Drug diffusion and release from a bioerodible spherical capsule

Controlled release of a drug contained in a spherical polymer capsule is of significant interest in many fields of medicine. There is growing interest in tailoring the erosion properties of the drug to help control and optimize the drug release process. Theoretical understanding of the nature of drug release from a bioerodible capsule is, therefore, important for designing effective drug delivery systems. While drug release from a fixed-radius capsule is relatively easier to model, the shrinking nature of a bioerodible capsule due to surface erosion presents several difficulties in theoretical modeling. This work presents a closed-form solution for the drug concentration distribution and drug delivery characteristics from a spherical capsule undergoing linear surface erosion. This problem is solved by a transformation that converts the moving boundary problem into a fixed boundary problem. For uniform initial drug distribution, the solution is shown to depend on a single non-dimensional parameter. The theoretical model is used to develop an understanding of the impact of varying the drug diffusion coefficient and rate of erosion on drug delivery characteristics. It is found that, in general, the nature of drug release in a bioerodible sphere is determined by a delicate balance between two simultaneously occurring processes - erosion and diffusion. This work improves the theoretical understanding of diffusion in drug delivery systems by accounting for the practical erosion phenomena, and may contribute towards the design and optimization of drug delivery systems.