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.

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...

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Autores principales:	Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J Catanzaro, Vaibhav A Diwadkar
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/f05de3bfb5d74a6d8c68193daffd092f
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spelling	oai:doaj.org-article:f05de3bfb5d74a6d8c68193daffd092f2021-12-02T20:18:15ZFrom 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.1932-620310.1371/journal.pone.0255859https://doaj.org/article/f05de3bfb5d74a6d8c68193daffd092f2021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0255859https://doaj.org/toc/1932-6203fMRI 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.Andrew SalchAdam RegalskiHassan AbdallahRaviteja SuryadevaraMichael J CatanzaroVaibhav A DiwadkarPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 8, p e0255859 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Andrew Salch Adam Regalski Hassan Abdallah Raviteja Suryadevara Michael J Catanzaro Vaibhav A Diwadkar 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.
description	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.
format	article
author	Andrew Salch Adam Regalski Hassan Abdallah Raviteja Suryadevara Michael J Catanzaro Vaibhav A Diwadkar
author_facet	Andrew Salch Adam Regalski Hassan Abdallah Raviteja Suryadevara Michael J Catanzaro Vaibhav A Diwadkar
author_sort	Andrew Salch
title	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.
title_short	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.
title_full	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.
title_fullStr	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.
title_full_unstemmed	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.
title_sort	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.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/f05de3bfb5d74a6d8c68193daffd092f
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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.

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