An Algebraic Topological Method for Multimodal Brain Networks Comparisons

TL;DR

This paper introduces a formal algebraic topological method to compare structural and functional brain networks by embedding them in a shared metric space, enabling identification of significant differences and aggregation across subjects.

Contribution

It presents a novel formalism for comparing multimodal brain networks within a common metric space, facilitating new insights into brain connectivity differences.

Findings

Identified significant differences between structural and functional networks.

Developed a method for aggregating networks across subjects.

Revealed features not observable with classical averaging.

Abstract

Understanding brain connectivity has become one of the most important issues in neuroscience. But connectivity data can reflect either the functional relationships of the brain activities or the anatomical properties between brain areas. Although one should expect a clear relationship between both representations it is not straightforward. Here we present a formalism that allows for the comparison of structural (DTI) and functional (fMRI) networks by embedding both in a common metric space. In this metric space one can then find for which regions the two networks are significantly different. Our methodology can be used not only to compare multimodal networks but also to extract statistically significant aggregated networks of a set of subjects. Actually, we use this procedure to aggregate a set of functional (fMRI) networks from different subjects in an aggregated network that is compared with the anatomical (DTI) connectivity. The comparison of the aggregated network reveals some features that are not observed when the comparison is done with the classical averaged network.