Diffusion modeling of percutaneous absorption kinetics. 1. Effects of flow rate, receptor sampling rate, and viable epidermal resistance for a constant donor concentration

Permeable Cornified Envelope Layer Regulates the Solute Transport in Human Stratum Corneum

To unravel the diffusion mechanisms of percutaneous drug delivery, suitable numerical analysis of stratum corneum structure is essential. In this research paper, we accounted for the permeable envelope layer in the brick-and-mortar finite element models of human stratum corneum. Both penetration and desorption experiments for tritiated water were simulated by transient finite element analysis. Rivet-shaped corneodesmosomes were included in the brick and mortar model. Results showed that cornified lipid permeability (Penv) is a determinant in desorption of the solute, while lipid transverse diffusion coefficient (Dlip-trans) is prominent during penetration. These two major unknowns (Penv and Dlip-trans) were obtained by extensive fitting of the finite element model to the experimental water data. Penv and Dlip-trans were determined to be 1×10-2 cm/s and 5.7×10-10 cm2/s, respectively.

Human epidermal in vitro permeation test (IVPT) analyses of alcohols and steroids

This study examined a number of factors that can impact the outcomes of in vitro human epidermal permeation coefficients for aliphatic alcohols and steroids, including receptor phase composition and study conditions. We determined experimentally the solubilities and IVPT permeation of a homologous series of ¹⁴C labeled aliphatic alcohols (ethanol, propanol, pentanol, heptanol, octanol and decanol) in different receptor fluids as recommended by Organisation Economic Co-operation and Development (OECD). We used human epidermal membranes at 25°C and phosphate-buffered saline (PBS), 2% w/v bovine serum albumin (2%w/v BSA), 50% v/v ethanol and 0.1, 2 and 6% w/v Oleth-20 receptor phases. We also explored and confirmed the discrepancies between in vitro human epidermal permeability coefficients (k_p) and diffusion lag times for steroids from Scheuplein's group with our own work and that of others. The main reason for the observed differences is not clear but is likely to be multifactorial, including the effects of diffusion cell design, receptor phase solubility, unstirred receptor phase effects, epidermal membrane hydration, diffusion cell configuration, transport through appendageal pathways and steroid lipophilicity. We conclude with a summary of experimental conditions that should be considered in undertaking IVPT studies.

Compartmental modeling of skin absorption and desorption kinetics: Donor solvent evaporation, variable diffusion/partition coefficients, and slow equilibration process within stratum corneum

This work expands the recently developed compartmental model for skin transport to model variable diffusion and/or partition coefficients, and the presence of slow equilibration/slow binding kinetics within stratum corneum. The model was validated by comparing it with the diffusion model which was solved numerically using the finite element method. It was found that the new compartmental model predictions agreed well with that of the diffusion model, providing a sufficient number of compartments was used. The compartmental model was applied to two previously published experimental data sets: water penetration and desorption data and the finite dose dermal penetration of testosterone. Significant improvement of the fitting quality for all these data sets was achieved using the compartmental model.

Effect of Rubbing Application on the Skin Permeation of Active Ingredients from Lotion and Cream

Effect of rubbing application on the skin permeation of a hydrophilic drug caffeine (CAF) and lipophilic drug rhododendrol (RD) from lotion and cream were investigated. Skin permeation of CAF was markedly increased by rubbing action independent of the formulation type. In addition, the skin penetration-enhancement effect was affected by the rubbing direction: rubbing application against the direction of hair growth showed the highest permeation compared with rubbing applications along the direction of hair growth and in a circular pattern on the skin. On the other hand, no enhancement effect was observed by the rubbing actions on the skin permeation of RD, regardless of formulation type. Change in the infundibula orifice size of hair follicles by the rubbing and following skin stretching may be related to the higher skin permeation for CAF. In contrast, high RD distribution into the stratum corneum may be a reason why no enhancement effect was observed by the rubbing action. These results can be helpful to predict safety and effectiveness of topically applied formulations.

Relating transdermal delivery plasma pharmacokinetics with in vitro permeation test (IVPT) findings using diffusion and compartment-in-series models

Increasing emphasis is being placed on using in vitro permeation test (IVPT) results for topical products as a surrogate for their in vivo behaviour. This study sought to relate in vivo plasma concentration - time pharmacokinetic (PK) profiles after topical application of drug products to IVPT findings with mechanistic diffusion and compartment models that are now widely used to describe permeation of solutes across the main skin transport barrier, the stratum corneum. Novel in vivo forms of the diffusion and compartment-in-series models were developed by combining their IVPT model forms with appropriate in vivo disposition functions. Available in vivo and IVPT data were then used with the models in data analyses, including the estimation of prediction intervals for in vivo plasma concentrations derived from IVPT data. The resulting predicted in vivo plasma concentration - time profiles for the full models corresponded closely with the observed results for both nitroglycerin and rivastigmine at all times. In contrast, reduced forms of these in vivo models led to discrepancies between model predictions and observed results at early times. A two-stage deconvolution procedure was also used to estimate the in vivo cumulative amount absorbed and shown to be linearly related to that from IVPT, with an acceptable prediction error. External predictability was also shown using a separate set of in vitro and in vivo data for different nitroglycerin patches. This work suggests that mechanistic and physiologically based pharmacokinetic models can be used to predict in vivo behaviour from IVPT data for topical products.

Reflections on the OECD guidelines for in vitro skin absorption studies

At the 8th conference of Occupational and Environmental Exposure of the Skin to Chemicals (OEESC) (16-18 September 2019) in Dublin, Ireland, several researchers performing skin permeation assays convened to discuss in vitro skin permeability experiments. We, along with other colleagues, all of us hands-on skin permeation researchers, present here the results from our discussions on the available OECD guidelines. The discussions were especially focused on three OECD skin absorption documents, including a recent revision of one: i) OECD Guidance Document 28 (GD28) for the conduct of skin absorption studies (OECD, 2004), ii) Test Guideline 428 (TGD428) for measuring skin absorption of chemical in vitro (OECD, 2004), and iii) OECD Guidance Notes 156 (GN156) on dermal absorption issued in 2011 (OECD, 2011). GN156 (OECD, 2019) is currently under review but not finalized. A mutual concern was that these guidance documents do not comprehensively address methodological issues or the performance of the test, which might be partially due to the years needed to finalize and update OECD documents with new skin research evidence. Here, we summarize the numerous factors that can influence skin permeation and its measurement, and where guidance on several of these are omitted and often not discussed in published articles. We propose several improvements of these guidelines, which would contribute in harmonizing future in vitro skin permeation experiments.

Methods to Evaluate Skin Penetration In Vitro

Dermal and transdermal drug therapy is increasing in importance nowadays in drug development. To completely utilize the potential of this administration route, it is necessary to optimize the drug release and skin penetration measurements. This review covers the most well-known and up-to-date methods for evaluating the cutaneous penetration of drugs in vitro as a supporting tool for pharmaceutical research scientists in the early stage of drug development. The aim of this article is to present various experimental models used in dermal/transdermal research and summarize the novel knowledge about the main in vitro methods available to study skin penetration. These techniques are: Diffusion cell, skin-PAMPA, tape stripping, two-photon microscopy, confocal laser scanning microscopy, and confocal Raman microscopic method.

SAMPA: A free software tool for skin and membrane permeation data analysis

Skin and membrane permeation experiments comprise an important step in the development of a transdermal or topical formulation or toxicological risk assessment. The standard method for analyzing these data relies on the linear part of a permeation profile. However, it is difficult to objectively determine when the profile becomes linear, or the experiment duration may be insufficient to reach a maximum or steady state. Here, we present a software tool for Skin And Membrane Permeation data Analysis, SAMPA, that is easy to use and overcomes several of these difficulties. The SAMPA method and software have been validated on in vitro and in vivo permeation data on human, pig and rat skin and model stratum corneum lipid membranes using compounds that range from highly lipophilic polycyclic aromatic hydrocarbons to highly hydrophilic antiviral drug, with and without two permeation enhancers. The SAMPA performance was compared with the standard method using a linear part of the permeation profile and a complex mathematical model. SAMPA is a user-friendly, open-source software tool for analyzing the data obtained from skin and membrane permeation experiments. It runs on a Microsoft Windows platform and is freely available as a Supporting file to this article.

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.

Vehicle effects on human stratum corneum absorption and skin penetration

This study evaluated the effects of three vehicles-ethanol (EtOH), isopropyl alcohol (IPA), and isopropyl myristate (IPM)-on stratum corneum (SC) absorption and diffusion of the [¹⁴C]-model compounds benzoic acid and butenafine hydrochloride to better understand the transport pathways of chemicals passing through and resident in SC. Following application of topical formulations to human dermatomed skin for 30 min, penetration flux was observed for 24 h post dosing, using an in vitro flow-through skin diffusion system. Skin absorption and penetration was compared to the chemical-SC (intact, delipidized, or SC lipid film) binding levels. A significant vehicle effect was observed for chemical skin penetration and SC absorption. IPA resulted in the greatest levels of intact SC/SC lipid absorption, skin penetration, and total skin absorption/penetration of benzoic acid, followed by IPM and EtOH, respectively. For intact SC absorption and total skin absorption/penetration of butenafine, the vehicle that demonstrated the highest level of sorption/penetration was EtOH, followed by IPA and IPM, respectively. The percent doses of butenafine that were absorbed in SC lipid film and penetrated through skin in 24 h were greatest for IPA, followed by EtOH and IPM, respectively. The vehicle effect was consistent between intact SC absorption and total chemical skin absorption and penetration, as well as SC lipid absorption and chemical penetration through skin, suggesting intercellular transport as a main pathway of skin penetration for model chemicals. These results suggest the potential to predict vehicle effects on skin permeability with simple SC absorption assays. As decontamination was applied 30 min after chemical exposure, significant vehicle effects on chemical SC partitioning and percutaneous penetration also suggest that skin decontamination efficiency is vehicle dependent, and an effective decontamination method should act on chemical solutes in the lipid domain.

Estimating Maximal In Vitro Skin Permeation Flux from Studies Using Non-sink Receptor Phase Conditions

PURPOSE

This study explored the impact of non-sink receptor conditions on the in vitro skin permeation test (IVPT) and sought to estimate equivalent sink condition IVPT data.

METHODS

Simulated diffusion model and experimental IVPT data were generated for ethyl salicylate across human epidermal membranes in Franz diffusion cells using six different receptor phases, with a 10 fold variation in ethyl salicylate solubility.

RESULTS

Both simulated and experimental IVPT - time profiles were markedly affected by receptor phase solubility and receptor sampling rates. Similar sink condition equivalent estimated maximum fluxes were obtained by nonlinear regression and adjustment of linear regression estimates of steady state flux for relative saturation of the receptor phase over time for the four receptor phases in which the ethyl salicylate was relatively soluble. The markedly lower steady - state fluxes found for the other two phases in which ethyl salicylate was less soluble was attributed to an aqueous solution boundary layer effect.

CONCLUSIONS

Non-sink receptor phase IVPT data can be used to derive equivalent sink receptor phase IVPT data provided the receptor phase solubility and hydrodynamics are sufficient to minimise the impact of aqueous diffusion layers on IVPT data.

Mathematical models for dermal drug absorption

INTRODUCTION

Mathematical models of dermal transport offer the advantages of being much faster and less expensive than in vitro or in vivo studies. The number of methods used to create such models has been increasing rapidly, probably due to the steady rise in computational power. Although each of the various approaches has its own virtues and limitations, it may be difficult to decide which approach is best suited to address a given problem.

AREAS COVERED

Here we outline the basic ideas, drawbacks and advantages of compartmental and quantitative structure-activity relationship models, as well as of analytical and numerical approaches for solving the diffusion equation. Examples of special applications of the different approaches are given.

EXPERT OPINION

Although some models are sophisticated and might be used in future to predict transport through damaged or diseased skin, the comparatively low availability of suitable and accurate experimental data limits extensive usage of these models and their predictive accuracy. Due to the lack of experimental data, the possibility of validating mathematical models is limited.

Advances in the bioanalytical study of drug delivery across the skin

The study of a drug's dermal penetration profile provides important pharmaceutical data for the rational development of topical and transdermal delivery systems because the skin is a broadly used delivery route for local and systemic drugs and a potential route for gene therapy and vaccines. Monitoring drug penetration across the skin and quantifying its levels in different skin layers have been constant challenges due to the detection limitations of the available techniques, as well as the inherent interference in this tissue. This review explores and discusses several bionalytical methods that are indispensable tools to study drugs across the skin. In addressing the main topic, we structure the review highlighting the skin as an important route of drug administration and its structure, skin membrane models most used and its properties, in vitro and in vivo assays most used in the study of drug delivery to the skin, the techniques for processing the skin for subsequent analysis by bioanalytical methods that have a theoretical and practical approach showing its applicability, limitations and also including examples of its use. This review has a comprehensive approach in order to help researchers design their experiments and update the applicability and advances in this area of expertise.

On the selection of an opioid for local skin analgesia: Structure-skin permeability relationships

Recent studies demonstrated that post-herpetical and inflammatory pain can be locally managed by morphine gels, empirically chosen. Aiming to rationalize the selection of the most suitable opioid for the cutaneous delivery, we studied the in vitro penetration through human epidermis of eight opioids, evidencing the critical modifications of the morphinan core. Log P, log D, solid-state features and solubility were determined. Docking simulations were performed using supramolecular assembly made of ceramide VI. The modifications on position 3 of the morphinan core resulted the most relevant in determining both physicochemical characteristics and diffusion pattern. The 3-methoxy group weakened the cohesiveness of the crystal lattice structure and increased the permeation flux (J). Computational studies emphasized that, while permeation is essentially controlled by molecule apolarity, skin retention depends on a fine balance of polar and apolar molecular features. Moreover, ChemPLP scoring the interactions between the opioids and ceramide, correlated with both the amount retained into the epidermis (Qret) and J. The balance of the skin penetration properties and the affinity potency for μ-receptors evidenced hydromorphone as the most suitable compound for the induction of local analgesia.

Mathematical models for skin toxicology

INTRODUCTION

Our skin is exposed daily to substances; many of these are neutral and safe but others are potentially harmful. In order to estimate the degree of toxicity and damage to skin tissues when exposed to harmful substances, skin toxicology studies are required. If these studies are coupled with suitably designed mathematical models, they can provide a powerful tool that allows appropriate interpretation of data. This work reviews mathematical models that can be employed in skin toxicology studies.

AREAS COVERED

Two types of mathematical models and their suitability for assessing skin toxicology are covered in this review. The first is focused on predicting penetration rate through the skin from a solute's physicochemical properties, while the second type of models transport processes in skin layers using appropriate equations with the specific aim of predicting the concentration of a given solute in viable skin tissues.

EXPERT OPINION

Mathematical models are an important tool for accurate valuation of skin toxicity experiments, estimation of skin toxicity and for developing new formulations for skin disease therapy. Comprehensive mathematical models of drug transport in skin, especially those based on more physiologically detailed mechanistic considerations of transport processes, are required to further enhance their role in assessing skin toxicology.

Modelling skin penetration using the Laplace transform technique

The Laplace transform is a convenient mathematical tool for solving ordinary and partial differential equations. The application of this technique to problems arising in drug penetration through the skin is reviewed in this paper.

Modeling the human skin barrier--towards a better understanding of dermal absorption

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.

Finite and infinite dosing: difficulties in measurements, evaluations and predictions

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.

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.

Improved input parameters for diffusion models of skin absorption

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.

Mathematical and pharmacokinetic modelling of epidermal and dermal transport processes

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.

Measuring the stratum corneum reservoir: desorption kinetics from keratin

High keratin binding and slow desorption kinetics are assumed to be responsible for the formation of the stratum corneum (SC) reservoir. We measured equilibrium binding coefficients (K(b)) and desorption rate constants (k(off)) with bovine hoof/horn keratin and six solutes with similar molecular weight (180-288 Da) and varying lipophilicities [expressed as octanol-water distribution coefficient, i.e., a partition coefficient corrected for pH (log K(pH))-0.13 to 3.8]. Two ionizable solutes within this set were tested at different pH values as degree of ionization and lipophilicity were expected to influence equilibrium binding and desorption kinetics. The unbound fraction at equilibrium varied between 18% and 93%. All solutes exhibited linear binding isotherms within the investigated concentration range. Equilibrium binding and the rate of desorption are both functions of solute lipophilicity [log K(b) = 1.23 + 0.32 log K(pH); log k(off) = 1/(25.75 + 8.35 K(pH) (0.34))]. Our results prove that slow desorption from keratin may be a major contributor to the SC reservoir. Also, they prove that reservoir formation is relevant for lipophilic solutes independent of drug class, thus allowing new options for topical pharmacotherapy.

Modelling dermal drug distribution after topical application in human

PURPOSE

To model and interpret drug distribution in the dermis and underlying tissues after topical application which is relevant to the treatment of local conditions.

METHODS

We created a new physiological pharmacokinetic model to describe the effect of blood flow, blood protein binding and dermal binding on the rate and depth of penetration of topical drugs into the underlying skin. We used this model to interpret literature in vivo human biopsy data on dermal drug concentration at various depths in the dermis after topical application of six substances. This interpretation was facilitated by our in vitro human dermal penetration studies in which dermal diffusion coefficient and binding were estimated.

RESULTS

The model shows that dermal diffusion alone cannot explain the in vivo data, and blood and/or lymphatic transport to deep tissues must be present for almost all of the drugs tested.

CONCLUSION

Topical drug delivery systems for deeper tissue delivery should recognise that blood/lymphatic transport may dominate over dermal diffusion for certain compounds.

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.

Diffusion modelling of percutaneous absorption kinetics: 4. Effects of a slow equilibration process within stratum corneum on absorption and desorption kinetics

One of the main functions of the skin is to control the ingress and egress of water into and out of the body. The transport kinetics of water in the stratum corneum (SC), the dominant site of resistance in the skin, is normally described assuming a homogeneous membrane model. In the present work, the desorption of water from SC was studied and profiles obtained for amount desorbed versus time profiles that were more consistent with water transport occurring in a heterogeneous membrane. Analysis of the resulting profiles yields a model that is consistent with a slow equilibration/slow binding of water within SC as well as its permeation through the SC. Diffusion model solutions were used to derive the steady-state flux, lag time and mean desorption time for water in SC. The slow binding kinetics of water in the SC are limited and most pronounced in the early transient stages of transport and are not easily discerned using steady-state penetration studies. The practical importance of this work is in its use of desorption experiments to recognise and define the skin reservoir for water and other solutes as well as penetration parameters in defining their transdermal kinetics.

A model of solute transport through stratum corneum using solute capture and release

A one-dimensional model of solute transport through the stratum corneum is presented. Solute is assumed to diffuse through lipid bi-layers surrounding impermeable corneocytes. Transverse diffusion (perpendicular to the skin surface) through lipids separating adjacent corneocytes, is modeled in the usual way. Longitudinal diffusion (parallel to the skin surface) through lipids between corneocyte layers, is modeled as temporary trapping of solute, with subsequent release in the transverse direction. This leads to a linear equation for one-dimensional transport in the transverse direction. The model involves an arbitrary function whose precise form is uncertain. For a specific choice of this function, closed form expressions for the Laplace transform of solute out-flux at the inner boundary, and for the time lag are obtained in the case that a constant solute concentration is maintained at the outer skin surface, with the inner boundary of the stratum corneum kept at zero concentration, and with the stratum corneum initially free of solute.

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.

Percutaneous Absorption of Steroids: Determination of in vitro Permeability and Tissue Reservoir Characteristics in Human Skin Layers

The skin localization of steroids following topical application is largely unknown. We determined the distribution of five steroids in human skin using excised epidermal, dermal, and full-thickness membranes in vitro. There was no significant difference in steroid maximum flux through epidermal and full-thickness membranes, other than significantly lower fluxes for the most polar steroid, aldosterone. Hydrocortisone had the highest dermal diffusivity and dermal penetration, and the accumulation of hydrocortisone and corticosterone was higher than that of the other steroids. Slower penetration and higher accumulation in the viable epidermis of progesterone in full-thickness skin were consistent with dermal penetration limitation effects associated with high lipophilicity.

In vitro percutaneous absorption of all-trans retinoic acid applied in free form or encapsulated in stratum corneum lipid liposomes

The objective of this study was to design an all-trans retinoic acid (RA) topical release system that modifies drug diffusion parameters in the vehicle and the skin in order to reduce systemic absorption and the side-effects associated with topical application of the drug to skin. Three cases of application of hydrogels containing RA either in free form or encapsulated in stratum corneum lipid liposomes (SCLLs) have been considered. For this purpose, we have evaluated the RA in formulations with combinations of Carbopol Ultrez 10 (U10) and hyaluronic acid (HA) for percutaneous absorption. In vitro permeability experiments with [3H]-t-RA were carried out using a Franz-type diffusion cell in abdominal rat skin samples. Accumulation of the drug in the surface and skin layers was evaluated by both the tape stripping method and a dissection technique, and subsequently, all the radiolabelled samples were analyzed by liquid scintillation counting. The results show that RA encapsulation not only prolongs drug release but also promotes drug retention by the viable skin. At the same time, interaction between RA and HA has an obstructive effect on diffusion, which contributes to the formation of a reservoir of the latter.

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC.

Factors affecting the formation of a skin reservoir for topically applied solutes

The reservoir function of the skin is an important determinant of the duration of action of a topical solute. The reservoir can exist in the stratum corneum, in the viable avascular tissue (viable epidermis and supracapillary dermis) and in the dermis. A steroid reservoir in the stratum corneum has been demonstrated by the reactivation of a vasoconstrictor effect by occlusion or application of a placebo cream to the skin some time after the original topical application of steroid. Other solutes have also been reported to show a reservoir effect in the skin after topical application. A simple compartmental model is used to understand why reactivation of vasoconstriction some time after a topical steroid application shows dependency on time, topical solute concentration and the product used to cause reactivation. The model is also used to show which solutes are likely to show a reservoir effect and could be potentially affected by desquamation, especially when the turnover of the skin is abnormally rapid. A similar form of the model can be used to understand the promotion of reservoir function in the viable tissue and in the dermis in terms of effective removal by blood perfusing the tissues.

Steady-state flux and lag time in the stratum corneum lipid pathway: results from finite element models

Finite element model (FEM) solutions of the diffusion through two-dimensional representations of the stratum corneum (SC) lipid pathway are presented. Both simplified, regular "brick and mortar" models and a more complex, irregular model are analyzed. It is assumed that diffusion occurs only within the SC lipids and the lipids are isotropic. The steady-state flux and lag time are solved and compared with the corresponding values for a homogeneous membrane of the same thickness consisting of lipid material. Results confirm that the heterogeneous SC model behaves like a homogeneous membrane, meaning that FEM diffusion simulations are well approximated by an appropriate solution of the diffusion equation for a homogeneous membrane. Additionally, both steady-state flux and lag time (relative to these values in a homogeneous membrane) can be predicted from algebraic equations based on simple dimensionless descriptors of SC geometry. However, values for diffusivity derived from homogeneous membrane approximations to the FEM solutions (effective diffusivity, D*) are not equal to the intrinsic diffusivity of the chemical in lipid. Furthermore, the pathlength derived from homogeneous membrane approximations to FEM solutions (effective pathlength, l*) is not equal to the lipid pathlength and is not dependent on SC tortuosity. Whereas l* is not a function of corneocyte overlap, D* is. These model results suggest that diffusion properties of the SC lipid pathway can be correlated to SC geometry, but intrinsic diffusion coefficients and SC tortuosity cannot be derived from common diffusion cell experiments. Use of the model equations to predict permeability and lag time of lipophilic solutes is described.

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.

Acyclovir permeation through rat skin: mathematical modelling and in vitro experiments

The aim of this work is to characterise the skin permeation properties of a male rat by means of a purely diffusive mathematical model based on Fick's second law. Additionally, in the attempt of proposing a reliable tool allowing the skin permeability (or resistance) determination on the basis of experimental data, the model automatically accounts also for two typical experimental conditions. In particular, drug dissolution in the donor environment and receiver sampling technique (part of the receiver volume is withdrawn and immediately replaced by fresh solvent) are considered. The results of this characterisation are then compared with those coming from a common simplified approach. Acyclovir is chosen as model drug and a thermostatic (37 degrees C) Franz cell apparatus is used to perform permeation experiments. This study suggests that Acyclovir permeation through the rat skin can be well described by the proposed model and that some differences arise in the evaluation of the full-skin resistance performed by means of our model or the usual simpler approach.

A random walk model of skin permeation

A new mathematical model for permeability of chemicals in aqueous vehicle through skin is presented. The rationale for this model is to represent diffusion by its fundamental molecular mechanism, i.e., random thermal motion. Diffusion is modeled as a two-dimensional random walk through the biphasic (lipid and corneocyte) stratum corneum (SC). This approach permits calculations of diffusion phenomena in a morphologically realistic SC structure. Two concepts are key in the application of the model to the prediction of steady-state skin permeability coefficients: "effective diffusivity" and "effective path length," meaning the diffusivity and thickness of a homogeneous membrane having identical permeation properties as the stratum corneum. Algebraic expressions for these two variables are developed as functions of the molecular weight and octanol-water partition coefficient of the diffusing substance. Combining these with expressions for membrane-vehicle partition coefficient and permeability of the aqueous epidermis enables the calculation of steady-state skin permeability coefficients. The resulting four-parameter algebraic model was regressed against the "Flynn data base" with excellent results (R2 = 0.84: SE = 0.0076; F = 154; N = 94). The model provides insight into the contributions of stratum corneum diffusivity and effective path lengths to overall skin permeability and may prove useful in the prediction of non-steady-state diffusion phenomena.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations.