Multiscale Causal Geometric Deep Learning for Modeling Brain Structure

Multimodal MRI offers complementary multi-scale information to characterize the brain structure. However, it remains challenging to effectively integrate multimodal MRI while achieving neuroscience interpretability. Here we propose to use Laplacian harmonics and spectral graph theory for multimodal alignment and multiscale integration. Based on the cortical mesh and connectome matrix that offer multi-scale representations, we devise Laplacian operators and spectral graph attentions to construct a shared latent space for model alignment. Next, we employ a disentangled learning combined with Graph Variational Autoencoder architectures to separate scale-specific and shared features. Lastly, we design a mutual information-informed bilevel regularizer to separate causal and non-causal factors based on the disentangled features, achieving robust model performance with enhanced interpretability. Our model outperforms baselines and other state-of-the-art models. The ablation studies confirmed the effectiveness of the proposed modules. Our model promises to offer a robust and interpretable framework for multi-scale brain structure analysis.

💡 Research Summary

The paper introduces La‑MuSe, a multiscale causal geometric deep‑learning framework that jointly leverages cortical surface meshes derived from T1‑weighted MRI and white‑matter connectomes derived from diffusion MRI. The authors first construct Laplacian matrices for each modality (mesh Laplacian Lₘ and connectome Laplacian L𝚌) using cotangent weighting for the mesh and standard adjacency for the connectome. By solving the eigen‑decomposition of these Laplacians, they obtain Laplacian harmonics (eigenvectors) that capture geometric information at multiple spatial frequencies. The harmonics are projected into a shared latent space via the Rayleigh quotient, aligning the eigen‑vectors of the two modalities. Initial graphs Gₘ and G𝚌 are built from cosine similarity of dominant eigenvectors, and a Spectral Graph Attention Network iteratively refines edge weights while preserving spectral properties (eᵢⱼ = LeakyReLU(aᵀ