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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i6.10
pages 1-11

Modeling and Optimization of Microneedle Systems

Gennadiy V. Sandrakov
Kiev National Taras Shevchenko University, Kiev
Sergey I. Lyashko
Kiev National Taras Shevchenko University Kiev, Ukraine
Elena S. Bondar
Kiev National Taras Shevchenko University, Kiev
Nataliya I. Lyashko
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev

Краткое описание

A mathematical model and a variational method of computation of optimal parameters for transdermal (hypodermic) medicine delivery by microneedle systems are developed. Such systems are formed by a large number of microneedles, which are fixed on the plane base and used for vaccine, protein and insulin injections. Numerous publications confirm the high efficiency of the microneedle system applications for transdermal medicine injections at the treatment of different diseases. Microneedles of such systems, as a rule, are not ordinary medical needles. The microneedles are synthesized from biodegradable polymers that are dissolved with the prescribed rate after transdermal drug injections. Homogenization methods for computation of the optimum parameters of microneedles are developed, which consider that the system consists of a great number of microneedles. The problem of computation of parameters of elastic interaction of with taking into account microneedle system with the surface is considered as a problem of approximation and homogenization of solutions of the problem of minimization of an integral functional, which is determined as an obstacle problem. The obtained values of microneedle parameters guarantee the effective application of such systems for transdermal medicine delivery. We prove the statement that such values of parameters are independent of the shape of the base and configuration of microneedles. This independence is connected first of all with needles microthickness. It was confirmed that the systems with circular cylindrical microneedles are most optimal since such microneedles have the best properties for injections.


  1. Park J.H., Allen M.G., Prausnitz M.R., Biodegradable polymer microneedles: fabrication, mechanics and transdermal drug delivery, J. Controlled Release, 2005, 104, 51-66. .

  2. Olatunji O., Das D.B., Garland M.J., Belaid L., Donnelly R.F., Influence of array interspacing on the force required for successful microneedle skin penetration: theoretical and practical approaches, J. Pharmaceutical Sciences, 2013, 102, 1209-1221. .

  3. ItaK., Transdermal delivery of drugs with microneedles potential and challenges, Pharmaceutics, 2015, 7, 397-405. .

  4. RipolinA., QuinnJ., LarranetaE., Vicente-Perez E.M., Barry J., Donnelly R.F., Successful application of large microneedle patches by human volunteers, International J. Pharmaceutics, 2017, 521, 92-101. .

  5. Bhatnagar S., Dave K., Venuganti V.V.K., Microneedles in the clinic, J. Controlled Release, 2017, 260, 164-182. .

  6. Mitra A.K., Cholkar C., Mandal A. (ed.), Emerging nanotechnologies for diagnostics, drug delivery and medical devises, Elsevier, Amsterdam, Oxford, Cambridge, 2017. .

  7. Tekko I., LarranetaE., Rodgers A.M., Scott C.J., Kissenpfennig A., Donnelly R.F., Microneedles in nanomedicine delivery, In book: Nanotechnologies in preventive and regenerative medicine, Elsevier, Amsterdam, 2018. .

  8. Gomaa Y.A., Morrow D.I.J., Garland M.J., Donnelly R.F., El-Khordagui L.K., Effects of microneedle length, density, insertion time and multiple applications on human skin barrier function: Assessments by transdermal water loss, Toxicol in Vitro, 2010, 24, 1971-1978. .

  9. Olatunji O., Das D.B., Nassehi V., Modelling transdermal drug delivery using microneedles: Effect of geometry on drug transport behavior, J. Pharmaceutical Sciences, 2012, 101(1), 164-175. .

  10. RomgensA.M., BaderD.L., Bouwstra J.A., Baaijens F.P.T., Oomens C.W.J., Monitoring the penetration process of single microneedles with varying tip diameters, J. Mechanical Behavior of Biomedical Materials, 2014, 40, 397-405. .

  11. Carbone L., Colombini F., On convergence of functionals with unilateral constraints, J. Math. Pures Appl., 1980, 59, 465-500. .

  12. Attouch H., Picard C., Variational inequalities with varying obstacles: the general form, J. Fund. Anal., 1983, 50, 329-386. .

  13. Sandrakov G.V., Homogenization of variational inequalities for problems with regular obstacles, DokladyMath., 2004, 70(1), 539-542. .

  14. Sandrakov G.V., Homogenization of variational inequalities for obstacle problems, Sbornik Math., 2005, 196(4), 541-560. .

  15. Sandrakov G.V., Homogenization of nonlinear equations and variational inequalities with obstacles, Doklady Math., 2006, 73(2), 178-181. .

  16. Sandrakov G.V., Homogenization of variational inequalities and equations defined by pseudomonotone operators, Sbornik Math., 2008, 199(1), 67-98. .

  17. Kinderlehrer D., Stampacchia G., An introduction to variational inequalities and their applications, Academic Press, New York, 1980, Russian transl., Mir, Moscow 1983. .

  18. Rodrigues J.F., Obstacle problems in mathematical physics, North-Holland, Amsterdam, 1987. .

  19. CioranescuD., MuratF., A strange term coming from nowhere. Topics in the Mathematical Modelling of Composite Materials, Birkhauser, Boston, 1997, 45-93. .

  20. Lyashko S.I., KlyushinD.A., Nomirovsky D.A., SemenovV.V., Identification of age-structured contamination sources in ground water, Optimal control of age-structured populations in economy, demography, and the environment (ed. by R. Boucekkline et. al.), Routledge, London-New York, 2013, 277-292. .

  21. Lyashko S.I., KlyushinD.A., Pavlychko V.V., Model-based analysis of biological tissue heating by point ultrasound sources, J. Automation and Information Sciences, 2010, 42(2), 44-50. .

  22. Lyashko S.I., KlyushinD.A., Onotskyi V.V., Lyashko N.I., Optimal control of drug delivery from microneedle systems, Cybernetics and systems analysis, 2018, 54(3), 357-365. .

  23. Tymoshenko A., KlyushinD., Lyashko S., Optimal control of point sources in Richards-Klute equation, Advances in Intelligent Systems and Computing, 2019, 754, 194-203. .

  24. Sandrakov G.V., Homogenization of variational inequalities for non-linear diffusion problems in perforated domains, Izvestiya Math., 2005, 69(5), 1035-1059. .

  25. KlyushinD.A., Onotskyi V.V., Numerical simulation of 3D unsaturated infiltration from point sources in porous media, J. Coupled Systems and Multiscale Dynamics, 2016, 4, 187-193. .

  26. Petryk M.R., Khimich A.N., Petryk M.M., Simulation of adsorption and desorption of hydrocarbons in nanoporous catalysts of neutralization systems of exhaust gases using nonlinear Langmuir isotherm, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal "Problemy upravleniya i informatiki", 2018, No. 5, 59-72. .

  27. Sandrakov G.V., The homogenization of nonstationary equations with contrast coefficients, Doklady Mathematics, 1997, 56(1), 586-589. .

  28. Sandrakov G.V., Multiphase models of nonstationary diffusion arising from homogenization, Computational Mathematics and Mathematical Physics, 2004, 44(10), 1741-1756. .

  29. Sandrakov G.V., Multiphase homogenized diffusion models for problems with several parameters, Izvestiya Math., 2007, 71(6), 1193-1252. .

  30. DiazJ.I., Gomez-Castro D., Podol'skii A.V., Shaposhnikova T.A., On the asymptotic limit of the effectiveness of reaction-diffusion equations in periodically structured media, J. Math. Anal. Appl., 2017, 455, 1597-1613. .

  31. ZubovaM.N., Shaposhnikova T.A., Homogenization of the variational inequality corresponding to a problem with rapidly varying boundary conditions, Math. Notes, 2007, 82(4), 481-491. .

  32. Verlan D.A., Semenov V.V., Chabak L.M., A strongly convergent modified extragradient method for variational inequalities with non-Lipschitz operators, J. Automation and Information Sciences, 2015, 47(7), 31-46. .

  33. Semenov V.V., A version of the mirror descent method to solve variational inequalities, Cybernetics and Systems Analysis, 2017, 53(2), 234-243. .

  34. Semenov V.V., Inertial hybrid splitting methods for operator inclusion problems, Cybernetics and Systems Analysis, 2018, 54(6), 936-943. .

  35. Lyashko S.I., Semenov V.V., On the controllability of linear distributed systems in classes of generalized actions, Cybernetics and Systems Analysis, 2001, 37(1), 13-32. .

  36. Lyashko S.I., Nomirovsky D.A., Sergienko T.I., Trajectory and terminal controllability in hyperbolic and pseudohyperbolic systems with generalized actions, Cybernetics and Systems Analysis, 2001, 37(5), 756-763. .

  37. Semenov V.V., Solvability of a parabolic transmission problem with the condition of a generalized proper lumped source, Differential Equations, 2005, 41(6), 878-886. .

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