Lemaire V, Bélair J, Hildgen P
Département de Physique, Centre de Recherches Mathématiques, Université de Montréal, Que., Montréal, Canada.
Int J Pharm. 2003 Jun 4;258(1-2):95-107. doi: 10.1016/s0378-5173(03)00165-0.
Biodegradable, porous microspheres exhibit a wide range of release profiles. We propose in this paper a unifying approach based on the dual action of diffusion and erosion to establish which mechanisms are responsible for the variety of release kinetics observed during in vitro experiments. Our modeling procedure leads to the partitioning of the matrix into multiple, identical elements, thus simplifying significantly the mathematical and numerical treatment of the problem. The model equations cannot be solved analytically, since the domain contains a moving interface, and must therefore be solved numerically, using specific methods designed for that purpose. Our model confirms the major role that the relative dominance between diffusion and erosion plays in the release kinetics. In particular, the velocity of erosion, the effective diffusion coefficient of the drug molecule in the wetted polymer, the average pore length, and the initial pore diameter are sensitive parameters, whereas the porosity and the effective diffusion coefficient of the drug in the solvent-filled pores is seen to have little influence, if any, on the release kinetics. The model is confirmed by using release data from biodegradable microspheres with different ratios of low and high molecular weight PLA. Excellent goodness of fit is achieved by varying two parameters for all types of experimental kinetics: from the typical square root of time profile to zero-order kinetics to concave release curves. We are also able to predict, by interpolation, release curves from microspheres made of intermediate, untested ratios of PLA by using a relation between two model parameters.
可生物降解的多孔微球呈现出广泛的释放曲线。我们在本文中提出一种基于扩散和侵蚀双重作用的统一方法，以确定在体外实验中观察到的各种释放动力学的 responsible 机制。我们的建模过程导致将基质划分为多个相同的元素，从而显著简化了该问题的数学和数值处理。由于域中包含一个移动界面，模型方程无法解析求解，因此必须使用为此目的设计的特定方法进行数值求解。我们的模型证实了扩散和侵蚀之间的相对主导作用在释放动力学中所起的主要作用。特别是，侵蚀速度、药物分子在湿润聚合物中的有效扩散系数、平均孔径和初始孔径是敏感参数，而孔隙率和药物在充满溶剂的孔隙中的有效扩散系数对释放动力学的影响很小（如果有影响的话）。通过使用具有不同低分子量和高分子量聚乳酸比例的可生物降解微球的释放数据，证实了该模型。通过针对所有类型的实验动力学改变两个参数，实现了极好的拟合优度：从典型的时间平方根曲线到零级动力学再到凹形释放曲线。我们还能够通过插值预测由中间的、未经测试的聚乳酸比例制成的微球的释放曲线，方法是使用两个模型参数之间的关系。
