Dynamical

Alzheimer's disease is characterised by the pathological interaction of two proteins, amyloid-beta (Aβ) and tau, which collectively drive neurodegeneration and cognitive decline. The progression of Aβ, tau, and neurodegeneration biomarkers is captured by the ATN framework, which is a powerful tool for disease classification. However, since the ATN framework is mainly descriptive, it cannot quantify or predict relationships between biomarkers over time. We address this limitation by introducing a dynamical ATN (dATN) model that mechanistically simulates the spatiotemporal progression of Aβ, tau, and neurodegeneration. The dATN model integrates mechanisms of prion-like protein aggregation of Aβ and tau, network-based tau propagation, Aβ-driven catalysis of tau progression, and tau-driven neurodegeneration. We calibrated the model using multimodal longitudinal imaging data from both the ADNI and BioFINDER-2 cohorts and show that it accurately fits longitudinal regional Aβ, tau, and neurodegeneration data. Using the dATN model, we show that Aβ-induced effects predict Braak-like cortical tau progression, that the spatial colocalisation of Aβ and tau is a crucial biomarker of disease acceleration, and that tau-driven atrophy strongly correlates with observed neurodegeneration. Furthermore, by integrating the disease progression model with pharmacokinetic-pharmacodynamic simulations, we present a powerful tool that facilitates regional evaluation of therapeutic strategies targeting Aβ, identification of critical intervention windows, and prediction of heterogeneous treatment effects across brain regions. This framework unifies mechanistic understanding with clinical imaging biomarkers, offering a quantitative approach for forecasting disease progression, testing mechanistic hypotheses, and optimising personalised treatment strategies in AD.