A study on structural and diffusion properties of porcine stratum corneum based on very small angle neutron scattering data

Transdermal and lateral effective diffusivities for drug transport in stratum corneum from a microscopic anisotropic diffusion model

This paper presents a computational model of molecular diffusion through the interfollicular stratum corneum. Specifically, it extends an earlier two-dimensional microscopic model for the permeability in two ways: (1) a microporous leakage pathway through the intercellular lipid lamellae allows slow permeation of highly hydrophilic permeants through the tissue; and (2) the model yields explicit predictions of both lateral (D‾_‖^sc) and transdermal (D‾_⊥^sc) effective (average, homogenized) diffusivities of solutes within the tissue. We present here the mathematical framework for the analysis and a comparison of the predictions with experimental data on desorption of both hydrophilic and lipophilic solutes from human stratum corneum in vitro. Diffusion in the lipid lamellae is found to make the effective diffusivity highly anisotropic, with the predicted ratio D‾_‖^sc/D‾_⊥^sc ranging from 34-39 for fully hydrated skin and 150 to more than 1000 for partially hydrated skin. The diffusivities and their ratio are in accord with both experimental data and the results of mathematical analyses performed by others.

Surging footprints of mathematical modeling for prediction of transdermal permeability

In vivo skin permeation studies are considered gold standard but are difficult to perform and evaluate due to ethical issues and complexity of process involved. In recent past, a useful tool has been developed by combining the computational modeling and experimental data for expounding biological complexity. Modeling of percutaneous permeation studies provides an ethical and viable alternative to laboratory experimentation. Scientists are exploring complex models in magnificent details with advancement in computational power and technology. Mathematical models of skin permeability are highly relevant with respect to transdermal drug delivery, assessment of dermal exposure to industrial and environmental hazards as well as in developing fundamental understanding of biotransport processes. Present review focuses on various mathematical models developed till now for the transdermal drug delivery along with their applications.

Skin membrane electrical impedance properties under the influence of a varying water gradient

The stratum corneum (SC) is an effective permeability barrier. One strategy to increase drug delivery across skin is to increase the hydration. A detailed description of how hydration affects skin permeability requires characterization of both macroscopic and molecular properties and how they respond to hydration. We explore this issue by performing impedance experiments on excised skin membranes in the frequency range 1 Hz to 0.2 MHz under the influence of a varying gradient in water activity (aw). Hydration/dehydration induces reversible changes of membrane resistance and effective capacitance. On average, the membrane resistance is 14 times lower and the effective capacitance is 1.5 times higher when the outermost SC membrane is exposed to hydrating conditions (aw = 0.992), as compared to the case of more dehydrating conditions (aw = 0.826). Molecular insight into the hydration effects on the SC components is provided by natural-abundance (13)C polarization transfer solid-state NMR and x-ray diffraction under similar hydration conditions. Hydration has a significant effect on the dynamics of the keratin filament terminals and increases the interchain spacing of the filaments. The SC lipids are organized into lamellar structures with ∼ 12.6 nm spacing and hexagonal hydrocarbon chain packing with mainly all-trans configuration of the acyl chains, irrespective of hydration state. Subtle changes in the dynamics of the lipids due to mobilization and incorporation of cholesterol and long-chain lipid species into the fluid lipid fraction is suggested to occur upon hydration, which can explain the changes of the impedance response. The results presented here provide information that is useful in explaining the effect of hydration on skin permeability.

Neutron Radiation Tests about FeCr Slag and Natural Zeolite Loaded Brick Samples

Neutron shielding performances of new brick samples are investigated. Brick samples including 10, 20, and 30 percentages of ferrochromium slag (FeCr waste) and natural zeolite are prepared and mechanical properties are obtained. Total macroscopic cross sections are calculated by using results of 4.5 MeV neutron transmission experiments. As a result, neutron shielding capacity of brick samples increases with increasing FeCr slag and natural zeolite percentages. This information could be useful in the area of neutron shielding.

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.

Application of numerical methods for diffusion-based modeling of skin permeation

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.

Detailed modeling of skin penetration--an overview

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.

Computational modeling of the skin barrier

A simulation environment for the numerical calculation of permeation processes through human skin has been developed. In geometry models that represent the actual cell morphology of stratum corneum (SC) and deeper skin layers, the diffusive transport is simulated by a finite volume method. As reference elements for the corneocyte cells and lipid matrix, both three-dimensional tetrakaidecahedra and cuboids as well as two-dimensional brick-and-mortar models have been investigated. The central finding is that permeability and lag time of the different membranes can be represented in a closed form depending on model parameters and geometry. This allows a comparison of the models in terms of their barrier effectiveness at comparable cell sizes. The influence of the cell shape on the barrier properties has been numerically demonstrated and quantified. It is shown that tetrakaidecahedra in addition to an almost optimal surface-to-volume ratio also has a very favorable barrier-to-volume ratio. A simulation experiment was successfully validated with two representative test substances, the hydrophilic caffeine and the lipophilic flufenamic acid, which were applied in an aqueous vehicle with a constant dose. The input parameters for the simulation were determined in a companion study by experimental collaborators.

In-silico model of skin penetration based on experimentally determined input parameters. Part II: Mathematical modelling of in-vitro diffusion experiments. Identification of critical input parameters

This work describes a framework for in-silico modelling of in-vitro diffusion experiments illustrated in an accompanying paper [S. Hansen, A. Henning, A. Naegel, M. Heisig, G. Wittum, D. Neumann, K.-H. Kostka, J. Zbytovska, C.M. Lehr, U.F. Schaefer, In-silico model of skin penetration based on experimentally determined input parameters. Part I: experimental determination of partition and diffusion coefficients, Eur. J. Pharm. Biopharm. 68 (2008) 352-367 [corrected] A mathematical model of drug permeation through stratum corneum (SC) and viable epidermis/dermis is presented. The underlying geometry for the SC is of brick-and-mortar character, meaning that the corneocytes are completely embedded in the lipid phase. The geometry is extended by an additional compartment for the deeper skin layers (DSL). All phases are modelled with homogeneous diffusivity. Lipid-donor and SC-DSL partition coefficients are determined experimentally, while corneocyte-lipid and DSL-lipid partition coefficients are derived consistently with the model. Together with experimentally determined apparent lipid- and DSL-diffusion coefficients, these data serve as direct input for computational modelling of drug transport through the skin. The apparent corneocyte diffusivity is estimated based on an approximation, which uses the apparent SC- and lipid-diffusion coefficients as well as corneocyte-lipid partition coefficients. The quality of the model is evaluated by a comparison of concentration-SC-depth-profiles of the experiment with those of the simulation. Good agreements are obtained, and by an analysis of the underlying model, critical parameters of the models can be identified more easily.

Fatty acid interdigitation in stratum corneum model membranes: a neutron diffraction study

The influence of the chain length of the free fatty acid (FFA) in a stratum corneum (SC) lipid model membrane composed of N-(alpha-hydroxyoctadecanoyl)-phytosphingosine (CER [AP]), cholesterol (Ch), FFA and cholesterol sulphate (ChS) was investigated by neutron diffraction. The internal nanostructure of the SC lipid membrane in addition to the water distribution function was determined via calculation of the neutron scattering length density profile (Fourier profile). The Fourier profiles of the studied SC model membranes revealed that such membranes have a repeat distance approximately equal to the membrane thickness. Increasing the chain length of the FFA in the CER[AP] based model membrane did not cause an alteration of the internal nanostructure but led to a decrease in the membrane repeat distance from 45.6 angstroms (palmitic acid, C16:0) to 43.7 angstroms (cerotic acid, C26:0) due to a partial interdigitation of the FFA chains. Ceramide [AP] forces the long chain fatty acids to incorporate into the unchanged spacing of the bilayer, thereby obligating the FFA protrude partly through opposing leaflet. Furthermore, the longer chained free fatty acids tend to form a new separate so-called "fatty acid rich phase". Therefore, the elongation of the chain length of the FFA decreases the solubility of the FFA in the SC model membrane based on CER[AP].

Properties of ceramides and their impact on the stratum corneum structure. Part 2: stratum corneum lipid model systems

The stratum corneum (SC) represents the outermost layer of the mammalian skin, exhibits the main skin barrier and plays an important role in the water penetration pathway through the SC. Knowing the structure and properties of the SC at the molecular level is essential for studying drug penetration through the SC and for the development of new dermal drug delivery systems. Therefore, research interest is focused on the SC lipid matrix and on water diffusion through it. Thus, the ultimate aim is to design a lipid mixture that mimics the barrier properties of the human SC to a high extent and that can substitute the SC in drug delivery systems. This review summarizes various studies performed on either isolated animal or human ceramide based SC model systems, coming to the result that using synthetic lipids with a well-defined architecture allows good extrapolation to the in vivo situation. This review is the continuation of part 1 that is focused on a detailed description of the thermotropic and/or lyotropic phase behaviour of single ceramide types obtained by various experimental techniques. The objective of part 2 is to reflect the numerous studies on SC lipid model systems, namely binary, ternary and multicomponent systems, during the last decade. In this context, neutron diffraction as a prospective tool for analyzing the internal membrane structure is addressed in particular. Based on these new insights, current SC models are presented, whose validations are still under discussion. A profound knowledge about SC lipid organization at the molecular level is still missing.

A multiphase microscopic diffusion model for stratum corneum permeability. II. estimation of physicochemical parameters, and application to a large permeability database

The full parameterization for the stratum corneum biphasic microtransport model presented previously in this Journal [95:620-648 (2006)] is developed through a combination of fundamental transport theory and calibration with existing data. Of the five microscopic transport properties, four (D(cor), K(cor/w), D(lip), K(lip/w)) are developed from sources independent of the existing steady-state permeability database. The fifth parameter, k(trans) (the mass transfer coefficient for transbilayer hopping), is derived from a fit of the model to the permeability data according to a modified free surface area function of the form log(10) k(trans) = A-B x (MW)(1/3). Examination of the experimental data in terms of the two dimensionless groups, R and sigma, arising from the analysis leads to the conclusion that SC permeation for most compounds is dominated by the transcellular pathway regardless of their lipophilicity, a striking departure from recent skin permeability models. Overall fit of the developed model(s) to the permeability data is somewhat better than for the Potts-Guy equation and variants thereof; however, marked improvement is seen in the estimation of lag times and the related potential for predicting skin hydration effects and transient skin permeation profiles. Simple approximations to the full numerical solution are presented that allow the developed model(s) to be implemented on a spreadsheet.

Thermodynamics of water interaction with human stratum corneum I: measurement by isothermal calorimetry

A thermodynamic study of water interaction with human stratum corneum (SC) is presented. The procedure consisted of conjoint water vapor sorption and heat flow measurements. Heat of sorption of water in excised human SC at various relative humidities was measured in an isothermal calorimeter at 32 degrees C using back and thigh skin from three different donors. These measurements, combined with the gravimetric sorption isotherm, were used to calculate the integral and differential enthalpies and entropies associated with binding of water to SC. Differential enthalpy values suggest hydrogen-bonding interactions similar to those for water in wool keratin. The changes in differential enthalpy and entropy with increasing water content followed a pattern similar to that seen in wool and other hydrophilic polymers. The results are partially interpreted in terms of a BET isotherm with monolayer volume v(m) = 0.022 g H(2)O/g dry SC and binding parameter C = 6.5 x 10(8).

A multiphase microscopic diffusion model for stratum corneum permeability. I. Formulation, solution, and illustrative results for representative compounds

A two-dimensional microscopic transport model of the stratum corneum (SC) incorporating corneocytes of varying hydration and permeability embedded in an anisotropic lipid matrix is presented. Results are expressed in terms of a dimensionless permeability (P(SC/w)(comp), which is a function of two dimensionless parameters, R and sigma. R is a ratio of transbilayer to lateral molecular flows within a lipid bilayer and sigma is the ratio of (lateral) permeability in the lipid phase, D(lip)K(lip/w), to that in the corneocyte phase, D(cor)K(cor/w.) The shape of the dimensionless permeability surface is also governed by the arrangement of the SC lipids, where Model 1 represents the extreme in which lipid-phase transport can occur with no transbilayer transport, whereas Model 2 entails maximum transbilayer transport. Model calculations are exemplified by characterizing the skin permeability of four representative permeants: water, ethanol, nicotinamide, and testosterone. A comparison with experimental steady state permeability and partition data supports that the transport properties of the SC lipids are highly anisotropic, with lateral diffusivities several orders of magnitude higher than the equivalent diffusivity calculated from transbilayer hopping. Nevertheless, the calculations suggest that corneocyte-phase transport plays a major role for all four permeants. These results confirm our previous calculations on water permeability and present a marked contrast to the commonly stated doctrine that the SC transport pathway is primarily intercellular.

A Two-Phase Analysis of Solute Partitioning into the Stratum Corneum

An analysis is presented of partition coefficients K(SC/w) describing solute distribution into fully hydrated stratum corneum (SC) from dilute aqueous solution (w). A comprehensive database is compiled from the experimental literature covering more than eight decades in the octanol/water partition coefficient K(o/w). It is analyzed according to a two-phase model following that of Anderson, Raykar, and coworkers (1988, 1989), which accounts for uptake by intercellular lipid and corneocyte (keratin plus water) phases having inherently different lipophilicities, as characterized by an SC lipid/water partition coefficient K(lip/w) and a partition coefficient PC(pro/w) quantifying cornoeocyte-phase binding. Regression of 72 data points yields useful best-fit recalibrations of power laws (or linear free energy relationships) giving K(lip/w) and PC(pro/w) as functions of K(o/w). The specific conclusions of the analysis are as follows: (i) The two-phase model offers substantial improvements over previously proposed analytical representations of K(SC/w), yielding an rms error in log(10)K(SC/w) of 0.30 limited by the scatter in the data. (ii) The best-fit description of the lipid phase is given by the power law K(lip/w) = 0.43 (K(o/w))(0.81), suggesting about half the absolute value of K(lip/w) relative to previous estimates. (iii) The best-fit description of corneocyte-phase binding differs negligibly from the correlation found by Anderson, Raykar, and coworkers for the more limited set of compounds studied by them. Explicit consideration of the two-phase nature of the SC also furnishes a rational basis for predicting the effects of varying hydration state upon K(SC/w).

New insights into the structure and hydration of a stratum corneum lipid model membrane by neutron diffraction

The structure and hydration of a stratum corneum (SC) lipid model membrane composed of N-(alpha-hydroxyoctadecanoyl)-phytosphingosine (CER6)/cholesterol (Ch)/palmitic acid (PA)/cholesterol sulfate (ChS) were characterized by neutron diffraction. The neutron scattering length density across the SC lipid model membrane was calculated from measured diffraction peak intensities. The internal membrane structure and water distribution function across the bilayer were determined. The low hydration of the intermembrane space is a major feature of the SC lipid model membrane. The thickness of the water layer in the SC lipid model membrane is about 1 A at full hydration. For the composition 55% CER6/25% Ch/15% PA/5% ChS, in a partly dehydrated state (60% humidity) and at 32 degrees C, the lamellar repeat distance and the membrane thickness have the same value of 45.6 A . The hydrophobic region of the membrane has a thickness of 31.2 A . A decrease of the Ch content increases the membrane thickness. The water diffusion through the SC lipid model multilamellar membrane is a considerably slow process relative to that through phospholipid membranes. In excess water, the membrane hydration follows an exponential law with two characteristic times of 93 and 44 min. At 81 degrees C and 97% humidity, the membrane separates into two phases with repeat distances of 45.8 and 40.5 A . Possible conformations of CER6 molecules in the dry and hydrated multilayers are discussed.

Lipid vesicles and other colloids as drug carriers on the skin

Colloids from an aqueous suspension can cross the skin barrier only through hydrophilic pathways. Various colloids have a different ability to do this by penetrating narrow pores of fixed size in the skin, or the relevant nano-pores in barriers modelling the skin. Such ability is governed by colloid adaptability, which must be high enough to allow penetrant deformation to the size of a pore in such barrier: for a 100 nm colloid trespassing the skin this means at least 5-fold deformation/elongation. (Lipid) Bilayer vesicles are normally more adaptable than the comparably large (lipid coated) fluid droplets. One of the reasons for this, and an essential condition for achieving a high bilayer adaptability and pore penetration, is a high bilayer membrane elasticity. The other reason is the relaxation of changing colloid's volume-to-surface constraint during pore penetration; it stands to reason that such relaxation requires a concurrent, but only transient and local, bilayer permeabilisation. Both these phenomena are reflected in bilayer composition sensitivity, which implies non-linear pressure dependency of the apparent barrier penetrability, for example. Amphipats that acceptably weaken a membrane (surfactants, (co)solvents, such as certain alcohols, etc.) consequently facilitate controlled, local bilayer destabilisation and increase lipid bilayer flexibility. When used in the right quantity, such additives thus lower the energetic expense for elastic bilayer deformation, associated with pore penetration. Another prerequisite for aggregate transport through the skin is the colloid-induced opening of the originally very narrow ( approximately 0.4 nm) gaps between cells in the barrier to pores with diameter above 30 nm. Colloids incapable of enforcing such widening-and simultaneously of self-adapting to the size of 20-30 nm without destruction-are confined to the skin surface. All relatively compact colloids seem to fall in this latter category. This includes mixed lipid micelles, solid (nano)particles, nano-droplets, biphasic vesicles, etc. Such colloids, therefore, merely enter the skin through the rare wide gaps between groups of skin cells near the organ surface. Transdermal drug delivery systems based on corresponding drug formulations, therefore, rely on simple drug diffusion through the skin; the colloid then, at best, can modulate drug transport through the barrier. In contrast, the adaptability-and stability-optimised mixed lipid vesicles (Transfersomes, a trademark of IDEA AG) can trespass much narrower pathways between most cells in the skin; such highly adaptable colloids thus mediate drug transport through the skin. Sufficiently stable ultra-adaptable carriers, therefore, can ensure targeted drug delivery deep below the application site. This has already been shown in numerous preclinical tests and several phase I and phase II clinical studies. Drug delivery by means of highly adaptable drug carriers, moreover, allows highly efficient and well-tolerated drug targeting into the skin proper. Sustained drug release through the skin into systemic blood circulation is another field of ultradeformable drug carrier application.

Visualization of the lipid barrier and measurement of lipid pathlength in human stratum corneum

Detailed models of solute transport through the stratum corneum (SC) require an interpretation of apparent bulk diffusion coefficients in terms of microscopic transport properties. Modern microscopy techniques provide a tool for evaluating one key property-lipid pathway tortuosity-in more detail than previously possible. Microscopic lipid pathway measurements on alkali expanded human SC stained with the lipid-soluble dyes methylene blue, Nile red, and oil red O are described. Brightfield, differential interference contrast, fluorescence, and laser scanning confocal optics were employed to obtain 2-dimensional (2-D) and 3-dimensional (3-D) images. The 2-D techniques clearly outlined the corneocytes. Confocal microscopy using Nile red yielded a well-delineated 3-D structure of expanded SC. Quantitative assessment of the 2-D images from a small number of expanded SC samples led to an average value of 3.7 for the ratio of the shortest lipid-continuous pathway to the width of the membrane. This was corrected for the effect of alkaline expansion to arrive at an average value of 12.7 for the same ratio prior to swelling.