Message Passing on Cortical Simplicial Complex for Cortical Surface Analysis

The complex folding structure of the cerebral cortex remains a major challenge for cortical surface analysis. Contrary to volume-based methods, recent advances in non-Euclidean spaces have led to the development of various surface-based networks for cortical surface analysis. While graph convolutional networks applied to the surface mesh offer the most straightforward approach, recent spherical convolutional networks have shown promising results across various analysis tasks. In this paper, we model the cortical surface as a higher-order structure: a simplicial complex. First, we introduce a simple yet effective method to construct higher-order descriptors on the icosahedral mesh representation of the cortical surface. Then, we propose a hierarchical architecture that consists of novel message-passing layers and a pooling layer. Lastly, our carefully designed Cortical Simplex Neural Network is evaluated through in-depth experiments on a large-scale dataset. It showcases competitive results in multiple tasks: Alzheimer’s disease classification, brain age regression, and subject-sex classification. Through extensive experiments, we demonstrate the advantages of our new approach and highlight the potential value of leveraging simplicial complex neural networks for cortical surface analysis.