Vol. 8, No. 4, 2020

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Models for drug release of gentamicin in a polylactic acid matrix

Anna S. Morozova, Elena N. Vilchevskaya, Wolfgang H. Müller and Nikolay M. Bessonov

Vol. 8 (2020), No. 4, 307–320
DOI: 10.2140/memocs.2020.8.307

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.

diffusion parameter identification, drug release, diffusion models, finite volumes
Mathematical Subject Classification
Primary: 60K50
Received: 30 April 2020
Revised: 6 July 2020
Accepted: 28 September 2020
Published: 9 November 2020

Communicated by Francesco dell'Isola
Anna S. Morozova
Peter the Great Saint Petersburg Polytechnic University
Saint Petersburg
Elena N. Vilchevskaya
Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences
Saint Petersburg
Wolfgang H. Müller
Fachgebiet Kontinuumsmechanik und Materialtheorie
Institut für Mechanik
Technische Universität Berlin
Nikolay M. Bessonov
Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences
Saint Petersburg