Neural operator-based digital twins for modeling amyloid-β and tau propagation and treatment optimization in Alzheimer's disease
Authors: Xiaofeng Xu, Tingting Dan, Zifan Zhou, Bin Li, Guorong Wu, Wenrui Hao
Organizations: Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA · Department of Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA · School of Electrical Engineering and Computer Science, Pennsylvania State University, University Park, PA 16802, USA · Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA · Department of Statistics and Operation Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA · UNC Neuroscience Center, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
Accurately predicting the spatiotemporal evolution of amyloid-β and tau proteins at the individual level is critical for improving the diagnosis and treatment of Alzheimer's disease. We consider the problem of constructing patient-specific digital twins that model the propagation of these biomarkers on the cortical surface using reaction--diffusion dynamics. A major challenge is that the underlying nonlinear aggregation mechanisms are unknown and must be inferred from sparse, noisy, and heterogeneous longitudinal PET imaging data. To address this, we develop a data-driven framework that learns biomarker dynamics directly from clinical observations. The approach combines operator learning with reduced-order representations to infer governing equations of disease progression from data. Using this framework, we achieve predictive accuracies of 87% for amyloid-β and 81% for tau. Building on the learned dynamics, we further formulate a PDE-constrained optimal control problem to design personalized therapeutic strategies that regulate pathological protein propagation. By integrating data-driven dynamical modeling with treatment optimization, the proposed digital twin framework provides an interpretable and predictive platform for understanding disease progression and enabling precision interventions in neurodegenerative disorders.
Alzheimer's disease (AD) progression is highly heterogeneous and is typically observed through sparse and irregular longitudinal data, posing challenges for prediction and personalised monitoring. Existing machine learning approaches have improved AD prediction using multimodal data, yet often focus on static classification or cohort-level risk estimation, providing limited support for subject-specific modelling and uncertainty-aware reasoning. To address these limitations, we present a personalised digital twin framework for AD prediction and scenario-based analysis using multimodal longitudinal data. The proposed approach integrates complementary modelling strategies to capture clinical transitions and temporal dependencies across visits. Using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), including cognitive assessments, clinical variables, and MRI-derived phenotypes, the framework predicts cognitive status and diagnostic categories while quantifying predictive uncertainty and enabling patient-specific what-if trajectory analysis. Evaluation on leak-free subject-level splits demonstrates strong performance in score forecasting and diagnosis classification. In this sparse and irregular ADNI setting, transition-based modelling of adjacent visits achieved higher predictive accuracy than the sequence-based branch, suggesting that local transition modelling may be more data-efficient. While sequence models remain valuable for uncertainty-aware trajectory forecasting, local transition modelling offers a more data-efficient and robust predictive strategy. These findings highlight the importance of aligning temporal modelling strategies with clinical data structure and suggest that transition-based digital twin formulations may provide a practical and interpretable approach for personalised disease forecasting in neurodegenerative disorders.
Alzheimer's disease (AD) progression is often described through the amyloid-tau-neurodegeneration, or AT(N), cascade. However, most longitudinal models represent this cascade either as a fixed sequence of biomarkers or as a black-box forecasting task. This makes it difficult to determine when biologically guided biomarker relationships influence future regional pathology. In this study, we introduce Bayesian Networks with Latent Time Embedding (BN-LTE), a Bayesian structural framework for stage-aware modeling of AD progression. BN-LTE estimates disease pseudotime from baseline biomarker profiles and constrains directed dependencies according to biologically plausible AT(N) ordering. Posterior spline-varying structural equations are then used to link initial multimodal measurements with future annualized regional tau-PET change. Across repeated subject-disjoint evaluations using ADNI data, BN-LTE shows strong spatial reconstruction of tau progression compared with the included forecasting baselines. Beyond spatial reconstruction, BN-LTE recovers posterior stage-varying AT(N)-constrained effects and identifies a mid-pseudotime window of amyloid sensitivity. This window is supported by model-implied g-formula contrasts, root-adjusted AIPW, mechanism-sensitive ablations, and robustness analyses across spline and prior specifications. Overall, these findings position BN-LTE as a Bayesian structural framework for forecasting tau progression while examining stage-dependent AT(N)-cascade mechanisms in observational longitudinal neuroimaging data. Our code is available at https://github.com/danleneurocom/BN-LTE.
While longitudinal brain PET imaging is the gold standard for quantifying the spatiotemporal accumulation of Beta-amyloid, its widespread clinical utility is constrained by high operational costs and cumulative radiation risks. Recent deep generative models show promise in longitudinal image synthesis; however, they often fail to capture subtle pathological progression due to identity drift and a persistent bias toward trivially replicating baseline signal intensities rather than modeling temporal transition. To this end, we propose Delta-Diffusion, a novel progression-aware framework that redefines longitudinal PET synthesis as a conditional Poisson Diffusion Bridge (PDB) process. Unlike standard diffusion models that start from Gaussian noise, our PDB formulation is mathematically anchored to the subject's baseline PET, effectively transforming the generative task into a conditional distribution transition of the amyloid trajectory. To handle heteroscedastic nature of PET imaging, we introduce a physically-grounded Poisson perturbation within a Diffusion Transformer (DiT). This architecture uses adaptive scale-shift modulation to precisely calibrate the synthesis with the elapsed clinical interval and structural MRI context. A volume-of-interest balanced objective is designed to emphasize sparse, high-risk regions of amyloid accumulation. Validated on two cohorts with 542 subjects, Delta-Diffusion demonstrates superior performance in capturing longitudinal variations in amyloid deposition compared to state-of-the-art methods, offering a robust computational framework for tracking disease progression.