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September  2009, 12(2): 401-414. doi: 10.3934/dcdsb.2009.12.401

Mathematical models of subcutaneous injection of insulin analogues: A mini-review

Jiaxu Li 1, and  James D. Johnson 2,

1. 

Department of Mathematics, University of Louisville, Louisville, KY 40292, United States
2. 

Department of Cellular and Physiological Sciences; Department of Surgery, University of British Columbia, Vancouver, BC, Canada

Received  December 2008 Revised  May 2009 Published  July 2009

In the last three decades, several models relevant to the subcutaneous injection of insulin analogues have appeared in the literature. Most of them model the absorption of insulin analogues in the injection depot and then compute the plasma insulin concentration. The most recent systemic models directly simulate the plasma insulin dynamics. These models have been and/or can be applied to the technology of the insulin pump or to the coming closed-loop systems, also known as the artificial pancreas. In this paper, we selectively review these models in detail and at point out that these models provide key building blocks for some important endeavors into physiological questions of insulin secretion and action. For example, it is not clear at this time whether or not picomolar doses of insulin are found near the islets and there is no experimental method to assess this in vivo. This is of interest because picomolar concentrations of insulin have been found to be effective at blocking beta-cell death and increasing beta-cell growth in recent cell culture experiments.
Keywords: insulin analogues, differential equations., type 1 diabetes, insulin.
Mathematics Subject Classification: 34K20, 92C50, 92D2.
Citation: Jiaxu Li, James D. Johnson. Mathematical models of subcutaneous injection of insulin analogues: A mini-review. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 401-414. doi: 10.3934/dcdsb.2009.12.401
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