Department of Engineering, University of Leicester, Leicester LE1 7RH, UK.
Acta Biomater. 2018 Jan 15;66:192-199. doi: 10.1016/j.actbio.2017.11.023. Epub 2017 Nov 8.
For aliphatic polyesters such as PLAs and PGAs, there is a strong interplay between the hydrolytic degradation and erosion - degradation leads to a critically low molecular weight at which erosion starts. This paper considers the underlying physical and chemical processes of hydrolytic degradation and erosion. Several kinetic mechanisms are incorporated into a mathematical model in an attempt to explain different behaviours of mass loss observed in experiments. In the combined model, autocatalytic hydrolysis, oligomer production and their diffusion are considered together with surface and interior erosion using a set of differential equations and Monte Carlo technique. Oligomer and drug diffusion are modelled using Fick's law with the diffusion coefficients dependent on porosity. The porosity is due to the formation of cavities which are a result of polymer erosion. The model can follow mass loss and drug release up to 100%, which cannot be explained using a simple reaction-diffusion. The model is applied to two case studies from the literature to demonstrate its validity. The case studies show that a critical molecular weight for the onset of polymer erosion and an incubation period for the polymer dissolution are two critical factors that need to be considered when predicting mass loss and drug release.
In order to design bioresorbable implants, it is important to have a mathematical model to predict polymer degradation and corresponding drug release. However, very different behaviours of polymer degradation have been observed and there is no single model that can capture all these behaviours. For the first time, the model presented in this paper is capable of capture all these observed behaviours by switching on and off different underlying mechanisms. Unlike the existing reaction-diffusion models, the model presented here can follow the degradation and drug release all the way to the full disappearance of an implant.
对于脂肪族聚酯如 PLA 和 PGA，水解降解和侵蚀降解之间存在强烈的相互作用 - 降解会导致临界分子量降低，从而开始侵蚀降解。本文考虑了水解降解和侵蚀降解的潜在物理和化学过程。几种动力学机制被纳入到一个数学模型中，试图解释实验中观察到的不同质量损失行为。在组合模型中，自动催化水解、低聚物生成及其扩散与使用一组微分方程和蒙特卡罗技术的表面和内部侵蚀一起被考虑。低聚物和药物扩散使用依赖于孔隙率的菲克定律进行建模。由于聚合物侵蚀形成空腔，因此会产生孔隙率。该模型可以跟踪质量损失和药物释放高达 100%，这是无法用简单的反应-扩散解释的。该模型应用于文献中的两个案例研究，以证明其有效性。案例研究表明，聚合物侵蚀开始的临界分子量和聚合物溶解的潜伏期是预测质量损失和药物释放时需要考虑的两个关键因素。
为了设计可生物吸收的植入物，拥有能够预测聚合物降解和相应药物释放的数学模型非常重要。然而，已经观察到非常不同的聚合物降解行为，并且没有一个单一的模型可以捕捉到所有这些行为。本文提出的模型是首次能够通过打开和关闭不同的基础机制来捕捉到所有这些观察到的行为。与现有的反应-扩散模型不同，本文提出的模型可以一直跟踪降解和药物释放，直到植入物完全消失。
