# Evaluating topological and graph-theoretical approaches to extract complex multimodal brain connectivity patterns in multiple sclerosis

## TL;DR

This study compares topological and graph-based methods to identify brain connectivity patterns in multiple sclerosis, finding that topological methods perform better.

## Contribution

The study introduces a novel comparison of Betti curves and graph-theoretical metrics for brain connectivity analysis in multiple sclerosis.

## Key findings

- Betti curves outperform graph-theoretical metrics in distinguishing multiple sclerosis patients from healthy volunteers.
- Multimodal integration using feature concatenation and multilayer graphs improves classification performance.
- Topological features capture complex brain alterations associated with multiple sclerosis more effectively.

## Abstract

Brain networks, or graphs, derived from magnetic resonance imaging (MRI) offer a powerful framework for representing the structural, morphological, and functional organization of the brain. Graph-theoretical metrics have been widely employed to characterize properties such as efficiency, integration, and communication within these networks. More recently, topological data analysis techniques, such as persistent homology and Betti curves, have emerged as complementary approaches for capturing higher-order network patterns. In this study, we present a comparative analysis of these feature-generation methodologies in the context of neurodegenerative disease. Specifically, we evaluate the effectiveness of Betti curves and graph-theoretical metrics in extracting features for distinguishing people with multiple sclerosis (PwMS) from healthy volunteers (HV). Features are derived from structural connectivity, morphological gray matter, and resting-state functional networks, using both single layer and multilayer graph architectures. Our experiments, conducted on a cohort of PwMS and HV, demonstrate that features extracted using Betti curves generally outperform those based on graph-theoretical metrics. Furthermore, we show that multimodal data in terms of feature concatenation and multilayer graph architectures provide a more comprehensive representation of alterations in complex brain mechanisms associated with MS, leading to improved classification performance. These findings highlight the potential of topological features and multimodal integration for enhancing the understanding and diagnosis of neurodegenerative disorders.