We’re getting there…

Hey there!

Today really a major update!! The class is in it’s final stage an so are an example and two tutorials. One including more compact information about morphing, whereas the second provides detailed background info!

First download the necessary data for example 6 from GitHub. Replace the respective file in your mne root folder and run

python setup.py install to apply the changes and register the new class.

If you wish, you could navigate to mne-python/doc and run:

PATTERN=plot_background_morph.py make html_dev-pattern

This will render the detailed tutorial. You can then open it in your browser, by clicking mne-python/doc/_build/html/auto_tutorials

Here I will post very similar content to the above mentioned tutorial (I will not post the part about surface morphing here, since I am not the creator of this part):

Problem statement

Modern neuro imaging techniques such as souce reconstruction or fMRI analyses, make use of advanced mathematical models and hardware to map brain activation patterns into a subject specific anatomical brain space. This enables the study of spatio-temporal brain activity. Amongst many others, the representation of spatio-temporal activation patterns is often done by overlaying the actual anatomical brain structure, with the respective activation at the respective anatomical location. Hereby volumetric anatomical MR images are often used as such or are transformed into an inflated surface.

It becomes obvious that in order to compute group level statistics, data representations across subjects must be morphed to a common frame, such that anatomically / functional similar structures are represented at the same spatial location.

Morphing basics

Morphing describes the procedure of transforming a data representation in n- dimensional space into another data representation in the same space. In the context of neuroimaging data this space will mostly be 3-dimensional and necessary to bring individual subject spaces into a common frame. In general morphing operations can be split into two different kinds of transformation: linear and non-linear morphs or mappings.

A mapping is linear if it satisfies the following two conditions:

f(u+v)=f(u)+f(v) ,
f(cu)=cf(u) ,

where u and v are from the same vector space and c can be any scalar. This means that any linear transform is a mixture of additive and multiplicative operations and hence is often represented in terms of a transformation matrix.

In turn, a non-linear mapping can include linear components, but furthermore functions that are not limited by the above constraints. However it needs to be understood that including non-linear operations will alter the relationship of data points within a vector and thus cannot be represented as a transformation matrix. Instead every data point can be mapped independent of other data points. This becomes especially handy when morphing volumetric brain data. To achieve a mapping of structurally similar areas between subjects, it is inevitable to employ non-linear operations to account for morphological differences that cannot be represented by a linear transform.

In MNE-Python “brain space” data is represented as source estimate data, obtained by one of the implemented source reconstruction methods. See Source localization with MNE/dSPM/sLORETA/eLORETA

It is thus represented as SourceEstimate, VectorSourceEstimate, VolSourceEstimate or a mixture of those.

The data in the first two cases is represented as “surfaces”. This means that the data is represented as vertices on an inflated brain surface representation. In the last case the data is represented in a 4-dimensional space, were the last dimension refers to the data’s sample points.

Computing an inflated surface representation can be accomplished using FreeSurfer. Thereby, spherical morphing of the surfaces can be employed to bring data from different subjects into a common anatomical frame. When dealing with volumetric data, a non-linear morph map – or better morph volume – based on two different anatomical reference MRIs can be computed.

Volumetric morphing

The key difference in volumetric morphing as compared to morphing surfaces, is that the data is represented as a volume. A volume is a 3-dimensional data representation. It is necessary to understand that the difference to a mesh (what’s commonly meant when referring to “3D model”) is that the mesh is “empty”, while the volume is not. Whereas the mesh is defined by the vertices of the outer hull, the volume is defined by that and the points it is containing. Hence morphing volumetric data does not only require to map the surface data, but also it’s content in the correct way.

It becomes more easy to understand, when thinking about morphing one brain to another. We not only want the cortices to overlap anatomically as good as possible, but also all sub-cortical structures.

In MNE-Python the implementation of volumetric morphing is achieved by wrapping the corresponding functionality from DiPy. See this dipy example for reference.

The volumetric morphed is implemented as a two stage approach. First two reference brains are are aligned using an affine linear registration and later a non-linear Symmetric Diffeomorphic Registration in 3D.

 

Affine registration

See dipy affine example for reference.

Our goal is to pre-align both reference volumes as good as possible, to make it easier for the later non-linear optimization to converge to an acceptable minimum. The quality of the pre-alignment will be assessed using the mutual information that is aimed to be maximal [3].

Mutual information can be defined as the amount of predictive value two variables share. Thus how much information about a random variable B can be obtained through variable A.

It can further be expressed in terms of entropy as the difference between the joined entropy of A and B the respective conditional entropies. Hence the higher the joint entropy, the lower the conditional and hence one variable is more predictive for the respective other. Aiming for maximizing the mutual information can thus be seen as reducing the conditional entropy and thus the amount of information required from a second variable, to describe the system.

If we find a transformation such, that both volumes are overlapping as good as possible, then the location of a particular area in one brain, would be highly predictive for the same location on the second brain. In turn mutual information is high, whereas the conditional entropy is low.

The specific optimization algorithm used for mutual information driven affine registration is described in Mattes et al. 2003 [4].

In essence, a gradient decent is used to minimize the negative mutual information, while optimizing the set of parameters of the image discrepancy function.

 

Symmetric Diffeomorphic Registration

See dipy sdr example for reference.

Symmetric Diffeomorphic Image Registration is described in Avants et al. 2009 [2].

A map between two objects (manifolds that need to be differentiable) is diffeomorphic if it is invertable (so is it’s inverse). Hence it can be seen as a locally linear, smooth map, that describes how each point on one object relates to the same point on a second object. Imagine a scrambled and an intact sheet of paper. There is a clear mapping between each point of the first, to each point of the second object.

The introduced “symmetry” refers to symmetry after implementation. That is that morphing A to B yields computationally the same result as morphing B to A.

As optimization criterion the cross-correlation was chosen, which is a description of similarity between two data series.

 

SourceMorph

SourceMorph is MNE-Python’s source estimation morphing operator. It can perform all necessary computations, to achieve the above transformations on surface source estimate representations as well as for volumetric source estimates. This includes SourceEstimate and VectorSourceEstimate for surface representations and VolSourceEstimate for volumetric representations.

SourceMorph can take general a type specific keyword arguments. The following general keyword arguments are accepted:

  • subject_from: string pointing to the respective subject folder representing the subject the is going to be morphed. E.g. subject_from=’Bert’. Within the respective subject folder (e.g. SUBJECTS_DIR/Bert), the result of an anatomical segmentation, done with FreeSurfer should be present. More specifically FreeSurfer surface data is employed to achieve surface morph operations, whereas for volume source estimates brain.mgz will be used by default. The default is subject_from=None. If this is the case subject_from will be derived from the source space or source estimate if present.
  • subject_to: string pointing to the respective subject folder representing the subject the is used as reference for the respective morph. Hence this it represents the target space. Similar data as for subject_from is used. The default is subject_to=’fsaverage’, hence is not otherwise specified fsaverage will be the target space. Note that it is possible as well to specify a path pointing to any brain.mgz that is used as reference volume.
  • subjects_dir: FreeSurfer subject directory. If not defined in SUBJECTS_DIR, subjects_dir should be define, otherwise the default is None, utilizing the path set in the environment.
  • src: The list of source space corresponding to the source estimate that is targeted as a morph. While for VolSourceEstimates, src is must be set, it is not necessary to be set when attempting to perform a surface morph. Hence the default is src=None. If no src is provided (only possible for surface morphs), then the SourceMorph operator is only set up and the computation of the morph takes place, once the object is called. In the case of volumetric data, src must be provided, in order to obtain the relevant information of how the data maps to anatomical data, that is used to compute the morph.
  • spacing: This parameter is fundamentally different depending on the underlying morph. Please see surface source estimates for information related to surface morphs and volumetric source estimates for information related to volumetric morphs. Default is spacing=5
  • precomputed: If precomputed morph data is already present, or custom made morph data will be used, it can be set by the keyword argument precomputed. If not None, the argument must be a dictionary, carrying type specific morphing information set up in the same way as used by SourceMorph. Please see surface source estimates and volumetric source estimates for information about type specific morph parameters. precomputed=morph_params will thus override my_morph.params The default is precomputed=None

A SourceMorph object can be created, by initializing an instance and setting desired key word arguments like so: my_morph = mne.SourceMorph(...)

my_morph will have all arguments set or their default values as attributes. Furthermore it indicates of which kind it is my_morph.kind and what are the respective morphing parameters my_morph.params.

my_morph.params is a dictionary, that varies depending on the type of morph, all relevant information is stored. See surface source estimates and volumetric source estimates for information about type specific morph parameters.

Surface morphing.

surface source estimates. In addition to general keyword arguments SourceMorph can take multiple arguments depending on the underlying morph. For (Vector) SourceEstimate, those keyword arguments include:

  • spacing: In case of (Vector)SourceEstimate spacing can be an integer a list of 2 np.array or None. The defaut is spacing=5. Spacing refers to what was known as grade in previous versions of MNE-Python. It defines the esolution of the icosahedral mesh (typically 5). If None, all vertices will be used (potentially filling the surface). If a list, then values will be morphed to the set of vertices specified in in spacing[0] and spacing[1]. Note that specifying the vertices (e.g., grade=[np.arange(10242), np.arange(10242)] for fsaverage on a standard grade 5 source space) can be substantially faster than computing vertex locations. Note that if subject=’fsaverage’ and ‘spacing=5’, this set of vertices will automatically be used (instead of computed) for speed, since this is a common morph.
  • smooth: Number of iterations for the smoothing of the surface data. If None, smooth is automatically defined to fill the surface with non-zero values. The default is None.
  • xhemi: If True data can be morphed between hemispheres by setting. The full cross-hemisphere morph matrix maps left to right and right to left. A matrix for cross-mapping only one hemisphere can be constructed by specifying the appropriate vertices, for example, to map the right hemisphere to the left: vertices_from=[[], vert_rh], vertices_to=[vert_lh, []]. Cross-hemisphere mapping requires appropriate sphere.left_right morph-maps in the subject’s directory. These morph maps are included with the fsaverage_sym FreeSurfer subject, and can be created for other subjects with the mris_left_right_register FreeSurfer command. The fsaverage_sym subject is included with FreeSurfer > 5.1 and can be obtained as described here. For statistical comparisons between hemispheres, use of the symmetric fsaverage_sym model is recommended to minimize bias [5].

 

volumetric source estimates

In addition to general keyword arguments SourceMorph can take multiple arguments depending on the underlying morph. For mne.VolSourceEstimate, those keyword arguments include:

  • spacing: In case of VolSourceEstimate spacing can be an integer, float, tuple of integer or float or None. The default is spacing=5. Spacing refers to the voxel size that is used to compute the volumetric morph. Since two volumes are compared “point wise” the number of slices in each orthogonal direction has direct influence on the computation time and accuracy of the morph. See Symmetric Diffeomorphic Registration to understand why this is the case. Spacing thus can also be seen as the voxel size to which both reference volumes will be resliced before computing the symmetric diffeomorphic volume. An integer or float value, will be interpreted as isotropic voxel size in mm. Setting a tuple allows for anisotropic voxel sizes e.g. (1., 1., 1.2). If None the full resolution of the MRIs will be used. Note, that this can cause long computation times.
  • niter_affine: As described in Affine registration an iterative process is used to find the transformation that maps one image to another. This iterative process is performed in multiple levels and a number of iterations per level. A level is a stage of iterative refinement with a certain level of precision. The higher or later the level the more refined the iterative optimization will be, requiring more computation time. The number of levels and the number of iterations per level are defined as a tuple of integers, where the number of integers or the length of the tuple defines the number of levels, whereas the integer values themselves represent the number of iterations in that respective level. The default is niter_affine=(100, 100, 10) referring to a 3 stage optimization using 100, 100 and 10 iterations for the 1st, 2nd and 3rd level. Note, that internally a 3 step approach is computed internally: A translation, followed by a rigid body transform (adding rotation), followed by an affine transform (adding scaling). Thereby the result of the first step will be the initial morph of the second and so on. Thus the defined number of iterations actually applies to 3 different computations.
  • niter_sdr: As described in Symmetric Diffeomorphic Registration an iterative process is used to find the transformation that maps one image to another. This iterative process is performed in multiple levels similar to the affine optimization (Affine registration). The default is niter_sdr=(5, 5, 3) referring to a 3 stage optimization using 5, 5 and 3 iterations for the 1st, 2nd and 3rd level.

 

SourceMorph’s methods

Once an instance of SourceMorph was created, it exposes 3 methods:

  • my_morph() Calling an instance of SourceMorph on SourceEstimate, VectorSourceEstimate or VolSourceEstimate, will apply the precomputed morph to the input data and return the morphed source estimate (stc_morphed = my_morph(stc)). If a surface morph was attempted and no source space was provided during instantiation of SourceMorph, then the actual computation of the morph will take place, using the input data as reference data, rather then precomputing it based on the source space data. Additionally the method takes the same keyword arguments as my_morph.as_volume(), given that as_volume=True. This means that the result will not be a source estimate, but instead NIfTI image representing the source estimate data in the specified way. If as_volume=False all other volume related arguments will be ignored.

  • my_morph.as_volume() This method only works with VolSourceEstimate. It returns a NIfTI image of the source estimate. mri_resolution can be defined to change the resolution of the output image. mri_resolution=True will output an image in the same resolution as the MRI information stored in src. If mri_resolution=False the output image will have the same resolution as defined in ‘spacing’ when instantiating the morph. Furthermore, mri_resolution can be defined as integer, float or tuple of integer or float to refer to the desired voxel size in mm. A single value will be interpreted as isotropic voxel size, whereas anisotropic dimensions can be defined using a tuple. Note, that a tuple must have a length of 3 referring to the 3 orthogonal spatial dimensions. The default is mri_resolution=False. The keyword argument mri_space asks, whether to use the same reference space as the reference MRI of the reference space of the source estimate. The default is mri_space=True. Furthermore a keyword argument called apply_morph can be set, indicating whether to apply the precomputed morph. In combination with the keyword argument ‘as_volume’, this can be used to produce morphed and unmorphed NIfTIs. The default is apply_morph=False.

  • my_morph.save() Saves the morph object to disk. The only input argument is the filename. Since the object is stored in HDF5 (‘.h5’) format, the filename will be extended by ‘-morph.h5’ if no file extension was initially defined. To read saved SourceMorph objects, use mne.read_source_morph().

  • Shortcuts:

    stc_fsaverage = SourceMorph(src=src)(stc)

    img = SourceMorph(src=src)(stc, as_volume=True)

 

Alternative API

Some operations can be performed using the respective source estimate itself. This is mostly to support the API of previous versions of MNE-Python.

Un-morphed VolSourceEstimate can be converted into NIfTI images using stc.as_volume

Un-morphed SourceEstimate and VectorSourceEstimate can morphed using stc.morph

Note that in any of the above cases SourceMorph will be used under the hood to perform the requested operation.

 

Step by step hands on tutorial

In this tutorial we will morph different kinds of source estimates between individual subject spaces using mne.SourceMorph.

We will use precomputed data and morph surface and volume source estimates to a common space. The common space of choice will be FreeSurfer’s “fsaverage”.

Furthermore we will convert our volume source estimate into a NIfTI image using morph.as_volume.

Setup

We first import the required packages and define a list of file names for various data sets we are going to use to run this tutorial.

import os

import matplotlib.pylab as plt
import nibabel as nib
from mne import (read_evokeds, SourceMorph, read_source_estimate)
from mne.datasets import sample
from mne.minimum_norm import apply_inverse, read_inverse_operator
from nilearn.image import index_img
from nilearn.plotting import plot_glass_brain

# We use the MEG and MRI setup from the MNE-sample dataset
sample_dir_raw = sample.data_path()
sample_dir = sample_dir_raw + '/MEG/sample'
subjects_dir = sample_dir_raw + '/subjects'

fname_evoked = sample_dir + '/sample_audvis-ave.fif'

fname_surf = os.path.join(sample_dir, 'sample_audvis-meg')
fname_vol = os.path.join(sample_dir,
                         'sample_audvis-grad-vol-7-fwd-sensmap-vol.w')

fname_inv_surf = os.path.join(sample_dir,
                              'sample_audvis-meg-eeg-oct-6-meg-eeg-inv.fif')
fname_inv_vol = os.path.join(sample_dir,
                             'sample_audvis-meg-vol-7-meg-inv.fif')

fname_t1_fsaverage = subjects_dir + '/fsaverage/mri/brain.mgz'

Data preparation

First we load the respective example data for surface and volume source estimates. In order to save computation time we crop our time series to a short period around the peak time, that we already know. For a real case scenario this might apply as well if a narrow time window of interest is known in advance.

stc_surf = read_source_estimate(fname_surf, subject='sample')

# The surface source space
src_surf = read_inverse_operator(fname_inv_surf)['src']

# The volume inverse operator
inv_src = read_inverse_operator(fname_inv_vol)

# The volume source space
src_vol = inv_src['src']

# Ensure subject is not None
src_vol[0]['subject_his_id'] = 'sample'

# For faster computation we redefine tmin and tmax
stc_surf.crop(0.09, 0.1)  # our prepared surface source estimate

# Read pre-computed evoked data
evoked = read_evokeds(fname_evoked, condition=0, baseline=(None, 0))

# Apply inverse operator
stc_vol = apply_inverse(evoked, inv_src, 1.0 / 3.0 ** 2, "dSPM")

# For faster computation we redefine tmin and tmax
stc_vol.crop(0.09, 0.1)  # our prepared volume source estimate

Setting up SourceMorph for SourceEstimate

As explained in Surface morphing and surface source estimates we have several options to instantiate SourceMorph. We know, that if src is not provided, the morph will not be pre-computed but instead will be prepared for morphing when calling the instance. This works only with (Vector) SourceEstimate. Below you will find a common setup that will apply to most use cases.

morph_surf = SourceMorph(subject_from='sample',  # Default: None
                         subject_to='fsaverage',  # Default
                         subjects_dir=subjects_dir,  # Default: None
                         src=None,  # Default
                         spacing=5,  # Default
                         smooth=None,  # Default
                         xhemi=False)  # Default

Setting up SourceMorph for VolSourceEstimate

From Volumetric morphing and volumetric source estimates we know, that src has to be provided when morphing VolSourceEstimate. Furthermore we can define the parameters of the in general very costly computation. Below an example was chosen using a non-default spacing of isotropic 3 mm. The default is 5 mm and you will experience a noticeable difference in computation time, when changing this parameter. Ideally subject_from can be inferred from src, subject_to is ‘fsaverage’ by default and subjects_dir is set in the environment. In that case mne.SourceMorph can be initialized taking only src as parameter. For demonstrative purposes all available keyword arguments were set nevertheless.

morph_vol = SourceMorph(subject_from='sample',  # Default: None
                        subject_to='fsaverage',  # Default
                        subjects_dir=subjects_dir,  # Default: None
                        spacing=(3., 3., 3.),  # Default: 5
                        src=src_vol,  # Default: None
                        niter_affine=(100, 100, 10),  # Default
                        niter_sdr=(5, 5, 3))  # Default

Applying an instance of SourceMorph

Once we computed the morph for our respective dataset, we can morph the data by giving it as an argument to the SourceMorph instance. This operation applies pre-computed transforms to stc or computes the morph if instantiated without providing src. Default keyword arguments are valid for both types of morph. However, changing the default only makes real sense when morphing VolSourceEstimate See SourceMorph’s methods for more information.

stc_surf_m = morph_surf(stc_surf,  # SourceEstimate | VectorSourceEstimate
                        as_volume=False,  # Default
                        mri_resolution=False,  # Default
                        mri_space=False,  # Default
                        apply_morph=True)  # Default

stc_vol_m = morph_vol(stc_vol)  # VolSourceEstimate

Transforming VolSourceEstimate into NIfTI

In case of a VolSourceEstimate, we can further ask SourceMorph to output a volume of our data in the new space. We do this by calling the morph.as_volume. Note, that un-morphed source estimates still can be converted into a NIfTI by using stc.as_volume. The shape of the output volume can be modified by providing the argument mri_resolution. This argument can be boolean, a tuple or an int. If mri_resolution=True, the MRI resolution, that was stored in src will be used. Setting mri_resolution to False, will export the volume having voxel size corresponding to the spacing of the computed morph. Setting a tuple or single value, will cause the output volume to expose a voxel size of that values in mm. We can play around with those parameters and see the difference.

# Create full MRI resolution output volume
img_mri_res = morph_vol.as_volume(stc_vol_m, mri_resolution=True)

# Create morph resolution output volume
img_morph_res = morph_vol.as_volume(stc_vol_m, mri_resolution=False)

# Create output volume of manually defined voxel size directly from SourceMorph
img_any_res = morph_vol(stc_vol,  # use un-morphed source estimate and
                        as_volume=True,  # output NIfTI with
                        mri_resolution=2,  # isotropic voxel size of 2mm
                        mri_space=True,  # in MRI space
                        apply_morph=True)  # after applying the morph

Plot results

# Plot morphed volume source estiamte

# Load fsaverage anatomical image
t1_fsaverage = nib.load(fname_t1_fsaverage)

# Initialize figure
fig, [axes1, axes2, axes3] = plt.subplots(1, 3)
fig.subplots_adjust(top=0.8, left=0.1, right=0.9, hspace=0.5)
fig.patch.set_facecolor('white')

for axes, img, res in zip([axes1, axes2, axes3],
                          [img_mri_res, img_morph_res,
                           img_any_res],
                          ['Full MRI\nresolution',
                           'Morph\nresolution',
                           'isotropic\n7 mm']):
    # Setup nilearn plotting
    display = plot_glass_brain(t1_fsaverage,
                               display_mode='x',
                               cut_coords=0,
                               draw_cross=False,
                               axes=axes,
                               figure=fig,
                               annotate=False)

    # Transform into volume time series and use first one
    overlay = index_img(img, 0)

    display.add_overlay(overlay, alpha=0.75)
    display.annotate(size=8)
    axes.set_title(res, color='black', fontsize=12)
plt.show()

# save some memory
del stc_vol_m, morph_vol, morph_surf, img_mri_res, img_morph_res, img_any_res

Plot morphed surface source estimate

surfer_kwargs = dict(
    hemi='lh', subjects_dir=subjects_dir,
    clim=dict(kind='value', lims=[8, 12, 15]), views='lateral',
    initial_time=0.09, time_unit='s', smoothing_steps=5)
brain = stc_surf_m.plot(**surfer_kwargs)
brain.add_text(0.1, 0.9, 'Morphed to fsaverage', 'title', font_size=16)

Summary

Morphing is the process of transforming a representation in one space to another. This is particularly important for neuroimaging data, since individual differences across subject’s brains have to be accounted.

In MNE-Python, morphing is achieved using SourceMorph. This class can morph surface and volumetric source estimates alike.

Instantiate a new object by calling and use the new instance to morph the data:

morph = mne.SourceMorph(src=src)
stc_fsaverage = morph(stc)

Furthermore the data can be converted into a NIfTI image:

img_fsaverage = morph.as_volume(stc_fsaverage)

References

[1] Gramfort, A., Luessi, M., Larson, E., Engemann, D. A., Strohmeier, D., Brodbeck, C., … & Hämäläinen, M. (2013). MEG and EEG data analysis with MNE-Python. Frontiers in neuroscience, 7, 267.
[2] (1, 2) 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. Medical image analysis, 12(1), 26-41.
[3] Viola, P., & Wells III, W. M. (1997). Alignment by maximization of mutual information. International journal of computer vision, 24(2), 137-154.
[4] 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.
[5] Greve D. N., Van der Haegen L., Cai Q., Stufflebeam S., Sabuncu M. R., Fischl B., Brysbaert M. A Surface-based Analysis of Language Lateralization and Cortical Asymmetry. Journal of Cognitive Neuroscience 25(9), 1477-1492, 2013.

This was quite a bunch of info…

Fortunately there is a short version available 😉

Just render it and see yourself:

PATTERN=plot_morph.py make html_dev-pattern

Cheers,

Tommy

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