Document Type
Article
Abstract
fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. “Structure” within fMRI data is determined by dynamic fluctuations in spatially distributed signals over time, and TDA is well positioned to help researchers better characterize mass dynamics of the signal by rigorously capturing shape within it. To accurately motivate this idea, we a) survey an established method in TDA (“persistent homology”) to reveal and describe how complex structures can be extracted from data sets generally, and b) describe how persistent homology can be applied specifically to fMRI data. We provide explanations for some of the mathematical underpinnings of TDA (with expository figures), building ideas in the following sequence: a) fMRI researchers can and should use TDA to extract structure from their data; b) this extraction serves an important role in the endeavor of functional discovery, and c) TDA approaches can complement other established approaches toward fMRI analyses (for which we provide examples). We also provide detailed applications of TDA to fMRI data collected using established paradigms, and offer our software pipeline for readers interested in emulating our methods. This working overview is both an inter-disciplinary synthesis of ideas (to draw researchers in TDA and fMRI toward each other) and a detailed description of methods that can motivate collaborative research.
Disciplines
Algebraic Geometry | Data Science | Geometry and Topology | Investigative Techniques | Radiology | Statistical Methodology
Recommended Citation
Salch A, Regalski A, Abdallah H, Suryadevara R, Catanzaro MJ, Diwadkar VA (2021) From mathematics to medicine: A practical primer on topological data analysis (TDA) and the development of related analytic tools for the functional discovery of latent structure in fMRI data. PLoS ONE 16(8): e0255859. https://doi.org/10.1371/journal.pone.0255859
Included in
Algebraic Geometry Commons, Data Science Commons, Geometry and Topology Commons, Investigative Techniques Commons, Radiology Commons, Statistical Methodology Commons
Comments
© 2021 Salch et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The fMRI data are included in the Supporting information file data.zip. The software we wrote to analyze this data is freely available at https://github.com/regalski/Wayne-State-TDA.
This work is supported by the National Institutes of Health (MH111177 and MH059299), the Jack Dorsey Endowment, the Cohen Neuroscience Endowment, and the Lycaki-Young Fund from the State of Michigan.