Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix
Applied and Computational Mathematics
Volume 6, Issue 2, April 2017, Pages: 111-128
Received: Mar. 15, 2017; Accepted: Mar. 28, 2017; Published: Apr. 27, 2017
Views 1444      Downloads 73
K. Saranya, Thiagarajar College of Engineering, Madurai, India
V. Mohan, Thiagarajar College of Engineering, Madurai, India
L. Rajendran, Department of Mathematics, Sethu Institute of Technology, Kariapatti, India
Article Tools
Follow on us
In this paper the theoretical model of glucose–oxidaise loaded in chitosan-aliginate microsphere and hydrogen peroxide production is discussed. The glucose and oxygen in the medium diffuse into the microsphere and react, as a catalyst by glucose oxidase, to produce gluconic acid and hydrogen peroxide. The model involves the system of nonlinear nonsteady-state reaction-diffusion equations. Analytical expressions for the concentrations of glucose, oxygen, gluconic acid and hydrogen peroxide are derived from these equations using homotopy perturbation and the reduction of order method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed. The effect of various parameters (glucose concentration in the external solution, particle size, enzyme loading and Michaelis constant etc.) on the concentration of gluconic acid and hydrogen peroxide release is discussed. Sensitivity analysis of parameters is also discussed.
Mathematical Modeling, Enzyme–Encapsulated Polymer, Microspheres, Hydrogen Peroxide Generation, Release Kinetics
To cite this article
K. Saranya, V. Mohan, L. Rajendran, Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix, Applied and Computational Mathematics. Vol. 6, No. 2, 2017, pp. 111-128. doi: 10.11648/j.acm.20170602.16
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Szatrowski TP, Nathan CF (1991) Production of large amounts of hydrogen peroxide by human tumor cells. Cancer Research 51: 794-798.
Abdekhodaie MJ, Wu XY (2009) Modeling of a glucose sensitive composite membrane for closed-loop insulin delivery. J.Membr.Sci.335: 21-31.
Albin G, Horbett TA, Ratner BD (1990) Glucose sensitive membranes for controlled deliver of insulin. J. Kost (Ed.), pulsed and self-regulated drug delivery, CRC Press, Boca Raton, F:159–185.
Rajendran L,Bieniasz LK (2012) Analytical expressions for the steady-state concentrations of glucose, oxygen and gluconic acid in a composite membrane for closed-loop insulin delivery. J Membrane Biol.246: 121-129.
Joy RA, Rajendran L (2012) Mathematical modeling and transient analytical solution of a glucose sensitive composite membrane for closed-loop insulin delivery using He’s Variational iteration method. Int.Rev.Chem.Eng4: 516-523
Yu, J, Zhang, Y, Ye, DiSanto, R,Sun, W,Ranson ,D,Ligler, FS, Buse, JB, Gu, Z(2015). Micro needle-array patches loaded with hypoxia-sensitive vesicles provide fast glucose-responsive insulin delivery. Proceeding s of the National Academy of Sciences 112: 8260-8265.
Abdekhodaie MJ, Wu XY (2005) Modeling of a cationic glucose sensitive membrane with consideration of oxygen limitation.J.Membr.Sci.245: 119–127.
Abdekhodaie MJ, Cheng JI, Wu XY (2015). Effect of formulation factors on the bioactivity of glucose oxidase encapsulated chitosan-alginate microspheres: In vitro investigation and mathematical model prediction. Chemical Engineering Science125: 4-12
GhorbaniA, Nadjfi JS (2007) He’s homotopy perturbation method for calculating Adomian’s polynomials. Int. J. Nonlin. Sci. Num. Simul. 8(2): 229-332
He JH (2006) Homotopy perturbation method for solving boundary value problems. Phy. Lett. A. 350: 87-88
He JH (2004) Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156: 527-539
He JH (2006) Addendum: New interpretation of homotopy perturbation method. Int. J. Mod. Phys. 20: 2561-2568.
He JH, Feng Mo Lu(2013) Comments on Analytical solution of amperometric enzymatic reactions based on homotopy perturbation method, by A. Shanmugarajan, S. Alwarappan, S. Somasundaram, R. Lakshmanan [Electrochim. Acta 56 (2011) 3345]. 102: 472-473
He JH (2004) The Homotopy perturbation method for non linear oscillators with discontinuities Appl. Math. Comput. 151: 287-292.
He JH (2005) Homotopy perturbation method for bifurcation of non linear problems. Int. J. Non lin. Sci Numer. Simul. 6(2): 207-208
He JH, Hong Wu Xu (2006) construction of solitary solution and compacton-like solution by variational iteration method. chaos, Solitons & Fractols 29: 108-113
He JH, Wu XH (2007) variational iteration method: new development and applications. Computers & Mathematics with Applications. 54: 881-894.
Adomian G, Witten M (1994) Computation of solutions to the generalized Michaelis-Menton equation. Applied Mathematics Letters 7: 45–48
Adomian G (1995) Solving the mathematical models of neurosciences and medicine. Mathematics and Computers in Simulation 40(1-2): 107-114
Wazwaz AM, Gorguis A (2004) Ananalytic study of Fisher’s equation by using Adomian decomposition method. Appl Math Comput 154(3): 609–620.
Loghambal Shunmugham and Rajendran.L (2013) Analytical expressions for steady-state concentrations of substrate and oxidized and reduced mediator in an amperometric biosensor. International Journal of Electrochemistry.
He JH (2006) Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30: 700-708
He JH (1999) Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering 178: 257-262.
Rajendran L, AnithaS(2013) Reply to comments on analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method by Ji-Huan He, Lu-Feng Mo. Electro chimica Acta 102: 474–476.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186