  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.
