Quantifying Contributions from TopologicalCycles in the Brain Network towards Cognition

This study proposes a novel metric called Homological Vertex Importance Profile (H-VIP), utilizing topological data analysis tool persistent homology, to analyze human brain structural and functional connectomes. Persistent homology is a useful tool for identifying topological features such as cycles and cavities within a network. The salience of persistent homology lies in the fact that it offers a global view of the network as a whole. However, it falls short in precisely determining the relative relevance of the vertices of the network that contribute to these topological features. Our aim is to quantify the contribution of each individual vertex in the formation of homological cycles and provide insight into local connectivity. Our proposed H-VIP metric captures, quantifies, and compresses connectivity information from vertices even at multiple degrees of separation and projects back onto each vertex. Using this metric, we analyze two independent datasets: structural connectomes from the Human Connectome Project and functional connectomes from the Alzheimers Disease Neuroimaging Initiative. Our findings indicate a positive correlation between various cognitive measures and H-VIP, in both anatomical and functional brain networks. Our study also demonstrates that the connectivity in the frontal lobe has a higher correlation with cognitive performance compared to the whole brain network. Furthermore, the H-VIP provides us with a metric to easily locate, quantify, and visualize potentially impaired connectivity for each subject and may have applications in the context of personalized medicine for neurological diseases and disorders.