 4×4 transformation matrix, a column of ones was appended to the Nx3 array containing the old coordinates.

def morph_slice_indices(slice_indices, transmat): # make sure array is 2D slice_indices = np.atleast_2d(slice_indices) # add a column of ones slice_indices = np.append(slice_indices, np.ones((slice_indices.shape[0], 1)), axis=1) # matrix multiplication with transformation matrix slice_indices_out = np.einsum('...j,ij', slice_indices, transmat) # round to select valid slices and remove last column return np.round(slice_indices_out[:, :-1])

As a last – mostly for convenience – we define a function that prepares our morph template data. This includes loading the example data and re-slicing. The first argument to give to the function is the result we obtained from *compute_lcmv_example_data.* The function returns the pre-processed volumes (functional, moving MRI, static MRI).

def prepare_volume_example_data(img_in, t1_m_path, t1_s_path, voxel_size=(3., 3., 3.)): # load lcmv inverse if isinstance(img_in, str): img_vol = nib.load(img_in) else: img_vol = img_in # reslice lcmv inverse img_vol_res, img_vol_res_affine = reslice.reslice( img_vol.get_data(), img_vol.affine, img_vol.header.get_zooms()[:3], voxel_size) img_vol_res = nib.Nifti1Image(img_vol_res, img_vol_res_affine) # load subject brain (Moving) t1_m_img = nib.load(t1_m_path) # reslice Moving t1_m_img_res, t1_m_img_res_affine = reslice.reslice( t1_m_img.get_data(), t1_m_img.affine, t1_m_img.header.get_zooms()[:3], voxel_size) t1_m_img_res = nib.Nifti1Image(t1_m_img_res, t1_m_img_res_affine) # load fsaverage brain (Static) t1_s_img = nib.load(t1_s_path) # reslice Static t1_s_img_res, t1_s_img_res_affine = reslice.reslice( t1_s_img.get_data(), t1_s_img.affine, t1_s_img.header.get_zooms()[:3], voxel_size) t1_s_img_res = nib.Nifti1Image(t1_s_img_res, t1_s_img_res_affine) return img_vol_res, t1_m_img_res, t1_s_img_res

Lastly we execute the example:

# Setup path data_path = sample.data_path() results_path = data_path + '/subjects/LCMV-results' # create results directory if it doesn't exist if not path.exists(results_path): makedirs(results_path) # compute LCMV beamformer inverse example img = compute_lcmv_example_data(data_path) # load and reslice volumes img_vol_res, t1_m_img_res, t1_s_img_res = prepare_volume_example_data( img, data_path + '/subjects/sample/mri/brain.mgz', data_path + '/subjects/fsaverage/mri/brain.mgz', voxel_size=(5., 5., 5.)) # compute morph map from Moving to Static mapping, affine = compute_morph_map(t1_m_img_res, t1_s_img_res) save_mapping(results_path + '/volume_morph', [mapping, affine]) mapping, affine = load_mapping(results_path + '/volume_morph') # apply morph map (test if saving and loading worked) img_vol_morphed = morph_precomputed(img_vol_res, mapping, affine) # make transformed ndarray a nifti img_vol_morphed = nib.Nifti1Image(img_vol_morphed, affine=t1_s_img_res.affine) # save morphed result nib.save(img_vol_morphed, results_path + '/lcmv-fsaverage.nii.gz')

The plotting can be done using:

# select image overlay imgs = [index_img(img_vol_res, 0), index_img(img_vol_res, 0), index_img(img_vol_morphed, 0)] # select anatomical background images t1_imgs = [t1_m_img_res, t1_s_img_res, t1_s_img_res] # slices to show for Static volume slices_s = (-10, 0, 0) # slices to show for Moving volume # to show roughly the same view, we transform the selected Static slices using # the inverse affine transformation. Note that due to rotation and the # non-linear transform, both views do not overlap perfectly (pre computed for # this example) slices_m = morph_slice_indices(np.atleast_2d(slices_s), affine.affine_inv)[0] slices = [slices_s, slices_s, tuple(slices_m)] # define titles for plots titles = ['subject brain', 'fsaverage brain', 'fsaverage brain morphed result'] # plot results figure, (axes1, axes2, axes3) = plt.subplots(3, 1) figure.subplots_adjust(top=0.8, left=0.1, right=0.9, hspace=0.5) figure.patch.set_facecolor('black') for axes, img, t1_img, cut_coords, title in zip([axes1, axes2, axes3], imgs, t1_imgs, slices, titles): display = plot_anat(t1_img, display_mode='ortho', cut_coords=cut_coords, draw_cross=False, axes=axes, figure=figure, annotate=False) display.add_overlay(img, alpha=0.75) display.annotate(size=8) axes.set_title(title, color='white', fontsize=12) plt.text(plt.xlim()[1], plt.ylim()[0], 't = 0.087s', color='white') plt.suptitle('morph subject results to fsaverage', color='white', fontsize=16) plt.show()

… but the results shown below will are an animated t-series, whereas the plot produced by the above code will only show a single time-point.

As clearly visible the morph was successful as before, but now got a much nicer API and can be used as hands-on example.

Furthermore the above code computes within a minute, so don’t hesitate to try it out! ðŸ˜‰

As usual the source code will be provided via GitHub.

Stay tuned!

Cheers,

Tommy