Abstract

In this paper, we propose a graphlet-based topological algorithm for the investigation of the brain network at resting state (RS). To this aim, we model the brain as a graph, where (labeled) nodes correspond to specific cerebral areas and links are weighted connections determined by the intensity of the functional magnetic resonance imaging (fMRI). Then, we select a number of working graphlets, namely, connected and non-isomorphic induced subgraphs. We compute, for each labeled node, its Graphlet Degree Vector (GDV), which allows us to associate a GDV matrix to each one of the 133 subjects of the considered sample, reporting how many times each node of the atlas “touches” the independent orbits defined by the graphlet set. We focus on the 56 independent columns (i.e., non-redundant orbits) of the GDV matrices. By aggregating their count all over the 133 subjects and then by sorting each column independently, we obtain a sorted node table, whose top-level entries highlight the nodes (i.e., brain regions) most frequently touching each of the 56 independent graphlet orbits. Then, by pairwise comparing the columns of the sorted node table in the top-k entries for various values of k, we identify sets of nodes that are consistently involved with high frequency in the 56 independent graphlet orbits all over the 133 subjects. It turns out that these sets consist of labeled nodes directly belonging to the default mode network (DMN) or strongly interacting with it at the RS, indicating that graphlet analysis provides a viable tool for the topological characterization of such brain regions. We finally provide a validation of the graphlet approach by testing its power in catching network differences. To this aim, we encode in a Graphlet Correlation Matrix (GCM) the network information associated with each subject then construct a subject-to-subject Graphlet Correlation Distance (GCD) matrix based on the Euclidean distances between all possible pairs of GCM. The analysis of the clusters induced by the GCD matrix shows a clear separation of the subjects in two groups, whose relationship with the subject characteristics is investigated.

Highlights

  • “Resting-state brain activity” is defined as the activity in the brain when a subject is awake but not performing a specific cognitive task or responding to external sensory stimuli

  • The main goal of this paper is to provide a topological characterization of the rs-functional magnetic resonance imaging (fMRI) network, i.e., the resting state (RS) network generated by employing resting-state functional magnetic resonance imaging (rs-fMRI) data

  • There is a general consensus on the fact that the areas forming the default mode network (DMN) are the posterior cingulate cortex (PCC), the precuneus (PCUN), the medial prefrontal cortex, and the medial, lateral, and inferior parietal regions, which contribute to adaptive function, attention, and internal maintenance (Acheson and Hagoort, 2013)

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Summary

Introduction

“Resting-state brain activity” is defined as the activity in the brain when a subject is awake but not performing a specific cognitive task or responding to external sensory stimuli. Other authors (Andrews-Hanna et al, 2010, 2014), consider the DMN as a wider set of interconnected and anatomically defined brain regions They speculate that the DMN consists of the following cerebral areas: The PCC, the PCUN, the mPFC, and the angular gyrus (AnG) should act as hubs, while the temporoparietal junction (TPJ), the lateral temporal cortex, and the anterior temporal pole constitute the dorsal medial system; and the hippocampus (HF+), the parahippocampus (PHC), the retrosplenial cortex (RSC), and the posterior inferior parietal lobe (pIPL) are the medial temporal subsystem. In agreement with (Finotelli et al, 2018), where an extended version of the DMN based on a graph theoretical and statistical analysis was provided, and with reference to Table 1, we consider the DMN defined by the left and right frontal poles (respectively, nodes 1 and 48); the left and right superior temporal gyrus, posterior division (respectively, nodes 10 and 57); the left and right middle temporal gyrus, posterior division (respectively, nodes 12 and 59); the left and right supramarginal gyrus, posterior division (respectively, nodes and 67); the left and right angular gyrus (respectively, nodes and 68); the left and right frontal medial cortices (respectively, nodes 25 and 72); the left and right cingulate gyrus, posterior division (respectively, nodes and 77); and the left and right precuneus (respectively, nodes and 78)

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