Models for the insulin response to intravenous glucose

MATHEMATICAL MODELING OF INTRA-VENOUS GLUCOSE TOLERANCE TEST MODEL WITH TWO DISCRETE DELAYS

A mathematical model for Intra-Venous Glucose Tolerance Test (IVGTT) with explicit glucose–insulin interaction is presented as a system of delay differential equation with discrete time delays and its important mathematical features are analyzed. This model includes the positivity and boundedness of the solution. An unique equilibrium point is found and its local stability is investigated. Using the Lyapunov functional approach, we show the global stability of the unique equilibrium point. The length of delay that preserves the stability is estimated. Sensitivity analysis is performed on a delay differential equation model for IVGTT that suggests the parameter value has a major impact on the model dynamics. Numerical calculations are performed to support and elaborate the analytical findings.

Advancing our understanding of the glucose system via modeling: a perspective

The glucose story begins with Claude Bernard's discovery of glycogen and milieu interieur, continued with Banting's and Best's discovery of insulin and with Rudolf Schoenheimer's paradigm of dynamic body constituents. Tracers and compartmental models allowed moving to the first quantitative pictures of the system and stimulated important developments in terms of modeling methodology. Three classes of multiscale models, models to measure, models to simulate, and models to control the glucose system, are reviewed in their historical development with an eye to the future.

Selective effects of secretagogues on insulin secretion: a mathematical model

A mathematical model of the secretion of insulin from pancreatic islets of Langerhans is proposed. Previously proposed mathematical models of insulin secretion have dealt solely with glucose-stimulated release, and not with the more complex patterns of secretion (such as "off-responses") in response to other secretagogues or combinations of secretagogues. We conclude that an off-response is consistent with a compartmental model; and the facilitating effect of a constant concentration of glucose on leucine-stimulated insulin secretion is consistent with a selective effect of glucose on a single compartment of the model.