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.
Highlights
IntroductionThe human brain is a complex system composed of a set of regions, which are segregated in order to perform specific tasks and are efficiently integrated in order to share information [1]
The human brain is a complex system composed of a set of regions, which are segregated in order to perform specific tasks and are efficiently integrated in order to share information [1].The mapping of the structure and the functionality of brain networks is a main challenge in understanding the functioning, as it cannot be studied as a group of independent elements.An important first step to understand how the information is shared, is the generation of a comprehensive map
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
Summary
The human brain is a complex system composed of a set of regions, which are segregated in order to perform specific tasks and are efficiently integrated in order to share information [1]. Global measures have been proposed to describe the overall network structure of the brain Studies such as Kennedy et al [19] suggested that a functional and structural central circuit with different areas acting as a cluster governed the information distribution and integration in the brain. We use a brain network model, where regions correspond to states of a Markov process, to model impulses as random walks on the brain network [38] Please note that this model differs from the previous ones [24,27,28], where correlations between subsets are used to study the centrality and segregation. To evaluate the proposed measures different synthetic model networks, and structural and functional human networks at different scales are considered
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