Date on Master's Thesis/Doctoral Dissertation

5-2025

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Li, Jiaxu

Committee Member

Gill, Ryan

Committee Member

Li, Bingtuan

Committee Member

Hu, Changbing

Committee Member

Mokshagundam, Sri Prakash L.

Author's Keywords

Diabetes; glucose; insulin; fatty acids; insulin sensitivity; β-cell mass.

Abstract

Existing mathematical models investigating the progression of type 2 diabetes (T2D) over time primarily focus on glucose, insulin, β-cell mass, and other related factors, while often omitting fatty acids (FA) as an explicit variable—despite FA being a major energy source for the body. There exists a complex network of dynamical interactions among glucose, insulin, FA, and β-cell mass. To gain deeper insights into the metabolic dynamics and pathophysiology of T2D, it is essential to incorporate FA into such models. In this study, we extend the classic Topp’s GIβ model by explicitly incorporating FA and exploring its interactions with glucose, insulin, and β-cell mass. A new formulation for insulin sensitivity (SI) is proposed to better capture the impaired effect of FA on SI, enabling the exploration of diabetes development pathways and strategies for prevention or delay. Model simulations align well with clinical data and successfully replicate key characteristics of T2D progression, including declining SI, β-cell loss, sedentary lifestyle, and excessive dietary intake. Our results demonstrate a strong positive correlation between glucose and FA levels, indicating that elevated FA is associated with increased glucose concentrations. Model analysis shows that FA levels in diabetic subjects rise significantly because of T2D development. Numerical analyses indicate that maintaining adequate physical activity or reducing dietary excess effectively preserves SI and β-cell mass, thereby reducing the risk of developing T2D.

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