NDLI: Modeling Impulsive Injections of Insulin: Towards Artificial Pancreas

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Huang, Mingzhan Li, Jiaxu Song, Xinyu Guo, Hongjian
Copyright Year	2012
Abstract	We propose two novel mathematical models with impulsive injection of insulin or its analogues for type 1 and type 2 diabetes mellitus. One model incorporates the periodic impulsive injection of insulin. We analytically show the existence and uniqueness of a positive globally asymptotically stable periodic solution for type 1 diabetes, which implies that the perturbation caused by insulin injection will not disturb homeostasis but amend the glucose from a pathological level toward a healthier level. We also show that the system is uniformly permanent for type 2 diabetes, that is, the glucose concentration level is uniformly bounded above and below. The other model determines the insulin injection by closely monitoring the glucose level when it reaches or passes a predefined but adjustable threshold value. We analytically prove the existence and stability of the order one periodic solution, which ensures that the perturbation by the injection in such an automated way can keep the blood glucose concentration under control. Our numerical analysis confirms and further enhances the usefulness and robustness of our models. The first model has clinical implications in that the glucose level of a diabetic can be controlled within a desired level by adjusting the values of two model parameters, injection period and injection dose. A method for choosing these two parameters is described. The second model is, to the best of our knowledge, the first attempt to conquer some critical issues in the design of an artificial pancreas with closed-loop approach. For the former case, our numerical analysis reveals that a regime with a smaller insulin dose and more frequent deliveries is more efficient and effective, but surprisingly, for the latter case, a larger dose is more effective. This can be significant in the design and development of the insulin pump and artificial pancreas.
Starting Page	1524
Ending Page	1548
Page Count	25
File Format	PDF
ISSN	00361399
DOI	10.1137/110860306
e-ISSN	1095712X
Issue Number	5
Volume Number	72
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-10-04
Access Restriction	Subscribed
Subject Keyword	glucose level control insulin impulsive delivery semicontinuous dynamical system Qualitative investigation and simulation of models Population dynamics Medical applications artificial pancreas orbital stability insulin pump
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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