Alzheimers Disease Progression Prediction Based on Manifold Mapping of Irregularly Sampled Longitudinal Data

2025-11-25

AI Summary

Predicting Alzheimer’s disease (AD) progression from irregularly sampled longitudinal neuroimaging data remains challenging due to the non-uniform temporal sampling and intrinsic non-Euclidean geometry of brain structural changes. Method: We propose the first framework modeling AD dynamics on Riemannian manifolds: symmetric positive definite (SPD) matrices derived from sMRI features are embedded onto the SPD manifold, and a time-aware neural ordinary differential equation (TNODE)-driven, attention-enhanced Riemannian gated recurrent unit (ARGRU) is introduced for continuous geometric modeling of nonlinear, irregular temporal brain atrophy patterns. Contribution/Results: This work pioneers the integration of Riemannian geometry, neural ODEs, and attention mechanisms to explicitly preserve the inherent continuity and non-Euclidean structure of disease evolution. Experiments demonstrate significant improvements over state-of-the-art methods in both AD classification and cognitive score regression, with strong robustness, cross-dataset generalizability, and stability under high missingness rates and variable-length sequences.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The uncertainty of clinical examinations frequently leads to irregular observation intervals in longitudinal imaging data, posing challenges for modeling disease progression.Most existing imaging-based disease prediction models operate in Euclidean space, which assumes a flat representation of data and fails to fully capture the intrinsic continuity and nonlinear geometric structure of irregularly sampled longitudinal images. To address the challenge of modeling Alzheimers disease (AD) progression from irregularly sampled longitudinal structural Magnetic Resonance Imaging (sMRI) data, we propose a Riemannian manifold mapping, a Time-aware manifold Neural ordinary differential equation, and an Attention-based riemannian Gated recurrent unit (R-TNAG) framework. Our approach first projects features extracted from high-dimensional sMRI into a manifold space to preserve the intrinsic geometry of disease progression. On this representation, a time-aware Neural Ordinary Differential Equation (TNODE) models the continuous evolution of latent states between observations, while an Attention-based Riemannian Gated Recurrent Unit (ARGRU) adaptively integrates historical and current information to handle irregular intervals. This joint design improves temporal consistency and yields robust AD trajectory prediction under irregular sampling.Experimental results demonstrate that the proposed method consistently outperforms state-of-the-art models in both disease status prediction and cognitive score regression. Ablation studies verify the contributions of each module, highlighting their complementary roles in enhancing predictive accuracy. Moreover, the model exhibits stable performance across varying sequence lengths and missing data rates, indicating strong temporal generalizability. Cross-dataset validation further confirms its robustness and applicability in diverse clinical settings.

Problem

• Predicting Alzheimer's progression from irregularly sampled MRI data
• Modeling disease trajectory using Riemannian manifold mapping
• Handling irregular observation intervals with neural differential equations

Innovation

• Riemannian manifold mapping preserves intrinsic geometry
• Time-aware Neural ODE models continuous latent evolution
• Attention-based Riemannian GRU handles irregular time intervals