An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume
An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume
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DOI：
10.3934/jimo.2009.5.127
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发表时间：
2008-12
影响因子：
1.3
通讯作者：
Song Wang;X. Lou
中科院分区：
文献类型：
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作者：
Song Wang;X. Lou
本文提出了一种新的基于最优拟合法的数学模型，用于估算药物从二维盘状给药装置到外部有限体积的有效扩散系数。在这个模型中，我们假设扩散过程发生在外部流体的边界层内，而在边界层外，由于对流控制，药物浓度是均匀的。利用分离变量技术，在适当的初始条件和边界条件下，得到了相应扩散方程的解析解。还得到了任意$t>；0$在时间间隔$[0，t]$内释放的质量与无限时间内释放的总质量之比的公式。此外，我们将该模型推广到具有两个不同有效扩散系数的问题，以处理“初始猝发”现象。后一种模型包含多个未知参数，因此提出了确定有效扩散系数、临界时间和有效边界层宽度的优化过程。用强的松龙2-半琥珀酸钠盐在聚甲基丙烯酸羟乙酯水凝胶多孔盘中的扩散实验数据对这些模型进行了验证。数值结果表明，这些模型具有较高的实用性和准确性。
In this paper we propose a new mathematical model based on optimal fitting for estimating effective diffusion coefficients of a drug from a delivery device of 2D disc geometry to an external finite volume. In this model, we assume that the diffusion process occurs within the boundary layer of the external fluid, while outside the layer the drug concentration is uniform because of the convection-domination. An analytical solution to the corresponding diffusion equation with appropriate initial and boundary conditions is derived using the technique of separation of variables. A formula for the ratio of the mass released in the time interval $[0,t]$ for any $t>0$ and the total mass released in infinite time is also obtained. Furthermore, we extend this model to one for problems with two different effective diffusion coefficients, in order to handle the phenomenon of 'initial burst'. The latter model contains more than one unknown parameter and thus an optimization process is proposed for determining the effective diffusion coefficient, critical time and width of the effective boundary layer. These models were tested using experimental data of the diffusion of prednisolone 2-hemisuccinate sodium salt from porous poly(2-hydroxyethylmethacrylate) hydrogel based discs. The numerical results show that the usefulness and accuracy of these models.