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.

Percutaneous absorption of steroids from finite doses: Predicting urinary excretion from in vitro skin permeation testing.

Pharmacokinetic (PK) models are widely used to describe drug permeation across the epidermal membrane barrier, the stratum corneum (SC). Here, we extend our previously reported diffusion and compartment-in-series models to describe plasma concentrations, urinary excretion-time profiles and exposure estimates after topically applied finite doses of solvent deposited solids. In vivo models were derived by convolution of a skin absorption input function for finite dosing with that for in vivo disposition PK. In vitro skin permeation test (IVPT) and in vivo urinary excretion data for cortisone, desoxycorticosterone, and testosterone were extracted from literature for model validation and establishment of in vitro - in vivo relationships (IVIVR). Both SC diffusion and SC 3-compartment-in-series PK models adequately described experimental in vitro and in vivo permeation data, with similar model parameter estimates for SC diffusion time and bioavailability. A satisfactory IVIVR was generated for cortisone, whereas testosterone and desoxycorticosterone showed higher bioavailability in vitro compared to in vivo. In recognising that future prospective studies need to both have an adequate sampling schedule and be harmonized for robust IVIVRs, we developed expressions for predicting extent of absorption and time for peak absorption for both in vitro and in vivo studies. Other study parameters, such as application site, applied dose, and application techniques, can also affect drug permeability through skin during dosage form metamorphosis after finite dose application, and a lack of correlation may result if these are poorly matched.

Predicting Viable Skin Concentration: Modelling the Subpapillary Plexus.

The skin concentration of a substance after a topical application or exposure determines both local treatment outcomes and the dermal toxicity assessment of various products. However, quantifying the time course of those concentrations at skin effect sites, such as the viable epidermal, superficial dermis and appendages in humans is especially problematic in vivo, making physiologically based mathematical modelling an essential tool to meet this need. This work further develops our published physiologically based pharmacokinetic and COMSOL based dermal transport modelling by considering the impact of the superficial subpapillary dermal plexus, which we represent as two well stirred compartments. The work also studied the impact on dermal concentrations of subpapillary plexus size, depth, blood velocity and density of subpapillary plexus vessels. Sensitivity analyses are used to define the most important transport determinants of skin concentrations after topical application of a substance, with previously published results used to validate the resulting analyses. This resulting model describes the available experimental data better than previous models, especially at deeper dermal depths.

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.

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.

Retinal Tissue Bioengineering, Materials and Methods for the Treatment of Glaucoma.

BACKGROUND: Glaucoma, a characteristic type of optic nerve degeneration in the posterior pole of the eye, is a common cause of irreversible vision loss and the second leading cause of blindness worldwide. As an optic neuropathy, glaucoma is identified by increasing degeneration of retinal ganglion cells (RGCs), with consequential vision loss. Current treatments only postpone the development of retinal degeneration, and there are as yet no treatments available for this disability. Recent studies have shown that replacing lost or damaged RGCs with healthy RGCs or RGC precursors, supported by appropriately designed bio-material scaffolds, could facilitate the development and enhancement of connections to ganglion cells and optic nerve axons. The consequence may be an improved retinal regeneration. This technique could also offer the possibility for retinal regeneration in treating other forms of optic nerve ailments through RGC replacement. METHODS: In this brief review, we describe the innovations and recent developments in retinal regenerative medicine such as retinal organoids and gene therapy which are specific to glaucoma treatment and focus on the selection of appropriate bio-engineering principles, biomaterials and cell therapies that are presently employed in this growing research area. RESULTS: Identification of optimal sources of cells, improving cell survival, functional integration upon transplantation, and developing techniques to deliver cells into the retinal space without provoking immune responses are the main challenges in retinal cell replacement therapies. CONCLUSION: The restoration of visual function in glaucoma patients by the RGC replacement therapies requires appropriate protocols and biotechnology methods. Tissue-engineered scaffolds, the generation of retinal organoids, and gene therapy may help to overcome some of the challenges in the generation of clinically safe RGCs.

Diffusion modelling of percutaneous absorption kinetics. Predicting urinary excretion from in vitro skin permeation tests (IVPT) for an infinite dose.

In this work, we developed a number of generalised skin diffusion based pharmacokinetic models to relate published in vivo urinary excretion data to matching experimentally generated in vitro human skin permeation test (IVPT) data for a series of topically applied salicylate esters. A simplified linear in vivo model was found to inadequately describe the time course of urinary excretion over the entire sampling period. We represented the skin barrier as both a one layer (stratum corneum) and a two-layer (stratum corneum with viable epidermis) diffusion model and convoluted their Laplace solutions with that for a single exponential disposition phase to describe the urinary excretion profiles in the Laplace domain. We also derived asymptotic approximations for the model and estimated the conditions under which they could be used. We then sought to develop in vitro - in vivo relationships (IVIVR) for topically applied methyl, ethyl and glycol salicylates using our experimental IVPT data and the literature urinary excretion data. Good linear IVIVRs for ethyl and glycol salicylates were obtained, but the IVIVR for methyl salicylate was poor, perhaps because of topical stimulation of local skin blood flow by methyl salicylate. The ratio of the hydrated to dehydrated skin permeation for all salicylate esters was the same in both the IVPT and in vivo studies. A diffusion based one compartment pharmacokinetic model was also developed to describe the urinary excretion of solutes after removal of topical products and to compare the methyl salicylate skin permeation for five different body sites. The work presented here is consistent with the development of skin IVIVRs, but suggests that different skin conditions, application sites and local skin effects may affect model predictions.

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.

Investigation of the Size Distribution for Diffusion-Controlled Drug Release From Drug Delivery Systems of Various Geometries.

Various drug delivery systems (DDSs) are often used in modern medicine to achieve controlled and targeted drug release. Diffusional release of drugs from DDSs is often the main mechanism, especially at early times. Generally, average dimensions of DDS are used to model the drug release, but our recent work on drug release from fibers demonstrated that taking into account diameter distribution is essential. This work systematically investigated the effect of size distribution on diffusional drug release from DDSs of various geometric forms such as membranes, fibers, and spherical particles. The investigation clearly demonstrated that the size distribution has the largest effect on the drug release profiles from spherical particles compared to other geometric forms. Published experimental data for drug release from polymer microparticles and nanoparticles were fitted, and the diffusion coefficients were determined assuming reported radius distributions. Assuming the average radius when fitting the data leads to up to 5 times underestimation of the diffusion coefficient of drug in the polymer.

Numerical Investigation of Analytical Models of Drug Flux Through Microporated Skin.

In this study, drug flux through microporated skin was modeled using detailed numerical solution of the diffusion equation. The results of the modeling were compared to previously published simplified and easy to use analytical equations. Limitations and accuracy of these equations were investigated. Appropriate modifications of the equations were identified to expand them to wider practical applications when pore shape is not circular. Numerical simulations have shown a good accuracy of the new simple equations when these are used within their limits of application.

Using a simple equation to predict the microporation-enhanced transdermal drug flux.

The mathematical model describing drug flux through microporated skin was previously developed. Based on this model, two mathematical equations can be used to predict the microporatio-enhanced transdermal drug flux: the complex primal equation containing a variety of experimentally-determined variables, and the simplified straightforward equation. In this study, experimental transdermal fluxes of three corticosteroids through split-thickness human skin treated with a microneedle roller were measured, and the values of fluxes compared with those predicted using both the more complex and simplified equations. According to the results of the study, both equations demonstrated high accuracy in the prediction of the fluxes of corticosteroids. The simplified equation was validated and confirmed as robust using regression analysis of literature data. Further, its capability and ease of use was exemplified by predicting the flux of methotrexate through the skin microporated with laser and comparing with published experimental data.

Microneedles as the technique of drug delivery enhancement in diverse organs and tissues.

Microneedles is the technique of drug delivery enhancement, which was primarily designed for facilitating percutaneous drug delivery. Started from the development of simple solid microneedles, providing microporation of stratum corneum and therefore enhancement of topical drug delivery, for two decades the technique has progressed in various modifications such as hollow, coated, dissolving and hydrogel forming microneedles. In their turn, the modifications have resulted in new mechanisms of drug delivery enhancement and followed by the expansion of applicability range in terms of targeted tissues and organs. Thus, in addition to percutaneous drug delivery, microneedles have been considered as an efficient technique facilitating ocular, oral mucosal, gastrointestinal, ungual and vaginal drug administration. It is anticipated that the technique of microneedle-assisted drug delivery will soon become relevant for majority of organs and tissues.

Modelling drug flux through microporated skin.

A simple mathematical equation has been developed to predict drug flux through microporated skin. The theoretical model is based on an approach applied previously to water evaporation through leaf stomata. Pore density, pore radius and drug molecular weight are key model parameters. The predictions of the model were compared with results derived from a simple, intuitive method using porated area alone to estimate the flux enhancement. It is shown that the new approach predicts significantly higher fluxes than the intuitive analysis, with transport being proportional to the total pore perimeter rather than area as intuitively anticipated. Predicted fluxes were in good general agreement with experimental data on drug delivery from the literature, and were quantitatively closer to the measured values than those derived from the intuitive, area-based approach.

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.

Aspects of Mathematical Modelling of Pressure Retarded Osmosis.

In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed.

Temperature effect on the build-up of exponentially growing polyelectrolyte multilayers. An exponential-to-linear transition point.

In this study, the effect of temperature on the build-up of exponentially growing polyelectrolyte multilayer films was investigated. It aims at understanding the multilayer growth mechanism as crucially important for the fabrication of tailor-made multilayer films. Model poly(L-lysine)/hyaluronic acid (PLL/HA) multilayers were assembled in the temperature range of 25-85 °C by layer-by-layer deposition using a dipping method. The film growth switches from the exponential to the linear regime at the transition point as a result of limited polymer diffusion into the film. With the increase of the build-up temperature the film growth rate is enhanced in both regimes; the position of the transition point shifts to a higher number of deposition steps confirming the diffusion-mediated growth mechanism. Not only the faster polymer diffusion into the film but also more porous/permeable film structure are responsible for faster film growth at higher preparation temperature. The latter mechanism is assumed from analysis of the film growth rate upon switching of the preparation temperature during the film growth. Interestingly, the as-prepared films are equilibrated and remain intact (no swelling or shrinking) during temperature variation in the range of 25-45 °C. The average activation energy for complexation between PLL and HA in the multilayers calculated from the Arrhenius plot has been found to be about 0.3 kJ mol(-1) for monomers of PLL. Finally, the following processes known to be dependent on temperature are discussed with respect to the multilayer growth: (i) polymer diffusion, (ii) polymer conformational changes, and (iii) inter-polymer interactions.

Pathway Distribution Model for Solute Transport in Stratum Corneum.

One of the main functions of the skin is to reduce the amount of water evaporating from the surface of a human body with outermost layer of the epidermis, stratum corneum (SC), forming a barrier, which protects underlying tissue from dehydration. Empirical data obtained for water penetration in SC are normally analysed using mathematical models, among which the homogeneous membrane (HM) model is commonly employed to describe transport kinetics in SC. However, the HM model failed to fit simultaneously the experimental data for water permeation and desorption (Anissimov YG, Roberts MS. 2009. J Pharm Sci 98:772-781), as the model does not account for a complex structure of SC and irregular distribution of corneocytes. Our previous work (Anissimov YG, Roberts MS. 2009. J Pharm Sci 98:772-781) introduced a slow binding (SB) model that is more aligned with the true biological structure of SC. This report provides an alternative/additional model to both the HM and SB models and takes into account the distribution of effective pathways across SC for water transport.

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.

Iontophoretic skin permeation of peptides: an investigation into the influence of molecular properties, iontophoretic conditions and formulation parameters.

The transdermal route offers advantages for delivery of peptides and proteins. However, these polar and large molecules do not permeate the skin barrier well. Various enhancement methods have been employed to address this problem. Iontophoresis is one of the methods that shows promise but its application to peptide delivery has yet to be fully explored. This study investigates the effects of different molecular properties and iontophoretic conditions on the skin permeation of peptides. In this study, the permeation of alanine-tryptophan dipeptide (MW 276 Da), alanine-alanine-proline-valine tetrapeptide (MW 355 Da), Argireline® (Acetyl hexapeptide-3, MW 889 Da) and Triptorelin acetate (decapeptide, MW 1311 Da) through excised human skin under passive or iontophoretic current of 0.4 mA was investigated. The effects of pH change (3.0-7.4, to provide different net negative, neutral, and positive charges) to the peptide, donor concentration (1-10 mg/ml), background electrolyte (34-137 mM NaCl and/or 5-20 mM HEPES) and current direction (anodal vs cathodal) were also studied. Peptides were analysed by high-performance liquid chromatography or liquid scintillation counting. Iontophoresis led up to a 30 times increase in peptide permeation relative to passive permeation for the peptides. Electroosmosis was an important determinant of the total flux for the high molecular weight charged peptides. Electrorepulsion was found to be considerable for low molecular weight charged moieties. Permeation was decreased at lower pH, possibly due to decreased electroosmosis. Results also showed that 10 times increase in donor peptide concentration increases permeation of peptides by about 2-4 times and decreases iontophoretic permeability coefficients by about 2.5-5 times. The addition of extra background electrolyte decreased the iontophoretic permeation coefficient of peptides by 2-60 times. This study shows that iontophoretic permeation of peptides is affected by a number of parameters that can be optimized for effective transdermal peptide delivery.