Modelling functionalized drug release for a spherical capsule

Advances in material design has led to the rapid development of novel materials with increasing complexity and functions in bioengineering. In particular, functionally graded materials (FGMs) offer important advantages in various fields of application. In this work, we consider a heterogeneous reaction-diffusion model for an FGM spherical drug releasing system that generalizes the multi-layer configuration to arbitrary spatially-variable coefficients. Our model proposes a possible form for the drug diffusivity and reaction rate functions exhibiting fixed average material properties and a drug release profile that can be continuously varied between the limiting cases of a homogeneous system (constant coefficients) and two-layer system (stepwise coefficients). A hybrid analytical-numerical solution is then used to solve the model, which provides closed-form expressions for the drug concentration and drug release profiles in terms of generalized Fourier series. The resulting concentration and mass profiles show how the release rate can be controlled and continuously varied between a fast (homogeneous) and slow (two-layer) release.