Optimization of transdermal and transmucosal drug delivery systems utilizing thin-plate spline interpolation

多变量样条插值响应面法是一种有效的药物配方优化方法。然而，目前还没有令人满意的方法来评估最优解的可靠性。我们将bootstrap （BS）重采样和Kohonen’s自组织图谱（SOM）整合到RSM-S中，以经皮和经黏膜给药系统的处方优化以及常规片剂为模型实验。基于所获得的数据集，利用RSM-S估计了同时最优解。留一交叉验证结果表明，最优解是可靠的。同时，对原始数据集进行BS重采样，生成大量BS样本，并估计每个BS样本的同时最优解（BS最优解）。BS最优解的分布远非正态分布，是全局最优解和局部最优解的混合分布。然后使用SOM聚类来识别全局最优解集。SOM聚类将BS最优解划分为多个聚类，从包含最优解的聚类中评估最优解的可靠性。本文提出的方法为评价非线性最优解的鲁棒性提供了一种很有前途的方法。

The response surface method incorporating multivariate spline interpolation (RSM-S) is a powerful technique for the formulation optimization of pharmaceuticals. However, no satisfactory method has been developed to evaluate the reliability of the optimal solution. We integrated bootstrap (BS) resampling and Kohonen's self-organizing maps (SOM) into RSM-S using the formulation optimization of transderaml and transmucosal drug delivery systems as well as conventional tablets as the model experiments. Based on the data set obtained, the simultaneous optimal solution was estimated using RSM-S. Leave-one-out cross-validation showed the optimal solution to be reliable.Concurrently, a large number of BS samples were generated from the original data set using BS resampling, and simultaneous optimal solutions for each BS sample (BS optimal solutions) were estimated. The distribution of the BS optimal solutions was far from a normal distribution, suggesting a mixture of global and local optimal solutions. SOM clustering was then used to identify the set of global optimal solutions. SOM clustering divided the BS optimal solutions into several clusters, and the reliability of the optimal solution was evaluated from the cluster that included the optimal solution. The method proposed in this study offers a promising way to evaluate the robustness of nonlinear optimal solutions.