Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression

Zhang, Zhen; Zou, Zongren; Kuhl, Ellen; Karniadakis, George Em

doi:10.1016/j.cma.2023.116647

Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression

Journal Article · Mon Nov 27 00:00:00 EST 2023 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2023.116647· OSTI ID:2440706

Zhang, Zhen ^[1]; Zou, Zongren ^[2]; ^[3]; Karniadakis, George Em ^[2]

Brown University, Providence, RI (United States); Brown University
Brown University, Providence, RI (United States)
Stanford University, CA (United States)

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. Furthermore, 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.

View Accepted Manuscript (DOE)

Research Organization:: Brown University, Providence, RI (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: SC0023191

OSTI ID:: 2440706

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 419; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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60 APPLIED LIFE SCIENCES
Alzheimer’s disease
Misfolded tau protein
Model discovery
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Uncertainty quantification

Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression

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