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Analysis of a convection-diffusion-reaction problem in a surface-based biosensor using the method of lines
Carlos A. M. Silva, Enanuel N. Macêdo and João N. N. Quaresma

The Method of Lines (MOL) was used to study the mass-transfer process and the underlying biomolecular interaction process on the surface based on biosensors, a new optical sensor technology of optical sensors that uses the surface plasmon resonance technique (SPR) to generate the extension of the kinetic process. A mathematical model was developed involving the convection-diffusion equation of mass transport coupled with an equation that describes the reversible chemical reaction between analyte and immobilized reactant. A computer code in FORTRAN 90/95 programming language using the subroutine DIVPAG from the IMSL library was developed to numerically solve the system of ordinary differential equations resulting from the application of the MOL in the original model. The parameter values used for the simulation were chosen from the literature data to simulate typical cases. Therefore, the mathematical model proposed in this paper based on a problem of convection-diffusion-reaction was used to describe the biomolecular interactions process, and numerical results were generated to predict the time course for average free analyte concentration and average concentration of bound analyte-receptor complex to the phases of association and dissociation. These results were compared with those obtained with solution methodologies from other works in order to validate the mathematical model developed.

Keywords: Convection-diffusion-reaction model, Mass transport, Method of Lines, Mathematical modeling

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