Total fraction of drug released from diffusion-controlled delivery systems with binding reactions

In diffusion-controlled drug delivery, it is possible for drug molecules to bind to the carrier material and never be released. A common way to incorporate this phenomenon into the governing mechanistic model is to include an irreversible first-order reaction term, where drug molecules become permanently immobilised once bound. For diffusion-only models, all the drug initially loaded into the device is released, while for reaction-diffusion models only a fraction of the drug is ultimately released. In this short paper, we show how to calculate this fraction for several common diffusion-controlled delivery systems. Easy-to-evaluate analytical expressions for the fraction of drug released are developed for monolithic and core-shell systems of slab, cylinder or sphere geometry. The developed formulas provide analytical insight into the effect that system parameters (e.g. diffusivity, binding rate, core radius) have on the total fraction of drug released, which may be helpful for practitioners designing drug delivery systems.Comment: 10 pages, 5 figure

Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [Appl. Math. Model., 46:450-464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work.Comment: 24 pages, 8 figures, accepted version of paper published in Applied Mathematics and Computatio

On the equivocal nature of the mass absorption curves

The idea behind the research presented is based upon apparently contradictory experimental results obtained here by means of photoacoustics modalities for the same drug donor/acceptor membrane system, serving as a surrogate for a transdermal delivery system. The first modality allowed for the monitoring of the total amount of mass uptake (m(t)-type data), while the second technique allowed for the quantification of time-dependent concentration distribution within the acceptor membrane (c(x,t)-type data). Despite of a very good agreement between the m(t) data and the 1st-order uptake fitting model (standard Fickian diffusion with constant source boundary condition), the standard approach failed during the c(x,t) data analysis. The results led to the analysis of the interfacial transfer contribution to the overall mass transfer efficiency, which eventually allowed to question reliability of the m(t) data analysis for the determination and quantification of the mass transport parameters. A more detailed analysis of the c(x,t) by means of the newly introduced transport rate number parameter revealed, that the mass uptake by the acceptor is almost equally influenced by interfacial and bulk transport processes. The analyses performed were translated into a model-free characteristic times, i.e. parameters common for any of the model scheme used.Comment: 31 pages total, 10figs including 3 in the supplementary materials sectio