A robust Reeb graph model of white matter fibers with application to Alzheimer's disease progression

Tractography generates billions of complex curvilinear fibers (streamlines) in 3D that exhibit the geometry of white matter pathways. Analysis of raw streamlines on such a large scale is time-consuming and intractable. Further, it is well known that tractography computations produce noisy streamlines, and this in turn severely affect their use in structural brain connectivity analysis. Prompted by these challenges, we propose a novel method to model the bundling structures of streamlines using the construct of a Reeb graph. Three key parameters in our method capture the geometry and topology of the streamlines: (i){epsilon} - distance between a pair of streamlines in a bundle that defines its sparsity; (ii) - spatial length of the bundle that introduces persistence; and (iii){delta} - the bundle thickness. Together, these parameters control the robustness and granularity of the model to provide a compact signature of the streamlines and their underlying anatomic fiber structure. We validate the robustness of the bundling structure using synthetic and ISMRM datasets. Next, we demonstrate the potential of this approach as a tool for efficient tractogram comparison by quantifying the fiber densities in the progression of Alzheimers disease. Our results on ADNI data localize the maximal bundles of various brain regions and show a significant depletion in the fiber density as Alzheimers disease progresses. The source code for the implementation is available on GitHub.