Theses and Dissertations

Advisor

Shantia, Yarahmadian

Committee Member

Swan, J. Edward, II

Committee Member

Chuanxi, Qian

Committee Member

Young, Maxwell

Committee Member

Zhang, Jialin

Date of Degree

12-12-2025

Original embargo terms

Visible MSU Only 2 Years

Document Type

Dissertation - Campus Access Only

Major

Computational Engineering

Degree Name

Doctor of Philosophy (Ph.D.)

College

James Worth Bagley College of Engineering

Department

Computational Engineering Program

Abstract

Alzheimer’s disease has long posed a serious challenge for humanity, with no promising cure in sight. Researchers worldwide strive to deepen understanding of this condition through math- ematical, biological, and computational approaches, aiming to develop more effective therapies. In this study, we model the progression of Alzheimer’s disease by examining the aggregation of amyloid beta, which leads to filament formation, using a stochastic method. We treat aggregation and fragmentation of amyloid beta (����) filaments as a random chemical reaction process and employ Monte Carlo simulations to analyze the kinetics. This allows us to simulate aggregation and analyze filament growth across lengths. By conceptualizing disease progression in terms of aggregation dynamics and treating it as a stochastic process, we evaluate the inherent randomness and convergence patterns in filament propagation. Our analysis explores primary and secondary aggregation, and fragmentation under varying propensities, including random switching to assess its effect on convergence. The findings indicate that stochastic modeling helps elucidate the progression of ���� aggregation, which drives plaque formation and disease onset. This framework can also extend to protein aggregation in other disorders. To advance the simulation, we have implemented preliminary interactive simulations in Compucell3D with plans for full spatial and 3D modeling. We also approach this from a data perspective, using the National Alzheimer’s Coordinating Center (NACC) dataset to analyze biomarkers such as ���� and Tau proteins in relation to disease progression. We investigate relationships between phosphorylated tau (Ptau), ����, total tau (Ttau), their ratios, and cognitive status, including CSF biomarkers, PET imaging, and hippocampal atrophy. The results reveal significant associations between severe cognitive impairment and the ratios of Ptau/���� and Ttau/����. Severe cases showed lower ���� and higher Ptau and Ttau, consistent with AD pathology. These findings suggest that biomarker ratios strongly relate to cognitive decline, though this study does not account for other confounders. Therefore, this dissertation is comprehensive and interdisciplinary, combining mathematical modeling, computational simulation, and patient data analysis. As a minor project, it includes an industrial research project on the adoption of post-quantum cryptography in blockchain networks and decentralized systems.

Sponsorship (Optional)

The Study was financially supported by Naoris Protocol Inc.

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