# Drug delivery from microcapsules: how can we estimate the release time?

## TL;DR

This paper introduces two methods based on temporal moments to estimate drug release time from multi-layer spherical microcapsules, enabling quick comparison of different capsule designs without full simulations.

## Contribution

It presents novel moment-based approaches for predicting drug release times from multi-layer microcapsules, avoiding complex transient solution calculations.

## Key findings

- Both methods accurately estimate release times.
- Approaches are computationally inexpensive.
- Methods enable comparison of capsule configurations.

## Abstract

Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. 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 that provide useful indicators of 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 versus time curve 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 simple algebraic expressions involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) to characterize the release time 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 measure to compare \textit{a priori} the release time of different composite microcapsule configurations.