Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

Abstract

Functional magnetic resonance imaging (fMRI) is a crucial technology for gaining insights into cognitive processes in humans. Data amassed from fMRI measurements result in volumetric data sets that vary over time. However, analysing such data presents a challenge due to the large degree of noise and person-to-person variation in how information is represented in the brain. To address this challenge, we present a novel topological approach that encodes each time point in an fMRI data set as a persistence diagram of topological features, i.e. high-dimensional voids present in the data. This representation naturally does not rely on voxel-by-voxel correspondence and is robust to noise. We show that these time-varying persistence diagrams can be clustered to find meaningful groupings between participants, and that they are also useful in studying within-subject brain state trajectories of subjects performing a particular task. Here, we apply both clustering and trajectory analysis techniques to a group of participants watching the movie 'Partly Cloudy'. We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.

arXiv commentAccepted at the Conference on Neural Information Processing Systems (NeurIPS) 2020; camera-ready version

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Cited by in corpus (5)

• Noise robustness of persistent homology on greyscale images, across filtrations and signatures
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• TopOC: Topological Deep Learning for Ovarian and Breast Cancer Diagnosis