The dynamic mechanism comprising an enzymatic reaction and the diffusion of reactants and products inside a glucose-sensitive composite membrane is described using a mathematical model created by Abdekhodaie and Wu. A set of non-linear steady-state reaction-diffusion equations is presented in this theoretical model. These equations have been meticulously and accurately solved analytically, considering the concentrations of glucose, oxygen, and gluconic acid, using a novel approach of Akbari Ganji and differential transform methods. The high level of agreement between these analytical results and the numerical results for steady-state conditions is a testament to the model's precision. A numerical simulation was produced via the precise and widely used MATLAB software. A comprehensive graphic representation of the model's various kinetic parameters' effects has also been provided. Additionally, a theoretical analysis of the kinetic parameters, such as the maximal reaction velocity (Vmax) and the Michaelis-Menten constants (Kg and Kox) for oxygen and glucose, pH profiles with membranes is presented. This expressed model is incredibly helpful when creating glucose-responsive composite membranes for closed-loop insulin delivery.
| Published in | American Journal of Applied Mathematics (Volume 13, Issue 3) |
| DOI | 10.11648/j.ajam.20251303.12 |
| Page(s) | 194-204 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Membrane Responsive to Glucose, Delivery of Insulin, Enzymatic Process, Equation of Reaction-diffusion, Akbari-Ganji Method, Differential Transform Method
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APA Style
Kesavan, R., Rajagopal, S., Ramasamy, K. (2025). Mathematical Modelling and Analytical Expressions for Steady-state Concentrations of Non-linear Glucose-responsive Composite Membranes for Closed-loop Insulin Delivery: Akbari-Ganji and Differential Transform Methods. American Journal of Applied Mathematics, 13(3), 194-204. https://doi.org/10.11648/j.ajam.20251303.12
ACS Style
Kesavan, R.; Rajagopal, S.; Ramasamy, K. Mathematical Modelling and Analytical Expressions for Steady-state Concentrations of Non-linear Glucose-responsive Composite Membranes for Closed-loop Insulin Delivery: Akbari-Ganji and Differential Transform Methods. Am. J. Appl. Math. 2025, 13(3), 194-204. doi: 10.11648/j.ajam.20251303.12
AMA Style
Kesavan R, Rajagopal S, Ramasamy K. Mathematical Modelling and Analytical Expressions for Steady-state Concentrations of Non-linear Glucose-responsive Composite Membranes for Closed-loop Insulin Delivery: Akbari-Ganji and Differential Transform Methods. Am J Appl Math. 2025;13(3):194-204. doi: 10.11648/j.ajam.20251303.12
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Download@article{10.11648/j.ajam.20251303.12,
author = {Ranjani Kesavan and Swaminathan Rajagopal and Karpagavalli Ramasamy},
title = {Mathematical Modelling and Analytical Expressions for Steady-state Concentrations of Non-linear Glucose-responsive Composite Membranes for Closed-loop Insulin Delivery: Akbari-Ganji and Differential Transform Methods
},
journal = {American Journal of Applied Mathematics},
volume = {13},
number = {3},
pages = {194-204},
doi = {10.11648/j.ajam.20251303.12},
url = {https://doi.org/10.11648/j.ajam.20251303.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251303.12},
abstract = {The dynamic mechanism comprising an enzymatic reaction and the diffusion of reactants and products inside a glucose-sensitive composite membrane is described using a mathematical model created by Abdekhodaie and Wu. A set of non-linear steady-state reaction-diffusion equations is presented in this theoretical model. These equations have been meticulously and accurately solved analytically, considering the concentrations of glucose, oxygen, and gluconic acid, using a novel approach of Akbari Ganji and differential transform methods. The high level of agreement between these analytical results and the numerical results for steady-state conditions is a testament to the model's precision. A numerical simulation was produced via the precise and widely used MATLAB software. A comprehensive graphic representation of the model's various kinetic parameters' effects has also been provided. Additionally, a theoretical analysis of the kinetic parameters, such as the maximal reaction velocity (Vmax) and the Michaelis-Menten constants (Kg and Kox) for oxygen and glucose, pH profiles with membranes is presented. This expressed model is incredibly helpful when creating glucose-responsive composite membranes for closed-loop insulin delivery.
},
year = {2025}
}
TY - JOUR T1 - Mathematical Modelling and Analytical Expressions for Steady-state Concentrations of Non-linear Glucose-responsive Composite Membranes for Closed-loop Insulin Delivery: Akbari-Ganji and Differential Transform Methods AU - Ranjani Kesavan AU - Swaminathan Rajagopal AU - Karpagavalli Ramasamy Y1 - 2025/06/11 PY - 2025 N1 - https://doi.org/10.11648/j.ajam.20251303.12 DO - 10.11648/j.ajam.20251303.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 194 EP - 204 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20251303.12 AB - The dynamic mechanism comprising an enzymatic reaction and the diffusion of reactants and products inside a glucose-sensitive composite membrane is described using a mathematical model created by Abdekhodaie and Wu. A set of non-linear steady-state reaction-diffusion equations is presented in this theoretical model. These equations have been meticulously and accurately solved analytically, considering the concentrations of glucose, oxygen, and gluconic acid, using a novel approach of Akbari Ganji and differential transform methods. The high level of agreement between these analytical results and the numerical results for steady-state conditions is a testament to the model's precision. A numerical simulation was produced via the precise and widely used MATLAB software. A comprehensive graphic representation of the model's various kinetic parameters' effects has also been provided. Additionally, a theoretical analysis of the kinetic parameters, such as the maximal reaction velocity (Vmax) and the Michaelis-Menten constants (Kg and Kox) for oxygen and glucose, pH profiles with membranes is presented. This expressed model is incredibly helpful when creating glucose-responsive composite membranes for closed-loop insulin delivery. VL - 13 IS - 3 ER -
PG & Research Department of Mathematics, Vidhyaa Giri College of Arts and Science (Affiliated to Alagappa University), Puduvayal, India
PG & Research Department of Mathematics, Vidhyaa Giri College of Arts and Science (Affiliated to Alagappa University), Puduvayal, India
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