Bidirectional Graph GAN: Representing Brain Structure-Function Connections for Alzheimer's Disease

The relationship between brain structure and function is critical for revealing the pathogenesis of brain disease, including Alzheimer's disease (AD). However, it is a great challenge to map brain structure-function connections due to various reasons. In this work, a bidirectional graph generative adversarial networks (BGGAN) is proposed to represent brain structure-function connections. Specifically, by designing a module incorporating inner graph convolution network (InnerGCN), the generators of BGGAN can employ features of direct and indirect brain regions to learn the mapping function between structural domain and functional domain. Besides, a new module named Balancer is designed to counterpoise the optimization between generators and discriminators. By introducing the Balancer into BGGAN, both the structural generator and functional generator can not only alleviate the issue of mode collapse but also learn complementarity of structural and functional features. Experimental results using ADNI datasets show that the both the generated structure connections and generated function connections can improve the identification accuracy of AD. More importantly, based the proposed model, it is found that the relationship between brain structure and function is not a complete one-to-one correspondence. Brain structure is the basis of brain function. The strong structural connections are almost accompanied by strong functional connections.