# American Institute of Mathematical Sciences

2009, 6(1): 41-58. doi: 10.3934/mbe.2009.6.41

## Systemically modeling the dynamics of plasma insulin in subcutaneous injection of insulin analogues for type 1 diabetes

 1 Department of Mathematics, University of Louisville, Louisville KY 40292, United States 2 Department of Math & Statistics, College of Liberal Arts and Sciences, Arizona State University, Tempe, AZ 85287 - 1804

Received  May 2008 Revised  July 2008 Published  December 2008

Type 1 diabetics must inject exogenous insulin or insulin analogues one or more times daily. The timing and dosage of insulin administration have been a critical research area since the invention of insulin analogues. Several pharmacokinetical models have been proposed, and some are applied clinically in modeling various insulin therapies. However, their plasma insulin concentration must be computed separately from the models' output. Furthermore, minimal analytical study was performed in these existing models. We propose two systemic and simplified ordinary differential equation models to model the subcutaneous injection of rapid-acting insulin analogues and long-acting insulin analogues, respectively. Our models explicitly model the plasma insulin and hence have the advantage of computing the plasma insulin directly. The profiles of plasma insulin concentrations obtained from these two models are in good agreement with the experimental data. We also study the dynamics of insulin analogues, plasma insulin concentrations, and, in particular, the shape of the dynamics of plasma insulin concentrations.
Citation: Jiaxu Li, Yang Kuang. Systemically modeling the dynamics of plasma insulin in subcutaneous injection of insulin analogues for type 1 diabetes. Mathematical Biosciences & Engineering, 2009, 6 (1) : 41-58. doi: 10.3934/mbe.2009.6.41
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