FOCUS FEATURE:
Topological Neuroscience
Editorial: Topological Neuroscience
Paul Expert1,2,3,4, Louis-David Lord5, Morten L. Kringelbach5,6, and Giovanni Petri7,8
1Department of Mathematics, Imperial College London, London, UK
2EPSRC Centre for Mathematics of Precision Healthcare, Imperial College London, London, UK
3Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience, Kings College London, London, UK
4Global Digital Health Unit, School of Public Health, Faculty of Medicine, Imperial College London, London, UK
5Department of Psychiatry, University of Oxford, Oxford, UK
6Center for Music in the Brain, Aarhus University, Aarhus, Denmark
7ISI Foundation, Turin, Italy
8ISI Global Science Foundation, New York, New York, USA
Keywords: Topological data analysis, Neuroscience, Multiple scales, Higher order interactions
a n o p e n a c c e s s
j o u r n a l
ABSTRACT
Topology, in its many forms, describes relations. It has thus long been a central concept
in neuroscience, capturing structural and functional aspects of the organization of the
nervous system and their links to cognition. Recent advances in computational topology have
extended the breadth and depth of topological descriptions. This Focus Feature offers a
unified overview of the emerging field of topological neuroscience and of its applications
across the many scales of the nervous system from macro-, over meso-, to microscales.
From the early drawings of Ramon y Cajal to today, topological descriptions have played a
central role in neuroscience. In recent years, thanks to advancements in both mathematical
tools and data availability, the range and diversity of such descriptions are expanding rapidly,
spanning theoretical, computational, and experimental approaches to brain connectivity. Questo
Focus Feature on “Topological Neuroscience” aims at presenting the breadth of applicability
of topological data analysis (TDA) methods in neuroscience across scales and modalities.
Computational topology offers new frameworks for both the analytical description and the un-
derstanding of brain function. A common denominator to these new tools is their ability to find
meaningful simplifications of high-dimensional data. As such, TDA aims to capture mesoscale
patterns of disconnectivity and explicitly encode higher order interactions, questo è, interactions
between more than two regions or components (Giusti, Ghrist, & Bassett, 2016). Inoltre
to the description of the shape of spaces derived from neuroimaging data, topology might play
an even more fundamental role in brain organization, as indicated by mounting evidence for
how the brain encodes space and memories (Dabaghian, Mémoli, Frank, & Carlsson, 2012).
Finalmente, the intrinsic robustness of TDA methods and the features they identify make them
powerful candidates not only to characterize healthy brain function but also potentially as
biomarkers for disease (Romano et al., 2014).
Recent seminal research has shown the potential and impact of topological approaches. Topo-
logical differences have been found at the population and individual levels in functional con-
nectivity (Lee, Chung, Kang, Kim, & Lee, 2011; Lee, Kang, Chung, Kim, & Lee, 2012) in both
healthy and pathological subjects. Higher dimensional topological features have been em-
ployed to detect differences in brain functional configurations in neuropsychiatric disorders
and altered states of consciousness relative to controls (Chung et al., 2017; Petri et al., 2014),
and to characterize intrinsic geometric structures in neural correlations (Giusti, Pastalkova,
Curto, & Itskov, 2015; Rybakken, Baas, & Dunn, 2017). Structurally, persistent homology
Citation: Expert, P., Lord, l. D., Morten
l. Kringelbach, M. L., & Petri, G. (2019).
Editorial: Topological Neuroscience.
Network Neuroscience, 3(3), 653–655
https://doi.org/10.1162/netn_e_00096
DOI:
https://doi.org/10.1162/netn_e_00096
Received: 9 May 2019
Competing Interests: The authors have
declared that no competing interests
exist.
Corresponding Author:
Paul Expert
paul.expert08@imperial.ac.uk
Handling Editor:
Olaf Sporns
Copyright: © 2019
Istituto di Tecnologia del Massachussetts
Pubblicato sotto Creative Commons
Attribuzione 4.0 Internazionale
(CC BY 4.0) licenza
The MIT Press
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Editorial: Topological Neuroscience
techniques have been used to detect nontrivial topological cavities in white-matter networks
(Sizemore et al., 2018), discriminate healthy and pathological states in developmental (Lee
et al., 2017) and neurodegenerative diseases (Lee, Chung, Kang, & Lee, 2014), and also to
describe the brain arteries’ morphological properties across the lifespan (Bendich, Marron,
Mugnaio, Pieloch, & Skwerer, 2016). Finalmente, the properties of topologically simplified activity
have identified backbones associated with behavioral performance in a series of cognitive
compiti (Saggar et al., 2018).
This Focus Feature offers a unified overview of this emerging field of topological neuroscience
and of its applications across many scales of the nervous system from macro-, over meso-, A
microscales. Primo, Sizemore, Phillips-Cremins, Ghrist, and Bassett (2019) provide an accessible
introduction to the language of topological data analysis and investigate its potential in struc-
tural and genetic connectivity datasets. Chung, Lee, DiChristofano, Ombao, and Solo (2019)
focus instead on differences in whole-brain functional topology in a cohort of twins and pro-
pose a novel topological metric that captures the heritability of topological features. Nel
context of event-related fMRI, Ellis, Lesnick, Henselman-Petrusek, Keller, and Cohen (2019)
investigate the feasibility of topological techniques for recovering signal representations un-
der different conditions. At the mesoscopic scale, Babichev, Morozov, and Dabaghian (2019)
propose a computational model to assess the effect of memory replays in parahippocampal net-
works on the development and stabilization of hippocampal topological maps of space. At an
even smaller scale, Bardin, Spreemann, and Hess (2019) show that topological features of spike-
train data can be used to understand how individual neurons give rise to network dynamics,
and hence to classify topologically such emergent behaviors. From a methodological point
of view, Patania, Selvaggi, Veronese, Dipasquale, Expert, and Petri (2019) build topological
gene expression networks that robustly capture the relationships between genetic pathways
and brain function. Finalmente, Geniesse, Sporns, Petri, and Saggar (2019) present open-source
tools designed to explore graphical representations of high-dimensional neuroimaging data
extracted using topological data analysis at the individual level and without spatial nor tem-
poral averaging.
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It is now high time to put topological neuroscience center stage and to bring together the grow-
ing but often separate communities involved in applied topological analysis. Ancora, numerous
challenges and questions remain before TDA methods become widely accepted and can come
to realize their full potential. Notably, more research is needed both in terms of contextualiza-
tion and functional interpretation of topological features (Lord et al., 2016; Verovsek, Kurlin,
& Lesnik, 2017), and of scalability and computability of some of these features (Otter, Porter,
Tillmann, Grindrod, & Harrington, 2017). Tuttavia, there are already encouraging signs com-
ing from academic conferences and schools in related fields (per esempio., Netsci, Conference on Com-
plex Systems, Applied Machine Learning Days), where tracks or satellites dedicated to TDA
methods are already being organized. In this context, and considering that network-based
methods sit in the larger realm of TDA, the journal Network Neuroscience is a natural venue
to nurture and grow topological neuroscience in the coming years.
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