Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence
This work addresses the problem of analyzing time-varying fMRI data for neuroscientists, offering a robust method to study brain activity patterns, though it is incremental as it applies existing topological techniques to a specific domain.
The authors tackled the challenge of analyzing noisy and variable fMRI data by introducing a topological approach that encodes time points as persistence diagrams, which they applied to clustering and trajectory analysis of participants watching a movie, revealing significant differences in brain state trajectories and topological activity between adults and children.
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.