RIEMANNIAN GEOMETRY APPLIED TO STATIC AND DYNAMIC FUNCTIONAL CONNECTOMES AND THE IMPLICATIONS IN SUBJECT AND COGNITIVE FINGERPRINTS
Creators: name: Liu, Mintao
Publisher: name: Purdue University Graduate School
Year: 2025
Subjects: classificationCode: 320904
subject: Computational neuroscience (incl. mathematical neuroscience and theoretical neuroscience)

description: Functional connectomes (FCs) contain all pairwise estimations of functional couplings between brain regions. Neural activity of brain regions is estimated for subjects, sessions and tasks based on fMRI BOLD data. FCs are commonly represented as correlation matrices that are symmetric positive definite (SPD) matrices lying on or inside the SPD manifold. Since the geometry on the SPD manifold is non-Euclidean, the inter-related entries of FCs undermine the use of Euclidean-based distances and its stability when using them as features in machine learning algorithms. By projecting FCs into a tangent space, we can obtain tangent functional connectomes (tangent-FCs), whose entries would not be inter-related, and thus, allow the use of Euclidean-based methods. Tangent-FCs have shown a higher predictive power of behavior and cognition, but no studies have evaluated the effect of such projections with respect to fingerprinting.To some extent, FCs possess a recurrent and reproducible individual fingerprint that can identify if two FCs belong to the same participant. This process is referred to as fingerprinting or subject-identification. As research objects, FCs are expected to be reliable, which means FCs of the same person doing the same thing are expected to be more similar to each other compared to FCs of other individuals/conditions. The level of fingerprint, usually estimated by identification rate, tries to capture this expectation of reliability. When focusing on the dynamic functional connectivity (dFC) of a single fMRI scan, we proposed the concept of cognitive fingerprinting where the timing of functional reconfiguration is identified. This suggests that the changes of cognitive states can be reflected by the similarities/dissimilarities among dFCs.In this dissertation, we hypothesize that comparing FCs in tangent space by using Euclidean algebra should result in higher subject fingerprinting for static FCs and higher cognitive fingerprinting for dynamic FCs. This hypothesis is evaluated by addressing three research questions. The first question investigates the impact of tangent space projection on subject identification rates for static FCs. The second and third questions focus on dFCs, examining their performance in uncovering cognitive fingerprinting on the manifold and in tangent space, respectively. The timing of functional reconfiguration is identified by performing recurrence quantification analysis on dFCs on the manifold. And then, dFCs are projected onto tangent space to assess the influence of this projection on cognitive fingerprinting. Results reveal that identification rates improve systematically with tangent-FCs. Additionally, critical timepoints of functional reconfigurations align closely with ground truth for both manifold-based and tangent-space dFCs.Lastly, we tested those research questions together with data-driven mapping methods, connectome-based predictive modeling (CPM) and partial least squares (PLS), on a dataset of FCs that includes healthy controls and HIV patients as a case study. In conclusion, our findings support the proposed hypothesis, demonstrating that tangent space projection enhances comparisons and offers strong advantages as a transformation for FCs before their use in other analysis/applications.