Engineering Diffusion-Controlled Drug Delivery Systems to Achieve a Desired Drug Release Profile: Mathematical Modelling and Optimisation

OBJECTIVE: Drug delivery devices offer a promising strategy for the localized treatment of disease while minimising systemic side effects. However, designing diffusion-controlled systems to achieve a prescribed drug release profile remains a major challenge due to their inherently time-varying release rates. This study aims to develop a mathematical framework to enable the rational design of such systems to achieve desired therapeutic release profiles. METHODS: We develop a continuum-scale mathematical model describing diffusion-controlled drug release from a spherical microcapsule composed of a functionally graded polymer with spatially varying diffusivity and non-uniform initial drug distribution. These spatial design variables are parameterised using Bézier curves and identified via an inverse optimisation procedure based on a hybrid imperialist competitive algorithm. The framework is applied to two inverse design problems: (i) achieving near constant (zero-order) drug release over a specified time window, and (ii) reproducing prescribed release profiles defined by target checkpoints. RESULTS: The results show that a constant release rate can be achieved by tailoring the initial drug distribution while selecting an appropriate constant diffusivity. In contrast, more general release profiles require simultaneous optimisation of both spatially varying diffusivity and initial drug loading. CONCLUSIONS: The proposed framework demonstrates how mathematical modelling and optimisation can enable the rational design of diffusion-controlled drug delivery systems capable of producing tailored therapeutic release behaviours.