Systemically modeling the dynamics of plasma insulin in
subcutaneous injection of insulin analogues for type 1 diabetes
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Department of Mathematics, University of Louisville, Louisville KY 40292
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Department of Math & Statistics, College of Liberal Arts and Sciences, Arizona State University, Tempe, AZ 85287 - 1804
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Received:
01 May 2008
Accepted:
29 June 2018
Published:
01 December 2008
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MSC :
Primary: 92C50, 34C60
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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 insubcutaneous injection of insulin analogues for type 1 diabetes[J]. Mathematical Biosciences and Engineering, 2009, 6(1): 41-58. doi: 10.3934/mbe.2009.6.41
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Abstract
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.
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