An interpretable physics-informed graph neural network for forecasting longitudinal tau progression in Alzheimer's disease

Forecasting the progression of tau pathology by modeling its spatiotemporal dynamics is critical for characterizing Alzheimer’s disease (AD), where tau is a key driver of disease progression. Tau is an important prognostic biomarker for AD and is a primary endpoint for many ongoing clinical therapeutic trials. Tau burden can be quantified in vivo using positron emission tomography (PET), while its propagation is hypothesized to follow the structural connectome derived from diffusion tensor imaging (DTI), providing a framework for modeling network-driven tau spread. Deep learning approaches, particularly graph neural networks (GNNs), enable data-driven learning of regional changes in tau burden by leveraging brain connectivity. However, purely data-driven models are prone to overfitting and may fail to capture biologically meaningful propagation patterns. To address this, we present here a physics-informed GNN framework for tau forecasting that incorporates prior models of tau propagation, specifically the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation and the epidemic spreading model (ESM), as regularization terms in the latent space of the network. Our analysis relies on PET and DTI data from N=462 amyloid-positive human subjects from the Alzheimer’s Disease Neuroimaging Initiative. Our results demonstrate that physics-informed models improve model performance over the unregularized baseline across multiple evaluation metrics, with regularization in the latent space improving robustness compared to that in the feature space. The FKPP formulation achieves the best mean predictive performance, followed closely by ESM. We further implement post-hoc interpretability using Integrated Gradients to identify key regions and connections driving the model’s predictions. The interpretability analysis is consistent with the observed performance gains, indicating that physics-based regularization yields more localized attribution within biologically relevant regions. Overall, our findings demonstrate that integrating prior formulations of tau propagation with GNNs enhances predictive accuracy and interpretability, providing a promising framework for modeling network-driven spread of tau pathology.