Estimating the asymptotic characteristic time scales for diffusion-controlled drug release systems using partially sampled data

Abstract

Drug release experiments and numerical simulations only give access to partial release data (i.e., within a finite time range t∈[0,tf]). In this article, we propose fitting-based procedures to estimate the asymptotic time scales of the release process, namely the global relaxation time τ∗ and the longest (or terminal) relaxation time τ0, from partially sampled data of diffusion-controlled drug release systems. We test these procedures on both synthetic and experimental data using, as an example, the well-known Weibull function. Our results show that the Weibull function must be used with great care because the values of the fitting parameters can vary significantly depending on the ratio tf/τ0. Beyond their practical simplicity, the usefulness of our procedures is evidenced by the fact that: (1) the initial loading profile does not need to be known and (2) the chosen fitting function does not require any physical basis. These two advantages allow us to determine the diffusion coefficient of the molecules directly from the characteristic time τ0.