A physics-informed geometric learning model for pathological tau spread in Alzheimer's disease

Tau tangles are a pathophysiological hallmark of Alzheimer's disease (AD) and exhibit a stereotypical pattern of spatiotemporal spread which has strong links to disease progression and cognitive decline. Preclinical evidence suggests that tau spread depends on neuronal connectivity rather than physical proximity between different brain regions. Here, we present a novel physics-informed geometric learning model for predicting tau buildup and spread that learns patterns directly from longitudinal tau imaging data while receiving guidance from governing physical principles. Implemented as a graph neural network with physics-based regularization in latent space, the model enables effective training with smaller data sizes. For training and validation of the model, we used longitudinal tau measures from positron emission tomography (PET) and structural connectivity graphs from diffusion tensor imaging (DTI) from the Harvard Aging Brain Study. The model led to higher peak signal-to-noise ratio and lower mean squared error levels than both an unregularized graph neural network and a differential equation solver. The method was validated using both two-timepoint and three-timepoint tau PET measures. The effectiveness of the approach was further confirmed by a cross-validation study.