PDF e-Pub

## Section: New Results

### An Algebraic Topological Method for Multimodal Brain Networks Comparisons

Participants : Tiago Simas, Mario Chavez [Correspondant] , Pablo Rodriguez, Albert Diaz-Guilera.

Understanding brain connectivity is one of the most important issues in neuroscience. Nonetheless, connectivity data can reflect either functional relationships of brain activities or anatomical connections between brain areas. Although both representations should be related, this relationship is not straightforward. We have devised a powerful method that allows different operations between networks that share the same set of nodes, by embedding them in a common metric space, enforcing transitivity to the graph topology. Here, we apply this method to construct an aggregated network from a set of functional graphs, each one from a different subject. Once this aggregated functional network is constructed, we use again our method to compare it with the structural connectivity to identify particular brain regions that differ in both modalities (anatomical and functional). Remarkably, these brain regions include functional areas that form part of the classical resting state networks. We conclude that our method -based on the comparison of the aggregated functional network- reveals some emerging features that could not be observed when the comparison is performed with the classical averaged functional network.

More details in [23]

Figure 8. Schematic representation of the main steps for the described networks aggregation and metric embedding (defined here for the algebra $L$)