Two complementary approaches to modelling a biosensor

The paper outlines two approaches to the modelling of a biosensor which serves for the detection and quantitative measurement of microscopic amounts of biological substances. The operation principle of this device is based on the excitation, propagation, and detection of acoustic surface shear waves in a multilayered structure that contacts a fluid containing a protein to be detected. The mathematical model of such a structure involves large systems of coupled partial differential equations that describe piezoelectric, elastic, and hydrodynamic properties of the structure. Because of the short wavelength, the implementation of such a model with finite elements in three dimensions requires a very fine mesh and, therefore, forces to use parallel computing. Thus, it would be useful to have a simple tool for a fast preliminary analysis which would provide information about the structure of solutions. The paper presents such a tool developed using harmonic analysis techniques that are based on the construction of travelling wave solutions in the multilayered structure of the biosensor under assumption that the structure is unbounded in horizontal and downward directions. These assumptions are reasonable because the real biosensor chip is embedded up to the surface into a very viscose damping medium to exclude the reflection of waves on side and bottom faces, which imitates the above mentioned unboundedness.