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Advanced Drug Delivery Reviews (v.65, #2)
Modeling the human skin barrier — Towards a better understanding of dermal absorption
by Owen G. Jepps; Yuri Dancik; Yuri G. Anissimov; Michael S. Roberts (pp. 152-168).
Many drugs are presently delivered through the skin from products developed for topical and transdermal applications. Underpinning these technologies are the interactions between the drug, product and skin that define drug penetration, distribution, and elimination in and through the skin. Most work has been focused on modeling transport of drugs through the stratum corneum, the outermost skin layer widely recognized as presenting the rate-determining step for the penetration of most compounds. However, a growing body of literature is dedicated to considering the influence of the rest of the skin on drug penetration and distribution. In this article we review how our understanding of skin physiology and the experimentally observed mechanisms of transdermal drug transport inform the current models of drug penetration and distribution in the skin. Our focus is on models that have been developed to describe particular phenomena observed at particular sites of the skin, reflecting the most recent directions of investigation.Display Omitted
Keywords: Modeling; Human skin; Barrier; Dermal absorption; Transdermal drug transport; Transdermal penetration; Distribution
Mathematical and pharmacokinetic modelling of epidermal and dermal transport processes
by Yuri G. Anissimov; Owen G. Jepps; Yuri Dancik; Michael S. Roberts (pp. 169-190).
Topical delivery to the various regions of the skin and underlying tissues, transdermal drug delivery and dermal exposure to environmental chemicals are important areas of research. Mathematical models of epidermal and dermal transport, involving penetration of a solute through various layers of the skin, metabolism in the skin and its subsequent distribution and clearance into systemic circulation from underlying tissues, play an essential role in this research area and are reviewed in this work.Display Omitted
Keywords: Percutaneous drug delivery; Mathematical modelling
Detailed modeling of skin penetration—An overview
by Nagel Arne Naegel; Michael Heisig; Gabriel Wittum (pp. 191-207).
In recent years, the combination of computational modeling and experiments has become a useful tool that is proving increasingly powerful for explaining biological complexity. As computational power is increasing, scientists are able to explore ever more complex models in finer detail and to explain very complex real world data.This work provides an overview of one-, two- and three-dimensional diffusion models for penetration into mammalian skin. Besides diffusive transport this includes also binding of substances to skin proteins and metabolism. These models are based on partial differential equations that describe the spatial evolution of the transport process through the biological barrier skin.Furthermore, the work focuses on analytical and numerical techniques for this type of equations such as discretization schemes or homogenization (upscaling) techniques. Finally, the work compares different geometry models with respect to the permeability.A multi-scale representation of the skin as barrier.Display Omitted
Keywords: Abbreviations; RW; random walk; LT; Laplace transform; FD; finite difference; FE; finite element; FV; finite volume; IE; implicit Euler; RK; Runge–Kutta method; BDF; backward difference formula; TKD; tetrakaidekahedron; DON; donor; SC; stratum corneum; EPI; Epidermis; DER; Dermis; DSL; Deeper skin layers (viable epidermis/dermis); 1D; one-dimensional; 2D; two-dimensional; 3D; three-dimensional; PDE; partial differential equation; ODE; ordinary differential equation; w.r.t.; with respect toSkin; Stratum corneum; Geometry models; Brick-and-mortar; Cuboid; Tetrakaidekahedra; Mathematical modeling; Numerical simulation; Homogenization; Drug diffusion
Application of numerical methods for diffusion-based modeling of skin permeation
by H. Frederick Frasch; Ana M. Barbero (pp. 208-220).
The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions.Display Omitted
Keywords: Transdermal drug delivery; Stratum corneum; Unit cell problem; Finite difference method; Method of lines; Finite element method; Finite volume method; Random walk; Cellular automata; Smoothed particle hydrodynamics
Design and performance of a spreadsheet-based model for estimating bioavailability of chemicals from dermal exposure
by Yuri Dancik; Matthew A. Miller; Joanna Jaworska; Gerald B. Kasting (pp. 221-236).
A comprehensive transient model of chemical penetration through the stratum corneum, viable epidermis and dermis formulated in terms of an Excel™ spreadsheet and associated add-in is presented. The model is a one-dimensional homogenization of underlying microscopic transport models for stratum corneum and dermis; viable epidermis is treated as unperfused dermis. The model's salient features are a detailed structural description of the skin layers, a combination of first-principles based transport equations and empirical partition and diffusion coefficients, and the capability of simulating a variety of exposure scenarios. Model predictions are compared with representative in vitro skin permeation data obtained from the literature using as summary parameters total absorption ( Qabs), maximum flux ( Jmax) and skin permeability coefficient ( kp). The results of this evaluation demonstrate the current state-of-the-art in prediction of transient skin absorption and highlight areas in which further elaborations are needed to obtain satisfactory predictions.Display Omitted
Keywords: Transdermal drug transport; Stratum corneum (SC); Lipids; Corneocytes; Viable epidermis (VE); Dermis; Mathematical model
Breaching the skin barrier — Insights from molecular simulation of model membranes
by Rebecca Notman; Jamshed Anwar (pp. 237-250).
Breaching the skin's barrier function by design is an important strategy for delivering drugs and vaccines to the body. However, while there are many proposed approaches for reversibly breaching the skin barrier, our understanding of the molecular processes involved is still rudimentary. Molecular simulation offers an unprecedented molecular-level resolution with an ability to reproduce molecular and bulk level properties. We review the basis of the molecular simulation methodology and give applications of relevance to the skin lipid barrier, focusing on permeation of molecules and chemical approaches for breaching the lipid barrier by design. The bulk kinetic model based on Fick's Law describing absorption of a drug through skin has been reconciled with statistical mechanical quantities such as the local excess chemical potential and local diffusion coefficient within the membrane structure. Applications of molecular simulation reviewed include investigations of the structure and dynamics of simple models of skin lipids, calculation of the permeability of molecules in simple model membranes, and mechanisms of action of the penetration enhancers, DMSO, ethanol and oleic acid. The studies reviewed illustrate the power and potential of molecular simulation to yield important physical insights, inform and rationalize experimental studies, and to predict structural changes, and kinetic and thermodynamic quantities.Display Omitted
Keywords: Transdermal drug delivery; Percutaneous penetration; Skin lipids; Model membrane; Ceramides; Lipid bilayers; Computer modeling; Molecular dynamics simulation
Improved input parameters for diffusion models of skin absorption
by Steffi Hansen; Claus-Michael Lehr; Ulrich F. Schaefer (pp. 251-264).
To use a diffusion model for predicting skin absorption requires accurate estimates of input parameters on model geometry, affinity and transport characteristics. This review summarizes methods to obtain input parameters for diffusion models of skin absorption focusing on partition and diffusion coefficients. These include experimental methods, extrapolation approaches, and correlations that relate partition and diffusion coefficients to tabulated physico-chemical solute properties. Exhaustive databases on lipid–water and corneocyte protein–water partition coefficients are presented and analyzed to provide improved approximations to estimate lipid–water and corneocyte protein–water partition coefficients. The most commonly used estimates of lipid and corneocyte diffusion coefficients are also reviewed. In order to improve modeling of skin absorption in the future diffusion models should include the vertical stratum corneum heterogeneity, slow equilibration processes, the absorption from complex non-aqueous formulations, and an improved representation of dermal absorption processes. This will require input parameters for which no suitable estimates are yet available.Display Omitted
Keywords: Abbreviations; A; area; C; solute concentration; Cor; corneocyte; D; diffusion coefficient; Der; dermis; DMPC; dipalmitoyl phosphatidycholine; Epi; epidermis; f; hydro; hydrodynamic hindrance factor; f; steric; steric hindrance factor; h; thickness; J; ss; steady state flux; K; partition coefficient; k; B; Boltzman constant; k; off; desorption rate constant; k; on; adsorption rate constant; K; ow; octanol–water partition coefficient; k; P; permeability coefficient; K; pH; octanol–water distribution coefficient at a defined pH; K; SC/w; SC partition coefficient based on molar concentrations, defined as (moles of solute absorbed in the SC per unit volume of the hydrated SC)/(mol/volume solute concentration in the adjacent solution); k; trans; mass transfer coefficient; Lip; lipids; MV; the molar volume; MW; the molar weight; N; a; Avogadro's number; PC; intrinsic; SC partition coefficient based on mass ratio concentrations and dry SC weight, defined as (weight of solute absorbed in SC per unit weight of the original dry SC); /; (wt/wt solute concentration in the adjacent solution); PC; SC/w; partition coefficients based on weight ratio concentrations and hydrated SC weight, defined as (weight of solute absorbed in protein or lipid phase per unit weight of hydrated protein or lipid phase); /; (wt/wt solute concentration in the adjacent solution); Pro; protein; P; ^; S; C; /; w; comp; dimensionless SC permeability; Q; amount of solute diffusing across the skin membrane; QSA(P)R; quantitative structure activity (or permeability) relationship models; R; Resistance; r; solute radius assuming a spherical shape of the molecule; R; the ratio of trans-bilayer to lateral diffusivity; SC; stratum corneum; T; temperature; t; time period; t; lag; lag-time; γ; (; r; pore; )d; r; pore; pore size distribution as a function of pore radius; γ; e; Euler's constant; Δ; c; s; concentration gradient; η; 0; dynamic solvent viscosity; η; cor; dynamic viscosity of the corneocytes; ϑ; constant describing pore size distribution; λ; ratio of solute to keratin fiber radius; μ; constant describing pore size distribution; ν; are the weight fractions of water; ρ; density; σ; the ratio of lipid to corneocyte permeability; φ; cor; volume fractions of corneocytes; φ; lip; volume fractions of lipids; φ; pro; volume fractions of protein; ω; lip; weight fractions of lipids; ω; pro; weight fractions of proteinsPartition coefficient; Diffusion coefficient; Stratum corneum; Lipid bilayer; Keratin; Corneocyte
Predicting skin permeability from complex vehicles
by Daniela Karadzovska; James D. Brooks; Nancy A. Monteiro-Riviere; Jim E. Riviere (pp. 265-277).
It is now widely accepted that vehicle and formulation components influence the rate and extent of passive chemical absorption through skin. Significant progress, over the last decades, has been made in predicting dermal absorption from a single vehicle; however the effect of a complex, realistic mixture has not received its due attention. Recent studies have aimed to bridge this gap by extending the use of quantitative structure–permeation relationship (QSPR) models based on linear free energy relationships (LFER) to predict dermal absorption from complex mixtures with the inclusion of significant molecular descriptors such as a mixture factor that accounts for the physicochemical properties of the vehicle/mixture components. These models have been compiled and statistically validated using the data generated from in vitro or ex vivo experimental techniques. This review highlights the progress made in predicting skin permeability from complex vehicles.Display Omitted
Keywords: Chemical mixtures; Formulations; Percutaneous/dermal absorption; Quantitative structure–permeation relationship (QSPR); QSAR; Linear free energy relationships (LFER); Mixture factor; Topical drug delivery enhancers
Finite and infinite dosing: Difficulties in measurements, evaluations and predictions
by Dominik Selzer; Mona M.A. Abdel-Mottaleb; Tsambika Hahn; Schafer Ulrich F. Schaefer; Dirk Neumann (pp. 278-294).
Due to the increased demand for reliable data regarding penetration into and permeation across human skin, assessment of the absorption of xenobiotics has been gaining in importance steadily. In vitro experiments allow for determining these data faster and more easily than in vivo experiments. However, the experiments described in literature and the subsequent evaluation procedures differ considerably. Here we will give an overview on typical finite and infinite dose experiments performed in fundamental research and on the evaluation of the data. We will point out possible difficulties that may arise and give a short overview on attempts at predicting skin absorption in vitro and in vivo.Display Omitted
Keywords: Penetration; Permeation; Tape stripping; Concentration-depth profile; In vitro; In vivo
Recent advances in predicting skin permeability of hydrophilic solutes
by Longjian Chen; Lujia Han; Guoping Lian (pp. 295-305).
Understanding the permeation of hydrophilic molecules is of relevance to many applications including transdermal drug delivery, skin care as well as risk assessment of occupational, environmental, or consumer exposure. This paper reviews recent advances in modeling skin permeability of hydrophilic solutes, including quantitative structure–permeability relationships (QSPR) and mechanistic models. A dataset of measured human skin permeability of hydrophilic and low hydrophobic solutes has been compiled. Generally statistically derived QSPR models under-estimate skin permeability of hydrophilic solutes. On the other hand, including additional aqueous pathway is necessary for mechanistic models to improve the prediction of skin permeability of hydrophilic solutes, especially for highly hydrophilic solutes. A consensus yet has to be reached as to how the aqueous pathway should be modeled. Nevertheless it is shown that the contribution of aqueous pathway can constitute to more than 95% of the overall skin permeability. Finally, future prospects and needs in improving the prediction of skin permeability of hydrophilic solutes are discussed.Display Omitted
Keywords: Abbreviations; MSE; mean squared error; NMF; natural moisturizing factors; QSPR; Quantitative structure–permeability relationships; SC; stratum corneumAqueous porous pathway; Brick-and-mortar; Hydrophilic; Quantitative structure–permeability relationships; Skin permeability; Stratum corneum; Transdermal permeation
Predicting the absorption of chemical vapours
by Matias Rauma; Anders Boman; Gunnar Johanson (pp. 306-314).
The focus of this review is on the systemic absorption of vapours via skin, including experimental data as well as regression and pharmacokinetic models. Dermal contribution ratios (DCR), i.e. amount absorbed through skin relative to total intake (skin and inhalation) at specified conditions, could be identified or calculated from published data for 33 chemical vapours. The ratios vary from ~0.0002 (vinyl chloride) to ~0.8 (2-butoxyethanol), with hydrophilic chemicals having a higher ratio than lipophilic ones. Multiple regression analysis of these data suggests that the DCR is largely explained by the octanol:water partition coefficient, vapour pressure and molecular weight (R2=0.69). Several physiologically-based pharmacokinetic models were identified; however, all describe the absorption of single substances. Regarding predictive models, only two models were found. In conclusion, dermal uptake of chemical vapours needs more attention, as such exposures are common, data are scarce and few predictive models exist.Display Omitted
Keywords: Linear regression models; Predictive models; PBPK model; Organic solvents; Dermal to inhalation ratio; Dermal contribution ratio; DIR; DCR
Mathematical models to describe iontophoretic transport in vitro and in vivo and the effect of current application on the skin barrier
by Taís Gratieri; Yogeshvar N. Kalia (pp. 315-329).
The architecture and composition of the stratum corneum make it a particularly effective barrier against the topical and transdermal delivery of hydrophilic molecules and ions. As a result, different strategies have been explored in order to expand the range of therapeutic agents that can be administered by this route. Iontophoresis involves the application of a small electric potential to increase transport into and across the skin. Since current flow is preferentially via transport pathways with at least some aqueous character, it is ideal for hydrosoluble molecules containing ionisable groups. Hence, the physicochemical properties that limit partitioning and passive diffusion through the intercellular lipid matrix are beneficial for electrically-assisted delivery. The presence of fixed ionisable groups in the skin (pI 4–4.5) means that application of the electric field results in a convective solvent flow (i.e., electroosmosis) in the direction of ion motion so as to neutralise membrane charge. Hence, under physiological conditions, cation electrotransport is due to both electromigration and electroosmosis—their relative contribution depends on the formulation conditions and the physicochemical properties of the permeant. Different mathematical models have been developed to provide a theoretical framework in order to explain iontophoretic transport kinetics. They usually involve solutions of the Nernst–Planck equation – using either the constant field (Goldman) or electroneutrality (Nernst) approximations – with or without terms for the convective solvent flow component. Investigations have also attempted to elucidate the nature of ion transport pathways and to explain the effect of current application on the electrical properties of the skin—more specifically, the stratum corneum. These studies have led to the development of different equivalent circuit models. These range from simple parallel arrangements of a resistor and a capacitor to the inclusion of the more esoteric “constant phase element”; the latter provides a better mathematical description of the “non-ideal” behaviour of skin impedance. However, in addition to simply providing a “mathematical” fit of the observed data, it is essential to relate these circuit elements to biological structures present in the skin. More recently, attention has also turned to what happens when the permeant crosses the epidermis and reaches the systemic circulation and pharmacokinetic models have been proposed to interpret data from iontophoretic delivery studies in vivo. Here, we provide an overview of mathematical models that have been proposed to describe (i) the effect of current application on the skin and the implications for potential iontophoretic transport pathways, (ii) electrotransport kinetics and (iii) the fate of iontophoretically delivered drugs once they enter the systemic circulation.Display Omitted
Keywords: Iontophoresis; Transdermal delivery; Membrane transport models; Equivalent circuit; Skin; Pharmacokinetics
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