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Mathematical simulation of an amperometric enzyme-substrate electrode with apO2 basic sensor

Part 1 Mathematical model and simulation of thepO2 basic sensor

  • Transducers and Electrodes
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Abstract

The mathematical model (of an enzyme-substrate electrode with a pO2 basic sensor) is described by two coupled inhomogeneous partial differential equations and a set of boundary conditions. Generalised boundary conditions are derived, which the concentration values at the interfaces between two layers of different materials have to fulfil. This model is applicable to all enzyme-based sensors which operate with immobilised oxidase, are characterised by diffusion transport and have a cylindrosymmetrical geometry. To test this model the dependencies of the measurement characteristics of a pO2 sensor on the various design parameters were simulated. The simulation results concerning the influence exerted by the characteristics of the covering membrane and of the internal electrolyte layer as well as of the geometry of the electrodes correspond well with both the theoretical expectations and the experimental results. This mathematical model is expected to be successfully applied for simulating the behaviour of the far more complicated enzyme-substrate electrode too.

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Abbreviations

A :

area

c :

concentration

D :

diffusion coefficient

E t :

total amount of enzyme

F :

Faraday constant

H :

height

I :

sensor current

K m :

Michaelis constant

\(\tilde k\) :

\(R_{CAT} = \tilde k\Delta r\)

k :

rate constant

L :

thickness

\(\hat P\) :

permeability coefficient

p :

partial pressure

Q :

source density

r :

correlation coefficient

R :

radius,R EL=RΔr

S :

Bunsen solubility coefficient

U :

normalised intensity quantity

v :

reaction rate

V max :

maximum reaction rate per unit volume

V j :

partial coefficient at the interface between two adjacent phasesj andj+1

V :

volume

γ:

stoichiometry factor

Z :

H EL=ZΔz

1:

boundary layer

2:

external coupling membrane

3:

reaction layer

4:

internal covering membrane of the basic sensor

5:

internal electrolyte layer

B :

value in the bulk solution

CAT :

cathode

cat :

catalytic

E :

external, enzyme

EL :

electrode

G :

glucose

GR :

z co-ordinate of the interface,z i=GR iΔz

I :

internal

O :

oxygen

S :

substrate

t :

total

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Authors and Affiliations

  1. Scientific Department of Biomedical Engineering & Bionics, Ilmenau Institute of Technology, 6300, Ilmenau, German Democratic Republic

    K. Lemke

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Lemke, K. Mathematical simulation of an amperometric enzyme-substrate electrode with apO2 basic sensor. Med. Biol. Eng. Comput. 26, 523–532 (1988). https://doi.org/10.1007/BF02441921

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