Quick example of cortical unfolding in LAYNII

In this Blog post, I seek to describe a quick example of how to analyze high-resolution data across layers and columns with LAYNII.

This post is motivated by Shinho Cho. I want to thank Shinho for providing the example data used here. 

There are 5 steps involved to unfold the cortex.

1.) Obtain boder lines of GM/WM and CSF.

This can be done with automatic segmentation algorithms or manually in FSLeyes.

Screenshot 2018-09-26 14.43.25.png
example of how it looks to draw borderlines manually in FSLeyes

2.) Calculating layers with LN_GROW_LAYERS

With this rim.nii file, LAYNII can generate the layers with the command:

LN_GROW_LAYERS -rim rim.nii -vinc 100

The result is a layer file layers.nii looking like this

Screenshot 2018-09-26 14.47.00.png
are calculated based on the rim file above

Note on single slice data (e.g. for Shinho Cho ): when the “-threeD” flag is not set, the program LN_GROW_LAYERS estimates the layers on a slice-by-slice basis. This is done assuming that the slice direction is the third dimension in the nii header according to the default of x-y-z,as phase-read-slice. If your data are not stored like this, consider using the “-threeD” option in LN_GROW_LAYERS. Alternatively, the dimentsion can be exchanged with fslswapdim input x z y  output.

3.) Setting landmarks

For the columnar distance calculation, you can choose a landmark manually anywhere in the layer.nii. E.g generate a new file that is everywhere zero except for one column, where the signal is 1.

Screenshot 2018-09-26 14.47.52.png
Manually set landmark in green. This file is saved as landmarks.nii

4.) Calculating columnar distances

The columnar distances are calculated in the LAYNII program LN_COLUMNAR_DIST

LN_COLUMNAR_DIST -layer_file layers.nii -landmarks landmarks.nii -vinc 400

Screenshot 2018-09-26 14.51.09.png
example of columnar distances from landmark

Algorithm to estimate columnar distances

The columnar distances are calculated in a 6-step algorithm. The intermediate result after every step can be written out with the “-verbose” flag.

  1. The algorithm starts with by estimating Euclidean distances from the manually drawn landmark. In order account for the fact that the GM of a neighboring sulcus can be closer than the distance of a column with in the sulcus, the distance is estimated with a local grow-algorithm that extends the local patch voxel-by-voxel (step-size=1).

    growing.gif
    Grow algorithm to obtain a measure of cortical distances. This is done with the assumption that the cortical curvature is much much larger than the distance between two voxels.
  2. Since the growing algorithm works in voxel space, it can only estimate distances in units of intager multiples of voxel distances. The resulting Pythagorus errors can be accounted for with a local smoothing step along the layer direction only.

    smoothing_path
    correcting for Pythagoras errors of the distance estimates
  3. In the next step, the columnar distances are extrapolated across layers. The columnar distance value of every voxel is simply copied from the next closest voxel that has a valid distance estimate. This is done within the GM ribbon only (to avoid leakage from neighboring sulci). This is by far the longest part of the program. The most superficial and the bottom layers are excluded for now, because it would not be clear which side of the sulcus the correspond to.

    extending_across_Layers.gif
    growing estimated of cortical distance across layers. 
  4. Again, this step comes along with some Pythagoras errors that can be accounted for with within-layer smoothing.

    pytagoras_correction.gif
    Correcting for Pythagoras errors across all layers now.
  5. Now, the entire rim of the cortex can be filled into pial voxels too. This final growing procedure is only local (in the vicinity of two voxels). Thus, signal leakage of neighboring sulci can be neglected.

    with_rim.gif
    Filling in the last remaining voxels that could not be filled in before. 
  6. In a final step, the user can choose how big the columns should be. This is done with the optional “-Ncolumns” flag.

    scaling.gif
    Redefining the number of columns ant the column width.

Underlying assumptions in this procedure:

  • The proposed algorithm only works properly, if the voxel distance is much much smaller than the spatial scale of the curvature.
  • The proposed algorithm only works properly, if the voxel distance is much much smaller than the spatial scale at which the cortical thickness changes.
  • If the cortical curvature radius is in the range of the cortical thickness, columns thicknesses are scaled accordingly. The middle cortical layer are defined to have a homogeneous distance.

    scaled.png
    Areas, where the underlying assumptions are not completely met. 

5.) Regriding

The layers and distances provide a orthogonal coordinate system that can be used to regrid the data into a 2-dim layer-column matrix.

LN_IMAGIRO -layer_file layers.nii -column_file coordinates_final.nii -data ANAT.nii

The output of IMAGIRO is the file “unfoleded*.nii”.

 

correspondence-01.png
example of unfolding. In the IMAGIRO view the x-axis refers to different columns and the y-axis refers to different layers.
Further information on the dataset

Subject: 8 weeks old female cat, Varian 9.4T at CMRR
FOV: 32mm x 32mm, Slice thickness: 0.5mm x 6 coronal slices
Matrix size: 256 x 256, Resolution: 0.125 x 0.125 x 0.5mm, GEMS sequence (T1+T2 weighted), TR/TE = 300ms/15ms
1.5 cm diameter, single loop surface coil (1 channel)

 

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