Document Type

Article

Publication Date

2018

DOI

10.1080/23737867.2018.1429332

Publication Title

Letters in Biomathematics

Volume

5

Issue

1

Pages

70-90

Abstract

A basic model highlighting the counter-regulatory roles of insulin and glucagon is proposed to start a series of models designed to explore continuous rein control and major aspects of glucose metabolism. The three-by-three dynamical system uses black boxes to model unit processes such as the dependencies of insulin secretion rate and the glucagon secretion rate on blood glucose concentration. The dependency of basal conditions on insulin resistance and any defects in insulin or glucagon secretion are shown. Since over-production of hepatic glucose exists early in the history of diabetes, it is important that mathematical models should account for this effect by inclusion of the dynamical equation governing glucagon concentration as this illustrative model does. All solutions are consistent with gross features of the metabolic process. The model is examined for explicit and implicit assumptions affecting its validity which determines that the first extension to the model should account for glucose storage and the release of stored glucose.

Rights

© 2018 The Authors

This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original work is properly cited.

Original Publication Citation

Adams, C. L., & Lasseigne, D. G. (2018). An extensible mathematical model of glucose metabolism. Part I: the basic glucose-insulin-glucagon model, basal conditions and basic dynamics. Letters in Biomathematics, 5(1), 70-90. https://doi.org/10.1080/23737867.2018.1429332

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