Mathematical modeling of the hypothalamic-pituitary-adrenal system activity

Model Status

Please note that this particular variant of the model is an extension of the basic core model. To the three variables described in the core model: plasma insulin concentration (x), glucose concentration (y) and the density of the pancreatic beta cells (z), we are adding a forth variable (u) which describes the temporal glucose absorption by the gastrointestinal tract.

Model Structure

The secretion of insulin, and its biological effectiveness in reducing blood glucose levels, is mainly dependent on the number and functional efficiency of the pancreatic beta-cells, and also the degree of peripheral insulin resistance. Diabetes can arise from either a deficiency in insulin secretion or from a resistance to insulin. Several mathematical models have been proposed to try and describe the relationships between the plasma concentrations of glucose and insulin. However, these models are often too complex for the available clinical data; which is usually based on glucose alone and is only for a relatively short time period. The current model described here in CellML is based on the published model of Lenbury et al. (2001) and involves just four variables:

• Plasma insulin concentration;

• Plasma glucose concentration;

• Pancreatic beta-cell density; and

• A term to define gastrointestinal glucose absorption.

Schematic diagram of the pancreatic beta-cells. Glucose production is by beta-cells and uptake is by gastrointestinal cells. Beta-cell formation and loss represent the rates at which beta-cells replicate and die.

The complete original paper reference is cited below:

Modeling insulin kinetics: responses to a single oral glucose administration or ambulatory-fed conditions., Yongwimon Lenbury, Sitipong Ruktamatakul, and Somkid Amornsamarnkul, 2001, Mathematical Biosciences , 59, 15-25. (Full text (HTML) and PDF versions of the article are available on the BioSystems website.) PubMed ID: 11226623