2026-05-24T20:40:40Zhttps://keep.lib.asu.edu/oai/request

oai:keep.lib.asu.edu:node-1559882024-12-20T18:25:12Zoai_pmh:alloai_pmh:repo_items

155988 https://hdl.handle.net/2286/R.I.46258 http://rightsstatements.org/vocab/InC/1.0/ All Rights Reserved 2017 110 pages Doctoral Dissertation Academic theses Text eng Burkow, Daniel Harrison Li, Jiaxu Castillo-Chavez, Carlos Kuang, Yang Holechek, Susan Arizona State University Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2017 Diabetes is a disease characterized by reduced insulin action and secretion, leading to elevated blood glucose. In the 1990s, studies showed that intravenous injection of fatty acids led to a sharp negative response in insulin action that subsided hours after the injection. The molecule associated with diminished insulin signalling response was a byproduct of fatty acids, diacylglycerol. This dissertation is focused on the formulation of a model built around the known mechanisms of glucose and fatty acid storage and metabolism within myocytes, as well as downstream effects of diacylglycerol on insulin action. Data from euglycemic-hyperinsulinemic clamp with fatty acid infusion studies are used to validate the qualitative behavior of the model and estimate parameters. The model closely matches clinical data and suggests a new metric to determine quantitative measurements of insulin action downregulation. Analysis and numerical simulation of the long term, piecewise smooth system of ordinary differential equations demonstrates a discontinuous bifurcation implicating nutrient excess as a driver of muscular insulin resistance. Applied Mathematics Diabetes Differential Equations Insulin Resistance piecewise smooth Theoretical Biology Intramyocellular Lipids and the Progression of Muscular Insulin Resistance