Enhancing structural to functional brain network prediction using topological graph learning

Understanding the relationship between structural and functional brain connectivity remains a fundamental challenge in network neuroscience. While structural connectivity constrains neural interactions, functional connectivity emerges from complex, nonlinear dynamics that are not fully explained by anatomical wiring alone. Existing graph-based and deep learning approaches often focus on pairwise relationships, thereby overlooking higher-order topological organization in brain networks.

We propose TopoGCN, a topology-informed graph convolutional network that integrates topological data analysis (TDA) into structure-function prediction. Persistent homology is used to extract multiscale topological features from structural connectomes, which are incorporated as node-level inputs. Additionally, a topology-aware loss function is incorporated to enforce preservation of higher-order structures in predicted functional networks. The model is evaluated on Human Connectome Project data (n = 998) using both edge-wise metrics and topological measures, including motif distributions, Betti curves, and Wasserstein distances between persistence diagrams.

TopoGCN achieves competitive accuracy in reconstructing functional connectivity while significantly improving the preservation of higher-order network organization. Compared to state-of-the-art models, it yields lower KL divergence for node strength and motif distributions, and smaller Wasserstein distances between persistence diagrams, indicating better recovery of multiscale topological structures. Furthermore, hypothesis tests on Betti curves show no significant differences between observed and predicted networks, demonstrating strong agreement in both connected-component and cycle-based topology.

Our findings show that incorporating persistent-homology information into graph learning improves the modeling of structure-function relationships in the human brain. By preserving multiscale topological features beyond pairwise connections, TopoGCN provides an improved framework for topology-aware connectome prediction and offers new opportunities for studying brain organization and individual variability.