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

TL;DR

This work tackles the challenge of predicting Alzheimer's disease progression from irregularly sampled longitudinal sMRI data by mapping high-dimensional imaging features to a Riemannian manifold and jointly modeling temporal dynamics with a Time-aware Neural ODE (TNODE) and an Attention-based Riemannian GRU (ARGRU). The proposed R-TNAG framework comprises a Riemannian Manifold Mapping (RMM) module for end-to-end spatial feature extraction and manifold embedding, and a TNODE-ARGRU module that alternates continuous-time evolution with interval-aware, attention-guided updates. Ablation studies show that each component—RMM, manifold-space TNODE, and ARGRU with interval-dependent scaling—contributes to superior disease-state classification and cognitive-score regression, with strong robustness across varying sequence lengths and missing data, plus cross-dataset generalization on ADNI. The model demonstrates consistent temporal stability and improved predictive accuracy under irregular sampling, offering a practical framework for longitudinal AD prognosis in diverse clinical settings.

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.

Figures (3)

• Figure 1: The figure presents a comparison between the predicted curves and the true curves for different models in addressing the irregular interval prediction problem. (a) RNN are limited by the assumption of equal time intervals. When data are interpolated, errors can be easily introduced, and the prediction trajectory exhibits a stepwise pattern. (b) RNN+ supports irregular time intervals, but the prediction trajectory still exhibits a stepwise pattern. (c) NODE enable continuous modeling of irregular interval data, but the prediction trajectory deviates from the true values as the sequence length increases. (d) NODE-RNN+ leverages the update ability of RNN+ to reduce the bias in fitting irregular interval data, but introduces the stepwise property of RNN. (e) NODE-RGRU introduces an interpolation-driven continuous modeling method, further reducing the bias in fitting irregular interval data. however, interpolation can introduce noise, and the stepwise property of RNNs remains. (f) The proposed model R-TNAG utilizes the update ability of the ARGRU for irregular interval data, and simultaneously incorporates dynamic time-aware parameters in NODE to smooth the stepwise behavior of the GRU model.
• Figure 2: The overall architecture of the R-TNAG model is shown, where longitudinal clinical scores and imaging sequences serve as inputs, and the outputs are predictions of diagnostic categories and cognitive scores. (a) The RMM module is responsible for high-dimensional feature extraction and manifold embedding. (b) The TNODE-ARGRU module performs disease progression modeling by alternating between TNODE and ARGRU submodules; (b1) the TNODE submodule is a time-aware NODE that continuously models state evolution over time; (b2) the ARGRU submodule is an attention-augmented GRU that refines trajectory updates at irregular observation intervals.
• Figure 3: Longitudinal Evaluation of Disease State Prediction over 1–5 Years.