Diffusion through skin in the light of a fractional derivative approach: progress and challenges
- PDF / 1,512,265 Bytes
- 17 Pages / 595.276 x 790.866 pts Page_size
- 72 Downloads / 227 Views
REVIEW PAPER
Diffusion through skin in the light of a fractional derivative approach: progress and challenges Michele Caputo1 • Cesare Cametti2 Received: 3 May 2020 / Accepted: 24 August 2020 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This review is focussed on modelling the transport processes of different drugs across the intact human skin by introducing a memory formalism based on the fractional derivative approach. The fundamental assumption of the classic transport equation in the light of the Fick’s law is that the skin barrier behaves as a pseudo-homogeneous membrane and that its properties, summarized by the diffusion coefficient D, do not vary with time and position. This assumption does not hold in the case of a highly heterogeneous system as the skin is, whose outermost layer (the stratum corneum) is comprised of a multi-layered structure of keratinocytes embedded in a lamellar matrix of hydrophobic lipids, followed by the dermis that contains a network of capillaries that connect to the systemic circulation. A possible way to overcome these difficulties resides in the introduction of mathematical models which involve fractional derivatives to describe complex systems with interactions in space and time, following the model originally developed by Caputo in order to consider the memory effects in materials. Although the introduction of fractional derivatives to model memory effects is completely phenomenological, i.e., characterized by a single parameter, i.e., the fractional derivative order m; a number of authors have found that this approach can provide a better comparison to experimental data and that this technique may be alternative to integer-order derivative models. In this review, we aim to summarize some our recent results, concerning the transport of different diffusing compounds of different structural complexity across the intact skin. Keywords Drug diffusion Fractional derivatives Mathematical models of drug diffusion through skin
Introduction The penetration of drugs through intact human skin is a complex process of molecular diffusion across a composite multilayer membrane composed of the stratum corneum, that represents the outermost layer, and the epidermis and the dermis, each of them characterized by different structural and physico-chemical properties. While epidermis and dermis exert a barrier towards lipophilic compounds, stratum corneum, consisting of several layers of hydrated & Cesare Cametti [email protected] Michele Caputo [email protected] 1
College of Geosciences, Texas A&M University, College Station, USA
2
Department of Physics, University of Rome ‘‘La Sapienza’’, Rome, Italy
and keratinized cells, suspended in an extracellular lipid matrix, acts as an impermeable layer to most of drugs and other hydrophilic substances. This biological system, because of its structural organization, must be necessarily described, as far as the drug permeation is concerned, by a diffusion coefficient able to take into account the in
Data Loading...
