Апроксимації для задач оптимізації медичних систем мікроголок: Fìz.-mat. model. ìnf. tehnol. 2021, 32:17-21

• Date: 2021
• Main Author: Sandrakov, Gennadiy
• Format: Article
• Language: English
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: Апроксимація; системи мікроголок; оптимізація; задачі мінімізації; гомогенізація
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/152
• Journal Title: Physico-mathematical modeling and informational technologies

Microneedle systems are used for transdermal (hypodermic) medicine injections at the treatment of different diseases. The efficiency of using such systems depends significantly on the size and parameters of microneedles. The problem of determining such dependencies and optimal parameters is considered as the problem of optimizing the interaction of microneedle systems with an elastic surface. Minimization problems for integral functional, whose solutions are approximations for solutions to the interaction problem, are obtained by the homogenization theory methods. Such problems are formulated in the form of classical problems with obstacles . References Bhatnagar, S., Dave, K., Venuganti, V. V. K. (2017). Microneedles in the clinic. J. Controlled Release 260 (2017), 164–182. doi:10.1016/j.jconrel.2017.05.029. DOI doi.org/10.1016/j.jconrel.2017.05.029 Ripolin, A., Quinn, J., Larraneta, E., Vicente-Perez, E. M., Barry, J., Donnelly, R. F. (2017). Successful application of large microneedle patches by human volunteers. Int. J. Pharmaceutics 521, 92–101. doi: 10.1016/j.ijpharm.2017.02.011. DOI doi.org/10.1016/j.ijpharm.2017.02.011 Plamadeala, C., Gosain, S. R., Hischen, F., Buchroithner, B., Puthukodan, S., Jacak, J., Bocchino, A., Whelan, D., O’Mahony, C., Baumgartner, W., Heitz, J. 2020. Bio-inspired microneedle design for efficient drug/vaccine coating, Biomed. Microdevices, 22(8). doi:10.1007/s10544-019-0456-z. DOI doi.org/10.1007/s10544-019-0456-z Carbone, L., Colombini, F. (1980). On convergence of functionals with unilateral constraints. J. Math. Pures Appl. 59, 465–500. Attouch, H., Picard, C. (1983). Variational inequalities with varying obstacles: The general form of the limit problem. J. Func. Analysis, 50(3), 329–386. doi: 10.1016/0022-1236(83)90009-5. DOI doi.org/10.1016/0022-1236(83)90009-5 Cioranescu, D., Murat, F. (1997). A strange term coming from nowhere, Topics in the Mathematical Modelling of Composite Materials. Birkhauser: Boston, 45–93. DOI doi.org/10.1007/978-1-4612-2032-9_4 Sandrakov, G. V. 2004. Homogenization of variational inequalities for problems with a regular obstacle. Doklady Mathematics, 70(1), 539–542. Sandrakov, G. V. (2005). Homogenization of variational inequalities for obstacle problems, Sbornik Mathematics, 196(3-4), 541–560. doi:10.1070/SM2005v196n04ABEH000891. DOI dx.doi.org/10.1070/SM2005v196n04ABEH000891 Sandrakov, G. V. (2006). Homogenization of nonlinear equations and variational inequalities with obstacles. Doklady Mathematics, 73(2), 178–181. doi:10.1134/S1064562406020062. DOI doi.org/10.1134/s1064562406020062 Sandrakov, G. V., Lyashko, S. I., Bondar, E. S., Lyashko, N. I. Modeling and optimization of microneedle systems. J. Automation and Information Sciences, 51(6), 1–11. doi:10.1615/JAutomatInfScien.v51.i6.10. DOI doi.org/10.1615/jautomatinfscien.v51.i6.10 Sandrakov, G. V., Lyashko, S. I., Bondar, E. S., Lyashko, N. I., Semenov, V. V. (2020). Modeling of configurations formed under using microneedle systems. J. Automation and Information Sciences, 52(12). doi: 10.1615/JAutomatInfScien.v52.i12. DOI doi.org/10.1615/jautomatinfscien.v52.i12.10 Rodrigues, J. F. (1987). Obstacle problems in mathematical physics. North-Holland: Amsterdam.