Computer-aided modeling of a biosensor with selective and perforated membranes using a four-layered one-dimensional model

This article presents a one-dimensional model for a biosensor with perforated and selective membranes. This model is constructed by replacing the perforated membrane with two homogeneous layers. These layers are used to model parts of the perforated membrane, where holes are filled with an enzyme and where is no enzyme in the holes, separately. The proposed model was investigated by performing numerical experiments in order to determine conditions, under which the proposed model can be used to simulate an operation of a biosensor with an outer perforated membrane precisely. A preciseness of the model was measured by comparing its results with results of the corresponding two-dimensional model. Beside the measurement of the preciseness, results of the proposed model were compared to the results of the one-dimensional model, constructed by replacing the perforated membrane with one homogeneous layer. A biosensor was modeled using diffusion-reaction equations with a nonlinear member representing the Michaelis-Menten kinetic of an enzymatic reaction. These equations were solved numerically, using the method of finite differences