Simon Laurent
Otto H. York Department of Chemical, New Jersey Institute of Technology, Newark, NJ 07029, USA.
Math Biosci. 2009 Feb;217(2):151-8. doi: 10.1016/j.mbs.2008.11.004. Epub 2008 Nov 25.
Design tools are provided to assist in the development of drug-release devices that can control the time to establish a steady-state flux in addition to a desired delivery rate. In this contribution, the primary focus is placed on passive, heat-aided, and electrically assisted transport through planar membranes. Approximate analytical methods, that describe process dynamics, were applied to appropriate mathematical models to derive relationships between the system properties (e.g., diffusion coefficient, temperature and voltage potential) and the flux response time. Three case studies were investigated to illustrate the theoretical results. A steady-state benzocaine flux through ethylene-vinyl acetate membranes was achieved in 40min as predicted by a first-moment time constant approach. It took 5h and 45min to reach a constant delivery rate of amitriptyline HCl across human skin for a donor cell concentration of 0.032M and an electric current of 0.4mA/cm(2). Based on the upper limit and range estimates of the first eigenvalue, the onset of steady-state flux occurred between 3.4 and 3.5min when the donor and receiver cells were maintained at 47 and 37 degrees C, respectively. These predictions were confirmed by simulation, experimental evidence and graphical examination of drug-release data.
提供了设计工具,以协助开发药物释放装置,该装置除了能控制所需的给药速率外,还能控制达到稳态通量的时间。在本论文中,主要关注的是通过平面膜的被动、热辅助和电辅助传输。将描述过程动力学的近似分析方法应用于适当的数学模型,以推导系统特性(如扩散系数、温度和电势)与通量响应时间之间的关系。研究了三个案例研究以说明理论结果。通过一阶矩时间常数方法预测,在40分钟内可实现苯佐卡因通过乙烯-醋酸乙烯酯膜的稳态通量。对于供体细胞浓度为0.032M和电流为0.4mA/cm²的情况,盐酸阿米替林穿过人体皮肤达到恒定给药速率需要5小时45分钟。根据第一特征值的上限和范围估计,当供体和受体细胞分别保持在47和37摄氏度时,稳态通量的起始时间在3.4至3.5分钟之间。这些预测通过模拟、实验证据和药物释放数据的图形检验得到了证实。