Modeling and Optimization of Microneedle Systems

摘要

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 thehigh 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 microneedlesare 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 problemof 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. Weprove 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 thesystems with circular cylindrical microneedles are most optimal since such microneedles have the best properties for injections.