Network alignment and similarity reveal atlas-based topological differences in structural connectomes

Matteo Frigo (1, 2) , Emilio Cruciani (3, 2) , David Coudert (3, 2) , Rachid Deriche (1, 2) , Samuel Deslauriers-Gauthier (1, 2) , Emanuele Natale (3, 2)

1 ATHENA - Computational Imaging of the Central Nervous System
2 UniCA - Université Côte d'Azur
3 COATI - Combinatorics, Optimization and Algorithms for Telecommunications

The interactions between different brain regions can be modeled as a graph, called connectome, whose nodes correspond to parcels from a predefined brain atlas. The edges of the graph encode the strength of the axonal connectivity between regions of the atlas which can be estimated via diffusion Magnetic Resonance Imaging (MRI) tractography. Herein, we aim at providing a novel perspective on the problem of choosing a suitable atlas for structural connectivity studies by assessing how robustly an atlas captures the network topology across different subjects in a homogeneous cohort. We measure this robustness by assessing the alignability of the connectomes, namely the possibility to retrieve graph matchings that provide highly similar graphs. We introduce two novel concepts. First, the graph Jaccard index (GJI), a graph similarity measure based on the well-established Jaccard index between sets; the GJI exhibits natural mathematical properties that are not satisfied by previous approaches. Second, we devise WL-align, a new technique for aligning connectomes obtained by adapting the Weisfeiler-Lehman (WL) graph-isomorphism test. We validated the GJI and WL-align on data from the Human Connectome Project database, inferring a strategy for choosing a suitable parcellation for structural connectivity studies. Code and data are publicly available.

Mots clés: Network alignment; graph matching; brain network; brain parcellation; OPAL-Meso; neuroscience; brain network topology; structural connectome; graph alignment; graph Jaccard index; Weisfeiler-Lehman

Domaines: Algorithme et structure de données [cs.DS]; Traitement du signal et de l'image [eess.SP]; Imagerie médicale; Traitement du signal et de l'image [eess.SP]

Matteo Frigo, Emilio Cruciani, David Coudert, Rachid Deriche, Samuel Deslauriers-Gauthier, et al.. Network alignment and similarity reveal atlas-based topological differences in structural connectomes. Network Neuroscience, 2021, ⟨10.1162/netn_a_00199⟩. ⟨hal-03033777v2⟩