期刊
JOURNAL OF THEORETICAL BIOLOGY
卷 206, 期 4, 页码 605-619出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1006/jtbi.2000.2150
关键词
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Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta -cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a system of three nonlinear ordinary differential equations, where glucose and insulin dynamics are fast relative to beta -cell mass dynamics. For normal parameter values, the model has two stable fixed points (representing physiological and pathological steady states), separated on a slow manifold by a saddle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of the beta -cell mass (positive feedback). The model predicts that there are three 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) progressive defects in glucose and/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of the beta -cell mass which can drive glucose levels down (dynamical hyperglycemia). (C) 2000 Academic Press.
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