Department of Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States.
Mol Pharm. 2012 May 7;9(5):1052-66. doi: 10.1021/mp2002818. Epub 2012 Apr 17.
Dissolution models require, at their core, an accurate diffusion model. The accuracy of the model for diffusion-dominated dissolution is particularly important with the trend toward micro- and nanoscale drug particles. Often such models are based on the concept of a "diffusion layer." Here a framework is developed for diffusion-dominated dissolution models, and we discuss the inadequacy of classical models that are based on an unphysical constant diffusion layer thickness assumption, or do not correctly modify dissolution rate due to "confinement effects": (1) the increase in bulk concentration from confinement of the dissolution process, (2) the modification of the flux model (the Sherwood number) by confinement. We derive the exact mathematical solution for a spherical particle in a confined fluid with impermeable boundaries. Using this solution, we analyze the accuracy of a time-dependent "infinite domain model" (IDM) and "quasi steady-state model" (QSM), both formally derived for infinite domains but which can be applied in approximate fashion to confined dissolution with proper adjustment of a concentration parameter. We show that dissolution rate is sensitive to the degree of confinement or, equivalently, to the total concentration C(tot). The most practical model, the QSM, is shown to be very accurate for most applications and, consequently, can be used with confidence in design-level dissolution models so long as confinement is accurately treated. The QSM predicts the ratio of diffusion layer thickness to particle radius (the Sherwood number) as a constant plus a correction that depends on the degree of confinement. The QSM also predicts that the time required for complete saturation or dissolution in diffusion-controlled dissolution experiments is singular (i.e., infinite) when total concentration equals the solubility. Using the QSM, we show that measured differences in dissolution rate in a diffusion-controlled dissolution experiment are a result of differences in the degree of confinement on the increase in bulk concentration independent of container geometry and polydisperse vs single particle dissolution. We conclude that the constant diffusion-layer thickness assumption is incorrect in principle and should be replaced by the QSM with accurate treatment of confinement in models of diffusion-controlled dissolution.
溶解模型核心要求准确的扩散模型。在向微纳米级药物颗粒发展的趋势下，扩散主导溶解模型的准确性尤为重要。通常，此类模型基于“扩散层”的概念。本文为扩散主导溶解模型建立了一个框架，并讨论了基于不实际的常数扩散层厚度假设或由于“约束效应”而不正确修正溶解速率的经典模型的不足：（1）由于溶解过程的约束导致主体浓度增加，（2）通过约束修正通量模型（舍伍德数）。我们推导出了在具有不可渗透边界的受限流体中球形颗粒的精确数学解。使用该解，我们分析了时间相关的“无限域模型”（IDM）和“准稳态模型”（QSM）的准确性，这两种模型都是针对无限域正式推导的，但可以通过适当调整浓度参数以近似方式应用于受限溶解。我们表明，溶解速率对约束程度或等效的总浓度 C(tot) 敏感。最实用的模型 QSM 在大多数应用中非常准确，因此，只要准确处理约束，就可以在设计级别的溶解模型中放心使用。QSM 预测扩散层厚度与颗粒半径的比值（舍伍德数）为常数加上取决于约束程度的修正。QSM 还预测，在总浓度等于溶解度的情况下，扩散控制溶解实验中完全饱和或溶解所需的时间是奇异的（即无限的）。使用 QSM，我们表明，在扩散控制溶解实验中，溶解速率的差异是由于约束程度的差异引起的，而与容器几何形状和多分散性与单颗粒溶解无关的主体浓度增加无关。我们得出结论，在原理上，常数扩散层厚度假设是不正确的，应在扩散控制溶解模型中用准确处理约束的 QSM 代替。
