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Entropy 2018, 20(7), 491; https://doi.org/10.3390/e20070491

Novel Brain Complexity Measures Based on Information Theory

Graphics and Imaging Laboratory, University of Girona, 17003 Girona, Spain
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Received: 26 April 2018 / Revised: 6 June 2018 / Accepted: 19 June 2018 / Published: 25 June 2018
(This article belongs to the Special Issue Information Theory in Neuroscience)
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Abstract

Brain networks are widely used models to understand the topology and organization of the brain. These networks can be represented by a graph, where nodes correspond to brain regions and edges to structural or functional connections. Several measures have been proposed to describe the topological features of these networks, but unfortunately, it is still unclear which measures give the best representation of the brain. In this paper, we propose a new set of measures based on information theory. Our approach interprets the brain network as a stochastic process where impulses are modeled as a random walk on the graph nodes. This new interpretation provides a solid theoretical framework from which several global and local measures are derived. Global measures provide quantitative values for the whole brain network characterization and include entropy, mutual information, and erasure mutual information. The latter is a new measure based on mutual information and erasure entropy. On the other hand, local measures are based on different decompositions of the global measures and provide different properties of the nodes. Local measures include entropic surprise, mutual surprise, mutual predictability, and erasure surprise. The proposed approach is evaluated using synthetic model networks and structural and functional human networks at different scales. Results demonstrate that the global measures can characterize new properties of the topology of a brain network and, in addition, for a given number of nodes, an optimal number of edges is found for small-world networks. Local measures show different properties of the nodes such as the uncertainty associated to the node, or the uniqueness of the path that the node belongs. Finally, the consistency of the results across healthy subjects demonstrates the robustness of the proposed measures. View Full-Text
Keywords: brain network; complex networks; connectome; information theory; graph theory brain network; complex networks; connectome; information theory; graph theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Bonmati, E.; Bardera, A.; Feixas, M.; Boada, I. Novel Brain Complexity Measures Based on Information Theory. Entropy 2018, 20, 491.

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