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.

翻译：脑结构与功能之间的关系对于揭示包括阿尔茨海默病（AD）在内的脑疾病发病机制至关重要。然而，由于多种原因，构建脑结构-功能连接图谱仍面临巨大挑战。本文提出一种双向图生成对抗网络（BGGAN），用于表征脑结构-功能连接。具体而言，通过设计一个融合内图卷积网络（InnerGCN）的模块，BGGAN的生成器能够利用直接与间接脑区的特征，学习结构域与功能域之间的映射函数。此外，本文设计了一个名为Balancer的新模块，用以平衡生成器与判别器之间的优化过程。通过将Balancer引入BGGAN，结构生成器与功能生成器不仅能缓解模式崩溃问题，还能学习结构特征与功能特征的互补性。基于ADNI数据集的实验结果表明，生成的结构连接与功能连接均能提升AD识别准确率。更重要的是，基于所提模型发现，脑结构与功能之间的关系并非完全一一对应——脑结构是脑功能的基础，强结构连接几乎总是伴随强功能连接。