BioModels

A Model of β -Cell Mass, Insulin, and Glucose Kinetics: Pathways to Diabetes
BRIANTOPP, KEITHPROMISLOW, GERDADEVRIES, ROBERT MMIURA, DIANE TFINEGOOD

Diabetes is  a  disease of  the glucose  regulatory system that  is associated with  increasedmorbidity and early mortality. The primary variables of this system areb-cell mass, plasmainsulin concentrations, and plasma glucose concentrations. Existing mathematical models ofglucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novelmodel ofb-cell mass, insulin, and glucose dynamics, which consists of a system of threenonlinear ordinary di!erential equations, where glucose and insulin dynamics are fast relativetob-cell mass dynamics. For normal parameter values, the model has two stable"xed points(representing physiological and pathological steady states), separated on a slow manifold bya saddle point. Mild hyperglycemia leads to the growth of theb-cell mass (negative feedback)while extreme hyperglycemia leads to the reduction of theb-cell mass (positive feedback). Themodel predicts that there are three pathways in prolonged hyperglycemia: (1) the physiological"xed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physio-logical and saddle points can be eliminated (bifurcation), and (3) progressive defects in glucoseand/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of theb-cell mass which can drive glucose levels down (dynamical hyperglycemi