Modelling functionalized drug release for a spherical capsule

TL;DR

This paper develops a generalized reaction-diffusion model for spherical drug-releasing FGMs, providing analytical solutions that enable continuous control of drug release rates between homogeneous and layered configurations.

Contribution

It introduces a flexible heterogeneous model with analytical solutions for drug release, extending previous models to arbitrary spatially-variable coefficients.

Findings

The model offers closed-form expressions for drug concentration and release profiles.

The release rate can be continuously tuned between fast and slow regimes.

Analytical solutions facilitate design of customizable drug delivery systems.

Abstract

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.