Mathematical modeling in amperometric oxidase enzyme–membrane electrodes

Loghambal, S.; Rajendran, L.

doi:10.1016/j.memsci.2011.02.033

Cited by 35 publications

(22 citation statements)

References 40 publications

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“…(14), (15), (16), (18), (19), (20) Thiele modulus u 2 represents the ratio of the characteristic time of the enzymatic reaction to that of substrate diffusion. The variation in the Thiele modulus can be achieved by varying either the thickness of the enzyme layer or the amount of enzyme immobilized in the matrix.…”

Section: Resultsmentioning

confidence: 99%

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Analytical expressions for the concentrations of substrate, oxygen and mediator in an amperometric enzyme electrode

Indira¹,

Rajendran²

2013

Applied Mathematical Modelling

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a b s t r a c tThe theoretical model of Martens and Hall [N. Martens, E.A.H. Hall, Model for an immobilized oxidase enzyme electrode in the presence of two oxidants, Anal. Chem. 66 (1994) 2763-2770 in an immobilized oxidase enzyme electrodes is discussed. This model contains a non-linear term related to enzyme reaction system. In this paper, we obtain approximate analytical solutions for the non-linear equations under steady-state condition by using the homotopy perturbation method (HPM) and homotopy analysis method (HAM). Simple and approximate polynomial expressions for the concentration of substrate, oxygen, reduced mediator and current were obtained in terms of Thiele moduli and the normalized surface concentrations of species. Furthermore, in this work the numerical simulation of the problem is also reported using Scilab/Matlab program. An agreement between analytical and numerical results is noted.Crown

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Section: Resultsmentioning

confidence: 99%

“…Similarly we get Eqs. (15) and (16) in the text. The accuracy of the expression can be still improved by considering the higher-order terms (Solving Eq.…”

Section: Appendix B Basic Idea Of Liao's Homotopy Analysis Methodsmentioning

confidence: 99%

Analytical expressions for the concentrations of substrate, oxygen and mediator in an amperometric enzyme electrode

Indira¹,

Rajendran²

2013

Applied Mathematical Modelling

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“…This method is unique in its applicability, accuracy and efficiency. The HPM [24][25][26][27] uses the imbedding parameter p as a small parameter, and only a few iterations are needed to search for an asymptotic solution. The dimensionless rate constants k 1 , k 2 , k 3 , k 4 , k 5 and k 6 are related to one another, since the bulk solution is at equilibrium in the non-steady state.…”

Section: Mathematical Formulation Of the Boundary Value Problemmentioning

confidence: 99%

Analytical expression of non steady-state concentration for the CE mechanism at a planar electrode

Indira

Rajendran

2012

J Math Chem

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The analytical solutions of the non-steady-state concentrations of species at a planar microelectrode are discussed. The analytical expression of the kinetics of CE mechanism under first or pseudo-first order conditions with equal diffusion coefficients at planar electrode under non-steady-state conditions are obtained by using Homotopy perturbation method. These simple new approximate expressions are valid for all values of time and possible values of rate constants. Analytical equations are given to describe the current when the homogeneous equilibrium position lies heavily in favour of the electroinactive species. Working surfaces are presented for the variation of limiting current with a homogeneous kinetic parameter and equilibrium constant. In this work we employ the Homotopy perturbation method to solve the boundary value problem. Furthermore, in this work the numerical simulation of the problem is also reported using Scilab program. The analytical results are found to be in excellent agreement with the numerical results.

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“…The diffusion equations [14], containing a nonlinear term related to the enzymatic reaction, are carried out using the implicit difference scheme [15]. In recent years, analytical solutions are reported for various types of biosensors [16] [17] [18] [19]. The analytical results of diagnostic biosensor are relevant because their solutions describe important applications such as bioreactors and biofuel cells, among others [20] [21].…”

Section: Introductionmentioning

confidence: 99%

Reliable Method for Steady-State Concentrations and Current over the Diagnostic Biosensor Transducers

Preethi¹,

Meena²,

Poovazhaki³

2017

AJAC

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A mathematical modelling of diagnostic biosensors system at three basic types of enzyme kinetics is discussed in the presence of diffusion. Enzyme kinetics is adopted to be first order, Michaelis-Menten and ping-pong mechanism. In this paper, approximate analytical solutions are obtained for the non-linear equations under steady-state conditions by using the new Homotopy perturbation method. Simple and closed forms of analytical expressions for concentrations of substrate, product and co-substrate and corresponding current response have been derived for all possible values of parameters. Furthermore, the numerical simulation of the problem is also reported here by using Matlab program. Good agreement between analytical and numerical results is noted.

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Mathematical modeling in amperometric oxidase enzyme–membrane electrodes

Cited by 35 publications

References 40 publications

Analytical expressions for the concentrations of substrate, oxygen and mediator in an amperometric enzyme electrode

Analytical expressions for the concentrations of substrate, oxygen and mediator in an amperometric enzyme electrode

Analytical expression of non steady-state concentration for the CE mechanism at a planar electrode

Reliable Method for Steady-State Concentrations and Current over the Diagnostic Biosensor Transducers

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