Recovering Brain Structural Connectivity from Functional Connectivity via Multi-GCN Based Generative Adversarial Network

Understanding brain structure-function relationship, e.g., the relations between brain structural connectivity (SC) and functional connectivity (FC), is critical for revealing organizational principles of human brain. However, brain’s many-to-one function-structure mode, i.e., diverse functional patterns may be associated with the same SC, and the complex direct/indirect interactions in both structural and functional connectivity make it challenge to infer a reliable relationship between SC and FC. Benefiting from the advances in deep neural networks, many deep learning based approaches are developed to model the complex and non-linear relations that can be overlooked by traditional shallow methods. In this work, we proposed a multi-GCN based generative adversarial network (MGCN-GAN) to infer individual SC based on corresponding FC. The generator of MGCN-GAN is composed by multiple multi-layer graph convolution networks (GCNs) which have the capability to model complex indirect connections in brain connectivity. The discriminator of MGCN-GAN is a single multi-layer GCN which aims to distinguish predicted SC from real SC. To overcome the inherent unstable behavior of GAN, we designed a new structure-preserving (SP) loss function to guide the generator to learn the intrinsic SC patterns more effectively. We tested our model on Human Connectome Project (HCP) dataset and the proposed MGCN-GAN model can generate reliable individual SC based on FC. This result implies that there may exist a common regulation between specific brain structural and functional architectures across different individuals.