Mathematical modelling of three-layer amperometric biosensor and analytical expressions using homotopy perturbation method

Abstract

In this study, a biosensor based on an electrode that has been chemically altered is represented mathematically. The homotopy perturbation method analytically solves the model, and simulation results are verified against analytical solutions for various physical parameter values. The biosensor's mathematical model comprises three layers: an exterior diffusion layer, a dialysis membrane, and an enzyme layer. An effective diffusion coefficient is added to the mathematical model to integrate the diffusion layer with the dialysis membrane. Then, the problem is reduced to the two-layer model, which can effectively replace the three-layer model. The homotopy perturbation method (HPM) is used to solve the non-linear system of chemically modified electrode equations into an approximate analytical formulation. These formulations will be compared with MATLAB-based numerical simulations. Furthermore, an alternative to the current density in steady-state and the biosensor's sensitivity, resistance are explored.

Keywords

• Biosensor
• Mathematical modeling
• Effective diffusion coefficient
• Homotopy perturbation method