School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China.
Comput Math Methods Med. 2020 Aug 1;2020:8380691. doi: 10.1155/2020/8380691. eCollection 2020.
The optimization problem of drug release based on the multilaminated drug-controlled release devices has been solved in this paper under the inverse problem solution scheme. From the viewpoint of inverse problem, the solution of optimization problem can be regarded as the solution problem of a Fredholm integral equation of first kind. The solution of the Fredholm integral equation of first kind is a well-known ill-posed problem. In order to solve the severe ill-posedness, a modified regularization method is presented based on the Tikhonov regularization method and the truncated singular value decomposition method. The convergence analysis of the modified regularization method is also given. The optimization results of the initial drug concentration distribution obtained by the modified regularization method demonstrate that the inverse problem solution scheme proposed in this paper has the advantages of the numerical accuracy and antinoise property.
本文基于多层药物控释装置，采用反问题求解方案，解决了药物释放的最优化问题。从反问题的角度来看，优化问题的解可以看作是第一类 Fredholm 积分方程的解问题。第一类 Fredholm 积分方程的解是一个众所周知的不适定问题。为了解决严重的不适定性，本文提出了一种基于 Tikhonov 正则化方法和截断奇异值分解方法的改进正则化方法。还给出了改进正则化方法的收敛性分析。通过改进的正则化方法得到的初始药物浓度分布的优化结果表明，本文提出的反问题求解方案具有数值精度高和抗噪声性能好的优点。
