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 σ 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.