Simon L
Otto H. York Chemical Engineering Department, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA.
Math Biosci. 2007 Oct;209(2):593-607. doi: 10.1016/j.mbs.2007.03.009. Epub 2007 Apr 7.
The integral transform technique was implemented to solve a mathematical model developed for percutaneous drug absorption. The model included repeated application and removal of a patch from the skin. Fick's second law of diffusion was used to study the transport of a medicinal agent through the vehicle and subsequent penetration into the stratum corneum. Eigenmodes and eigenvalues were computed and introduced into an inversion formula to estimate the delivery rate and the amount of drug in the vehicle and the skin. A dynamic programming algorithm calculated the optimal doses necessary to achieve a desired transdermal flux. The analytical method predicted profiles that were in close agreement with published numerical solutions and provided an automated strategy to perform therapeutic drug monitoring and control.
采用积分变换技术求解为经皮药物吸收建立的数学模型。该模型包括贴片在皮肤上的反复贴敷和移除。利用菲克第二扩散定律研究药物通过载体的传输以及随后渗透进入角质层的过程。计算本征模和本征值，并将其引入反演公式以估计载体和皮肤中的给药速率及药物量。动态规划算法计算实现所需经皮通量所需的最佳剂量。该分析方法预测的曲线与已发表的数值解非常吻合，并提供了一种用于进行治疗药物监测和控制的自动化策略。
