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Talk Abstract
The $\beta$-Cell Mass, Insulin, and Glucose Model: Pathways to Diabetes

Robert M. Miura
Department of Mathematics
University of British Columbia
Vancouver, B.C. V6T 1Z2

Joint work with Brian Topp, Keith Promislow, Diane Finegood of Simon Fraser University and Gerda de Vries, University of Alberta.

Diabetes is a disease of the glucose regulatory system. The principal variables for this system are glucose, insulin, and $\beta$-cell mass. Previous models of glucose regulation have focussed on at most two of these variables. Here a model incorporating these three important variables is developed using novel data from our lab and data from the literature, resulting in a system of three nonlinear ordinary differential equations. Under normal conditions, we analyze the global and local behavior of the system. The model predicts at least three characteristic pathways to diabetes, namely a regulated hyperglycemia pathway, a bifurcation pathway, and a "catch-and-pass" pathway. The latter pathway is new, and it is particularly interesting because it relates the rate of change of insulin sensitivity to $\beta$-cell mass adaptation. This pathway allows for qualitative simulation of data from Zucker Diabetic Fatty rats, a model for spontaneous development of Type 2 diabetes, in the untreated and treated cases.

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1998-1999 Mathematics in Biology

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