VILNIUS TECH Library invites you to follow the published new dissertations. The dissertation „Klasikinės ir trupmeninio laipsnio difuzijos-reakcijos modeliais paremtų biologinių jutiklių atvirkštinio uždavinio sprendimo algoritmai ir jų analizė“ („Analysis of algorithms for the solution of the inverse biosensor problem based on classical and fractional power diffusion-reaction models“) prepared by VILNIUS TECH, Ignas Dapšys. The dissertation was prepared in 2019–2023, Scientific Supervisor – Prof. Dr Habil. Raimondas Čiegis.
The dissertation was defended at the public meeting of the Dissertation Defence Council of the Scientific Field of Informatics in the SRA-I Meeting Hall of Vilnius Gediminas Technical University at 10 a. m. on 6 December 2023.
Biosensors are devices for the detection and analysis of chemical compounds, based on biochemical processes. To analyze samples in practice, the inverse biosensor problem needs to be solved – to determine component concentrations of the sample from its biosensor signal. The problem is ill-posed for multiple substrates – this property causes the biosensor to become sensitive to noise (e.g. electric noise), which is present in real devices. Due to this reason, the biosensor precision decreases. One of our objectives is to find methods to improve it. Since biosensors are used for important applications, such as environmental protection, medicine and quality control for food production, improving precision can bring clear benefits in these areas and improve the quality of life. In this dissertation, a virtual biosensor model is used in order to avoid expenses associated with the development of physical prototypes and to obtain biosensor signals faster. This may raise questions about the model's accuracy compared to real-life devices. Therefore, an alternative model has been investigated, where the classical diffusion operator is replaced by a fractional power elliptic operator (FPEO). Solving such equations requires specialized numerical methods – methods based on rational approximations and their parallel versions were developed and analyzed. These methods were applied to a modified biosensor model. The dissertation consists of an introduction, three main chapters and general conclusions. The first chapter describes the biosensor models used – the classical model and the one with FPEO diffusion, defines fractional power elliptic operators and discusses the inverse biosensor problem. The second chapter gives the description and analysis of solvers for the models in the first chapter, their parallel versions and experimental precision and stability results. The third chapter discusses the application of artificial neural networks and the parallel DIRECT global optimization algorithm for solving the inverse biosensor problem and the experimental results for the effect of noise and the permitted substrate concentration domain shrinkage procedure. The results of this dissertation show that FPEO equation solvers based on rational approximation have sufficient precision for practical purposes. Parallel versions of these methods scale well for large problems. The biosensor model with FPEO-based diffusion allows for a more precise fit to real data, while the results of neural network experiments lead to recommendations to improve the biosensor precision, based on the type of noise present and the analysis mode.
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