Missel P J
Drug Delivery, Alcon Research Ltd., Fort Worth, TX 76134, USA.
Ann Biomed Eng. 2000 Nov-Dec;28(11):1307-17. doi: 10.1114/1.1329886.
Four methods are proposed for modeling diffusion in heterogeneous media where diffusion and partition coefficients take on differing values in each subregion. The exercise was conducted to validate finite element modeling (FEM) procedures in anticipation of modeling drug diffusion with regional partitioning into ocular tissue, though the approach can be useful for other organs, or for modeling diffusion in laminate devices. Partitioning creates a discontinuous value in the dependent variable (concentration) at an intertissue boundary that is not easily handled by available general-purpose FEM codes, which allow for only one value at each node. The discontinuity is handled using a transformation on the dependent variable based upon the region-specific partition coefficient. Methods were evaluated by their ability to reproduce a known exact result, for the problem of the infinite composite medium (Crank, J. The Mathematics of Diffusion, 2nd ed. New York: Oxford University Press, 1975, pp. 38-39.). The most physically intuitive method is based upon the concept of chemical potential, which is continuous across an interphase boundary (method III). This method makes the equation of the dependent variable highly nonlinear. This can be linearized easily by a change of variables (method IV). Results are also given for a one-dimensional problem simulating bolus injection into the vitreous, predicting time disposition of drug in vitreous and retina.
本文提出了四种方法，用于对非均质介质中的扩散进行建模，其中扩散系数和分配系数在每个子区域中具有不同的值。本研究旨在验证有限元建模（FEM）程序，以期对药物在眼部组织中的区域分配扩散进行建模，不过该方法对其他器官或层压装置中的扩散建模也可能有用。分配在组织间边界处的因变量（浓度）中产生了一个不连续值，现有的通用有限元代码难以处理这种情况，因为这些代码在每个节点仅允许一个值。通过基于区域特定分配系数对因变量进行变换来处理这种不连续性。通过它们重现无限复合介质问题的已知精确结果的能力来评估这些方法（Crank, J.《扩散数学》，第2版。纽约：牛津大学出版社，1975年，第38 - 39页）。最符合物理直观的方法基于化学势的概念，化学势在相间边界处是连续的（方法III）。该方法使因变量方程高度非线性。通过变量变换可以很容易地将其线性化（方法IV）。还给出了一维问题的结果，该问题模拟了向玻璃体中推注药物，预测了药物在玻璃体和视网膜中的时间分布。
