Abstract

Recent experiments by Macha et al. (Front. Bioeng. Biotech. 7 (2019), art. id. 37) on the release of gentamicin embedded in a polylactic acid matrix film immersed in a body fluid solution have shown, first, a sudden burst phenomenon after several weeks and, second, a premature end to the release, such that a considerable amount of gentamicin is kept in the matrix. It is shown that such phenomena cannot be described adequately by assuming diffusion of the Fickian kind. In order to improve the modeling, extensions to Fickian diffusion are proposed as follows. The first one is of a phenomenological nature. A production term in the diffusion equation with intrinsic parameters is introduced, all of which can be interpreted intuitively and related to experimental data. The model allows one to capture the aforementioned departure from the timewise parabolic Fickian release characteristic eventually leading to complete release. Second, a micromodel is presented that provides a physical explanation for the proposed production: the drug is released from a carrier particle into the matrix, which eventually comes to an end due to the diminishing particle surface, and the drug adheres to a core due to surface tension. The material parameters of both models are determined by inverse analysis of experimental data.

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