Èlektron. model. 2018, 41(1):105-118
A numerical analysis of the stability of the cyber-physical model of the immunosensor on a rectangular grid using lattice differential equations has been carried out. A class of lattice difference equations with delay was proposed for modeling the interaction of antigen-antibody within immunopixels. The spatial operator used, simulates the interaction between immunopixels like diffusion phenomena. In the study of the cyber-physical model of the immunosensor, the electrical signal characterizes the number of immunopixel cells in which the fluorescence phenomenon occurs. Such an approach is of great importance from the point of view of the development of cyber-physical immunosensory systems. The obtained experimental results provide a complete analysis of the stability of the immunosensor model taking into account the delay in time.
cyber-physical immunosensor system, immunosensor, differential differential equations with delay.
- Mehrotra, (2016), “Biosensors and their applications – a review,” Journal of Oral Biology and Craniofacial Research, Vol. 6, no. 2, pp. 153-159.
- Jiang, and Spencer, M.G. (2010), “Electrochemical impedance biosensor with electrode pixels for precise counting of CD4+ cells: A microchip for quantitative diagnosis of HIV infection status of AIDS patients,” Biosensors and Bioelectronics, Vol. 25, no. 7, pp. 16221628.
- Luppa, B., Sokoll, L.J. and Chan, D.W. (2001), “Immunosensors principles and applications to clinical chemistry,” Clinica Chimica Acta, Vol. 314, no. 1, pp. 1-26.
- Lee, A. (2008), “Cyber physical systems: Design challenges,” available at: https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/ EECS-2008-8.pdf.
- Lee, , Bagheri, B. and Kao, H.A. (2015), “A cyber-physical systems architecture for industry 4.0-based manufacturing systems,” Manufacturing Letters, Vol. 3, pp. 18-23, available at: http://www.sciencedirect.com/science/article/pii/S221384631400025X.
- Platzer, (2008), “Differential dynamic logic for hybrid systems.”, J. Autom. Reas., Vol. 41, no. 2, pp. 143-189, DOI: 10.1007/s10817-008-9103-8.
- Berger, C., Hees, A., Braunreuther, S. and Reinhart, G. (2016), “Characterization of cyber-physical sensor systems,” Procedia CIRP, 41, pp. 638-643, available at: https:// doi.org/10.1016/j.procir. 2015.12.019.
- Martsenyuk, P., Klos-Witkowska, A. and Sverstiuk, A.S. (2018), “Study of classification of immunosensors from viewpoint of medical tasks”, Medical informatics and engineering, Vol. 1, no. 41, pp. 13-19.
- Bihuniak, V., Sverstiuk, A.S. and Bihuniak, K.O. (2018), “Some aspects of using immunosensors in medicine”, Medychnyi forum, Vol. 14, no. 14, pp. 8-11.
- Martsenyuk, P., Klos-Witkowska, A., Sverstiuk, A.S., Bihunyak, T.V. (2018), “On principles, methods and areas of medical and biological application of optical immunosensors”, Medical informatics and engineering, Vol. 2, no. 42, pp. 28-36.
- Cruz, J., Rosa, C.C. and Oliva, A.G. (2002), “Immunosensors for diagnostic applications”, Parasitology research, Vol. 88, S4-S7.
- Paek, H. and Schramm, W. (1991), “Modeling of immunosensors under nonequilibrium conditions: mathematic modeling of performance characteristics”, Analytical biochemistry, Vol. 196, no. 2, pp. 319-325.
- Marchuk, , Petrov, R., Romanyukha, A. and Bocharov, G. (1991), “Mathematical model of antiviral immune response. I. data analysis, generalized picture construction and parameters evaluation for hepatitis B”, Journal of Theoretical Biology, Vol. 151, no. 1, pp. 1-40.
- Forys, (2002), “Marchuk’s model of immune system dynamics with application to tumour growth,” Journal of Theoretical Medicine, Vol. 4, no. 1, pp. 85-93, DOI: 10.1080/10273660290052151.
- Nakonechny, and Marzeniuk, V. (2006), “Uncertainties in medical processes control”, Lecture Notes in Economics and Mathematical Systems, Vol. 581, pp. 185-192.
- Marzeniuk, (2001), “Taking into account delay in the problem of immune protection of organism”, Nonlinear Analysis: Real World Applications, Vol. 2, no. 4, pp. 483-496.
- Prindle, A., Samayoa, P., Razinkov, I., Danino, T., Tsimring, L.S. and Hasty, J. (2011), “A sensing array of radically coupled genetic ‘biopixels’ ”, Nature, Vol. 481, no. 7379, pp. 3944.