Progress Report:DTI Clustering

Collaborators: Lauren O'Donnell (MIT), Carl-Fredrik Westin (BWH), Karthik Krishnan (Kitware)

Project Description

We are developing tools in the 3D Slicer for automatic clustering of tractographic paths through diffusion tensor MRI (DTI) data. By grouping tractographic paths based on shape and location, the white matter architecture may be more clearly visualized, and interesting properties of the clusters (such as for example FA or Westin's linear measure) may be quantified.

The above image shows the slicer clustering interface and example clusters.

This image shows the same paths as the bright green cluster in the previous image (part of the corpus callosum). Here randomly sampled tensors are displayed along the paths and colored with Westin's linear measure.

Clustering Implementation

Our implementation uses spectral clustering, a method for grouping data using eigenvectors of a data affinity matrix. This image gives an overview of the method.

Steps in clustering: shape comparison, spectral embedding, and output clusters

On the left example input tractographic paths are shown (these were created by manually seeding in the 3D Slicer). The center image shows an embedding of the tracts as points in 2D, where the distance between points is related to their shape similarity. This embedding was calculated as an intermediate step during spectral clustering. The image on the right shows the final output in the 3D Slicer, where tractographic paths are colored by cluster membership.

The software employed in this process includes:

• Slicer DTMRI module VTK classes for tractography.
• Slicer VTK class to compute tract path affinity matrix.
  • This matrix contains results of shape comparisons between tract paths.
  • Several methods are available: endpoint distance, Hausdorff distance, and mean/covariance distance.
• New ITK class (itkSpectralClustering) clusters data based on an affinity matrix.
  • Generally applicable for clustering problems because input is just this matrix.
• New and improved ITK Statistics framework which allows our embedding vectors (such as those in the middle image above) to have variable length and therefore employ more shape information when it is present. Thank you to Karthik Krishnan for reworking the ITK Statistics classes.

All of the code is part of NA-MIC. The VTK classes are in the 3D Slicer DTMRI module, while the ITK class is currently located in the NA-MIC Sandbox and will be included in ITK in the future.

References

[1] Lauren O'Donnell and Carl-Fredrik Westin: White Matter Tract Clustering and Correspondence in Populations, accepted to MICCAI 2005.