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 to 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.

Impact of solvent dry down, vehicle pH and slowly reversible keratin binding on skin penetration of cosmetic relevant compounds: I. Liquids.

To measure progress and evaluate performance of the newest UB/UC/P&G skin penetration model we simulated an 18-compound subset of finite dose in vitro human skin permeation data taken from a solvent-deposition study of cosmetic-relevant compounds (Hewitt et al., J. Appl. Toxicol. 2019, 1-13). The recent model extension involved slowly reversible binding of solutes to stratum corneum keratins. The selected subset was compounds that are liquid at skin temperature. This set was chosen to distinguish between slow binding and slow dissolution effects that impact solid phase compounds. To adequately simulate the physical experiments there was a need to adjust the evaporation mass transfer coefficient to better represent the diffusion cell system employed in the study. After this adjustment the model successfully predicted both dermal delivery and skin surface distribution of 12 of the 18 compounds. Exceptions involved compounds that were cysteine-reactive, highly water-soluble or highly ionized in the dose solution. Slow binding to keratin, as presently parameterized, was shown to significantly modify the stratum corneum kinetics and diffusion lag times, but not the ultimate disposition, of the more lipophilic compounds in the dataset. Recommendations for further improvement of both modeling methods and experimental design are offered.

A Framework for Incorporating Transient Solute-Keratin Binding Into Dermal Absorption Models.

Interpretation of experiments involving transient solute binding to isolated keratin substrates is analyzed and discussed in terms of their impact on transient permeation of topically-applied compounds through human stratum corneum. The analysis builds upon an earlier model (Nitsche and Frasch 2011 Chem Eng Sci 66:2019-41) by adding a second level of homogenization (ultrascopic-to-microscopic) prior to the microscopic-to-macroscopic conversion. Here "ultrascopic" refers to isolated keratin suspensions, "microscopic" to corneocyte interiors and "macroscopic" to tissue-averaged properties in the stratum corneum. Results are interpreted in the context of current parameterizations of the underlying ultrascopic binding parameters. The present analysis, which is limited to linear binding isotherms common in dilute solutions, reveals a maximum in the macroscopic forward binding rate constant as a function of solute lipophilicity, whereas the underlying equilibrium constant increases monotonically and the macroscopic reverse binding rate constant decreases monotonically. The size and location of the maximum depends upon the hydration state of the stratum corneum. Explicit equations expressing these findings allow both equilibrium and kinetic binding data in isolated keratins to be applied to the kinetics of transient absorption through the skin. They will enable more quantitative estimation of the long-recognized stratum corneum reservoir function.

Conclusions about osmotically inactive volume and osmotic fragility from a detailed erythrocyte model.

This paper develops a detailed model of human and bovine erythrocytes quantifying the dependence of total cell volume upon composition of an aqueous solution in which it is immersed. The cytoplasm is represented as an aqueous solution of hemoglobin and salt (KCl or NaCl). Model-based analysis of literature data on human erythrocytes, and of new experiments with bovine erythrocytes, leads to two findings. First, the Boyle-van't Hoff plot for human erythrocytes is found to be well described based on a solid volume fraction of âˆ¼0.3 in complete agreement with desiccation experiments. The linear portion of the calculated curve turns out to be numerically indistinguishable from the commonly used ideal model parameterized with an apparent osmotically inactive volume fraction of âˆ¼0.5. This mathematical outcome explains the longstanding perceived (but actually nonexistent) disconnect between the aforementioned fractions âˆ¼0.3 and âˆ¼0.5. A corollarial implication is that the actual volume fraction of osmotically nonparticipant (vicinal) water is very small (∼0.035). Second, an initial crenation of bovine erythrocytes (which occurs in classical techniques for measuring membrane permeability) is found to increase their fragility to an extent which correlates well with the crenated cell volume, and would affect the permeability determination.

Microscopic Models of Drug/Chemical Diffusion Through the Skin Barrier: Effects of Diffusional Anisotropy of the Intercellular Lipid.

Owing to the systematic alignment and ordering of fatty acid and ceramide chains, lipid layers in biological membranes have strongly anisotropic diffusion properties. The diffusivity D∥lip for solute transport in the direction parallel to the lipid layer is typically 103-105 times the diffusivity D⊥lip for the perpendicular direction. This article explores the consequences of this strong degree of anisotropy on solute diffusion through the stratum corneum (barrier) layer of the skin based on a realistic representation of a unit cell of the microstructure. Complementary numerical methods (smoothed particle hydrodynamics, finite differences) are used to solve the steady-state unit-cell diffusion problem leading to the average (homogenized, coarse-grained) diffusion tensor characterizing the tissue as an effective continuum. A parametric study is presented characterizing solute concentration profiles in detail for testosterone- and caffeine-like permeants, and it is shown that the results cannot be mimicked by calculations based on an isotropic lipid-phase diffusivity. The ratio of lateral to transdermal effective diffusivities calculated by the present model is of the order of 40 and 300 for fully hydrated (in vitro) and partially hydrated (in vivo) states, respectively. These values compare favorably with the results of recent experiments.

How Predictable Are Human Stratum Corneum Lipid/Water Partition Coefficients? Assessment and Useful Correlations for Dermal Absorption.

Partition coefficients between human stratum corneum lipids and water (Ksclip/w) are collected or deduced from a variety of sources in a manner that approximately doubles the available data compared to the current state-of-the-art model (Hansen et al., Adv Drug Deliv Rev. 2013;65(2):251-264). An additional datum for water itself in porcine SC that considerably extends the molecular size and lipophilicity range of the data set is considered. The data are analyzed in terms of an extended linear free energy relationship involving octanol/water partition coefficients, Abraham solvation parameters, and a secondary, power law molecular weight dependence. The optimum fit to log Ksclip/w for the full data set reduces the standard error of prediction from 0.50 for a Hansen-like model to 0.39; corresponding multiplicative errors in Ksclip/w are reduced from a factor of 3.1 to one of 2.5. The difference in performance is driven by the water datum, which requires a more complex dependence on molecular size than that afforded by Abraham parameters. In the absence of the water value, the Hansen-like model, which does not include a dependence on molecular size, is essentially optimum. A comparison is presented to fluid-phase phospholipid-water systems, which have a demonstrably different structure-property relationship.

A Universal Correlation Predicts Permeability Coefficients of Fluid- and Gel-Phase Phospholipid and Phospholipid-Cholesterol Bilayers for Arbitrary Solutes.

The permeability of gel-phase phospholipids is typically about an order of magnitude lower than that of the same compositions in the fluid phase, yet a quantitative description of the ordering factors leading to this difference has been elusive. The present analysis examines these factors with particular focus on the area per phospholipid chain, Ac, and its relationship to the minimum area per molecule in the crystalline state, A0. It is shown that fluid- and gel-phase phospholipid permeabilities can be reconciled by postulating a minimum area per chain Ac,0 = 17.1 Å(2), substantially less than one would estimate by dividing the accepted value A0 = 40.8 Å(2) by 2. An extended data set of phospholipid and phospholipid-cholesterol bilayer permeability data extending over 9 orders of magnitude is analyzed and correlated according to the developed relationship (N = 85, s = 0.3024, r(2) = 0.9332). Individual permeability values are consequently predicted to within an average deviation of 10(0.3024) or about a factor of 2. The analysis is broadly applicable in the fluid phase but is restricted to gel-phase phospholipid compositions that do not contain cholesterol. Guidance for the latter scenario is provided.

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.

Permeability of fluid-phase phospholipid bilayers: assessment and useful correlations for permeability screening and other applications.

Permeability data (P(lip/w) ) for liquid crystalline phospholipid bilayers composed of egg lecithin and dimyristoylphosphatidylcholine (DMPC) are analyzed in terms of a mathematical model that accounts for free surface area and chain-ordering effects in the bilayer as well as size and lipophilicity of the permeating species. Free surface area and chain ordering are largely determined by temperature and cholesterol content of the membrane, molecular size is represented by molecular weight, and lipophilicity of the barrier region is represented by the 1,9-decadiene/water partition coefficient, following earlier work by Xiang, Anderson, and coworkers. A correlating variable χ = MW(n) σ/(1 -σ) is used to link the results from different membrane systems, where different values of n are tried, and σ denotes a reduced phospholipid density. The group (1 -σ)/σ is a measure of free surface area, but can also be interpreted in terms of free volume. A single exponential function of χ is developed that is able to correlate 39 observations of P(lip/w) for different compounds in egg lecithin at low density, and 22 observations for acetic acid in DMPC at higher densities, spanning nine orders of magnitude to within an rms error for log 10 P(lip/w) of 0.20. The best fit found for n = 0.87 ultimately makes χ much closer to the ratio of molecular to free volumes than surface areas. The results serve as a starting point for estimating passive permeability of cell membranes to nonionized solutes as a function of temperature and cholesterol content of the membrane.

A correlation for 1,9-decadiene/water partition coefficients.

An important series of papers by Xiang, Anderson, and coworkers has established the strong correlation between phospholipid bilayer membrane permeability and the 1,9-decadiene/water partition coefficient over a wide range of compounds, elevating the importance of K(decadiene/w) as a predictor of molecular bioavailability. On the basis of a 58-point dataset developed by these authors, this research note develops an optimal correlation predicting log(10) K(decadiene/w) in terms of the octanol/water partition coefficient and four of the Abraham solvation parameters, namely A (hydrogen bond acidity), S (polarity/polarizability), E (excess molar refraction), and V (McGowan characteristic volume). The fitted dataset is described to within a root-mean-square error of 0.42, and the probable error in making a prediction for a compound not present therein is 0.49. It is shown that this correlation error for K(decadiene/w) is the dominant source of uncertainty in applying a comprehensive new model of phospholipid bilayer membrane permeability developed in a companion paper (Nitsche and Kasting, submitted for publication), which superposes the effects of molecular size and lipid density upon the decadiene lipophilicity scale. Thus, more experimental studies to augment the limited existing database on K(decadiene/w) are called for.

Dermal clearance model for epidermal bioavailability calculations.

A computational model for estimating dermal clearance in humans of arbitrary, nonmetabolized solutes is presented. The blood capillary component employs slit theory with contributions from both small (10 nm) and large (50 nm) slits. The lymphatic component is derived from previously reported clearance measurements of dermal and subcutaneous injections of (131)I-albumin in humans. Model parameters were fitted to both blood capillary permeability data and lymphatic clearance data. Small molecules are cleared largely by the blood and large molecules by the lymph. The combined model shows a crossover behavior at approximately 29 kDa, in acceptable agreement with the reported value of 16 kDa. When combined with existing models for stratum corneum permeability and appropriate measures of tissue binding, the developed model has the potential to significantly improve tissue concentration estimates for large or highly protein-bound permeants following dermal exposure.

Tissue binding affects the kinetics of theophylline diffusion through the stratum corneum barrier layer of skin.

New data sets on both (i) equilibrium theophylline (TH) partitioning/binding in stratum corneum and (ii) transient TH diffusion through human epidermis are explained by an extended partition-diffusion model with reversible binding. Data conform to a linear binding isotherm within the tested concentration range (0-2000 µg/mL) with an equilibrium ratio of bound-to-free solute of approximately 1.4. The permeability coefficient for TH is 4.86 × 10(-5) cm/h, and the lag time is 20.1 h. Binding occurs as a slow process, significantly affecting the kinetics of dermal penetration.

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.

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).

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.

The permeability of gap junction channels to probes of different size is dependent on connexin composition and permeant-pore affinities.

Gap junctions have traditionally been characterized as nonspecific pores between cells passing molecules up to 1 kDa in molecular mass. Nonetheless, it has become increasingly evident that different members of the connexin (Cx) family mediate quite distinct physiological processes and are often not interchangeable. Consistent with this observation, differences in permeability to natural metabolites have been reported for different connexins, although the physical basis for selectivity has not been established. Comparative studies of different members of the connexin family have provided evidence for ionic charge selectivity, but surprisingly little is known about how connexin composition affects the size of the pore. We have employed a series of Alexa dyes, which share similar structural characteristics but range in size from molecular weight 350 to 760, to probe the permeabilities and size limits of different connexin channels expressed in Xenopus oocytes. Correlated dye transfer and electrical measurements on each cell pair, in conjunction with a three-dimensional mathematical model of dye diffusion in the oocyte system, allowed us to obtain single channel permeabilities for all three dyes in six homotypic and four heterotypic channels. Cx43 and Cx32 channels passed all three dyes with similar efficiency, whereas Cx26, Cx40, and Cx45 channels showed a significant drop-off in permeability with the largest dye. Cx37 channels only showed significant permeability for the smaller two dyes, but at two- to sixfold lower levels than other connexins tested. In the heterotypic cases studied (Cx26/Cx32 and Cx43/Cx37), permeability characteristics were found to resemble the more restrictive parental homotypic channel. The most surprising finding of the study was that the absolute permeabilities calculated for all gap junctional channels in this study are, with one exception, at least 2 orders of magnitude greater than predicted purely on the basis of hindered pore diffusion. Consequently, affinity between the probes and the pore creating an energetically favorable in-pore environment, which would elevate permeant concentration within the pore and hence the flux, is strongly implicated.

A transient diffusion model yields unitary gap junctional permeabilities from images of cell-to-cell fluorescent dye transfer between Xenopus oocytes.

As ubiquitous conduits for intercellular transport and communication, gap junctional pores have been the subject of numerous investigations aimed at elucidating the molecular mechanisms underlying permeability and selectivity. Dye transfer studies provide a broadly useful means of detecting coupling and assessing these properties. However, given evidence for selective permeability of gap junctions and some anomalous correlations between junctional electrical conductance and dye permeability by passive diffusion, the need exists to give such studies a more quantitative basis. This article develops a detailed diffusion model describing experiments (reported separately) involving transport of fluorescent dye from a "donor" region to an "acceptor" region within a pair of Xenopus oocytes coupled by gap junctions. Analysis of transport within a single oocyte is used to determine the diffusion and binding characteristics of the cellular cytoplasm. Subsequent double-cell calculations then yield the intercellular junction permeability, which is translated into a single-channel permeability using concomitant measurements of intercellular conductance, and known single-channel conductances of gap junctions made up of specific connexins, to count channels. The preceding strategy, combined with use of a graded size series of Alexa dyes, permits a determination of absolute values of gap junctional permeability as a function of dye size and connexin type. Interpretation of the results in terms of pore theory suggests significant levels of dye-pore affinity consistent with the expected order of magnitude of typical (e.g., van der Waals) intermolecular attractions.

Mobility of water in human stratum corneum.

At low water activities, stratum corneum (SC) water sorption resembles that in other keratinized tissues (i.e., wool and horn), whereas at high water activities, it resembles that in polymeric hydrogels. We propose that the concentration-dependent water diffusivity observed in these other systems applies to the corneocyte phase of the SC. An increase in SC hydration leads to increased water diffusivity in the corneocytes, in accordance with the predictions of both effective diffusion and free volume theories. Thus, theoretical results on effective diffusivity in a composite medium with random fiber obstacles and a free volume theory for water diffusivity in hydrogels (calibrated using data from wool and horn) have been applied to human SC water sorption data to estimate and establish theoretical limits on water diffusivity in corneocytes as a function of water activity. These results are used in conjunction with steady-state water permeability data to estimate the water permeability of both corneocyte and lipid phases of the SC under hydrated and partially hydrated conditions. The results of the analysis, when combined with previous spectroscopic analyses, strongly suggest that the lipids provide most of the SC water barrier in either case; thus, the diffusion pathway for water is primarily transcellular.