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

TL;DR

This paper introduces a topological method using cubical persistence diagrams to analyze noisy, time-varying fMRI data, enabling robust clustering and trajectory analysis of brain states across individuals.

Contribution

It presents a novel topological approach that encodes each fMRI time point as a persistence diagram, allowing noise-robust analysis without voxel correspondence.

Findings

Identified significant differences in brain state trajectories between adults and children.

Demonstrated the effectiveness of topological clustering in grouping participants.

Showed robustness of the method to noise and individual variability.

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.