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 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).
Topp
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B
Diabetes Research Laboratory, Simon Fraser University, Burnaby, BC, Canada V5A IS6.
Promislow
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K
deVries
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Miura
R M
RM
Finegood
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DT
D001786:Blood Glucose / Q000378:metabolism; D048429:Cell Size; D003920:Diabetes Mellitus / Q000097:blood / Q000473:pathology*; D006801:Humans; D007328:Insulin / Q000097:blood*; D007515:Islets of Langerhans / Q000378:metabolism / Q000473:pathology*; D008954:Models, Biological; D017711:Nonlinear Dynamics
D001786:Blood Glucose; D007328:Insulin