Understanding drug release from pharmaceutical granules is vital to the development of targeted release profiles. A model describing diffusion and solubility-limited drug dissolution and release from a porous spherical granule of drug and excipient is considered. Radially varying porosity and initial concentration profiles which can arise in pharmaceutical granules are incorporated. A range of boundary-value and moving-boundary-value problems arise, depending on the relationship between the drug saturation concentration in the solvent medium and the initial drug concentration and porosity profiles. The model is derived in detail for the case where the initial drug concentration is greater than the drug saturation concentration in all parts of the granule. In this case, a moving boundary forms at the granule surface and propagates inwards, separating an unextracted inner core from a shell region which undergoes extraction via diffusion. The full model is non-dimensionalised and analysed using asymptotic methods and numerical solution. A leading-order model is derived by exploiting a small parameter corresponding to the ratio of the drug saturation concentration to the maximum initial concentration in the granule, allowing estimation of the time taken for the moving boundary to reach the granule centre. The behaviour of the full model is considered by solving it using a boundary immobilisation method and the finite element method for a range of parameters and comparing to the leading-order model. Finally, the model outputs for the moving boundary position and normalised drug release are compared with experimental data from the literature.

了解药物颗粒的药物释放对于开发靶向释放曲线至关重要。考虑了描述扩散和溶解度限制的药物从药物和赋形剂的多孔球形颗粒溶出和释放的模型。结合了药物颗粒中可能出现的径向变化的孔隙率和初始浓度曲线。根据溶剂介质中药物饱和浓度与初始药物浓度和孔隙率分布之间的关系，会出现一系列边界值和移动边界值问题。该模型是针对初始药物浓度大于颗粒所有部分的药物饱和浓度的情况而详细推导出来的。在这种情况下，在颗粒表面形成移动边界并向内传播，将未提取的内核与通过扩散进行提取的壳区域分离。完整模型是无量纲化的，并使用渐近方法和数值解进行分析。通过利用与颗粒中药物饱和浓度与最大初始浓度之比相对应的小参数，可以推导出主阶模型，允许估计移动边界到达颗粒中心所需的时间。通过使用边界固定方法和有限元方法对一系列参数进行求解并与领先阶模型进行比较，来考虑完整模型的行为。最后，将移动边界位置和归一化药物释放的模型输出与文献中的实验数据进行比较。