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A Model of β-cell Mass, Insulin, Glucose, and Receptor Dynamics with Applications to Diabetes

Approximately 15.7 million people in the United States suffer from diabetes mellitus, of which about 90% are classified as type II. Most cases of type II diabetes mellitus are characterized by high blood glucose levels resulting from chronic insulin resistance, which then leads to significant beta-cell mass reduction from "beta-cell exhaustion" and/or "glucose toxicity". Existing mathematical models of beta-cell mass, insulin, and glucose kinetics contribute to the study of the disease by qualitatively and quantitatively describing different pathways to diabetes. Successful models of a complex system are often malleable, in that they can be extended to include further components, and consequently be a more complete representation of the system. Insulin receptor dynamics have not been previously considered in modeling the gluco-regulatory system, yet are important in the pathogenesis of the disease as chronic insulin resistance is associated with the down-regulation of these receptors at the surface of muscle cells. We incorporate the dynamics of insulin receptors into an existing mathematical model, resulting in a four dimensional system of nonlinear ordinary differential equations. Through analytical calculations and numerical simulations we conclude that coupling receptor dynamics is valuable in that our system extends previous models to include a fourth significant factor in diabetes, gives improved quantitative results in describing beta-cell mass, and provides a theoretical justification for experimentally observed receptor behavior.

  • Poster session award recipient at the 2002 AMS/MAA Joint Mathematics Meeting in San Diego, CA

Article Number:
BU-1579-M

Year:
2001

Authors:
Ryan D. Hernandez, Pitzer College
Danielle J. Lyles, University of Texas at San Antonio
Daniel B. Rubin, Stanford University
Thomas B. Voden, University of California, Riverside
Project supervisors:
Stephen Wirkus, California State Polytechnic University, Pomona
Ricardo Oliva, Cornell University

model_of_b_cell_mass_insluin_glucose_and_receptor_dynamics.pdf