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 sub-stances. The operation principle of this device is based on the excitation, propagation, and detection of acoustic sur-face shear waves in a multilayered structure that contacts a fluid containing a protein to be detected. The mathemat-ical model of such a structure involves large systems of coupled partial differential equations that describe piezo-electric, elastic, and hydrodynamic properties of the struc-ture. Because of the short wavelength, the implementation of such a model with finite elements in three dimensions re-quires 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 infor-mation 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 solu-tions in the multilayered structure of the biosensor under assumption that the structure is unbounded in horizontal and downward directions. These assumptions are reason-able 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 imi-tates the above mentioned unboundedness. KEY WORDS Love wave biosensor, multi-layered structures, dispersion relations, surface acoustic waves