Mathematical models of a biosensor

• Published in: Applied mathematical modelling 2004-06, Vol.28 (6), p.573-589
• Main Authors: Botkin, N.D., Turova, V.L.
• Format: Article
• Language: English
• Subjects: Finite element models; Fluid–solid interface; Love waves; Multi-layered structure
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2003.10.012

This paper studies mathematical models of a biosensor that serves for the measurement of small amounts of certain substances in liquids. The device works as follows: acoustic shear waves are excited due to an alternate voltage applied to electrodes deposited on a quartz crystal substrate; the waves are transmitted into a thin isotropic guiding layer in contact with a liquid containing molecules to be detected; these molecules adhere to a specific receptor, aptamer, immobilized on the surface of the guiding layer; the arising mass loading causes a phase shift in the electric signal which is measured on output electrodes. We state a three-dimensional mathematical model that describes a composite structure consisting of three coupled layers: two solid layers with different elastic and electric properties and a liquid layer treated as a weakly compressible viscous fluid. The full coupling between deformations and the electric field is assumed. A two-dimensional model is derived from the three-dimensional one by neglecting the non-homogeneity in x 2-direction. Another two-dimensional model is derived by the averaging of the three-dimensional model in x 3-direction under the assumption of an exponential attenuation of waves in the liquid and the substrate. The models are implemented numerically with finite elements. Computer simulations exhibit a good agreement with physical experiments.