Modelling and optimal control of blood glucose levels in the human body
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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Industrial and Management Optimization (JIMO) following peer review. The definitive publisher-authenticated version "Al Helal, Z. and Rehbock, V. and Loxton, R. 2015. Modelling and optimal control of blood glucose levels in the human body. Journal of Industrial and Management Optimization (JIMO). 11 (4): pp. 1149-1164" is available online at: http://dx.doi.org/10.3934/jimo.2015.11.1149
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 glucosesubsystem. 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 its 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 optimizedmodel 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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