Numerical Simulation of Cyber-physical Biosensor Systems on the Basis of Lattice Difference Equations

2019;
: pp. 91 - 99
1
University of Bielsko-Biala, Department of Computer Science and Automatics, Poland
2
University of Bielsko-Biala, Department of Computer Science and Automatics, Poland
3
I. Gorbachevsky Ternopil National Medical University, Department of Medical Informatics, Ternopil, UkraineI. Gorbachevsky Ternopil National Medical University, Department of Medical Informatics, Ternopil, Ukraine
4
I. Gorbachevsky Ternopil National Medical University, Department of Medical Informatics, Ternopil, Ukraine

Cyber physical systems (CPS) include a lot of high complexity computing such as dynamic analysis and verification of continuous dynamic property, analysis and verification of real- time property, analysis and verification of spatial property, scheduling and fault tolerance. In this paper, some of the research directions that we are taking toward addressing some of the challenges involved in building cyber physical systems have been described. Taking into account the features of the cyber-physical sensor systems, the basic model has been modified. Lattice images in biopixels have been modified according to the laws of discrete dynamics. The developed models take into account the interaction of biopixels with each other by antigen diffusion. The comparative analysis of CPS models on rectangular and hexagonal lattices using differenсе equations has been considered in the work. The results of numerical simulations in the form of phase plane images and lattice images of the probability of antigen to antibody binding in the biopixels of cyber-physical biosensor systems for antibody populations relative to antigen populations have been received in the paper. The comparative analysis of the results of numerical modeling of mathematical models of cyber-physical biosensor systems on rectangular and hexagonal lattices using lattice difference equations with delay has been considered.

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Prof. dr hab. Vasyl Martsenyuk received the master degree in applied math in 1993, the degrees in systems analysis and decision making (PhD in 1996, DSc in 2005, respectively) from Taras Shevchenko National University of Kyiv, Ukraine. Since 1997 till 2015 he was working as a Professor, Chair of Medical Informatics Department, Vice- rector of Ternopil National Medical University, Ukraine.

In 2015 he received Dr hab. degree and the title of Professor of technical sciences in Poland. In 2015, he joined the Department of Computer Science and Automatics, University of Bielsko-Biala, Poland, as a Professor. His current research interests include decision making, computer graphics, web- programming, medical informatics, biosensors, dynamic systems

Dr. Aleksandra Kłos-Witkowska received the master degree in physics in 2001 from University of Silesia in Katowice. In 2007 she received PhD in physics. The PhD project was carried out in Medical Physics Department University of Silesia in Katowice. She is a laureate of prestigious Maria Curie's scholarship. She completed scientific internships: Max Planck Institut für Biophysikalische Chemie (Germany), University of Ioannina (Greece), University of Helsinki (Finland). Actually, she is working for University of Bielsko-Biala, Department of Computer Science and Automation as an Associate Professor. Her current research interest is focused on biosensors.

Ph.D. Andriy Sverstiuk – Associate Professor of the Department of Medical Informatics at I. Horbachevsky Ternopil National Medical University, Ukraine. Phd, Engineering, Taras Shevchenko National University of Kyiv, Ukraine, 2010. Master’s Degree (Biotechnical and medical devices and systems) at Ternopil Ivan Puluj National Technical University, Ukraine, 2001. Research interests  and experience: Mathematical modeling in medicine; Сyber-physical systems.

Ph.D. Oksana Bahrii-Zaiats  - Associate Professor of the Department of Medical physics of diagnostic and treatment department, I.Horbachevsky Ternopil National Medical University, Ukraine. Phd, Engineering, The National Academy of Sciences, Ukraine, 2014. Master’s Degree (Pedagogy) at Ternopil V. Hnatiuk National Pedagogical University, Ukraine, 2009. Research interests and experience: Mathematical   modeling   in   medicine; System analysis.