Neural operator-based digital twins for modeling amyloid-$β$ and tau propagation and treatment optimization in Alzheimer's disease

2026-06-23

AI Summary

This study addresses the challenge of precisely predicting the spatiotemporal evolution of amyloid-β (Aβ) and tau proteins at the individual level in Alzheimer’s disease to enable early diagnosis and personalized intervention. To this end, we propose a patient-specific digital twin framework that integrates neural operators with reduced-order modeling, uniquely capable of learning unknown nonlinear protein aggregation dynamics from sparse, noisy, and heterogeneous longitudinal PET imaging data. By embedding an optimal control mechanism constrained by reaction–diffusion partial differential equations, our approach yields interpretable intervention strategies. Evaluated on individual subjects, the method achieves prediction accuracies of 87% for Aβ and 81% for tau propagation, substantially advancing the frontier of biomarker modeling and precision therapeutics in neurodegenerative diseases.

Abstract

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.

Problem

• Alzheimer's disease
• amyloid-β
• tau propagation
• digital twins
• spatiotemporal prediction

Innovation

• neural operator
• digital twin
• reaction-diffusion dynamics
• PDE-constrained optimization
• data-driven modeling