Novel Brain Complexity Measures Based on Information Theory

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.

Measuring the Non-linear Directed Information Flow in Schizophrenia by Multivariate Transfer Entropy

“…The GCA is initially formulated for linear models and later extended to nonlinear systems by applying to local linear models. Despite its success in detecting the direction of interactions in the brain, it either makes assumptions about the structure of the interacting systems or the nature of their interactions and as such, it may suffer from the shortcomings of modeling systems/signals of unknown structure (Lainscsek et al, 2013;Sohrabpour et al, 2016;Bonmati, 2018). Even though much has been achieved with the GCA, a different data-driven approach which involves information theoretic measures like Transfer entropy (TE) may play a critical role in elucidating the effective connectivity of non-linear complex systems that the GCA may fail to unearth (Schreiber, 2006;Madulara et al, 2012;Dejman et al, 2017).…”

“…To quantify the effective connectivity and exploring the corresponding network aberration in the SCZ, the reliable estimation of the brain network seems to be of great urgency. In this work, we used the TE in a multivariate fashion (Lainscsek et al, 2013;Alonso-Solís et al, 2015;Bonmati, 2018), i.e., multiple TE (MTE) (Montalto et al, 2014;Novelli et al, 2019;Wollstadt et al, 2019). The MTE has great ability to handle problems that the GCA and the BVTE cannot, such as spurious or redundant interactions, where multiple sources provide the same information about the target, the MTE also cannot miss synergistic interactions between multiple relevant sources and the target, where these multiple sources jointly transfer more information into the target than what could be detected from examining source contributions individually.…”

Spatiotemporal Graph Imaging Associated with Multilevel Atomic Excitations †

“…The graph structure is basically composed of nodes (vertices) and links (edges), as well as a connectivity matrix that describes the strength of links between nodes. The nature of vertices and edges of the graph is strongly dependent on the system considered [2][3][4][5]. A molecular quantum graph consists of a large number of vertices.…”

“…In such a quantum graph, the vertices correspond to energy minima on the potential energy surface of the compound system, and the links represent low-energy paths between vertices. In computational neuroscience contexts, has been demonstrated how the brain network can be represented by a graph [5]. The nodes in the brain graph correspond to a set of brain regions that perform specific tasks, and the edges correspond to functional connections.…”

Information Theory in Neuroscience

“…Two papers use the concept of maximum entropy [ 18 ] to develop maximum entropy models to measure the existence of functional interactions between neurons and understand their potential role in neural information processing [ 19 , 20 ]. Kitazono et al [ 21 ] and Bonmati et al [ 22 ] develop concepts relating information theory to measures of complexity and integrated information. These techniques have potential for a wide range of applications, not least of which is the study of how consciousness emerges from the dynamics of the brain.…”