Finite dissolution-rate drug release: From a continuous-field description to a moving-boundary problem

In this paper, a previously established model for drug release from a matrix layer is revisited from both analytical and numerical perspectives. The model was originally formulated using a continuous-field description in terms of two transient, one-dimensional, partial differential equations (PDEs) - one each for dissolved and solid drug concentrations. The PDE for the former is of reaction–diffusion type, whilst in the latter there is reaction, but no diffusion. We demonstrate how the problem can be re-posed as a sequence of three sub-problems, the second of which constitutes an embedded moving-boundary (sharp interface) problem, whilst the other two are conventional fixed-boundary problems; nevertheless, the stopping time for the first problem and the starting time for the third problem are unknown and have to be determined as part of the solution. The model equations are solved numerically in three different ways using finite-element methods, with the novel contribution being the application of boundary immobilization techniques for the embedded sub-problem, in tandem with the use of asymptotic methods to give detailed information regarding the motion of moving front at its inception and just prior to its extinction. For the diffusion-limiting case, we also obtain a closed-form expression for the fraction of drug released as a function of time that cannot be obtained via a continuous-field formulation.