| Abstract [eng] |
Biosensors are analytical devices mainly used to detect analytes and measure their concentrations. Mathematical modeling is widely used for optimizing and analyzing an operation of biosensors for reducing price of development of new biosensors. The object of this research is mathematical and computer models, describing an operation of biosensors, made of several parts with different properties. The dissertation covers models, formulated in one and two-dimensional spaces by partial differential equations with non-linear members, and solved numerically, using the method of finite differences. The numerical models are implemented by a computer program. An original mathematical model for a biosensor with a carbon nanotube electrode is presented in the dissertation. The conditions at which the one-dimensional mathematical model can be used instead of two-dimensional one for accurate prediction of the biosensor response are investigated. Elements, used to build models of biosensors with a complex structure, were systemized. The biosensor description language is proposed and the computer software, simulating an operation of biosensors in the one-dimensional space and a rectangular domain of the two-dimensional space, is developed. An adequateness of the model for the biosensor with the carbon nanotube electrode and the impact of structural and geometrical properties on a response of the biosensor were investigated, performing computer experiments using the developed software. |
