Small Molecule Pharmaceutical Sciences, Genentech, Inc., 1 DNA Way, South San Francisco, CA, 94080, USA.
Pharm Res. 2022 May;39(5):907-917. doi: 10.1007/s11095-022-03270-6. Epub 2022 Apr 26.
The purpose of the study is to present a mathematical model capable of describing drug particle dissolution in 3-dimensional (3D) space, and to provide experimental model verification. Through this study, we also aim to elaborate limitations of the classic, 1D-based Nernst-Brunner formalism in dissolution modeling.
The 3D dissolution model was derived by treating the dissolution of a spherical particle as a diffusion-driven process, and by solving Fick's 2 law of diffusion in spherical coordinates using numerical methods. The resulting model was experimentally verified through analyzing the dissolution behavior of single succinic acid particles in un-stirred water droplet under polarized light microscopy, in combination with image segmentation techniques.
A set of working equations was developed to describe drug particle dissolution in 3D space. The predicted dissolution time and profile are in good agreement with the experimental results. The model clearly shows that the concentration gradient within the diffusion layer, in realistic 3D condition, must not be a constant value as implicated in the Nernst-Brunner formalism. The actual concentration profile is a hyperbola, and the concentration gradient at the surface of the particle can be significantly higher than the classic 1D-based dissolution model.
The study demonstrates that the classic, 1D-based dissolution models may lead to significant under-estimation of drug dissolution rates. In contrast, modeling dissolution in 3D space yields more reliable results. This study merits further development of comprehensive 3D drug dissolution models, by considering polydispersed particle ensemble and imposing the changes of diffusion layer thickness during dissolution.
本研究旨在提出一种能够描述药物颗粒在三维（3D）空间中溶解的数学模型，并提供实验模型验证。通过本研究，我们还旨在阐述经典的一维 Nernst-Brunner 公式在溶解建模中的局限性。
通过将球形颗粒的溶解处理为扩散驱动过程，并使用数值方法在球坐标中求解 Fick 的第二扩散定律，推导出 3D 溶解模型。通过在偏振光显微镜下分析未搅拌的水滴滴中单琥珀酸颗粒的溶解行为，并结合图像分割技术，对该模型进行了实验验证。
开发了一组工作方程来描述药物颗粒在 3D 空间中的溶解。预测的溶解时间和曲线与实验结果吻合良好。该模型清楚地表明，在实际的 3D 条件下，扩散层内的浓度梯度不能像 Nernst-Brunner 公式所暗示的那样是一个常数。实际的浓度曲线是一个双曲线，颗粒表面的浓度梯度可以明显高于经典的一维溶解模型。
本研究表明，经典的一维溶解模型可能导致药物溶解速率的显著低估。相比之下，在 3D 空间中建模溶解可以得到更可靠的结果。这项研究值得进一步开发全面的 3D 药物溶解模型，考虑到多分散颗粒集合体，并在溶解过程中考虑扩散层厚度的变化。
