Authors:

• @uhussai7 (primary developer)
• @akhanf

gcnn_dmri incorporates gauge equivariance into cnns designed to process diffusion MRI (dMRI) data. The dmri signal is realized on an antipodally identified sphere, i.e the real projective space . Inspired by Cohen et al. we model this 'half-sphere' as the top of an icosahedron. Interestingly, invoking the correct padding naturally leads us to use the full dihedral group, , to include reflections in addition to rotations of the hexagon, as shown in the image on the right. Here we show the application of such gauge equivariant layers to de-noising Human Connectome Project dMRI data limited to six gradient directions, a problem similar to the work of Tian et al.

• Select random subject id's for training and testing, one approach is shown in dataHandling/subject_list_generator.py.
• Similar to Tian et al. we use a mask that avoids CSF. For this we need a grey matter and a white matter mask, which can be made from mri_binarize with the flags --all-wm and --gm respectively.
• Further steps are shown in niceData.py:
  • make_freesurfer_masks runs the shell script to make the mask mentioned above.
  • make_loss_mask_and_structural finalizes the mask, T1 and T2 images with the correct padding and resolution.
  • make_diffusion creates diffusion volumes with fewer gradient directions, directions are choosen in the sequence of the aquisition and then cut off at desired number.
  • dtifit_on_directions runs dtifit on the new diffusion volumes with fewer directions.
  • We obtain the following folder structure:

      ── <training/testing>
          ├── <subject_id>
          │   ├── diffusion
          │   │   └── <# of gradient directions>
          │   │       ├── diffusion
          │   │       │   ├── bvals
          │   │       │   ├── bvecs
          │   │       │   ├── data.nii.gz
          │   │       │   ├── nodif_brain_mask.nii.gz
          │   │       │   └── S0mean.nii.gz
          │   │       └── dtifit
          │   │           ├── dtifit_< >.nii.gz
          │   ├── freesurfer_mask
          │   │   ├── mask_all_wm.nii.gz
          │   │   └── mask_gm.nii.gz
          │   ├── masks
          │   │   ├── mask_all_wm.nii.gz
          │   │   ├── mask_gm.nii.gz
          │   │   └── mask.nii.gz
          │   └── structural
          │       ├── T1.nii.gz
          │       └── T2.nii.gz
    

Similar to Tian et al. (and references therein) we use a residual network architecture but with the addition of gauge equivariant convolutions on the half icosahedron. The training script with the parameters used is training_script.py. Note that structural mri images (T1.nii.gz and T2.nii.gz) are also used as inputs.

Predictions can be performed with the script predicting_script.py. This will create a diffusion volume file, data_network.nii.gz along with bvecs_network and bvals_network, upon which one may perform dtifit. Following are some results of the denoising, the left grey images are fractional anistropy and right colored images are the V1 vector:

Documentation: https://akhanf.github.io/gcnn_dmri

Source Code: https://github.com/akhanf/gcnn_dmri

PyPI: https://pypi.org/project/gcnn_dmri/

Graph-equivariant CNNs for diffusion MRI

pip install gcnn_dmri

• Clone this repository
• Requirements:
  • Poetry
  • Python 3.7
• Create a virtual environment and install the dependencies

poetry install

• Activate the virtual environment

poetry shell

pytest

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