Limitations of Topological Data Analysis for event-related fMRI

Recent fMRI research has shown that perceptual and cognitive representations are instantiated in high-dimensional multi-voxel 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 structures in patterns of data. Several recent studies have successfully applied TDA to the study of various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs in ways that reveal novel structure. 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 TDA 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 signal and design conditions. Our results suggest that TDA has limited usefulness for event-related fMRI using current methods, as fMRI data is too noisy to allow representations to be reliably identified using TDA.