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Gardener, C.S., Green, J.M., Kruskal, M.D. and Miura, R.M. (1967) Method for solving the Korteweg–de Vries Equation. Physical Review Letter, 19, 1095. doi:org/10.1103/PhysRevLett.19.1095

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• TITLE: Mathematical model for steady state current at ppo-modified micro-cylinder biosensors

  AUTHORS: K. Venugopal, A. Eswari, L. Rajendran

  KEYWORDS: Non-Linear Reaction/Diffusion Equation; Biosensors; Polymer- Modified Micro-Cylinder Electrode; Polyphenol Oxidase; Homotopy Perturbation Method

  JOURNAL NAME: Journal of Biomedical Science and Engineering, Vol.4 No.9, September 30, 2011

  ABSTRACT: A Mathemataical model for a modified micro- cylinder electrode in which polyphenol oxidase ( PPO) occurs for all values of the concentration of catechol and o-quinone is analysed. This model is based on system of reaction-diffusion Equations containing a non-linear term related to Michaelis Menten kinetics of the enzymatic reaction. Here a new analytical technique Homotopy Perturbation Method is used to solve the system of non-linear differential Equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Here we report an analytical expressions pretaining to the concentration of catechol and o-quinone and corresponding current in terms of dimensionless reaction-diffusion parameters in closed form. An excellent agreement with available limiting case is noticed.