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

Cutaneous Pharmacokinetics of Topically Applied Novel Dermatological Formulations

Novel formulations are developed for dermatological applications to address a wide range of patient needs and therapeutic challenges. By pushing the limits of pharmaceutical technology, these formulations strive to provide safer, more effective, and patient-friendly solutions for dermatological concerns, ultimately improving the overall quality of dermatological care. The article explores the different types of novel dermatological formulations, including nanocarriers, transdermal patches, microsponges, and microneedles, and the techniques involved in the cutaneous pharmacokinetics of these innovative formulations. Furthermore, the significance of knowing cutaneous pharmacokinetics and the difficulties faced during pharmacokinetic assessment have been emphasized. The article examines all the methods employed for the pharmacokinetic evaluation of novel dermatological formulations. In addition to a concise overview of earlier techniques, discussions on novel methodologies, including tape stripping, in vitro permeation testing, cutaneous microdialysis, confocal Raman microscopy, and matrix-assisted laser desorption/ionization mass spectrometry have been conducted. Emerging technologies like the use of microfluidic devices for skin absorption studies and computational models for predicting drug pharmacokinetics have also been discussed. This article serves as a valuable resource for researchers, scientists, and pharmaceutical professionals determined to enhance the development and understanding of novel dermatological drug products and the complex dynamics of cutaneous pharmacokinetics.

A regression analysis using simple descriptors for multiple dermal datasets: Going from individual membranes to the full skin

In silico methods to estimate and/or quantify skin absorption of chemicals as a function of chemistry are needed to realistically predict pharmacological, occupational, and environmental exposures. The Potts-Guy equation is a well-established approach, using multi-linear regression analysis describing skin permeability (Kp) in terms of the octanol/water partition coefficient (logP) and molecular weight (MW). In this work, we obtained regression equations for different human datasets relevant to environmental and cosmetic chemicals. Since the Potts-Guy equation was published in 1992, we explored recent datasets that include different skin layers, such as dermatomed (including dermis to a defined thickness) and full skin. Our work was consistent with others who have observed that fits to the Potts-Guy equation are stronger for experiments focused on the epidermis. Permeability estimates for dermatomed skin and full skin resulted in low regression coefficients when compared to epidermis datasets. An updated regression equation uses a combination of fitted permeability values obtained with a published 2D compartmental model previously evaluated. The resulting regression equation was: logKp = -2.55 + 0.65logP - 0.0085MW, R2  = 0.91 (applicability domain for all datasets: MW ranges from 18 to >584 g/mol and -4 to >5 for logP). This approach demonstrates the advantage of combining mechanistic with structural activity relationships in a single modeling approach. This combination approach results in an improved regression fit when compared to permeability estimates obtained using the Potts-Guy approach alone. The analysis presented in this work assumes a one-compartment skin absorption route; future modeling work will consider adding multiple compartments.

Predicting viable skin concentration: Diffusional and convective drug transport

Viable skin drug transport is an important concept to consider as it can have a significant impact on the local concentration of a drug. The concentration becomes even more critical for toxicological issues when implementing different permeability enhancement techniques. For this reason, it is important to develop models that can predict drug transport in the viable skin. This paper expands upon previous capillary modeling by representing the convective transport of a solute that has permeated into the capillary loops. As a result, convective transport caused the concentration profile to plateau within the deeper dermal layers, effectively matching the trend of previous experimental data. Furthermore, the new model also has a significantly quicker transient profile as the time required to reach steady-state is five-fold faster than predicted in previous homogenous models.

Modeling drug transport within the viable skin - a review

INTRODUCTION

In the past, mathematical modeling of the transport of transdermal drugs has been primarily focused on the stratum corneum. However, the development of pharmaceutical technologies, such as chemical enhancers, iontophoresis, and microneedles, has led to two outcomes; an increase in permeability in the stratum corneum or the ability to negate the layer entirely. As a result, these outcomes have made the transport of a solute in the viable skin far more critical when studying transdermal drug delivery.

AREAS COVERED

The review will explicitly show the various attempts to model drug transport within the viable skin. Furthermore, a brief review will be conducted on the different models that explain stratum corneum transport, microneedle dynamics and estimation of the diffusion coefficient.

EXPERT OPINION

Future development of mathematical models requires the focus to be changed from traditional diffusion-based tissue models to more sophisticated three-dimensional models that incorporate the physiology of the skin.

Physiologically based mathematical modelling of solute transport within the epidermis and dermis

The stratum corneum is the main barrier to transdermal drug delivery which has previously resulted in mathematical modelling of solute transport in the skin being primarily directed at this skin layer. However, for topical treatment and skin toxicity studies, the concentration in the epidermis and dermis is important and needs to be modelled mathematically. Hitherto, mathematical models for viable skin layers typically simplified the clearance of solute by blood, either assuming sink condition at the top of the skin capillary loops or assuming a distributed clearance in the dermis. This paper is an attempt to develop a physiologically based mathematical model of drug transport in the viable skin. It incorporates explicit modelling of the capillary loops within the dermis and employs COMSOL Multiphysics® software to model the transport in three dimensions. Previously derived simplified models were compared to the results from this new numerical model. The results of this comparison showed that the simplified model reasonably described the average concentration in the viable skin layers when parameters of the models were chosen appropriately. When the recruitment of the capillary loops in the dermis was full and the top of capillary loops was at a depth of 100μm, the effective depth to place a sink condition in the simpler models was found to be at 150μm. However, when there was only partial recruitment of the capillaries, the effective depth increased to 180μm. The presented modelling is also essential for determining a transdermal flux when the stratum corneum barrier is compromised by such methods as microporation, application of chemical enhancers or microneedles.

A Theoretical Study on Inhibition of Melanoma with Controlled and Targeted Delivery of siRNA via Skin Using SPACE-EGF

Melanoma is a potentially lethal skin cancer with high mortality rate. Recently, the peptide-mediated transdermal delivery of small interference RNA (siRNA) emerges as a promising strategy to treat melanoma by inducing the apoptosis of tumor cells, but the related theoretical model describing the delivery of siRNA under the effect of SPACE-EGF, the growth inhibition of melanoma and the dynamic expanding of the bump on the skin due to the growth of melanoma has not been reported yet. In this article, a theoretical model is developed to describe the percutaneous siRNA delivery mediated by SPACE-EGF to melanoma and the growth inhibition of melanoma. The results present the spatial-temporal distribution of siRNA and the growth of melanoma under the inhibition of siRNA, which shows a good consistency with the experimental results. In addition, this model represents the uplift process of tumors on the skin surface. The model presented here is a useful tool to understand the whole process of the SPACE-EGF-mediated delivery of the siRNA to melanoma through skin, to predict the therapeutic effect, and to optimize the therapeutic strategy, providing valuable references for the treatment of melanoma.

Predicting dermal absorption of gas-phase chemicals: transient model development, evaluation, and application

A transient model is developed to predict dermal absorption of gas-phase chemicals via direct air-to-skin-to-blood transport under non-steady-state conditions. It differs from published models in that it considers convective mass-transfer resistance in the boundary layer of air adjacent to the skin. Results calculated with this transient model are in good agreement with the limited experimental results that are available for comparison. The sensitivity of the modeled estimates to key parameters is examined. The model is then used to estimate air-to-skin-to-blood absorption of six phthalate esters for scenarios in which (A) a previously unexposed occupant encounters gas-phase phthalates in three different environments over a single 24-h period; (B) the same as 'A', but the pattern is repeated for seven consecutive days. In the 24-h scenario, the transient model predicts more phthalate absorbed into skin and less absorbed into blood than would a steady-state model. In the 7-day scenario, results calculated by the transient and steady-state models converge over a time period that varies between 3 and 4 days for all but the largest phthalate (DEHP). Dermal intake is comparable to or larger than inhalation intake for DEP, DiBP, DnBP, and BBzP in Scenario 'A' and for all six phthalates in Scenario 'B'.

PRACTICAL IMPLICATIONS

Dermal absorption from air has often been overlooked in exposure assessments. However, our transient model suggests that dermal intake of certain gas-phase phthalate esters is comparable to, or larger than, inhalation intake under commonly occurring indoor conditions. This may also be the case for other organic chemicals that have physicochemical properties that favor dermal absorption directly from air. Consequently, this pathway should be included in aggregate exposure and risk assessments. Furthermore, under conditions where the exposure concentrations are changing or there is insufficient time to achieve steady-state, the transient model presented in this study is more appropriate for estimating dermal absorption than is a steady-state model.

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.

Effects of age, gender, BMI, and anatomical site on skin thickness in children and adults with diabetes

Objective

We aimed to assess the effects of age, sex, body mass index (BMI), and anatomical site on skin thickness in children and adults with diabetes.

Methods

We studied 103 otherwise healthy children and adolescents with type 1 diabetes aged 5–19 years, and 140 adults with type 1 and type 2 diabetes aged 20–85 years. The thicknesses of both the dermis and subcutis were assessed using ultrasound with a linear array transducer, on abdominal and thigh skin.

Results

There was an age-related thickening of both dermis (p<0.0001) and subcutis (p = 0.013) in children and adolescents. Girls displayed a substantial pubertal increase in subcutis of the thigh (+54%; p = 0.048) and abdomen (+68%; p = 0.009). Adults showed an age-related decrease in dermal (p = 0.021) and subcutis (p = 0.009) thicknesses. Pubertal girls had a thicker subcutis than pubertal boys in both thigh (16.7 vs 7.5 mm; p<0.0001) and abdomen (16.7 vs 8.8 mm; p<0.0001). Men had greater thigh dermal thickness than women (1.89 vs 1.65 mm; p = 0.003), while the subcutis was thicker in women in thigh (21.3 vs 17.9 mm; p = 0.012) and abdomen (17.7 vs 9.8 mm; p<0.0001). In boys, men, and women, both dermis and subcutis were thicker on the abdomen compared to thigh; in girls this was only so for dermal thickness. In both children and adults, the skin (dermis and subcutis) became steadily thicker with increasing BMI (p<0.0001).

Conclusions

Skin thickness is affected by age, pubertal status, gender, BMI, and anatomical site. Such differences may be important when considering appropriate sites for dermal/subcutaneous injections and other transdermal delivery systems.

Microneedle-assisted percutaneous delivery of naltrexone hydrochloride in yucatan minipig: in vitro-in vivo correlation

Although microneedle-assisted transdermal drug delivery has been the subject of multiple scientific investigations, very few attempts have been made to quantitatively relate in vitro and in vivo permeation. The case of naltrexone hydrochloride is not an exception. In the present study, a pharmacokinetic profile obtained following a "poke and patch" microneedle application method in the Yucatan minipig is reported. The profile demonstrates a rapid achievement of maximum naltrexone hydrochloride plasma concentration followed by a relatively abrupt concentration decline. No steady state was achieved in vivo. In an attempt to correlate the present in vivo findings with formerly published in vitro steady-state permeation data, a diffusion-compartmental mathematical model was developed. The model incorporates two parallel permeation pathways, barrier-thickness-dependent diffusional resistance, microchannel closure kinetics, and a pharmacokinetic module. The regression analysis of the pharmacokinetic data demonstrated good agreement with an independently calculated microchannel closure rate and in vitro permeation data. Interestingly, full-thickness rather than split-thickness skin employed in in vitro diffusion experiments provided the best correlation with the in vivo data. Data analysis carried out with the model presented herein provides new mechanistic insight and permits predictions with respect to pharmacokinetics coupled with altered microchannel closure rates.

Basic considerations in the dermatokinetics of topical formulations

Assessing the bioavailability of drug molecules at the site of action provides better insight into the efficiency of a dosage form. However, determining drug concentration in the skin layers following topical application of dermatological formulations is a great challenge. The protocols followed in oral formulations could not be applied for topical dosage forms. The regulatory agencies are considering several possible approaches such as tape stripping, microdialysis etc. On the other hand, the skin bioavailability assessment of xenobiotics is equally important for topical formulations in order to evaluate the toxicity. It is always possible that drug molecules applied on the skin surface may transport thorough the skin and reaches systemic circulation. Thus the real time measurement of molecules in the skin layer has become obligatory. In the last two decades, quite a few investigations have been carried out to assess the skin bioavailability and toxicity of topical/dermatological products. This review provides current understanding on the basics of dermatokinetics, drug depot formation, skin metabolism and clearance of drug molecules from the skin layers following application of topical formulations.

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.

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.

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.

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.

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.

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.

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.

A thermodynamic study of the cyclodextrin-UC781 inclusion complex using a HPLC method

UC781, a very potent HIV-1 non-nucleoside reverse transcriptase inhibitor with extreme hydrophobicity and poor water solubility, is under development as a topical vaginal microbicide product to prevent HIV transmission. In this study, the thermodynamic behavior of the interaction between UC781 with three cyclodextrins (CDs): β-cyclodextrin (βCD), hydroxypropyl-β-cyclodextrin (HPβCD) and methyl-β-cyclodextrin (MβCD), was investigated using a reversed-phase HPLC method. A mobile phase consisting of acetonitrile: H₂O (30:70) solution containing various CD concentrations was used. The retention time at different temperatures was determined to evaluate the inclusion process. The influence of βCDs on the solubility and hydrophobicity of UC781 was characterized by retention time values. The results showed that the inclusion capacity of cyclodextrins follows the order MβCD > βCD > HPβCD. An enthalpy-entropy compensation effect was also observed. In addition, the results revealed that the change of ΔH is greater than that of ΔS. These results suggested that the complexation of UC781 with βCDs is an enthalpy driven process. The modification on β-cyclodextrin will influence the inclusion process.

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.

Effect of hydration on the permeation of ketoconazole through human nail plate in vitro

The impact of hydration on the permeation of the antifungal drug, ketoconazole, through excised human nails in vitro was evaluated in diffusion cell studies. Nails treated with [(3)H]ketoconazole solvent-deposited onto the dorsal surface were maintained in incubators at 32 degrees C and exposed sequentially to relative humidities (dorsal side) of 15, 40, 80 and 100% over a period of 40 days. The ventral side was bathed in a pH 7.4 phosphate buffer. Ascending and descending humidity regimens were tested. Increasing the ambient RH from 15 to 100% enhanced permeation of radiolabel associated with [(3)H]ketoconazole by a factor of three. Diffusivities estimated from these data and the associated nail water contents (estimated in a separate study) can be described by a free volume theory. Therefore, formulations or treatments, which increase nail hydration, have potential to improve topical therapy for onychomycosis, if a favorable balance between drug delivery and growth conditions for the dermatophytes can be achieved.

A geometrical model of dermal capillary clearance

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

Spatial distribution of cutaneous microvasculature and local drug clearance after drug application on the skin

We analysed quantitatively blood microvessels distribution in normal skin. We conclude that the segmental area of blood vessels peaks approximately 0.1 mm below the skin surface, where the upper cutaneous blood plexus resides. Total blood vessels area then decreases quasi-exponentially to a depth of approx. -0.75 mm, with a decay length of approximately 0.1 mm, which is site and skin condition dependent, but at greater depths the decrease is approx. 6-times less steep. The corresponding permeability sink exhibits a similar, but superficially steeper, depth-profile. The lateral localisation of superficial blood vessels is such that ensures maximum diffusion from and into the capillaries, which affects transdermal drug delivery: each hairpin-like loop is in the centre of a papilla that corresponds to a cluster of corneocytes surrounded by main diffusion pathways. The aggregate area of blood vessels in the skin is >or=2.5-fold greater than total organ surface area under normal physiological conditions. The molecules diffusing through the skin barrier are thus largely cleared in outermost 20% of the organ, which may create a drug concentration maximum in the dermis, if clearance increases significantly with time. Skin microdialysis data are therefore extremely sensitive to cutaneous blood flow (distribution) and sampling. Skin microvasculature and its distribution must consequently be considered in all topical or transdermal drug transport studies, for example, by including suitably formulated clearance term into generalised diffusion equation.

Kinetics of finite dose absorption through skin 2: Volatile compounds

A diffusion model to account for the disposition of an arbitrary dose of a (potentially) volatile compound applied to skin from a volatile vehicle is presented. In its most general form, the model allows for variable diffusivity of the permeant in the stratum corneum (SC) and must be solved numerically. However, for permeants having a constant diffusivity, absorption, and evaporation is characterized in terms of four dimensionless parameters-a reduced time tau, a fractional deposition depth in the SC f, a ratio of membrane capacity for the permeant to the applied dose beta, and a ratio of evaporative mass transfer coefficient to diffusive permeability chi. An important combination of these parameters arises as the reduced dose M(r) = (fbeta)(-1). Two cases are distinguished. In Case 1, corresponding to M(r) < or = 1, the dose is less than that required to saturate the upper layers of the SC, and the shape of the absorption and evaporation profiles is independent of the dose. Analytical solutions to Case 1 may be derived for arbitrary initial distributions of the permeant; the solution for a square wave is presented. In Case 2, corresponding to M(r) > 1, absorption and evaporation approach steady-state values as the dose is increased. Numerical evaluations of this behavior are shown. Limiting behavior for the case of a highly volatile solvent applied to skin is discussed. A companion paper discusses the application of the model to the absorption and evaporation of benzyl alcohol from human skin in vitro.