Part-2: Analytical Expressions of Concentrations of Glucose, Oxygen, and Gluconic Acid in a Composite Membrane for Closed-Loop Insulin Delivery for the Non-steady State Conditions
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- 作者：N. Mehala ; L. Rajendran ; V. Meena
- 关键词：Glucose ; sensitive membrane ; Gluconic acid ; Oxygen ; Homotopy perturbation method ; Reaction diffusion equation ; Insulin delivery ; Enzymatic reaction
- 刊名：The Journal of Membrane Biology
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：250
- 期：1
- 页码：89-101
- 全文大小：
- 刊物类别：Biomedical and Life Sciences
- 刊物主题：Biochemistry, general; Human Physiology;
- 出版者：Springer US
- ISSN：1432-1424
- 卷排序：250
文摘
A mathematical model developed by Abdekhodaie and Wu (J Membr Sci 335:21–31, 2009), which describes a dynamic process involving an enzymatic reaction and diffusion of reactants and product inside glucose-sensitive composite membrane has been discussed. This theoretical model depicts a system of non-linear non-steady state reaction diffusion equations. These equations have been solved using new approach of homotopy perturbation method and analytical solutions pertaining to the concentrations of glucose, oxygen, and gluconic acid are derived. These analytical results are compared with the numerical results, and limiting case results for steady state conditions and a good agreement is observed. The influence of various kinetic parameters involved in the model has been presented graphically. Theoretical evaluation of the kinetic parameters like the maximal reaction velocity (Vmax) and Michaelis–Menten constants for glucose and oxygen (Kg and Kox) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery.