A New Shape Similarity Framework for brain fibers classification

Diffusion Magnetic Resonance Imaging (dMRI) techniques provide a non-invasive way to explore organization and integrity of the white matter structures in human brain. dMRI quantifies in each voxel, the diffusion process of water molecules which are mechanically constrained in their motion by the axons of the neurons. This technique can be used in surgical planning and in the study of anatomical connectivity, brain changes and mental disorders. From dMRI data, white matter fiber tracts can be reconstructed using a class of technique called tractography. The dataset derived by tractography is composed by a large number of streamlines, which are sequences of points in 3D space. To simplify the visualization and analysis of white matter fiber tracts obtained from tracking algorithms, it is often necessary to group them into larger clusters or bundles. This step is called clustering. In order to perform clustering, a mathematical definition of fiber similarity (or more commonly a fiber distance) must be specified. On the basis of this metric, pairwise fiber distance can be computed and used as input for a clustering algorithm. The most common metrics used for distance measure are able to capture only the local relationship between streamlines but not the global structure of the fiber. The global structure refers to the variability of the shape. Together, local and global information, can define a better metric of similarity. We have extracted the global information using a mathematical representation based on the study of the tract with Frénet equations. In particular, we have defined some intrinsic parameters of the fibers that led to a classification of the tracts based on global geometrical characteristics. Using these parameters, a new distance metric for fiber similarity has been developed. For the evaluation of the goodness of the new metric, indices were used for a qualitative study of the results.