A Functional Geometry of fMRI BOLD Signal Interactions


We propose a method that captures the global patterns of functional connectivity [1] in the brain from a set of blood oxygenation level dependent (BOLD) signals in functional magnetic resonance imaging (fMRI) data acquired during a certain condition or task. The method represents the connectivity as a diffusion process on all points in the brain. By embedding the corresponding BOLD signals, into a diffusion map, or a so-called functional geometry we capture all pairwise relations of the signal in a Euclidean geometry. In this geometry proximity signifies close functional connectivity. The embedding captures relations on multiple scales, which are parameterized by the diffusion time. It establishes a space, wherein the roles of individual brain regions, their interaction with others, and the change and dynamics due to different conditions can be studied. The approach provides an explorative tool for the analysis of global interaction patterns in the brain, their correspondence with specific tasks, and their descriptiveness with regard to clinically relevant questions. The work is in the same vein as [2] where diffusion maps were used to perform dimensionality reduction by parameterizing entire brain states, to represent relations between brains. In Shen et al. [3] they were used to segment activated regions. In [4] initial density measurements of pre-chosen regions in functional geometries were related to certain tasks. In this work we present complete results of a method that detects regions of interest and measures their mutual relations, and relates them to clinically relevant variables. In the following we outline the method, present results, that indicate that the functional geometry is able to repeatably capture differences between subject sets. We conclude with a discussion of the method and its relation to existing approaches.

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@inproceedings{Langs2009AFG, title={A Functional Geometry of fMRI BOLD Signal Interactions}, author={Georg Langs and Dimitris Samaras and Nikos Paragios and Jean Honorio and Polina Golland and Nelly Alia-Klein and Dardo Tomasi and Nora D. Volkow and Rita Z. Goldstein}, year={2009} }