Uncovering Cortical Pathways of Prion-Like Pathology Spreading in Alzheimer’s Disease by Neural Optimal Mass Transport

Tremendous efforts have been made to investigate stereotypical patterns of tau aggregates in Alzheimer’s disease (AD), current positron emission tomography (PET) technology lacks the capability to quantify the dynamic spreading flows of tau propagation in disease progression, despite the fact that AD is characterized by the propagation of tau aggregates throughout the brain in a prion-like manner. We address this challenge by formulating the seek for latent cortical tau propagation pathways into a well-studied physics model of the optimal mass transport (OMT) problem, where the dynamic behavior of tau spreading across longitudinal tau-PET scans is constrained by the geometry of the brain cortex. In this context, we present a variational framework for dynamical system of tau propagation in the brain, where the spreading flow field is essentially a Wasserstein geodesic between two density distributions of spatial tau accumulation. Meanwhile, our variational framework provides a flexible approach to model the possible increase of tau aggregates and alleviate the issue of vanishing flows by introducing a total variation (TV) regularization on flow field. Following the spirit of physics-informed deep model, we derive the governing equation of the new TV-based unbalanced OMT model and customize an explainable generative adversarial network to (1) parameterize the population-level OMT using generator and (2) predict tau spreading flow for the unseen subject by the trained discriminator. We have evaluated the accuracy of our proposed model using the ADNI and OASIS datasets, focusing on its ability to herald future tau accumulation. Since our deep model follows the second law of thermodynamics, we further investigate the propagation mechanism of tau aggregates as AD advances. Compared to existing methodologies, our physics-informed approach delivers superior accuracy and interpretability, showcasing promising potential for uncovering novel neurobiological mechanisms.