ReeBundle: A Method for Topological Modeling of White Matter Pathways Using Diffusion MRI

Tractography can generate millions of complex curvilinear fibers (streamlines) in 3D that exhibit the geometry of white matter pathways in the brain. Common approaches to analyzing white matter connectivity are based on adjacency matrices that quantify connection strength but do not account for any topological information. A critical element in neurological and developmental disorders is the topological deterioration and irregularities in streamlines. In this paper, we propose a novel Reeb graph-based method "ReeBundle" that efficiently encodes the topology and geometry of white matter fibers. Given the trajectories of neuronal fiber pathways (neuroanatomical bundle), we re-bundle the streamlines by modeling their spatial evolution to capture geometrically significant events (akin to a fingerprint). ReeBundle parameters control the granularity of the model and handle the presence of improbable streamlines commonly produced by tractography. Further, we propose a new Reeb graph-based distance metric that quantifies topological differences for automated quality control and bundle comparison. We show the practical usage of our method using two datasets: (1) For International Society for Magnetic Resonance in Medicine (ISMRM) dataset, ReeBundle handles the morphology of the white matter tract configurations due to branching and local ambiguities in complicated bundle tracts like anterior and posterior commissures; (2) For the longitudinal repeated measures in the Cognitive Resilience and Sleep History (CRASH) dataset, repeated scans of a given subject acquired weeks apart lead to provably similar Reeb graphs that differ significantly from other subjects, thus highlighting ReeBundle's potential for clinical fingerprinting of brain regions.