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Mathematical modeling of anomalous diffusive behavior in transdermal drug-delivery including time-delayed flux concept

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  • Čukić, Milena
  • Galovic, Slobodanka

Abstract

Molecular transport through a composite multilayer membrane is a central process in transdermal drug delivery (TDD). Classical Fickean approach treats skin as a pseudo-homogenous membrane, while in reality skin is highly heterogeneous system as shown in basic physiological research. Particle transport across such systems shows anomalous diffusive behavior that is described by fractional models. These models don't consider experimentally observed dependence of particle transport nature on time scale. The possible way of inclusion of that observation in model of transdermal transport is presented in this paper. The generalized fractional models of the spectral functions of the concentration profile and the cumulative amount of the drug absorbed through the bloodstream are derived. The derived model predicts resonances in concentration profile and larger cumulative amount of the drug in both the short-time limit and the long-time limit, which can have significant physiological implications.

Suggested Citation

  • Čukić, Milena & Galovic, Slobodanka, 2023. "Mathematical modeling of anomalous diffusive behavior in transdermal drug-delivery including time-delayed flux concept," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s096007792300485x
    DOI: 10.1016/j.chaos.2023.113584
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    References listed on IDEAS

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    1. Caputo, Michele & Cametti, Cesare & Ruggero, Vittorio, 2008. "Time and spatial concentration profile inside a membrane by means of a memory formalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2010-2018.
    2. W. He & H. Song & Y. Su & L. Geng & B. J. Ackerson & H. B. Peng & P. Tong, 2016. "Dynamic heterogeneity and non-Gaussian statistics for acetylcholine receptors on live cell membrane," Nature Communications, Nature, vol. 7(1), pages 1-8, September.
    3. Zhiwei Ding & Ke Chen & Bai Song & Jungwoo Shin & Alexei A. Maznev & Keith A. Nelson & Gang Chen, 2022. "Observation of second sound in graphite over 200 K," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    4. Minho S. Song & Hyungseok C. Moon & Jae-Hyung Jeon & Hye Yoon Park, 2018. "Neuronal messenger ribonucleoprotein transport follows an aging Lévy walk," Nature Communications, Nature, vol. 9(1), pages 1-8, December.
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