2023/07/16 by Zhen Zhang, Zhang, Zhen, Zongren Zou +5 · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Advanced Neuroimaging Techniques and Applications #Bioinformatics and Genomic Networks #FOS: Biological sciences #FOS: Computer and information sciences #Machine Learning (cs.LG) #Quantitative Methods (q-bio.QM) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2307.08107
openalex publication_date 2023/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Misfolded tau proteins play a critical role in the progression and pathology of Alzheimer's disease. Recent studies suggest that the spatio-temporal pattern of misfolded tau follows a reaction-diffusion type equation. However, the precise mathematical model and parameters that characterize the progression of misfolded protein across the brain remain incompletely understood. Here, we use deep learning and artificial intelligence to discover a mathematical model for the progression of Alzheimer's disease using longitudinal tau positron emission tomography from the Alzheimer's Disease Neuroimaging Initiative database. Specifically, we integrate physics informed neural networks (PINNs) and symbolic regression to discover a reaction-diffusion type partial differential equation for tau protein misfolding and spreading. First, we demonstrate the potential of our model and parameter discovery on synthetic data. Then, we apply our method to discover the best model and parameters to explain tau imaging data from 46 individuals who are likely to develop Alzheimer's disease and 30 healthy controls. Our symbolic regression discovers different misfolding models f(c) for two groups, with a faster misfolding for the Alzheimer's group, f(c) = 0.23c3 - 1.34c2 + 1.11c, than for the healthy control group, f(c) = -c3 +0.62c2 + 0.39c. Our results suggest that PINNs, supplemented by symbolic regression, can discover a reaction-diffusion type model to explain misfolded tau protein concentrations in Alzheimer's disease. We expect our study to be the starting point for a more holistic analysis to provide image-based technologies for early diagnosis, and ideally early treatment of neurodegeneration in Alzheimer's disease and possibly other misfolding-protein based neurodegenerative disorders.