Alzheimer's disease diagnosis by applying Shannon entropy to Ricci flow-based surface indexing and extreme gradient boosting

Geometric surface models are extensively utilized in brain imaging to analyze and compare three-dimensional anatomical shapes. Due to the intricate nature of the brain surface, rather than examining the entire cortical surface, we are introducing a new set of signatures focused on characteristics of the hippocampal region, which is linked to aspects of Alzheimer's disease. Our approach focuses on Ricci flow as a conformal parameterization method, permitting us to calculate the conformal factor and mean curvature as conformal surface representations to identify distinct regions within a three-dimensional mesh. For the first time for such settings, we propose a simple while elegant formulation by employing the well-established concept of Shannon entropy on these well-known features. This compact while rich feature formulation turns out to lead to an efficient local surface encoding. We are validating its effectiveness through a series of preliminary experiments on 3D MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), with the aim of diagnosing Alzheimer's disease. The feature vectors generated and inputted into the XGBoost classifier demonstrate a remarkable level of accuracy, further emphasizing their potential as a valuable additional measure for surface-based cortical morphometry in Alzheimer's disease research.