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

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.

Skin permeability prediction with MD simulation sampling spatial and alchemical reaction coordinates

A molecular-level understanding of skin permeation may rationalize and streamline product development, and improve quality and control, of transdermal and topical drug delivery systems. It may also facilitate toxicity and safety assessment of cosmetics and skin care products. Here, we present new molecular dynamics simulation approaches that make it possible to efficiently sample the free energy and local diffusion coefficient across the skin's barrier structure to predict skin permeability and the effects of chemical penetration enhancers. In particular, we introduce a new approach to use two-dimensional reaction coordinates in the accelerated weight histogram method, where we combine sampling along spatial coordinates with an alchemical perturbation virtual coordinate. We present predicted properties for 20 permeants, and demonstrate how our approach improves correlation with ex vivo/in vitro skin permeation data. For the compounds included in this study, the obtained log KPexp-calc mean square difference was 0.9 cm2 h-2.

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.

Use of Silicone Membrane Permeation to Assess Thermodynamic Activities of Ionic Liquids and Their Component Cation and Anion

Ionic liquid (IL) was prepared by mixing lidocaine and ibuprofen as a cation and anion, respectively, at various ratios. We determined the permeation of both compounds from the IL through a silicone membrane selected as a model biological membrane, and mathematically analyzed the permeation data from the viewpoint of the thermodynamic activities of lidocaine, ibuprofen, and the IL. As a result, IL and ibuprofen diffusely permeated through the membrane in the case of applying IL preparations with a molar fraction of ibuprofen of 0.5 or higher. The IL was thought to separate into lidocaine and ibuprofen in the receiver. On the other hand, when applying IL preparations with a molar fraction of lidocaine of 0.5 or higher, IL and lidocaine permeated. The permeation rate of IL itself was maximized when the applied IL was prepared using equimolar amounts of lidocaine and ibuprofen, and it decreased when the fraction of lidocaine or ibuprofen increased by more than 0.5. Their membrane permeation rates increased with an increase in their activity, and no more increase was found when the drugs were saturated in the IL. These membrane permeation profiles reflected well the mathematically calculated ones according to the concept of activity.

Inverse Mechanistic Modeling of Transdermal Drug Delivery for Fast Identification of Optimal Model Parameters

Transdermal drug delivery systems are a key technology to administer drugs with a high first-pass effect in a non-invasive and controlled way. Physics-based modeling and simulation are on their way to become a cornerstone in the engineering of these healthcare devices since it provides a unique complementarity to experimental data and additional insights. Simulations enable to virtually probe the drug transport inside the skin at each point in time and space. However, the tedious experimental or numerical determination of material properties currently forms a bottleneck in the modeling workflow. We show that multiparameter inverse modeling to determine the drug diffusion and partition coefficients is a fast and reliable alternative. We demonstrate this strategy for transdermal delivery of fentanyl. We found that inverse modeling reduced the normalized root mean square deviation of the measured drug uptake flux from 26 to 9%, when compared to the experimental measurement of all skin properties. We found that this improved agreement with experiments was only possible if the diffusion in the reservoir holding the drug was smaller than the experimentally measured diffusion coefficients suggested. For indirect inverse modeling, which systematically explores the entire parametric space, 30,000 simulations were required. By relying on direct inverse modeling, we reduced the number of simulations to be performed to only 300, so a factor 100 difference. The modeling approach's added value is that it can be calibrated once in-silico for all model parameters simultaneously by solely relying on a single measurement of the drug uptake flux evolution over time. We showed that this calibrated model could accurately be used to simulate transdermal patches with other drug doses. We showed that inverse modeling is a fast way to build up an accurate mechanistic model for drug delivery. This strategy opens the door to clinically ready therapy that is tailored to patients.

A Predictive Self-Organizing Multicellular Computational Model of Infant Skin Permeability to Topically Applied Substances

Computational models of skin permeability are typically based on assumptions of fixed geometry and homogeneity of the whole epidermis or of epidermal strata and are often limited to adult skin. Infant skin differs quantitatively from that of the adult in its structure and its functional properties, including its barrier function to permeation. To address this problem, we developed a self-organizing multicellular epidermis model of barrier formation with realistic cell morphology. By modulating the parameters relating to cell turnover reflecting those in adult or infant epidermis, we were able to generate accordingly two distinct models. Emerging properties of these models reflect the corresponding experimentally measured values of epidermal and stratum corneum thickness. Diffusion of an externally applied substance (e.g., caffeine) was simulated by a molecular exchange between the model agents, defined by the individual cells and their surrounding extracellular space. By adjusting the surface concentration and the intercellular exchange rate, the model can recapitulate experimental permeability data after topical exposure. By applying these parameters to an infant model, we were able to predict the caffeine concentration profile in infant skin, closely matching experimental results. This work paves the way for a better understanding of skin physiology and function during the first years of life.

Development of a Predictive Monte Carlo Radiative Transfer Model for Ablative Fractional Skin Lasers

It is possible to enhance topical drug delivery by pretreatment of the skin with ablative fractional lasers (AFLs). However, the parameters to use for a given AFL to achieve the desired depth of ablation or the desired therapeutic or cosmetic outcome are hard to predict. This leaves open the real possibility of overapplication or underapplication of laser energy to the skin. In this study, we developed a numerical model consisting of a Monte Carlo radiative transfer (MCRT) code coupled to a heat transfer and tissue damage algorithm. The simulation is designed to predict the depth effects of AFL on the skin, verified with in vitro experiments in porcine skin via optical coherence tomography (OCT) imaging. Ex vivo porcine skin is irradiated with increasing energies (50-400 mJ/pixel) from a CO₂ AFL. The depth of microscopic treatment zones is measured and compared with our numerical model. The data from the OCT images and MCRT model complement each other well. Nonablative thermal effects on surrounding tissue are also discussed. This model, therefore, provides an initial step toward a predictive determination of the effects of AFL on the skin. Lasers Surg. Med. © 2020 The Authors. Lasers in Surgery and Medicine published by Wiley Periodicals LLC.

Predicting Transdermal Fentanyl Delivery Using Mechanistic Simulations for Tailored Therapy

Transdermal drug delivery is a key technology for administering drugs. However, most devices are “one-size-fits-all”, even though drug diffusion through the skin varies significantly from person-to-person. For next-generation devices, personalization for optimal drug release would benefit from an augmented insight into the drug release and percutaneous uptake kinetics. Our objective was to quantify the changes in transdermal fentanyl uptake with regards to the patient’s age and the anatomical location where the patch was placed. We also explored to which extent the drug flux from the patch could be altered by miniaturizing the contact surface area of the patch reservoir with the skin. To this end, we used validated mechanistic modeling of fentanyl diffusion, storage, and partitioning in the epidermis to quantify drug release from the patch and the uptake within the skin. A superior spatiotemporal resolution compared to experimental methods enabled in-silico identification of peak concentrations and fluxes, and the amount of stored drug and bioavailability. The patients’ drug uptake showed a 36% difference between different anatomical locations after 72 h, but there was a strong interpatient variability. With aging, the drug uptake from the transdermal patch became slower and less potent. A 70-year-old patient received 26% less drug over the 72-h application period, compared to an 18-year-old patient. Additionally, a novel concept of using micron-sized drug reservoirs was explored in silico. These reservoirs induced a much higher local flux (µg cm^-2 h^-1) than conventional patches. Up to a 200-fold increase in the drug flux was obtained from these small reservoirs. This effect was mainly caused by transverse diffusion in the stratum corneum, which is not relevant for much larger conventional patches. These micron-sized drug reservoirs open new ways to individualize reservoir design and thus transdermal therapy. Such computer-aided engineering tools also have great potential for in-silico design and precise control of drug delivery systems. Here, the validated mechanistic models can serve as a key building block for developing digital twins for transdermal drug delivery systems.

Salt water and skin interactions: new lines of evidence

In Health Resort Medicine, both balneotherapy and thalassotherapy, salt waters and their peloids, or mud products are mainly used to treat rheumatic and skin disorders. These therapeutic agents act jointly via numerous mechanical, thermal, and chemical mechanisms. In this review, we examine a new mechanism of action specific to saline waters. When topically administered, this water rich in sodium and chloride penetrates the skin where it is able to modify cellular osmotic pressure and stimulate nerve receptors in the skin via cell membrane ion channels known as "Piezo" proteins. We describe several models of cutaneous adsorption/desorption and penetration of dissolved ions in mineral waters through the skin (osmosis and cell volume mechanisms in keratinocytes) and examine the role of these resources in stimulating cutaneous nerve receptors. The actions of salt mineral waters are mediated by a mechanism conditioned by the concentration and quality of their salts involving cellular osmosis-mediated activation/inhibition of cell apoptotic or necrotic processes. In turn, this osmotic mechanism modulates the recently described mechanosensitive piezoelectric channels.

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that intracellular spatial dependence is a crucial component of virus life cycles. The hepatitis C virus-encoded NS5A protein is an endoplasmatic reticulum (ER)-anchored viral protein and an essential component of the virus replication machinery. Therefore, we simulate NS5A dynamics on realistic reconstructed, curved ER surfaces by means of surface partial differential equations (sPDE) upon unstructured grids. We match the in silico NS5A diffusion constant such that the NS5A sPDE simulation data reproduce experimental NS5A fluorescence recovery after photobleaching (FRAP) time series data. This parameter estimation yields the NS5A diffusion constant. Such parameters are needed for spatial models of HCV dynamics, which we are developing in parallel but remain qualitative at this stage. Thus, our present study likely provides the first quantitative biophysical description of the movement of a viral component. Our spatio-temporal resolved ansatz paves new ways for understanding intricate spatial-defined processes central to specfic aspects of virus life cycles.

How Sensitive Are Transdermal Transport Predictions by Microscopic Stratum Corneum Models to Geometric and Transport Parameter Input?

While predictive models of transdermal transport have the potential to reduce human and animal testing, microscopic stratum corneum (SC) model output is highly dependent on idealized SC geometry, transport pathway (transcellular vs. intercellular), and penetrant transport parameters (e.g., compound diffusivity in lipids). Most microscopic models are limited to a simple rectangular brick-and-mortar SC geometry and do not account for variability across delivery sites, hydration levels, and populations. In addition, these models rely on transport parameters obtained from pure theory, parameter fitting to match in vivo experiments, and time-intensive diffusion experiments for each compound. In this work, we develop a microscopic finite element model that allows us to probe model sensitivity to variations in geometry, transport pathway, and hydration level. Given the dearth of experimentally-validated transport data and the wide range in theoretically-predicted transport parameters, we examine the model's response to a variety of transport parameters reported in the literature. Results show that model predictions are strongly dependent on all aforementioned variations, resulting in order-of-magnitude differences in lag times and permeabilities for distinct structure, hydration, and parameter combinations. This work demonstrates that universally predictive models cannot fully succeed without employing experimentally verified transport parameters and individualized SC structures.

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.

Effect of stratum corneum heterogeneity, anisotropy, asymmetry and follicular pathway on transdermal penetration

The impact of the complex structure of the stratum corneum on transdermal penetration is not yet fully described by existing models. A quantitative and thorough study of skin permeation is essential for chemical exposure assessment and transdermal delivery of drugs. The objective of this study is to analyze the effects of heterogeneity, anisotropy, asymmetry, follicular diffusion, and location of the main barrier of diffusion on percutaneous permeation. In the current study, the solution of the transient diffusion through a two-dimensional-anisotropic brick-and-mortar geometry of the stratum corneum is obtained using the commercial finite element program COMSOL Multiphysics. First, analytical solutions of an equivalent multilayer geometry are used to determine whether the lipids or corneocytes constitute the main permeation barrier. Also these analytical solutions are applied for validations of the finite element solutions. Three illustrative compounds are analyzed in these sections: diethyl phthalate, caffeine and nicotine. Then, asymmetry with depth and follicular diffusion are studied using caffeine as an illustrative compound. The following findings are drawn from this study: the main permeation barrier is located in the lipid layers; the flux and lag time of diffusion through a brick-and-mortar geometry are almost identical to the values corresponding to a multilayer geometry; the flux and lag time are affected when the lipid transbilayer diffusivity or the partition coefficients vary with depth, but are not affected by depth-dependent corneocyte diffusivity; and the follicular contribution has significance for low transbilayer lipid diffusivity, especially when flux between the follicle and the surrounding stratum corneum is involved. This study demonstrates that the diffusion is primarily transcellular and the main barrier is located in the lipid layers.

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.

Anatomically Detailed and Large-Scale Simulations Studying Synapse Loss and Synchrony Using NeuroBox

The morphology of neurons and networks plays an important role in processing electrical and biochemical signals. Based on neuronal reconstructions, which are becoming abundantly available through databases such as NeuroMorpho.org, numerical simulations of Hodgkin-Huxley-type equations, coupled to biochemical models, can be performed in order to systematically investigate the influence of cellular morphology and the connectivity pattern in networks on the underlying function. Development in the area of synthetic neural network generation and morphology reconstruction from microscopy data has brought forth the software tool NeuGen. Coupling this morphology data (either from databases, synthetic, or reconstruction) to the simulation platform UG 4 (which harbors a neuroscientific portfolio) and VRL-Studio, has brought forth the extendible toolbox NeuroBox. NeuroBox allows users to perform numerical simulations on hybrid-dimensional morphology representations. The code basis is designed in a modular way, such that e.g., new channel or synapse types can be added to the library. Workflows can be specified through scripts or through the VRL-Studio graphical workflow representation. Third-party tools, such as ImageJ, can be added to NeuroBox workflows. In this paper, NeuroBox is used to study the electrical and biochemical effects of synapse loss vs. synchrony in neurons, to investigate large morphology data sets within detailed biophysical simulations, and used to demonstrate the capability of utilizing high-performance computing infrastructure for large scale network simulations. Using new synapse distribution methods and Finite Volume based numerical solvers for compartment-type models, our results demonstrate how an increase in synaptic synchronization can compensate synapse loss at the electrical and calcium level, and how detailed neuronal morphology can be integrated in large-scale network simulations.

Proposed human stratum corneum water domain in chemical absorption

Compounds with varying physical and chemical properties may have different affinities to the stratum corneum (SC) and/or its intercellular lipids, keratin protein, and possible water domains. To better understand the mechanism of percutaneous absorption, we utilized 21 carbon-14 labeled chemicals, with wide hydrophilicity (log P = -0.05 to 6.17), and quantified their absorption/adsorption properties for a short incubation time (15 min) with regards to intact SC membrane, delipidized SC membrane and SC lipid. A facile method was developed for SC/lipid absorption, providing a more equivalent procedure and comparable data. SC lipid absorption of chemical solutes positively correlated with the octanol/water partition coefficient (log P). Differences between the percent dose of chemical absorption to intact SC and the total percent dose contributed by the protein and lipid domains suggest the possibility and significance of a water domain. Absorption rate experiments showed a longer lag time for intact SC than for delipidized SC or SC lipid, suggesting that the water domain may delay chemical binding to protein and lipid domains, and may be a factor in the resistance of many chemicals to current decontamination methods. Copyright © 2015 John Wiley & Sons, Ltd.

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.

A strategy for in-silico prediction of skin absorption in man

For some time, in-silico models to address substance transport into and through the skin are gaining more and more importance in different fields of science and industry. In particular, the mathematical prediction of in-vivo skin absorption is of great interest to overcome ethical and economical issues. The presented work outlines a strategy to address this problem and in particular, investigates in-vitro and in-vivo skin penetration experiments of the model compound flufenamic acid solved in an ointment by means of a mathematical model. Experimental stratum corneum concentration-depth profiles (SC-CDP) for various time intervals using two different in-vitro systems (Franz diffusion cell, Saarbruecken penetration model) were examined and simulated with the help of a highly optimized three compartment numerical diffusion model and compared to the findings of SC-CDPs of the in-vivo scenario. Fitted model input parameters (diffusion coefficient and partition coefficient with respect to the stratum corneum) for the in-vitro infinite dose case could be used to predict the in-use conditions in-vitro. Despite apparent differences in calculated partition coefficients between in-vivo and in-vitro studies, prediction of in-vivo scenarios from input parameters calculated from the in-vitro case yielded reasonable results.

Numerical modelling of transdermal delivery from matrix systems: parametric study and experimental validation with silicone matrices

A model is presented for transdermal drug delivery from single-layered silicone matrix systems. The work is based on our previous results that, in particular, extend the well-known Higuchi model. Recently, we have introduced a numerical transient model describing matrix systems where the drug dissolution can be non-instantaneous. Furthermore, our model can describe complex interactions within a multi-layered matrix and the matrix to skin boundary. The power of the modelling approach presented here is further illustrated by allowing the possibility of a donor solution. The model is validated by a comparison with experimental data, as well as validating the parameter values against each other, using various configurations with donor solution, silicone matrix and skin. Our results show that the model is a good approximation to real multi-layered delivery systems. The model offers the ability of comparing drug release for ibuprofen and diclofenac, which cannot be analysed by the Higuchi model because the dissolution in the latter case turns out to be limited. The experiments and numerical model outlined in this study could also be adjusted to more general formulations, which enhances the utility of the numerical model as a design tool for the development of drug-loaded matrices for trans-membrane and transdermal delivery.

Skin permeation of organic gunshot residue: implications for sampling and analysis

Traditional gunshot residue (GSR) analysis is based on detection of particulates formed from metals found in the primer. Recent concerns regarding the interpretation of GSR evidence has led to interest in alternatives such as the organic constituents (organic gunshot residue, OGSR) found in propellants. Previous work has shown OGSR to be detectable on hands for several hours after a firing event, and given the lipophilic nature of these compounds, it was expected that losses due to secondary transfer (an issue with GSR particulates) would be negligible. However, other loss mechanisms have been identified, specifically skin permeation and evaporation. This paper describes experimental and modeling studies used to elucidate characteristics of skin permeation of 5 compounds present in OGSR. Pharmaceutical methods were adapted to characterize skin permeation using a skin surrogate and Franz diffusion cells. The amount of compounds deposited on skin after an authentic firing event (1 and 2 shots) was experimentally determined and applied for the permeation experiments. A fully validated selected ion monitoring GC/MS method was developed for quantitative analysis, and easily accessible online tools were employed for modeling. Results showed that OGSR residues should be detectable on skin for many hours after a firing event of as few as one or two shots, with detection capability being a function of the efficacy of sampling and sample preparation and the instrumental method employed. The permeation rates of the OGSR compounds were sufficiently different to suggest the potential to develop methods to approximate time-since-deposition.

Recent advances in predicting skin permeability of hydrophilic solutes

Understanding the permeation of hydrophilic molecules is of relevance to many applications including transdermal drug delivery, skin care as well as risk assessment of occupational, environmental, or consumer exposure. This paper reviews recent advances in modeling skin permeability of hydrophilic solutes, including quantitative structure-permeability relationships (QSPR) and mechanistic models. A dataset of measured human skin permeability of hydrophilic and low hydrophobic solutes has been compiled. Generally statistically derived QSPR models under-estimate skin permeability of hydrophilic solutes. On the other hand, including additional aqueous pathway is necessary for mechanistic models to improve the prediction of skin permeability of hydrophilic solutes, especially for highly hydrophilic solutes. A consensus yet has to be reached as to how the aqueous pathway should be modeled. Nevertheless it is shown that the contribution of aqueous pathway can constitute to more than 95% of the overall skin permeability. Finally, future prospects and needs in improving the prediction of skin permeability of hydrophilic solutes are discussed.

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.

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.

Design and performance of a spreadsheet-based model for estimating bioavailability of chemicals from dermal exposure

A comprehensive transient model of chemical penetration through the stratum corneum, viable epidermis and dermis formulated in terms of an Excel™ spreadsheet and associated add-in is presented. The model is a one-dimensional homogenization of underlying microscopic transport models for stratum corneum and dermis; viable epidermis is treated as unperfused dermis. The model's salient features are a detailed structural description of the skin layers, a combination of first-principles based transport equations and empirical partition and diffusion coefficients, and the capability of simulating a variety of exposure scenarios. Model predictions are compared with representative in vitro skin permeation data obtained from the literature using as summary parameters total absorption (Q(abs)), maximum flux (J(max)) and skin permeability coefficient (k(p)). The results of this evaluation demonstrate the current state-of-the-art in prediction of transient skin absorption and highlight areas in which further elaborations are needed to obtain satisfactory predictions.

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.

Finite dose skin mass balance including the lateral part: comparison between experiment, pharmacokinetic modeling and diffusion models

This work investigates in vitro finite dose skin absorption of the model compounds flufenamic acid and caffeine experimentally and mathematically. The mass balance in different skin compartments (donor, stratum corneum (SC), deeper skin layers (DSL), lateral skin parts and acceptor) is analyzed as a function of time. For both substances high amounts were found in the lateral skin compartment after 6h of incubation, which emphasizes not to elide these parts in the modeling. Here, three different mathematical models were investigated and tested with the experimental data: a pharmacokinetic model (PK), a detailed microscopic two-dimensional diffusion model (MICRO) and a macroscopic homogenized diffusion model (MACRO). While the PK model was fitted to the experimental data, the MICRO and the MACRO models employed input parameters derived from infinite dose studies to predict the underlying diffusion process. All models could satisfyingly predict or describe the experimental data. The PK model and MACRO model also feature the lateral parts.

Influence of skin type, race, sex, and anatomic location on epidermal barrier function

The intact skin represents a barrier to the uncontrolled loss of water, proteins, and plasma components from the organism. Owing to its complex structure, the epidermal barrier with its major layer, the stratum corneum, is the rate-limiting unit for the penetration of exogenous substances through the skin. The epidermal barrier is not a static structure. The status of different functions of the epidermis can be monitored by assessing specific biophysical parameters such as transepidermal water loss, stratum corneum hydration, and skin surface pH. Variables originating from the individual as well as exogenous factors have an important influence on the epidermal barrier parameters.

Mathematical modeling of process liquid flow and acetoclastic methanogenesis under mesophilic conditions in a two-phase biogas reactor

Acetoclastic methanogenesis in the second stage of a two-phase biogas reactor is investigated. A mathematical model coupling chemical reactions with transport of process liquid and with the variation of population of the microorganisms living on the plastic tower packing of the reactor is proposed. The evolution of the liquid is described by an advection-diffusion-reaction equation, while a monod-type kinetic is used for the reactions. Moreover, a new inhibition factor MO(max) is introduced, which hinders the growth of microorganisms when the plastic tower packing is overpopulated. After estimating the reaction parameters, the acetate outflow measured experimentally is in good agreement with that predicted by simulations. For coupling liquid transport with reaction processes, a spatial discretization of the reactor is performed. This yields essential information about the distribution of acetate and the production of methane in the reactor. This information allows for defining a measure of the effectiveness of the reactor.

Nanoparticles and their interactions with the dermal barrier

The dermal application of drugs is promising due to the ease of application. In this context nano-scale carrier systems were already evaluated in several studies with respect to the skin interaction and the impact on drug penetration. At the same time the upcoming production of engineered nano-scale materials requires a thorough safety evaluation. Drug delivery as well as risk assessment depends crucially on the ability of such carriers to overcome the skin barrier and reach deeper tissue layers. Therefore, the interaction of nanoparticles with skin and especially skin models is an intriguing field. However, the data obtained do not show a clear image on the effect of nano-carriers. Especially the penetration of such particles is an open and controversially discussed topic. The literature reports different results mainly on pig or murine skin showing strong penetration (pig and mouse) or the opposite. Looking only at the sizes of the particles also no conclusive picture can be obtained. Nevertheless, size is regarded to play an important role for skin penetration. Furthermore, the state of the skin influences penetration (hydration) and the mechanical stress is of outmost importance.

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.

Surgical approaches to create murine models of human wound healing

Wound repair is a complex biologic process which becomes abnormal in numerous disease states. Although in vitro models have been important in identifying critical repair pathways in specific cell populations, in vivo models are necessary to obtain a more comprehensive and pertinent understanding of human wound healing. The laboratory mouse has long been the most common animal research tool and numerous transgenic strains and models have been developed to help researchers study the molecular pathways involved in wound repair and regeneration. This paper aims to highlight common surgical mouse models of cutaneous disease and to provide investigators with a better understanding of the benefits and limitations of these models for translational applications.

In-silico model of skin penetration based on experimentally determined input parameters. Part I: experimental determination of partition and diffusion coefficients

Mathematical modeling of skin transport is considered a valuable alternative of in-vitro and in-vivo investigations especially considering ethical and economical questions. Mechanistic diffusion models describe skin transport by solving Fick's 2nd law of diffusion in time and space; however models relying entirely on a consistent experimental data set are missing. For a two-dimensional model membrane consisting of a biphasic stratum corneum (SC) and a homogeneous epidermal/dermal compartment (DSL) methods are presented to determine all relevant input parameters. The data were generated for flufenamic acid (M(W) 281.24g/mol; logK(Oct/H2O) 4.8; pK(a) 3.9) and caffeine (M(W) 194.2g/mol; logK(Oct/H2O) -0.083; pK(a) 1.39) using female abdominal skin. K(lip/don) (lipid-donor partition coefficient) was determined in equilibration experiments with human SC lipids. K(cor/lip) (corneocyte-lipid) and K(DSL/lip) (DSL-lipid) were derived from easily available experimental data, i.e. K(SC/don) (SC-donor), K(lip/don) and K(SC/DSL) (SC-DSL) considering realistic volume fractions of the lipid and corneocyte phases. Lipid and DSL diffusion coefficients D(lip) and D(DSL) were calculated based on steady state flux. The corneocyte diffusion coefficient D(cor) is not accessible experimentally and needs to be estimated by simulation. Based on these results time-dependent stratum corneum concentration-depth profiles were simulated and compared to experimental profiles in an accompanying study.