Geometric Modeling of Hippocampal Tau Deposition: A Surface-Based Framework for Covariate Analysis and Off-Target Contamination Detection

We introduce a framework combining geometric modeling with disease progression analysis to investigate tau deposition in Alzheimer's disease (AD) using positron emission tomography (PET) data. Focusing on the hippocampus, we construct a principal surface that captures the spatial distribution and morphological changes of tau pathology. By projecting voxels onto this surface, we quantify tau coverage, intensity, and thickness through bidirectional projection distances and interpolated standardized uptake value ratios (SUVR). This low-dimensional embedding preserves spatial specificity while mitigating multiple comparison issues. Covariate effects are analyzed using a two-stage regression model with inverse probability weighting to adjust for signal sparsity and selection bias. Using the SuStaIn model, we identify subtypes and stages of AD, revealing distinct tau dynamics: the limbic-predominant subtype shows age-related nonlinear accumulation in coverage and thickness, whereas the posterior subtype exhibits uniform SUVR increases across disease progression. Model-based predictions show that hippocampal tau deposition follows a structured spatial trajectory expanding bidirectionally with increasing thickness, while subtype differences highlight posterior hippocampal involvement consistent with whole-brain patterns. Finally, directional signal patterns on the principal surface reveal contamination from the choroid plexus, demonstrating the broader applicability of the proposed framework across modalities including amyloid PET.