Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview

Insulin sensitivity and pancreatic responsivity are the two main factors controlling glucose tolerance. We have proposed a method for measuring these two factors, using computer analysis of a frequently-sampled intravenous glucose tolerance test (FSIGT). This 'minimal modelling approach' fits two mathematical models with FSIGT glucose and insulin data: one of glucose disappearance and one of insulin kinetics. MINMOD is the computer program which identifies the model parameters for each individual. A nonlinear least squares estimation technique is used, employing a gradient-type of estimation algorithm, and the first derivatives (not known analytically) are computed according to the 'sensitivity approach'. The program yields the parameter estimates and the precision of their estimation. From the model parameters, it is possible to extract four indices: SG, the ability of glucose per se to enhance its own disappearance at basal insulin, SI, the tissue insulin sensitivity index, phi 1, first phase pancreatic responsivity, and phi 2, second phase pancreatic responsivity. These four characteristic parameters have been shown to represent an integrated metabolic portrait of a single individual. Show more

Kinetic analysis and integrated systems modeling have contributed substantially to our understanding of the physiology and pathophysiology of metabolic systems and the distribution and clearance of drugs in humans and animals. In recent years, many researchers have become aware of the usefulness of these techniques in the experimental design. With this has come the recognition that the discipline of kinetic analysis requires its own expertise. The expertise can impact experimental design in many ways, from the collaborative and service activities in which individuals interact in formal ways to the development of software tools to aid in kinetic analysis. The purpose of this report is to describe one such software tool, Simulation, Analysis, and Modeling Software II (SAAM II). In the first part, we describe in general how the user can take advantage of the capabilities of the software system, and in the second part, we give three specific examples using multicompartmental models found in lipoprotein (apolipoprotein B [apoB] kinetics) and diabetes (glucose minimal model) research. Show more

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). Copyright 2000 Academic Press. Show more