Cyber-physical model of the immunosensor system in a rectangular lattice with the use of lattice difference equations of population dynamics https://doi.org/10.33108/visnyk_tntu2018.04.112
Article Sidebar
Main Article Content
Abstract
The article developed a cyber-physical model for immunosensory systems. The main attention is paid to the mathematical description of the discrete dynamics of populations in combination with dynamic logic, which is used for discrete events. A class of solvable differential equations with time delay was introduced for modeling the interaction of antigen-antibodies within immunopicles. A spatial operator was used that simulates the interaction between immunopicles similar to the diffusion phenomenon. The paper presents the results of numerical simulation in the form of images of phase planes of the immunosensor model for antibody populations, with respect to antigenic populations. The experimental results obtained make it possible to analyze the stability of the model under consideration, taking into account the time delay.
Article Details
Issue
Section
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
1. E.A. Lee, «Cyber physical systems: Design challenges,» Center for Hybrid and Embedded Software Systems, EECS University of California, Berkeley, CA 94720, USA, Tech. Rep. UCB/EECS-2008-8, Jan. 2008, p. 10. [Online]. Avail- able: https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/ EECS-2008-8.pdf.
2. J. Lee, B. Bagheri, and H.-A. Kao, «A cyber-physical systems architecture for industry 4.0-based manufacturing systems,» Manufacturing Letters, vol. 3, pp. 18–23, 2015, ISSN: 2213-8463. https://doi.org/10.1016/j.mfglet.2014.12.001
3. K.-D. Kim and P.R. Kumar, «Cyber-physical systems: A perspective at the centennial,» Proceedings of the IEEE, vol. 100, no. Special Centennial Issue, pp. 1287 – 1308, May 2012. https://doi.org/10.1109/JPROC.2012.2189792
4. A. Platzer, «Differential dynamic logic for hybrid systems.,» J. Autom. Reas., vol. 41, no. 2, pp. 143 - 189, 2008, ISSN: 0168-7433. https://doi.org/10.1007/s10817-008-9103-8
5. Logical Foundations of Cyber-Physical Systems. Springer International Publishing, 2018.
6. V. Martsenyuk, A. Kłos-Witkowska, and A. Sverstiuk, «Stability, bifurcation and transition to chaos in a model of immunosensor based on lattice differential equations with delay,» Electronic Journal of Qualitative Theory of Differential Equations, no. 27, pp. 1 – 31, 2018. https://doi.org/10.14232/ejqtde.2018.1.27
7. A. Kłos-Witkowska, «The phenomenon of fluorescence in immunosensors.,» Acta Biochimica Polonica, vol. 63, no. 2, 2016. https://doi.org/10.18388/abp.2015_1231
8. X. Jiang and M.G. Spencer, «Electrochemical impedance biosensor with electrode pixels for precise counting of CD4+ cells: A microchip for quantitative diagnosis of HIV infec- tion status of AIDS patients,» Biosensors and Bioelectronics, vol. 25, no. 7, pp. 1622 – 1628, Mar. 2010. https://doi.org/10.1016/j.bios.2009.11.024
9. P.B. Luppa, L.J. Sokoll, and D.W. Chan, «Immunosensors- principles and applications to clinical chemistry,» Clinica Chimica Acta, vol. 314, no. 1, pp. 1 – 26, 2001, ISSN: 0009-8981. DOI: https://doi.org/10.1016/S0009-8981(01)00629-5. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0009898101006295. https://doi.org/10.1016/S0009-8981(01)00629-5
10. C. Berger, A. Hees, S. Braunreuther, and G. Reinhart, «Characterization of cyber-physical sensor systems,» Procedia CIRP, vol. 41, pp. 638 – 643, 2016. https://doi.org/10.1016/j.procir.2015.12.019
11. P. Soulier, D. Li, and J.R. Williams, «A survey of language- based approaches to cyber-physical and embedded system development,» Tsinghua Science and Technology, vol. 20, no. 2, pp. 130 – 141, 2015. https://doi.org/10.1109/TST.2015.7085626
12. H.J. Cruz, C.C. Rosa, and A.G. Oliva, «Immunosensors for diagnostic applications,» Parasitology research, vol. 88, S. 4 - S. 7, 2002. https://doi.org/10.1007/s00436-001-0559-2
13. S.-H. Paek and W. Schramm, «Modeling of immunosen- sors under nonequilibrium conditions: I. mathematic model- ing of performance characteristics,» Analytical biochemistry, vol. 196, no. 2, pp. 319 – 325, 1991. https://doi.org/10.1016/0003-2697(91)90473-7
14. V. Bloomfield and S. Prager, «Diffusion-controlled reactions on spherical surfaces. application to bacteriophage tail fiber attachment,» Biophysical journal, vol. 27, no. 3, pp. 447 – 453, 1979. https://doi.org/10.1016/S0006-3495(79)85228-5
15. O. Berg, «Orientation constraints in diffusion-limited macro- molecular association. the role of surface diffusion as a rate- enhancing mechanism,» Biophysical journal, vol. 47, no. 1, pp. 1 – 14, 1985. https://doi.org/10.1016/S0006-3495(85)83870-4
16. G. Marchuk, R. Petrov, A. Romanyukha, and G. Bocharov, «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, 1991, cited By 38. https://doi.org/10.1016/S0022-5193(05)80142-0
17. U. Forys, «Marchuk's model of immune system dynamics with application to tumour growth,» Journal of Theoretical Medicine, vol. 4, no. 1, pp. 85 – 93, 2002. https://doi.org/10.1080/10273660290052151
18. A. Nakonechny and V. Marzeniuk, «Uncertainties in medical processes control,» Lecture Notes in Economics and Mathe- matical Systems, vol. 581, pp. 185 – 192, 2006, cited By 2. https://doi.org/10.1007/3-540-35262-7_11
19. V. Marzeniuk, «Taking into account delay in the problem of immune protection of organism,» Nonlinear Analysis: Real World Applications, vol. 2, no. 4, pp. 483 – 496, 2001, cited By 2. https://doi.org/10.1016/S1468-1218(01)00005-0
20. A. Prindle, P. Samayoa, I. Razinkov, T. Danino, L.S. Tsim- ring, and J. Hasty, «A sensing array of radically coupled genetic 'biopixels',» Nature, vol. 481, no. 7379, pp. 39 – 44, Dec. 2011. https://doi.org/10.1038/nature10722