Simplicial and Topological Descriptions of Human Brain Dynamics

Abstract

ABSTRACTWhereas brain imaging tools like functional Magnetic Resonance Imaging (fMRI) afford measurements of whole-brain activity, it remains unclear how best to interpret patterns found amid the data’s apparent self-organization. To clarify how patterns of brain activity support brain function, one might identify metric spaces that optimally distinguish brain states across experimentally defined conditions. Therefore, the present study considers the relative capacities of several metric spaces to disambiguate experimentally defined brain states. One fundamental metric space interprets fMRI data topographically, i.e, as the vector of amplitudes of a multivariate signal, changing with time. Another perspective considers the condition-dependency of the brain’s Functional Connectivity (FC), i.e., the similarity matrix computed across the variables of a multivariate signal. More recently, metric spaces that think of the data topologically, e.g., as an abstract geometric object, have become available. In the abstract, uncertainty prevails regarding the distortions imposed by the mode of measurement upon the object under study. Features that are invariant under continuous deformations, such as rotation and inflation, constitute the features of topological data analysis. While there are strengths and weaknesses of each metric space, we find that metric spaces that track topological features are optimal descriptors of the brain’s experimentally defined states.AUTHOR SUMMARYTime-Varying Functional Connectivity (TVFC) leverages brain imaging data to interpret brain function as time-varying patterns of coordinating activity among brain regions. While many questions remain regarding the organizing principles through which brain function emerges from multi-regional interactions, advances in the mathematics of Topological Data Analysis (TDA) may provide new insights into the brain’s functional self-organization. One tool from TDA, “persistent homology”, observes the occurrence and persistence of n-dimensional holes in a sequence of simplicial complexes extracted from a weighted graph. The occurrence of such holes within the TVFC graph may indicate preferred routes of information flow among brain regions. In the present study, we compare the use of persistence homology versus more traditional metrics at the task of segmenting brain states that differ across experimental conditions. We find that the structures identified by persistence homology more accurately segment the stimuli, more accurately segment high versus low performance levels under common stimuli, and generalize better across volunteers. These findings support the topological interpretation of brain dynamics.