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Mathematical Modeling of Release Kinetics from Supramolecular Drug Delivery Systems

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Department of Applied Mathematics and Biostatistics, Faculty of Pharmacy, “Carol Davila” University of Medicine and Pharmacy, Bucharest 020956, Romania
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Department of Clinical Pharmacology, Toxicology and Psychopharmacology, Faculty of Medicine, “Carol Davila” University of Medicine and Pharmacy, Bucharest 020021, Romania
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Department of Physical and Colloidal Chemistry, Faculty of Pharmacy, “Carol Davila” University of Medicine and Pharmacy, Bucharest 020956, Romania
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Department of Pharmacy, G. D’Annunzio University of Chieti–Pescara, Chieti 66100, Italy
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Department of Clinical and Experimental Medicine, “Magna Græcia” University of Catanzaro, 88100 Germaneto (CZ), Italy
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Department of Health Sciences, School of Pharmacy, “Magna Græcia” University of Catanzaro, 88100 Germaneto (CZ), Italy
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Department of Applied Mathematics and Biostatistics, Titu Maiorescu University, Bucharest 004051, Romania
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Department of Biopharmacy and Pharmacokinetics, Titu Maiorescu University, Bucharest 004051, Romania
*
Author to whom correspondence should be addressed.
Pharmaceutics 2019, 11(3), 140; https://doi.org/10.3390/pharmaceutics11030140
Received: 31 January 2019 / Revised: 7 March 2019 / Accepted: 18 March 2019 / Published: 21 March 2019
Embedding of active substances in supramolecular systems has as the main goal to ensure the controlled release of the active ingredients. Whatever the final architecture or entrapment mechanism, modeling of release is challenging due to the moving boundary conditions and complex initial conditions. Despite huge diversity of formulations, diffusion phenomena are involved in practically all release processes. The approach in this paper starts, therefore, from mathematical methods for solving the diffusion equation in initial and boundary conditions, which are further connected with phenomenological conditions, simplified and idealized in order to lead to problems which can be analytically solved. Consequently, the release models are classified starting from the geometry of diffusion domain, initial conditions, and conditions on frontiers. Taking into account that practically all solutions of the models use the separation of variables method and integral transformation method, two specific applications of these methods are included. This paper suggests that “good modeling practice” of release kinetics consists essentially of identifying the most appropriate mathematical conditions corresponding to implied physicochemical phenomena. However, in most of the cases, models can be written but analytical solutions for these models cannot be obtained. Consequently, empiric models remain the first choice, and they receive an important place in the review. View Full-Text
Keywords: boundary conditions; diffusion equation; drug carriers; release kinetics boundary conditions; diffusion equation; drug carriers; release kinetics
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MDPI and ACS Style

Mircioiu, C.; Voicu, V.; Anuta, V.; Tudose, A.; Celia, C.; Paolino, D.; Fresta, M.; Sandulovici, R.; Mircioiu, I. Mathematical Modeling of Release Kinetics from Supramolecular Drug Delivery Systems. Pharmaceutics 2019, 11, 140.

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