A model of beta-cell mass, insulin, and glucose kinetics: Pathways to diabetes

Diabetes is a disease of the glucose regulatory system that is associated w ith increased morbidity and early mortality. The primary variables of this system are beta -cell mass, plasma insulin concentrations, and plasma gluco se concentrations. Existing mathematical models of glucose regulation incor porate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a syst em of three nonlinear ordinary differential equations, where glucose and in sulin dynamics are fast relative to beta -cell mass dynamics. For normal pa rameter values, the model has two stable fixed points (representing physiol ogical and pathological steady states), separated on a slow manifold by a s addle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of t he beta -cell mass (positive feedback). The model predicts that there are t hree pathways in prolonged hyperglycemia: (1) the physiological fixed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physiological and saddle points can be eliminated (bifurcation), and (3) p rogressive defects in glucose and/or insulin dynamics can drive glucose lev els up at a rate faster than the adaptation of the beta -cell mass which ca n drive glucose levels down (dynamical hyperglycemia). (C) 2000 Academic Pr ess.