TauFlowNet: Uncovering Propagation Mechanism of Tau Aggregates by Neural Transport Equation

Abstract

Alzheimer’s disease (AD) is characterized by the propagation of tau aggregates throughout the brain in a prion-like manner. Tremendous efforts have been made to analyze the spatiotemporal propagation patterns of widespread tau aggregates. However, current works focus on the change of focal patterns in lieu of a system-level understanding of the tau propagation mechanism that can explain and forecast the cascade of tau accumulation. To fill this gap, we conceptualize that the intercellular spreading of tau pathology forms a dynamic system where brain region is ubiquitously wired with other nodes while interacting with the build-up of pathological burdens. In this context, we formulate the biological process of tau spreading in a principled potential energy transport model (constrained by brain network topology), which allows us to develop an explainable neural network for uncovering the spatiotemporal dynamics of tau propagation from the longitudinal tau-PET images. We first translate the transport equation into a backbone of graph neural network (GNN), where the spreading flows are essentially driven by the potential energy of tau accumulation at each node. Further, we introduce the total variation (TV) into the graph transport model to prevent the flow vanishing caused by the ${\mathcal{l}}_{2}$-norm regularization, where the nature of system’s Euler-Lagrange equations is to maximize the spreading flow while minimizing the overall potential energy. On top of this min-max optimization scenario, we design a generative adversarial network (GAN) to depict the TV-based spreading flow of tau aggregates, coined TauFlowNet. We evaluate TauFlowNet on ADNI dataset in terms of the prediction accuracy of future tau accumulation and explore the propagation mechanism of tau aggregates as the disease progresses. Compared to current methods, our physics-informed method yields more accurate and interpretable results, demonstrating great potential in discovering novel neurobiological mechanisms.