From mathematics to medicine: Applying complex mathematics to analyze
fMRI data

Date:
August 18, 2021
Source:
Wayne State University - Office of the Vice President for Research
Summary:
Mathematical research is aiding in the analysis of fMRI data. fMRI
is the preeminent class of signals collected from the brain in
vivo and is irreplaceable in the study of brain dysfunction in
many medical fields, including psychiatry, neurology and pediatrics.



FULL STORY ========================================================================== Research led by a Wayne State University Department of Mathematics
professor is aiding researchers in Wayne State's Department of
Psychiatry and Behavioral Neurosciences in analyzing fMRI data. fMRI is
the preeminent class of signals collected from the brain in vivo and is irreplaceable in the study of brain dysfunction in many medical fields, including psychiatry, neurology and pediatrics.


========================================================================== Andrew Salch, Ph.D., associate professor of mathematics in Wayne State's College of Liberal Arts and Sciences, is leading the multidisciplinary
team that is investigating how concepts of topological data analysis, a subfield of mathematics, can be applied to recovering "hidden" structure
in fMRI data.

"We hypothesized that aspects of the fMRI signal are not easily
discoverable using many of the standard tools used for fMRI data
analysis, which strategically reduce the number of dimensions in the
data to be considered.

Consequently, these aspects might be uncovered using concepts from the mathematical field of topological data analysis, also called TDA, which
is intended for use on high-dimensional data sets," said Salch. "The
high dimensionality that characterizes fMRI data includes the three
dimensions of space -- that is, where in the brain the signal is being
acquired -- time -- or how the signal varies as brain states change
in time -- and signal intensity - - or how the strength of the fMRI
signal changes in response to the task. When related to task-induced
changes, the results reflect biologically meaningful aspects of brain
function and dysfunction. This is a unique collaborative work focused
on the complexities of both TDA and fMRI respectively, show how TDA
can be applied to real fMRI data collected, and provide open access computational software we have developed for implementing the analyses."
The research article, "From mathematics to medicine: A practical primer
on topological data analysis and the development of related analytic
tools for the functional discovery of latent structure in fMRI data,"
appears in the Aug. 12 issue of PLOS ONE.

In it, the team used TDA to discover data structures in the anterior
cingulate cortex, a critical control region in the brain. These
structures -- called non- contractible loops in TDA -- appeared in
specific conditions of the experiment, and were not identified using conventional techniques for fMRI analyses.

"We expect this work to become a citation classic," said Vaibhav Diwadkar, Ph.D., professor of psychiatry and behavioral neurosciences and research collaborator. "Instead of merely applying TDA to fMRI, we provide a
lucid argument for why medical researchers who use fMRI should consider
using TDA, and why topologists should turn their attention to the study
of complex fMRI data. Moreover, this important work provides readers
with empirical demonstrations of such applications, and we provide
potential users with the tools we used so they can in turn apply it to
their own data." "Our ongoing research utilizing TDA with fMRI will
provide a unique and complementary method for assessing brain function,
and will give medical researchers greater flexibility in tackling complex properties in their data," said Salch. "In particular, our work will
help fMRI researchers become aware of the significant power of TDA that
is designed to address complexity in data, and will enhance the value
of using fMRI in neuroscience and medicine." In addition to Salch and Diwadkar, co-authors on the paper include Adam Regalski, Wayne State mathematics graduate student; Hassan Abdallah, Wayne State mathematics department alumni and current graduate student at the University of
Michigan; and Michael Catanzaro, assistant professor of mathematics at
Iowa State University and Wayne State mathematics department alumni.

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 Funds from the State of Michigan.

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========================================================================== Journal Reference:
1. 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. PLOS ONE, 2021; 16
(8): e0255859 DOI: 10.1371/ journal.pone.0255859 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/08/210818135221.htm

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