Modelling and optimal control of blood glucose levels in the human body

Zahra Al Helal; Volker Rehbock; Ryan Loxton

doi:10.3934/jimo.2015.11.1149

Article Contents

2015, Volume 11, Issue 4: 1149-1164. Doi: 10.3934/jimo.2015.11.1149

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Modelling and optimal control of blood glucose levels in the human body

1.
Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845

Received: May 31, 2014

Revised: August 31, 2014

Published: September 2015

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Abstract

Regulating the blood glucose level is a challenging control problem for the human body. Abnormal blood glucose levels can cause serious health problems over time, including diabetes. Although several mathematical models have been proposed to describe the dynamics of glucose-insulin interaction, none of them have been universally adopted by the research community. In this paper, we consider a dynamic model of the blood glucose regulatory system originally proposed by Liu and Tang in 2008. This model consists of eight state variables naturally divided into three subsystems: the glucagon and insulin transition subsystem, the receptor binding subsystem and the glucose subsystem. The model contains 36 model parameters, many of which are unknown and difficult to determine accurately. We formulate an optimal parameter selection problem in which optimal values for the model parameters must be selected so that the resulting model best fits given experimental data. We demonstrate that this optimal parameter selection problem can be solved readily using the optimal control software MISER 3.3. Using this approach, significant improvements can be made in matching the model to the experimental data. We also investigate the sensitivity of the resulting optimized model with respect to the insulin release rate. Finally, we use MISER 3.3 to determine optimal open loop controls for the optimized model.

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Mathematics Subject Classification: Primary: 49M37; Secondary: 65P99, 92C45, 92C50.

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