Topological Data Analysis of Functional MRI Connectivity in Time and Space Domains

Abstract

The functional architecture of the brain can be described as a dynamical system where components interact in flexible ways, constrained by physical connections between regions. Using correlation, either in time or in space, as an abstraction of functional connectivity, we analyzed resting state fMRI data from 1003 subjects. We compared several data preprocessing strategies and found that independent component-based nuisance regression outperformed other strategies, with the poorest reproducibility in strategies that include global signal regression. We also found that temporal vs. spatial functional connectivity can encode different aspects of cognition and personality. Topological analyses using persistent homology show that persistence barcodes are significantly correlated to individual differences in cognition and personality, with high reproducibility. Topological data analyses, including approaches to model connectivity in the time domain, are promising tools for representing high-level aspects of cognition, development, and neuropathology.

Fig. 1:

Computing the persistent homology of a point cloud (image adapted from [27], Fig. 1).

Fig. 2:

Reproducibility of graph-theoretic and topological measures of functional connectivity by preprocessing strategy.

Fig. 3:

Reproducibility and cognitive correlation of persistent homology barcode analyses.