Wasserstein-Based Distance for Constructing Multi-Scale Individual Brain Networks from FDG-PET Images: Application to Alzheimer's Disease Diagnosis

This study introduces a novel method for constructing multi-scale individual brain networks from static Fluorodeoxyglucose Positron Emission Tomography (FDG-PET) images, with a primary focus on diagnosing Alzheimer's Disease (AD). Using Schaefer atlases, we partition the brain image into distinct regions, treating them as nodes in the graph. Subsequently, the Kernel Density Estimation (KDE) and Wasserstein Distance (WD) algorithms are used to estimate similarities between brain regions, forming graph connections. Addressing limitations inherent in fixed KDE settings, we propose employing several methods: the interquartile range, Sturges', and Freedman-Diaconis rules, to optimize KDE settings. WD, renowned for its ability to capture both probability and spatial differences, is used to enhance the comparison of similarities among graph nodes. The effectiveness of our method is validated using the ADNI dataset. Connectivity analysis across diagnostic groups-Cognitive Normal (CN), Mild Cognitive Impairment (MCI), and AD-reveals disruptions in information transmission within the FDG-PET-based brain network of MCI and AD subjects, compared to CN. Our findings support the effectiveness of KDE and WD in constructing multi-scale individual brain networks from FDG-PET images. This method shows promise for applications in other brain disorders, enabling personalized diagnosis.