Feasibility of topological data analysis for event-related fMRI

Abstract

Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multivoxel patterns in the brain. However, the methods for detecting these representations are limited. Topological data analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology—a popular TDA tool that identifies topological features in data and quantifies their robustness—can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations.

Facilitating open-science with realistic fMRI simulation: validation and application

“…The analyses described above provide an example of how fmrisim can validate the plausibility of an experimental analysis; however, fmrisim can also be used to show the implausibility of an experiment/analysis. We have taken this approach in other work using fmrisim to demonstrate what experimental design procedures can and cannot result in signal that can be recovered using a particular analysis procedure-topological data analysis (Ellis et al, 2019). Hence we believe that fmrisim can be used to demarcate what experiments and analyses are and are not plausible.…”

Peer Review #1 of "Facilitating open-science with realistic fMRI simulation: validation and application (v0.1)"

“…The analyses described above provide an example of how fmrisim can validate the plausibility of an experimental analysis; however, fmrisim can also be used to show the implausibility of an experiment/analysis. We have taken this approach in other work using fmrisim to demonstrate what experimental design procedures can and cannot result in signal that can be recovered using a particular analysis procedure -topological data analysis (Ellis, Lesnick, Henselman-Petrusek, Keller, & Cohen, 2019). Hence we believe that fmrisim can be used to demarcate what experiments and analyses are and are not plausible.…”

Topological insights into the neural basis of flexible behavior

“…We focused on topological data analysis (TDA; ( 11 ); ( 12 )), which is an emerging area in mathematics and data science that leverages groundbreaking advances in computational topology to summarize, visualize and discriminate complex data based on topological data summaries. These approaches, which have mostly been used in fields like astrophysics or large scale neural measurements (see, e.g., ( 13 ); ( 14 ); ( 15 )), are able to identify features in the data that are qualitatively distinct from those highlighted using traditional analytic methods.…”