Utilizing Neural Networks for Data-Driven Modeling of Alzheimer’s Disease

open_access
Open Access
Author:
Bohse, Emma
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Wenrui Hao, Thesis Supervisor
Aissa Wade, Thesis Honors Advisor
Keywords:
machine learning
mathematical modeling
physics informed neural networks
Alzheimer's Disease
data-driven modeling
Abstract:
Mathematical modeling is a powerful tool for studying complex diseases like Alzheimer’s disease (AD), providing deeper insights and enabling personalized simulation of disease progression. In this study, we leverage neural networks to develop a phase-field model that accurately captures brain geometry. Using MRI data, we train a convolutional neural network (CNN) to generate a high-fidelity three-dimensional brain model, achieving an accuracy of 99% under optimal parameters. We then integrate a mathematical model of AD, formulated as a system of differential equations. The system is based on the AD Biomarker Cascade model, a hypothetical framework that tracks the progression of Alzheimer’s disease by measuring various associated biomarkers. We solve it using physics-informed neural networks (PINNs), yielding a mean squared error under 10−5 when compared to an analytical solution. Finally, by combining these results with the phasefield function, we enable dynamic simulations of AD progression over time. This framework demonstrates the potential for creating highly personalized AD models from MRI data, offering a more ethical and precise approach to studying disease progression and evaluating treatment strategies.