Drug delivery from multi-layer micro-capsules: how can we estimate the release time?

In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model. The first approach, which uses the zeroth and first temporal moments only, provides a crude approximation of the release time taking the form of a simple algebraic expression involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) while the second approach yields an asymptotic estimate of the release time that depends on consecutive higher moments. Through several test cases, we show that both approaches provide a computationally- cheap and useful tool to quantify the release time of composite microcapsule configurations.