{"id":2111,"date":"2021-01-18T18:58:51","date_gmt":"2021-01-18T16:58:51","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=2111"},"modified":"2021-04-01T12:23:01","modified_gmt":"2021-04-01T09:23:01","slug":"%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d1%87%d0%bd%d1%96-%d0%bc%d0%be%d0%b4%d0%b5%d0%bb%d1%96-%d0%b1%d1%96%d0%be%d1%81%d0%b5%d0%bd%d1%81%d0%be%d1%80%d1%96%d0%b2-%d1%82%d0%b0-%d1%96%d0%bc","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=2111","title":{"rendered":"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0456 \u043c\u043e\u0434\u0435\u043b\u0456 \u0431\u0456\u043e\u0441\u0435\u043d\u0441\u043e\u0440\u0456\u0432 \u0442\u0430 \u0456\u043c\u0443\u043d\u043e\u0441\u0435\u043d\u0441\u043e\u0440\u0456\u0432"},"content":{"rendered":"

\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u041d\u0406 \u041c\u041e\u0414\u0415\u041b\u0406 \u0411\u0406\u041e\u0421\u0415\u041d\u0421\u041e\u0420\u0406\u0412 \u0422\u0410 \u0406\u041c\u0423\u041d\u041e\u0421\u0415\u041d\u0421\u041e\u0420\u0406\u0412<\/p>\n

MATHEMATICAL MODELS OF BIOSENSORS AND IMMUNOSENSORS<\/p>\n

<\/a> \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 174-182. \u041d\u043e\u043c\u0435\u0440: \u21162, 2019 (271)<\/strong>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u0412. \u041f. \u041c\u0410\u0420\u0426\u0415\u041d\u042e\u041a
\n\u0423\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0432 \u0411\u0454\u043b\u044c\u0441\u043a\u043e-\u0411\u044f\u043b\u0456\u0439, \u041f\u043e\u043b\u044c\u0449\u0430
\n\u0410. \u0421. \u0421\u0412\u0415\u0420\u0421\u0422\u042e\u041a, \u041e. \u0410. \u0411\u0410\u0413\u0420\u0406\u0419-\u0417\u0410\u042f\u0426\u042c
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u0434\u0435\u0440\u0436\u0430\u0432\u043d\u0438\u0439 \u043c\u0435\u0434\u0438\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406.\u042f. \u0413\u043e\u0440\u0431\u0430\u0447\u0435\u0432\u0441\u044c\u043a\u043e\u0433\u043e, \u0423\u043a\u0440\u0430\u0457\u043d\u0430
\n\u041d. \u0412. \u041a\u041e\u0417\u041e\u0414\u0406\u0419
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0432\u0430\u043d\u0430 \u041f\u0443\u043b\u044e\u044f, \u0423\u043a\u0440\u0430\u0457\u043d\u0430
\nV. P. MARTSENYUK<\/span>
\nUniversity in Belsko Biala, Poland
\nA. S. SVERSTIUK, O. A. BAGRII-ZAYATS<\/span>
\nTernopil State Medical University named after I.Ya. Gorbachevsky
\nN.V. KOZODII
\nIvan Pul’uj Ternopil National Technical University
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2019-271-2-174-182<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review :<\/strong> 20.03.2019 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed :<\/strong> 10.04.2019 \u0440.<\/p>\n

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\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430: <\/strong>\u0431\u0456\u043e\u0441\u0435\u043d\u0441\u043e\u0440, \u0456\u043c\u0443\u043d\u043e\u0441\u0435\u043d\u0441\u043e\u0440, \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c, \u0441\u0442\u0430\u0442\u0438\u0447\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c, \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0430\u043b\u044c\u043d\u0456 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

An overview of mathematical models of biosensors and immunosensors was carried out The classification of investigated devices, in relation to physical converters, is given. The static model of the biosensor based on the surface plasmon resonance is considered. Optical models of biosensors operating on the basis of prisms and fiber optics are presented. The principle of biosensors measurement on the basis of the phenomenon of surface plasmon resonance is described. The static mathematical model of evaluation of the lifetime of biosensors is analysed. The static model of biosensor with multilayered structure is considered. The mathematical model for determining the loss of performance characteristics of the biosensor, can be used for various enzyme biosensors, is proposed. It is concluded that electrochemical biosensors, with age at elevated temperatures, lose their operational characteristics more quickly. A biosensor for measuring glucose concentration with the ability to control food quality and medicine is considered. A dynamical model of an immunosensor based on a system of delay lattice differential equations that takes into account the presence of colonies of antigens and antibodies localized in pixels, as well as the diffusion of antigen colonies between pixels, is proposed. A class of solvable difference equations with delay in time for modelling the “antigen-antibody” interaction\u00a0 in an immunosensor was introduced. The model is based on a number of biological assumptions about the interaction of colonies of antigens and antibodies, as well as the diffusion of antigens. To describe discrete spaces in the space of colonies localized in corresponding pixels, the apparatus of differential equations on a rectangular solution is used. The models of biosensors and immunosensors, which can be used to design immunosensory devices with the ability to control parameters that would ensure their operational stability, are considered in this work.
\nKey words:<\/strong> biosensor, immunosensor, mathematical model, static mathematical model, differential equations.<\/p>\n

References<\/strong><\/p>\n

    \n
  1. Mosinska, K. Fabisiak, K. Paprocki, M. Kowalska, P. Popielarski, M. Szybowicz, A. Stasiak, et al., \u201cDiamond as a transducer material for the production of biosensors\u201d, Przemysl Chemiczny, vol. 92, no. 6, pp. 919\u2013923, 2013.<\/li>\n
  2. Adley, \u201cPast, present and future of sensors in food production\u201d, Foods, vol. 3, no. 3, pp. 491\u2013510, Aug. 2014. DOI: 10.3390\/foods3030491. [Online]. URL: https:\/\/doi.org\/10.3390\/foods3030491.<\/li>\n
  3. K\u0142os-Witkowska, \u201cEnzyme-based fluorescent biosensors and their environmental, clinical and industrial applications\u201d, Polish Journal of Environmental Studies, vol. 24, pp. 19\u201325, 2015. DOI: 10.15244\/pjoes\/28352. [Online]. URL: https:\/\/doi.org\/10.15244\/pjoes\/28352.<\/li>\n
  4. Burnworth, S. Rowan, and C. Weder, \u201cFluorescent sensors for the detection of chemical warfare agents\u201d, Chemistry – A European Journal, vol. 13, no. 28, pp. 7828\u20137836, Sep. 2007. DOI: 10.1002\/chem.200700720. [Online]. URL: https:\/\/doi.org\/10.1002\/chem.200700720.<\/li>\n
  5. Mehrotra, \u201cBiosensors and their applications \u2013 a review\u201d, Journal of Oral Biology and Craniofacial Research, vol. 6, no. 2, pp. 153\u2013159, May 2016. DOI: 10.1016\/j.jobcr.2015.12.002. [Online]. URL: https:\/\/doi.org\/10.1016\/j.jobcr.2015.12.002.<\/li>\n
  6. Martsenyuk V.P. Study of classification of immunosensors from viewpoint of medical tasks \/ A. Klos-Witkowska, A.S. Sverstiuk \/\/ Medical informatics and engineering. \u2013 2018. \u2013 \u2116 1(41). \u2013 pp. 13\u201319. DOI: https:\/\/dx.doi.org\/10.11603\/mie.1996-1960.2018.1.8887.<\/li>\n
  7. Bihuniak T.V. Deiaki aspekty vykorystannia imunosensoriv u medytsyni \/ T.V. Bihuniak, A.S.\u00a0Sverstiuk, K.O. Bihuniak \/\/ Medychnyi forum. \u2013 2018. \u2013 \u2116 14 (14). \u2013 S. 8\u201311.<\/li>\n
  8. Martsenyuk V.P. On principles, methods and areas of medical and biological application of optical immunosensors \/ A. Klos-Witkowska, A.S. Sverstiuk, T.V. Bihunyak \/\/ Medical informatics and engineering. \u2013 2018. \u2013\u2116 2 (42). \u2013 p 28\u201336. DOI: https:\/\/dx.doi.org\/10.11603\/mie.1996-1960.2018.2.9289.<\/li>\n
  9. Moina and G. Ybarra, \u201cFundamentals and applications of immunosensors\u201d, Advances in immunoassay technology, pp. 65\u201380, 2012.<\/li>\n
  10. K\u0142os-Witkowska, \u201cThe phenomenon of fluorescence in immunosensors\u201d, Acta Biochimica Polonica, vol. 63, no. 2, pp. 215\u2013221, 2016. DOI: 10.18388\/abp.2015_1231. [Online]. URL: https:\/\/doi.org\/10.18388\/abp.2015_1231.<\/li>\n
  11. D. Gibson, \u201cBiosensors: The stabilit\u00e9 problem\u201d, Analusis, vol. 27, no. 7, pp. 630\u2013638, 1999.<\/li>\n
  12. Saifur Rahman, Khaleda Akter Rikta, Labid Bin Bashar, M.S. Anower, Numerical analysis of graphene coated surface plasmon resonance biosensors for biomedical applications, Optik, Volume 156, 2018, Pages 384\u2013390, ISSN 0030-4026, https:\/\/doi.org\/10.1016\/j.ijleo.2017.11.057.<\/li>\n
  13. Achi, S. Bourouina-Bacha, M. Bourouina, A. Amine, Mathematical model and numerical simulation of inhibition based biosensor for the detection of Hg(II), Sensors and Actuators B: Chemical, Volume 207, Part A, 2015, pp. 413\u2013423, ISSN 0925-4005, URL: https:\/\/doi.org\/10.1016\/j.snb.2014.10.033.<\/li>\n
  14. Kuang, Delay differential equations with applications in population dynamics. New York: Academic Press, 1993.<\/li>\n
  15. \u041a\u0430\u0442\u0442\u0440\u0430\u043b\u043b \u0420. \u0412. \u0425\u0438\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0435\u043d\u0441\u043e\u0440\u044b \/ \u041a\u0430\u0442\u0442\u0440\u0430\u043b\u043b \u0420\u043e\u0431\u0435\u0440\u0442 \u0412. \u2013 \u041c. : \u041d\u0430\u0443\u0447\u043d\u044b\u0439 \u043c\u0438\u0440, 2000. \u2013 25 \u0441.<\/li>\n
  16. Nuno Miguel Matos Pires, Tao Dong , Ulrik Hanke, Nils Hoivik.Recent developments in Optical detection technologies in Lab-on-a-Chip devices for biosensing applications \/\/ Sensors 2014, 14, 15458\u201315479; DOI:10.3390\/s140815458.<\/li>\n
  17. Jonsson U., Fagerstam L., Ivarsson B. Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology \/\/ BioTechniques. \u2013 1991. \u2013 Vol.11 \u2013 pp. 620\u2013627.<\/li>\n
  18. Saifur Rahmana, Khaleda Akter Riktaa, Labid Bin Bashar, M.S. Anower, Numerical analysis of graphene coated surface plasmon resonance biosensors for biomedical applications, Optik 156 (2018), pp. 384\u2013390.<\/li>\n
  19. N. Shushama, M.M. Rana, R. Inum, M.B. Hossain, Graphene coated fiber optic surface plasmon resonance biosensor for the DNA hybridization detection: simulation analysis, Opt. Commun. 383 (2017), pp. 186\u2013190.<\/li>\n
  20. Fu, S. Zhang, H. Chen, J. Weng, Graphene enhances the sensitivity of fiber-Optic surface plasmon resonance biosensor, IEEE Sens. J. 15 (10) (2015).<\/li>\n
  21. Peter Panjan, Vesa Virtanen, Adama Marie Sesay, Determination of stability characteristics for electrochemical biosensors via thermally accelerated ageing, Talanta 170 (2017), pp. 331\u2013336.<\/li>\n
  22. Rossokhaty, N. Rossokhata, Mathematical model of a biosensor with multilayer charged membrane, Computer Physics Communications 147 (2002), pp. 366\u2013369.<\/li>\n
  23. Angad S. Kushwaha, Anil Kumar, Rajeev Kumar, S.K. Srivastava, A study of surface plasmon resonance (SPR) based biosensor with improved sensitivity, Photonics and Nanostructures – Fundamentals and Applications 31 (2018), 99\u2013106.<\/li>\n
  24. Yamamoto, Surface plasmon resonance (SPR) theory, Tutor., Rev. Polarogr. 48 (2002) 209.<\/li>\n
  25. Ma, G. Farrell, Y. Semenova, H.P. Chan, H. Zhang, Q. Wu, Sensitivity enhancement for a multimode fiber sensor with an axisymmetric metal grating layer, Photon. Nanostruct. \u2013 Fundam. Appl. 12 (2014), pp.69\u201374.<\/li>\n
  26. K. Maharana, R. Jha, Pu. Padhy, On the electric field enhancement and performance of SPR gas sensor based on graphene for visible and near infrared, Sens. Actuators B 207 (2015), pp. 117\u2013122.<\/li>\n
  27. Martsenyuk V. Stability, bifurcation and transition to chaos in a model of immunosensor based on lattice differential equations with delay \/ A. Klos-Witkowska, A. Sverstiuk \/\/ Electronic Journal of Qualitative Theory of Differential Equations: No. 2018(27), \u0440p. 1\u201331. DOI: 10.14232\/ejqtde.2018.1.27.<\/li>\n
  28. McCluskey, \u201cComplete global stability for an SIR epidemic model with delay \u2013 distributed or discrete\u201d, Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 55\u201359, Feb. 2010. DOI: 10.1016\/j.nonrwa.2008.10.014. [Online]. URL: https:\/\/doi.org\/10.1016\/j.nonrwa.2008.10.014.<\/li>\n
  29. Nakonechny and V. Marzeniuk, \u201cUncertainties in medical processes contro\u201d, Lecture Notes in Economics and Mathematical Systems, vol. 581, pp. 185\u2013192, 2006, cited By 2. DOI: 10.1007 \/ 3 – 540 – 35262 – 7 _ 11. [Online]. URL: https:\/\/www.scopus.com\/inward \/ record . uri ? eid = 2 – s2 . 0 – 53749093113 & doi = 10 . 1007 % 2f3 – 540 – 35262 – 7_11&partnerID=40&md5=03be7ef103cbbc1e94cacbb471daa03f.<\/li>\n
  30. Prindle, P. Samayoa, I. Razinkov, T. Danino, L. S. Tsimring, and J. Hasty, \u201cA sensing array of radically coupled genetic \u2018biopixels\u2019\u201d, Nature, vol. 481, no. 7379, pp. 39\u201344, Dec. 2011. DOI: 10.1038\/nature10722. [Online]. URL: https:\/\/doi.org\/10.1038\/nature10722.<\/li>\n
  31. Prindle, P. Samayoa, I. Razinkov, T. Danino, L. S. Tsimring, and J. Hasty, \u201cA sensing array of radically coupled genetic \u2018biopixels\u2019\u201d, Nature, vol. 481, no. 7379, pp. 39\u201344, Dec. 2011. DOI: 10.1038\/nature10722. [Online]. URL: https:\/\/doi.org\/10.1038\/nature10722.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

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