Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations - Homotopy perturbation approach

A mathematical model of amperometric and potentiometric biosensor is developed. The model is based on system of reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents an approximate analytical method (He's Homotopy perturbation method) to solve the non-linear differential equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Approximate analytical expressions for substrate concentration, product concentration and corresponding current response have been derived for all values of parameter a using perturbation method. These results are compared with available limiting case results and are found to be in good agreement. The obtained results are valid for the whole solution domain. (C) 2010 Elsevier B.V. All rights reserved.