BC-GTM: A Bidirectional Causal Graph Transformer Mapping for Modeling Brain Structural and Functional Connectivity

OBJECTIVE: Understanding the relationship between structural connectivity (SC) and functional connectivity (FC) is essential for advancing our understanding of brain function and organization. Recently, deep learning techniques, especially graph neural networks (GNNs), have shown promise in mapping the complex interactions between SC and FC. However, existing methods often fail to reveal the directed dependencies underlying the SC and FC mapping process and lack interpretability based on causal-inspired learning, limiting the reliability of the models. METHODS: We propose a Bidirectional Causal Graph Transformer Mapping (BC-GTM) model to learn the bidirectional mapping between SC and FC. The model consists of two key components: (1) a Bidirectional Causal Graph Transformer module, which leverages Directed Acyclic Graph (DAG) learning into Graph Transformer to identify the directed dependency subgraph between SC and FC; and (2) a Causal Invariance Graph Bidirectional Mapping module, which leverages causal invariance principle to enhance robustness in SC and FC mapping. RESULTS: Experimental results demonstrate that our model outperforms state-of-the-art methods in SC and FC bidirectional mapping tasks. Furthermore, it can identify key brain regions involved in the bidirectional mapping process, providing an interpretable, causal-inspired framework for understanding the interplay between SC and FC. CONCLUSION: BC-GTM overcomes the "black-box" limitations of previous GNN approaches by explicitly integrating causal-inspired directed dependencies. It ensures both superior mapping accuracy and model interpretability. SIGNIFICANCE: BC-GTM provides an effectiveness and interpretable GNN framework for advancing research in SC and FC bidirectional mapping.