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

Part-2: Analytical Expressions of Concentrations of Glucose, Oxygen, and Gluconic Acid in a... 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 (V max) and Michaelis–Menten constants for glucose and oxygen (K g and K ox) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Membrane Biology Springer Journals

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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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Life Sciences; Biochemistry, general; Human Physiology
ISSN
0022-2631
eISSN
1432-1424
D.O.I.
10.1007/s00232-016-9939-5
Publisher site
See Article on Publisher Site

Abstract

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 (V max) and Michaelis–Menten constants for glucose and oxygen (K g and K ox) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery.

Journal

The Journal of Membrane BiologySpringer Journals

Published: Nov 30, 2016

References

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