Multilayer Brain Networks
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Multilayer Brain Networks Michael Vaiana1 · Sarah Feldt Muldoon1
Received: 1 September 2017 / Accepted: 21 December 2017 © Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract The field of neuroscience is facing an unprecedented expanse in the volume and diversity of available data. Traditionally, network models have provided key insights into the structure and function of the brain. With the advent of big data in neuroscience, both more sophisticated models capable of characterizing the increasing complexity of the data and novel methods of quantitative analysis are needed. Recently, multilayer networks, a mathematical extension of traditional networks, have gained increasing popularity in neuroscience due to their ability to capture the full information of multi-model, multi-scale, spatiotemporal data sets. Here, we review multilayer networks and their applications in neuroscience, showing how incorporating the multilayer framework into network neuroscience analysis has uncovered previously hidden features of brain networks. We specifically highlight the use of multilayer networks to model disease, structure–function relationships, network evolution, and link multiscale data. Finally, we close with a discussion of promising new directions of multilayer network neuroscience research and propose a modified definition of multilayer networks designed to unite and clarify the use of the multilayer formalism in describing real-world systems. Keywords Multilayer network · Neuroscience · Brain structure · Brain function · Network Mathematics Subject Classification 05C82 · 92C42 · 92B20
Communicated by Danielle S. Bassett.
B 1
Sarah Feldt Muldoon [email protected] Department of Mathematics and CDSE Program, University at Buffalo, SUNY, Buffalo, NY, USA
123
J Nonlinear Sci
1 Introduction The human brain is a complex system organized by structural and functional relationships between its elements. Recent experimental advances have resulted in an unprecedented amount of data describing brain structure and function that now allows the brain to be modeled as a network through the measurement of pairwise interactions between its units. This modeling can occur across multiple scales, where the nodes of the network represent the units of the brain, whether they be proteins, neurons, brain regions, or some other measured unit (Feldt et al. 2011; Bassett and Sporns 2017). Edges of the network represent the strength of connection between two units and are typically chosen to measure either physical connections (structural networks) or statistical relationships between nodal dynamics (functional networks) (Bullmore and Sporns 2009). The rich theory of networks has been successfully utilized in studying the brain by quantifying network structure through the calculation of descriptive and inferential network statistics which expose otherwise hidden phenomenon. Measures of centrality, degree distribution, clustering, small-worldness, and more (Newman 2003; Boccaletti et al. 2006; Muldoon et al. 2016) h
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