Mathematical modelling of drug release from a porous granule

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.