Can we assign an upper limit to skin permeability?

A microscopic multiphase diffusion model of viable epidermis permeability

A microscopic model of passive transverse mass transport of small solutes in the viable epidermal layer of human skin is formulated on the basis of a hexagonal array of cells (i.e., keratinocytes) bounded by 4-nm-thick, anisotropic lipid bilayers and separated by 1-μm layers of extracellular fluid. Gap junctions and tight junctions with adjustable permeabilities are included to modulate the transport of solutes with low membrane permeabilities. Two keratinocyte aspect ratios are considered to represent basal and spinous cells (longer) and granular cells (more flattened). The diffusion problem is solved in a unit cell using a coordinate system conforming to the hexagonal cross section, and an efficient two-dimensional treatment is applied to describe transport in both the cell membranes and intercellular spaces, given their thinness. Results are presented in terms of an effective diffusion coefficient, D¯(epi), and partition coefficient, K¯(epi/w), for a homogenized representation of the microtransport problem. Representative calculations are carried out for three small solutes-water, L-glucose, and hydrocortisone-covering a wide range of membrane permeability. The effective transport parameters and their microscopic interpretation can be employed within the context of existing three-layer models of skin transport to provide more realistic estimates of the epidermal concentrations of topically applied solutes.

Analysis, Interpretation, and Extrapolation of Dermal Permeation Data Using Diffusion-Based Mathematical Models

New dermal penetration data have been measured in both "infinite" and finite dose experiments on a range of compounds of varying lipophilicities. The data are analyzed, using parameter fitting, to determine the values of parameters governing the overall skin absorption processes. Two one-dimensional diffusion models are used. The first is novel, and well suited to the modeling of dermal uptake in occupational exposure scenarios. The second is an implementation of a model taken from the literature. The models are compared in a variety of exposure scenarios, and exhibit good mutual agreement. Both successfully reproduce expected features of the absorption process. Penetration parameters are determined by analyzing both infinite and finite dose data. Prediction of dermal absorption with finite dose scenarios is carried out and compared with experimental data obtained under these conditions. Parameters determined may also have an important role in improving the reliability of predictive QSARs used to estimate the extent of penetration of untested molecules.

A geometrical model of dermal capillary clearance

A new microscopic model is developed to describe the dermal capillary clearance process of skin permeants. The physiological structure is represented in terms of a doubly periodic array of absorbing capillaries. Convection-dominated transport in the blood flow within the capillaries is coupled with interstitial diffusion, the latter process being quantified via a slender-body-theory approach. Convection across the capillary wall and in the interstitial phase is treated as a perturbation which may be added to the diffusive transport. The model accounts for the finite permeability of the capillary wall as well as for the geometry of the capillary array, based on realistic values of physiological parameters. Calculated dermal concentration profiles for permeants having the size and lipophilicity of salicylic acid and glucose illustrate the power and general applicability of the model. Furthermore, validation of the model with published in vivo experimental results pertaining to human skin permeation of hydrocortisone is presented. The model offers the possibility for in-depth theoretical understanding and prediction of subsurface drug distribution in the human skin following topical application, as well as rates of capillary clearance into the systemic circulation. A simpler approach that treats the capillary bed as a homogeneously absorbing zone is also employed. The latter may be used in conjunction with the capillary exchange model to estimate measurable dermal transport and clearance parameters in a straightforward manner.

Dermal capillary clearance: physiology and modeling

Substances applied to the skin surface may permeate deeper tissue layers and pass into the body's systemic circulation by entering blood or lymphatic vessels in the dermis. The purpose of this review is an in-depth analysis of the dermal clearance/exchange process and its constituents: transport through the interstitium, permeability of the microvascular barrier and removal via the circulation. We adapt an 'engineering' viewpoint with emphasis on quantifying the dermal microcirculatory physiology, providing the theoretical framework for the physics of key transport processes and reviewing the available computational clearance models in a comparative manner. Selected experimental data which may serve as valuable input to modeling attempts are also reported.

Distributed diffusion-clearance model for transient drug distribution within the skin

Quantitative predictions of molecular transport rates through the skin are key to the development of topically applied and transdermally delivered drugs, as well as risk assessment associated with dermal exposure. Most research to date has focused on correlations for the permeability of the stratum corneum, and transient diffusion models that oversimplify vascular clearance processes in terms of a perfect-removal boundary condition at an artificially introduced lower boundary. Considerations of the spatially distributed nature and action of blood vessels have usually been limited to the steady-state case. This article describes a more comprehensive transient model of percutaneous absorption formulated in terms of volumetric dispersion and clearance coefficients reflecting the spatial distribution of vascular processes. The model was implemented through an analysis of published experimental results on in vivo permeation of salicylic acid (SA) in de-epidermized rat skin. With regard to the characterization of SA in rat dermis ("de") in vivo, it was found that: (i) SA is likely to have a dermal effective partition coefficient (relative to pH 7.4 aqueous buffer "pH7.4") around unity (K(de/pH7.4) = 0.9 +/- 0.3); (ii) vascular processes seem not to increase drug dispersion significantly beyond molecular diffusion [D(de) approximately (D(de))(mol) = (8 +/- 3) . 10(-7) cm(2) s(-1)]; and (iii) vascular clearance is characterized by a rate coefficient k(de) = (7 +/- 2) . 10(-4) s(-1). Application of a whole-skin variant of the model (including the stratum corneum and viable epidermis) allowed realistic predictions to be made of transient subsurface concentration levels after application from a finite dose.

Human Skin Permeation and Partition: General Linear Free‐Energy Relationship Analyses

Literature values of the permeability coefficient for permeation of human skin from water have been adjusted for ionization in water and adjusted for temperature. The obtained values of log K(p) for 119 solutes at 37 degrees C have been correlated with Abraham descriptors to yield an equation with R(2) = 0.832 and SD = 0.46 log units. Three separate test sets of 60 compounds had log K(p) predicted with an SD of 0.48 log units. The main factors that influence log K(p) are solute hydrogen bond basicity that lowers the permeability coefficient and solute volume that increases the permeability coefficient. Human skin-water partition coefficients, as log K(sc), have been collected for 45 compounds and yield an equation with R(2) = 0.926 and SD = 0.22 log units. We have compared the log K(p) equation to equations for various other processes, but have found no process that appears to be similar to that for skin permeation. The nearest process to skin-water partition is the isobutanol-water partition system. An equation for lateral diffusion in the stratum corneum is shown to be reasonably close to various diffusion-related processes.

Mechanistic and empirical modeling of skin permeation of drugs

The skin forms a barrier to the external environment, maintaining body fluids within our system and excluding harmful substances, while the skin is a site of administration of drugs for topical and systemic chemotherapy. It is an important issue to predict the rate at which drugs or other xenobiotics penetrate the skin. In this article, we review modeling approaches for predicting skin permeation of compounds, including both mechanistic and empirical approaches. Mechanistic approaches can give us much information on understanding of skin permeation of the compounds, such as structure-permeability relationship, contribution of each barrier step, mechanism of penetration enhancers, and in vivo-in vitro relationship. On the other hand, empirical modeling can overcome any inaccuracies of mechanistic models caused by the existence of uncertainties and, therefore, give us better predictions from the practical point of view. Artificial neural networks are being available for empirical modeling of complex skin transport phenomenon.

Pharmacokinetic models of dermal absorption

Many studies have used pharmacokinetic (compartment) models for skin to predict or analyze dermal absorption of chemicals. Comparing these models is difficult because the relationships between rate constants and the physicochemical parameters were not always defined clearly, simplifying assumptions built into models sometimes were not stated, and which skin layers were included often were not specified. In this paper we review and compare published one- and two-compartment models for which rate constants were expressed in terms of the physicochemical and physical properties of the skin (i.e., diffusion coefficients, partition coefficients and thickness). Nine one-compartment and two two-compartment models are presented with a consistent nomenclature and clearly defined assumptions. In addition, methods used for estimating the physicochemical parameters required by the various are summarized. These eleven compartment models are compared with calculations from a two-membrane skin model that corresponds better with skin function. Many of the compartment models do not predict key characteristics of the two-membrane skin model, especially the effect of blood flow on skin concentration and penetration rates, even when the same input parameters were used. The compartment models developed by Kubota and by McCarley are better predictors of the two-membrane model results, because these models were developed to match characteristics of the membrane model.

A predictive algorithm for skin permeability: the effects of molecular size and hydrogen bond activity

PURPOSE

To develop a predictive algorithm of nonelectrolyte transport through skin based upon a partitioning-diffusion model.

METHODS

Drug permeability is described by a partitioning-diffusion equation. Through free-energy relationships, partitioning is related to the drug's molecular volume (MV), and hydrogen bond donor (Hd) and acceptor (Ha) activity. Diffusion is related to the drug's MV using a theory of diffusion through lipid lamellae based on free-volume fluctuations within the lipid domain. These two explicit descriptions are combined to give an equation describing permeability in terms of the permeant's physical properties. The aqueous permeability coefficients of 37 nonelectrolytes through human epidermis were evaluated as a function of these physical properties using a multiple regression analysis.

RESULT

The results of the regression analysis show that 94% of the variability in the data can be explained by a model which includes only the permeant's MV, Hd and Ha. These results further provide an algorithm to predict skin permeability based upon the values of these parameters. In addition, the relative contribution of various chemical functional groups (e.g., -COOH) is derived, and can be used to predict skin transport from drug structure alone.

CONCLUSIONS

A biophysically relevant model of drug transport through human skin is derived based solely on the physical properties of the drug. The model provides an algorithm to predict permeability from the drug's structure and/or physical properties. Moreover, the model is applicable to a number of lipid barrier membranes, suggesting a common transport mechanism in all.

Estimating skin permeation. The validation of five mathematical skin permeation models

This study provides an analysis of the reliability of five mathematical models, simulating permeation of substances through the skin from aqueous solutions. An extensive database was generated, containing data on 123 measured permeation coefficients of 99 different chemicals and their physicochemical properties. In addition, in this database all relevant experimental conditions are included. The coefficients of the different skin permeation models were estimated by non-linear multiple regression, using the octanol-water partition coefficient and the molecular weight as independent parameters. The reliability of the models was evaluated by testing variation of regression coefficients and of residual variance for subsets of data, randomly selected from the complete database. Three models were considered to provide reliable estimations of the skin permeation coefficient. These are based on the McKone and Howd model, the Guy and Potts model and the Robinson model. The last-mentioned two models were adaptations, because MW0.5 as independent parameter provided a better fit than MW (MW = molecular weight) in the original models. The McKone and Howd model and the Robinson model have the advantage, that they predict more precisely the skin permeation of highly hydrophilic and highly lipophilic chemicals compared to the Guy and Potts model. The revised Robinson model resulted always in the smallest residual variance.