МОДЕЛЮВАННЯ КОНФІГУРАЦІЙ, ЩО ВИНИКАЮТЬ ПРИ ВИКОРИСТАННІ СИСТЕМ МІКРОГОЛОК

• Datum: 2020
• Hauptverfasser: Sandrakov, G.V., Lyashko, S.I., Bondar, E.S., Lyashko, N.I., Semenov, V.V.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: моделювання конфігурацій; системи мікроголок; оптимізація параметрів; проблеми мінімізації; інтегральні функціонали
• Online Zugang: https://jais.net.ua/index.php/files/article/view/502
• Назва журналу: Problems of Control and Informatics

Microneedle systems are compiled by a sufficiently large number of microneedles, which are mounted on a flat base, and are used for injection of drugs in modern medicine. Such systems are often made in the form of a patch on which a large number of biosoluble microneedles are attached, which greatly simplifies the use of such systems for injecting drugs. As a rule, the width of the patch is fixed, but the length can be quite long. Therefore, such a patch can be considered as a periodic continuation of the selected fixed fragment. The efficiency of using such systems depends significantly on the size and number of microneedles, which are placed on such a fragment. The problem of determining such dependencies will be considered as the problem of optimizing the interaction of microneedle systems with an elastic surface. Such problems are formulated in the form of classical problems of minimization of integral functionals with obstacles, supplemented by periodic boundary conditions in one of the coordinates and homogeneous Dirichlet boundary conditions in the other coordinate. The homogenization theory methods are used to obtain homogenized minimization problems for such functionals, whose solutions are approximations for solutions of the interaction problem under consideration. The homogenized problems are also formulated in the form of classical minimization problems with an obstacle, which have a much simpler form in comparison with the original strongly oscillating obstacles. When obtaining these problems, it is essentially used that the systems under consideration are formed by a sufficiently large number of microneedles. Conditions are established for the explicit calculation of surface configurations arising from the interaction of microneedle systems with an elastic surface. Statements are proved that justify the form of such configurations. The condition of «appearance of a gap» between the surface and the base of the microneedle system is established and the height of such a «gap» is calculated.