Morphing source estimates: Moving data from one brain to another

Morphing refers to the operation of transferring source estimates from one anatomy to another. It is commonly referred as realignment in fMRI literature. This operation is necessary for group studies as one needs then data in a common space.

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

We will use precomputed data and morph surface and volume source estimates to a reference anatomy. The common space of choice will be FreeSurfer’s ‘fsaverage’ See FreeSurfer integration with MNE-Python for more information. Method used for cortical surface data in based on spherical registration [1] and Symmetric Diffeomorphic Registration (SDR) for volumic data [2].

Furthermore we will convert our volume source estimate into a NIfTI image using morph.apply(..., output='nifti1').

In order to morph labels between subjects allowing the definition of labels in a one brain and transforming them to anatomically analogous labels in another use mne.Label.morph().

Why morphing?

Modern neuroimaging techniques, such as source reconstruction or fMRI analyses, make use of advanced mathematical models and hardware to map brain activity patterns into a subject specific anatomical brain space.

This enables the study of spatio-temporal brain activity. The representation of spatio-temporal brain data is often mapped onto the anatomical brain structure to relate functional and anatomical maps. Thereby activity patterns are overlaid with anatomical locations that supposedly produced the activity. Anatomical MR images are often used as such or are transformed into an inflated surface representations to serve as “canvas” for the visualization.

In order to compute group level statistics, data representations across subjects must be morphed to a common frame, such that anatomically and functional similar structures are represented at the same spatial location for all subjects equally.

Since brains vary, morphing comes into play to tell us how the data produced by subject A, would be represented on the brain of subject B.

See also this tutorial on surface source estimation or this example on volumetric source estimation.

Morphing volume source estimates

A volumetric source estimate represents functional data in a volumetric 3D space. The difference between a volumetric representation and a “mesh” ( commonly referred to as “3D-model”), is that the volume is “filled” while the mesh is “empty”. Thus it is not only necessary to morph the points of the outer hull, but also the “content” of the volume.

In MNE-Python, volumetric source estimates are represented as mne.VolSourceEstimate. The morph was successful if functional data of Subject A overlaps with anatomical data of Subject B, in the same way it does for Subject A.

Setting up mne.SourceMorph for mne.VolSourceEstimate

Morphing volumetric data from subject A to subject B requires a non-linear registration step between the anatomical T1 image of subject A to the anatomical T1 image of subject B.

MNE-Python uses the Symmetric Diffeomorphic Registration [2] as implemented in dipy [3] (See tutorial from dipy for more details).

mne.SourceMorph uses segmented anatomical MR images computed using FreeSurfer to compute the transformations. In order tell SourceMorph which MRIs to use, subject_from and subject_to need to be defined as the name of the respective folder in FreeSurfer’s home directory.

See Morph volumetric source estimate usage and for more details on:

  • How to create a SourceMorph object for volumetric data
  • Apply it to VolSourceEstimate
  • Get the output is NIfTI format
  • Save a SourceMorph object to disk

Morphing surface source estimates

A surface source estimate represents data relative to a 3-dimensional mesh of the cortical surface computed using FreeSurfer. This mesh is defined by its vertices. If we want to morph our data from one brain to another, then this translates to finding the correct transformation to transform each vertex from Subject A into a corresponding vertex of Subject B. Under the hood FreeSurfer uses spherical representations to compute the morph, as relies on so called morphing maps.

The morphing maps

The MNE software accomplishes morphing with help of morphing maps which can be either computed on demand or precomputed. The morphing is performed with help of the registered spherical surfaces (lh.sphere.reg and rh.sphere.reg ) which must be produced in FreeSurfer. A morphing map is a linear mapping from cortical surface values in subject A (\(x^{(A)}\)) to those in another subject B (\(x^{(B)}\))

\[x^{(B)} = M^{(AB)} x^{(A)}\ ,\]

where \(M^{(AB)}\) is a sparse matrix with at most three nonzero elements on each row. These elements are determined as follows. First, using the aligned spherical surfaces, for each vertex \(x_j^{(B)}\), find the triangle \(T_j^{(A)}\) on the spherical surface of subject A which contains the location \(x_j^{(B)}\). Next, find the numbers of the vertices of this triangle and set the corresponding elements on the j th row of \(M^{(AB)}\) so that \(x_j^{(B)}\) will be a linear interpolation between the triangle vertex values reflecting the location \(x_j^{(B)}\) within the triangle \(T_j^{(A)}\).

It follows from the above definition that in general

\[M^{(AB)} \neq (M^{(BA)})^{-1}\ ,\]

i.e.,

\[x_{(A)} \neq M^{(BA)} M^{(AB)} x^{(A)}\ ,\]

even if

\[x^{(A)} \approx M^{(BA)} M^{(AB)} x^{(A)}\ ,\]

i.e., the mapping is almost a bijection.

Morphing maps can be computed on the fly or read with mne.read_morph_map(). Precomputed maps are located in $SUBJECTS_DIR/morph-maps.

The names of the files in $SUBJECTS_DIR/morph-maps are of the form:

<A> - <B> -morph.fif ,

where <A> and <B> are names of subjects. These files contain the maps for both hemispheres, and in both directions, i.e., both \(M^{(AB)}\) and \(M^{(BA)}\), as defined above. Thus the files <A> - <B> -morph.fif or <B> - <A> -morph.fif are functionally equivalent. The name of the file produced depends on the role of <A> and <B> in the analysis.

About smoothing

The current estimates are normally defined only in a decimated grid which is a sparse subset of the vertices in the triangular tessellation of the cortical surface. Therefore, any sparse set of values is distributed to neighboring vertices to make the visualized results easily understandable. This procedure has been traditionally called smoothing but a more appropriate name might be smudging or blurring in accordance with similar operations in image processing programs.

In MNE software terms, smoothing of the vertex data is an iterative procedure, which produces a blurred image \(x^{(N)}\) from the original sparse image \(x^{(0)}\) by applying in each iteration step a sparse blurring matrix:

\[x^{(p)} = S^{(p)} x^{(p - 1)}\ .\]

On each row \(j\) of the matrix \(S^{(p)}\) there are \(N_j^{(p - 1)}\) nonzero entries whose values equal \(1/N_j^{(p - 1)}\). Here \(N_j^{(p - 1)}\) is the number of immediate neighbors of vertex \(j\) which had non-zero values at iteration step \(p - 1\). Matrix \(S^{(p)}\) thus assigns the average of the non-zero neighbors as the new value for vertex \(j\). One important feature of this procedure is that it tends to preserve the amplitudes while blurring the surface image.

Once the indices non-zero vertices in \(x^{(0)}\) and the topology of the triangulation are fixed the matrices \(S^{(p)}\) are fixed and independent of the data. Therefore, it would be in principle possible to construct a composite blurring matrix

\[S^{(N)} = \prod_{p = 1}^N {S^{(p)}}\ .\]

However, it turns out to be computationally more effective to do blurring with an iteration. The above formula for \(S^{(N)}\) also shows that the smudging (smoothing) operation is linear.

From theory to practice

In MNE-Python, surface source estimates are represented as mne.SourceEstimate or mne.VectorSourceEstimate. Those can be used together with mne.SourceSpaces or without.

The morph was successful if functional data of Subject A overlaps with anatomical surface data of Subject B, in the same way it does for Subject A.

See Morph surface source estimate usage and for more details:

Please see also Gramfort et al. (2013) [4].

References

[1]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.
[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, 12(1), 26-41.
[3]Garyfallidis E, Brett M, Amirbekian B, Rokem A, van der Walt S, Descoteaux M, Nimmo-Smith I and Dipy Contributors (2014). DIPY, a library for the analysis of diffusion MRI data. Frontiers in Neuroinformatics, vol.8, no.8.
[4]Gramfort A., Luessi M., Larson E., Engemann D. A., Strohmeier D., Brodbeck C., Goj R., Jas. M., Brooks T., Parkkonen L. & Hämäläinen, M. (2013). MEG and EEG data analysis with MNE-Python. Frontiers in neuroscience, 7, 267.

Estimated memory usage: 9 MB

Gallery generated by Sphinx-Gallery