Volume entropy for modeling information flow in a brain graph

Abstract

Brain regions send and receive information through neuronal connections in an efficient way. In this paper, we modelled the information propagation in brain networks by a generalized Markov system associated with a new edge-transition matrix, based on the assumption that information flows through brain networks forever. From this model, we derived new global and local network measures, called a volume entropy and the capacity of nodes and edges on FDG PET and resting-state functional MRI. Volume entropy of a metric graph, a global measure of information, measures the exponential growth rate of the number of network paths. Capacity of nodes and edges, a local measure of information, represents the stationary distribution of information propagation in brain networks. On the resting-state functional MRI of healthy normal subjects, these measures revealed that volume entropy was significantly negatively correlated to the aging and capacities of specific brain nodes and edges underpinned which brain nodes or edges contributed these aging-related changes.

The balance between Bayesian inference and default mode determines the generation of tinnitus from decreased auditory input: A volume entropy‐based study

“…When edge paths pass through a node more frequently, the afferent node capacity at the node is larger. For an alternative method to convert weights on edges to weights on nodes, please refer to our recent study (Lee, Kim, et al, 2019 ).…”

“…To determine if there were differences in resting‐state cortical activity between the HL‐T and HL‐NT groups at the brain network level, we adopted the “volume entropy model” (Lee et al, 2019 ) and compared the groups with respect to information flow in the brain. The volume entropy of the brain network corresponds to the limit of asymptotic exponential growth rate of the number of paths in the network (Lee, Kim, et al, 2019 ). As a global measure of the brain network, volume entropy represents the global efficiency of the propagation of information throughout the brain network.…”

Maturational delay and asymmetric information flow of brain connectivity in SHR model of ADHD revealed by topological analysis of metabolic networks

“…The GMS with the volume entropy is a model for measuring information flow on a brain network. It found the volume entropy and edge capacity that measured network efficiency in the view of information flow and the amount and direction of information flow on edges, respectively 23 . Traditional approaches of directed brain networks have mainly considered effective connectivity where the direction of edges is estimated by causality between two nodes 16 .…”

“…where a ef is 1 if an edge e is connected to an edge f in the network, 0, otherwise, h is a nonnegative constant, and l(f) is the weight of the edge f 23,53 .…”

Notes on the values of volume entropy of graphs

“…Recently, there have been attempts to use the volume entropy as an invariant to distinguish brain networks of certain patients [6]. One way to obtain a local invariant is to remove a vertex and all the edges emanating from it.…”