Infinite Dose Conditions Research Articles

Integrating mathematical approaches (IMAS): Novel methodology for predicting dermal absorption rates of chemicals under finite dose conditions.

Quantitative structure permeation relationship (QSPR) models have gained prominence in recent years owing to their capacity to elucidate the influence of physicochemical properties on the dermal absorption of chemicals. These models facilitate the prediction of permeation coefficient (Kp) values, indicating the skin permeability of a chemical under infinite dose conditions. Conversely, obtaining dermal absorption rates (DAs) under finite dose conditions, which are crucial for skin product safety evaluation, remains a challenge when relying solely on Kp predictions from QSPR models. One proposed resolution involves using Kroes' methodology, categorizing DAs based on Kp values; however, refinement becomes necessary owing to discreteness in the obtained values. We previously developed a mathematical model using Kp values obtained from in vitro dermal absorption tests to predict DAs. The present study introduces a new methodology, Integrating Mathematical Approaches (IMAS), which combines QSPR models and our mathematical model to predict DAs for risk assessments without conducting in vitro dermal absorption tests. Regarding 40 chemicals (76.1 ≤ MW ≤ 220; -1.4 ≤ Log Ko/w ≤ 3.1), IMAS showed that 65.0% (26/40) predictions of DA values were accurate to within twofold of the observed values in finite dose experiments. Compared to Kroes' methodology, IMAS notably mitigated overestimation, particularly for hydrophilic chemicals with water solubility exceeding 57.0 mg/cm3. These findings highlight the value of IMAS as a tool for skin product risk assessments, particularly for hydrophilic compounds.

Lipid-coated membranes as skin surrogates for permeability assessment

There is a growing interest in developing in vitro skin models, particularly in the fields of skin care and drug delivery regarding optimization of topical drug formulations. The ban of animal experiments for cosmetic products testing has led to the development of alternative in vitro methods. The aim of this study was to develop and characterize simplified, cell-free, lipid-coated membrane models, exploring the usefulness and the potential application of these membranes in comparison to commercial synthetic membrane and to porcine skin. In these model membranes, lipids are deposited onto a polycarbonate membrane to create lipid-rich coated membranes. Two types of lipid-coated membranes were explored depending on the type of lipids used. In one type (phospholipidic), membranes were prepared depositing soybean phosphatidylcholine liposomes and in the other type (non-phospholipidic), major components of the stratum corneum lipid matrix were used to coat the polycarbonate membrane. Coating process was performed using drying and centrifugation steps. Under infinite dose conditions, and caffeine as permeant, high permeation correlation between developed membranes and pig skin was obtained, and similar permeation pro-files were obtained through phospholipidic and non-phospholipidic membranes. This study demonstrated the potential of the developed membranes to conduct permeation studies using Franz-type diffusion cells, and the simplication process to produce lipid-coated membranes.

Improvement of Skin Permeation of Caffeine, a Hydrophilic Drug, by the Application of Water Droplets Provided by a Novel Humidifier Device.

Recently, a novel humidifier that sprays water fine droplets equipped with a copolymer, poly(3,4-ethylene dioxythiophene)-poly(styrene sulfonate) (PEDOT/PSS) was developed. PEDOT/PSS in the humidifier absorbs water from the environment and releases fine water droplets by heating. In the present study, the effect of hydration on the skin barrier, stratum corneum, was first determined by the application of fine water droplets using the humidifier. The skin-penetration enhancement effect of a model hydrophilic drug, caffeine, was also investigated using the humidifier and compared with a conventional water-evaporative humidifier. More prolonged skin hydration effect was observed after application of the fine water droplet release humidifier using PEDOT/PSS than that using a conventional humidifier. In addition, markedly higher skin permeation of caffeine was observed in both infinite and finite dose conditions. Furthermore, higher skin permeation of caffeine from oil/water emulsion containing caffeine was observed in finite dose conditions by pretreatment with the humidifier using PEDOT/PSS. This device can provide water droplets without replenishing water, so it is more convenient for enhancing the skin permeation of chemical compounds from topical drugs and cosmetic formulations.

Polymeric micelle mediated follicular delivery of spironolactone: Targeting the mineralocorticoid receptor to prevent glucocorticoid-induced activation and delayed cutaneous wound healing

Impaired wound healing in patients receiving glucocorticoid therapy is a serious clinical concern: mineralocorticoid receptor (MR) antagonists can counter glucocorticoid-induced off-target activation of MR receptors. The aim of this study was to investigate the cutaneous delivery of the potent MR antagonist, spironolactone (SPL), from polymeric micelle nanocarriers, prepared using a biodegradable copolymer, methoxy-poly(ethylene glycol)-di-hexyl-substituted-poly(lactic acid). Immunofluorescent labelling of the MR showed that it was principally located in the pilosebaceous unit (PSU), justifying the study rationale since polymeric micelles accumulate preferentially in appendageal structures. Cutaneous biodistribution studies under infinite and finite dose conditions, demonstrated delivery of pharmacologically relevant amounts of SPL to the epidermis and upper dermis. Preferential PSU targeting was confirmed by comparing amounts of SPL in PSU-containing and PSU-free skin biopsies: SPL nanomicelles showed 5-fold higher delivery of SPL in the PSU-containing biopsies, 0.54 ± 0.18 ng/mm2vs. 0.10 ± 0.03 ng/mm2, after application of a hydrogel in finite conditions. Canrenone, an active metabolite of SPL, was also quantified in skin samples. In addition to being used for the treatment of delayed cutaneous wound healing by site-specific antagonism of the MR, the formulation might also be used to treat pilosebaceous androgen-related skin diseases, e.g. acne vulgaris, since SPL is a potent androgen receptor antagonist.

Prediction of skin permeation and concentration of rhododendrol applied as finite dose from complex cosmetic vehicles.

Finite dose experiments represent clinical use wherein depletion of dose, evaporation of excipients, and gradual change in vehicle composition may occur. In the present study, we attempted a mathematical approach for predicting skin permeation and concentration of a cosmetic active, rhododendrol (RD), from complex vehicle-based formulations applied in finite dose. In vitro skin permeation and concentration studies of RD were conducted from formulations containing water and polyols with concentrations ranging from 10 to 100% under infinite and finite dose conditions using vertical Franz diffusion cells. Observed data for skin permeation and the viable epidermis and dermis (VED) concentration of RD were estimated by the differential equations under Fick's second law of diffusion together with water evaporation kinetics and changes in the partition coefficient from vehicles to the stratum corneum. As a result, a goodness-of-fit was observed allowing accurate estimation of skin permeation and VED concentration of RD. This mathematical approach could become a useful tool to estimate the skin permeation and concentration of actives from topical formulation applied in finite dose conditions likened in actual use.

Usefulness of Artificial Membrane, Strat-M®, in the Assessment of Drug Permeation from Complex Vehicles in Finite Dose Conditions.

The ban on the use of animals in testing cosmetic products has led to the development of animal-free in vitro methods. Strat-M® is an artificial membrane engineered to mimic human skin and is recommended as a replacement for skin. However, its usefulness in the assessment of the permeation of cosmetics in in-use conditions remains unverified. No data have been published on its comparative performance with the membrane of choice, porcine skin. The comparative permeability characteristics of Strat-M® and porcine skin were investigated using Franz diffusion cells. Caffeine (CF) and rhododendrol (RD) in complex vehicles with varying concentrations of polyols were applied as finite and infinite doses. Good rank orders of permeation from finite dose experiments were observed for RD. High correlations were observed in RD permeation between Strat-M® and porcine skin under finite and infinite dose conditions, whereas only finite dose conditions for CF were associated with good correlations. Permeation from formulations with high polyol content and residual formulations was enhanced due to the disruption of the integrity of the Strat-M® barrier. The usefulness of Strat-M® in the assessment of dermal permeation may be limited to finite dose conditions and not applicable to infinite dose conditions or formulations applied in layers.

Topical delivery of niacinamide: Influence of neat solvents

Niacinamide (NIA) has been widely used in cosmetic and personal care formulations for several skin conditions. Permeation of topical NIA has been confirmed in a number of studies under infinite dose conditions. However, there is limited information in the literature regarding permeation of NIA following application of topical formulations in amounts that reflect the real-life use of such products by consumers. The aim of the present work was therefore to investigate skin delivery of NIA from single solvent systems in porcine skin under finite dose conditions. A secondary aim was to probe the processes underlying the previously reported low recovery of NIA following in vitro permeation and mass balance studies. The solubility and stability of NIA in various single solvent systems was examined. The solvents investigated included Transcutol® P (TC), propylene glycol (PG), 1-2 hexanediol (HEX), 1-2 pentanediol (1-2P), 1-5 pentanediol (1-5P), 1-3 butanediol (1-3B), glycerol (GLY) and dimethyl isosorbide (DMI). Skin permeation and deposition of the molecule was investigated in full thickness porcine skin in vitro finite dose Franz-type diffusion experiments followed by mass balance studies. Stability of NIA for 72h in the solvents was confirmed. The solubility of NIA in the solvents ranged from 82.9±0.8 to 311.9±4.5mg/mL. TC delivered the highest percentage permeation of NIA at 24h, 32.6±12.1% of the applied dose. Low total recovery of NIA after mass balance studies was observed for some vehicles, with values ranging from 55.2±12.8% to 106.3±2.3%. This reflected the formation of a number of NIA degradation by-products in the receptor phase during the permeation studies. Identification of other vehicles for synergistic enhancement of NIA skin delivery will be the subject of future work.

In vitro dermal absorption of carfentanil

There is growing concern regarding potential occupational exposures to the ultra-potent synthetic opioid carfentanil. However, little data are available on the toxicity of carfentanil in humans, particularly for dermal exposures. To begin to address this, permeation of carfentanil formulated in three vehicles, water, ethanol, and hand sanitizer was measured under infinite-dose conditions in an in vitro static diffusion cell system using the EpiDerm™ (EPI-606-X) RhE model. The permeation rate was fastest for carfentanil in water (3.9 × 10−3 cm/h), followed by hand sanitizer (1.2 × 10−3 cm/h), and slowest for carfentanil in ethanol (0.2 × 10−3 cm/h). In both ethanol and hand sanitizer, a lag-time between exposure and permeation of approximately 1.5 h was observed, while lag-time in water was approximately half an hour. Flux at steady-state was greater at 50.6 μg/ml than at 5.3 μg/ml for both water and ethanol; however, the percent of dose absorbed did not differ between doses for either vehicle. Slight differences in percutaneous permeation of carfentanil were observed between two brands of hand sanitizer, likely due to differences in relative proportion of alcohol and skin penetration enhancers. These data indicate that small skin exposures may not result in rapid, significant toxicity as previously reported.

The role of vehicle metamorphosis on triamcinolone acetonide delivery to the skin from microemulsions.

After application to the skin surface, a topical formulation is submitted to changes in composition produced by evaporation of volatile components, penetration of components into the skin and extraction of skin components ("vehicle metamorphosis"). The aim of this work was to study the effect of vehicle metamorphosis on skin delivery from microemulsions containing triamcinolone acetonide. The microemulsions were prepared and characterized for water evaporation kinetics, in vitro release and skin permeation and retention. Skin retention experiments were performed on full thickness pig ear skin, in both occluded infinite and un-occluded finite dose conditions. For comparison purposes, two creams, the commercial Ledercort® and a vanishing cream, were tested. With triamcinolone acetonide water evaporation does not modify skin retention, probably for the lipophilic nature of the drug. However, if water is eliminated from the microemulsions, the performance is reduced, probably because drug partitioning from vehicle to stratum corneum is disfavored. If a water-soluble drug (methyl prednisolone sodium succinate) is used, infinite dose application in occlusive conditions increases in a significant way the amount of drug retained in the skin. The involved mechanisms are probably stratum corneum swelling and increase of stratum corneum/viable epidermis partitioning.

Polymeric micelle nanocarriers for targeted epidermal delivery of the hedgehog pathway inhibitor vismodegib: formulation development and cutaneous biodistribution in human skin

ABSTRACTBackground: The aim was to investigate cutaneous delivery and biodistribution of the hedgehog pathway inhibitor, vismodegib (VSD), indicated for basal cell carcinoma (BCC), from polymeric micelle formulations under infinite/finite dose conditions.Methods: VSD-loaded micelles were characterized for drug content, particle size, and shape; a micelle gel was characterized for its rheological behavior. Cutaneous deposition and biodistribution of VSD were determined using porcine and human skin in vitro with quantification by UHPLC-MS/MS.Results: The optimal micelle solution (Zav 20–30 nm) increased the aqueous solubility of VSD by >8000-fold; drug content was stable after 4 weeks at 4°C. Application of micelle solution and micelle gel (0.086% w/v) to human skin for 12 h under infinite dose conditions resulted in statistically equivalent VSD deposition (0.62 ± 0.11 and 0.67 ± 0.14 μg/cm2, respectively). Cutaneous biodistribution in human skin under infinite (micelle solution and gel) and finite (micelle gel) dose conditions showed that the VSD concentrations obtained in the basal epidermis, at depths of 120–200 μm, were ˃3800- and ˃2300-fold greater than the IC50 reported for hedgehog signaling pathway inhibition in vitro.Conclusion: Cutaneous delivery of VSD from micelle-based formulations might enable targeted, topical treatment of superficial BCC with minimal risk of systemic exposure.

A comparison of the in vitro permeation of niacinamide in mammalian skin and in the Parallel Artificial Membrane Permeation Assay (PAMPA) model

The in vitro skin penetration of pharmaceutical or cosmetic ingredients is usually assessed in human or animal tissue. However, there are ethical and practical difficulties associated with sourcing these materials; variability between donors may also be problematic when interpreting experimental data. Hence, there has been much interest in identifying a robust and high throughput model to study skin permeation that would generate more reproducible results. Here we investigate the permeability of a model active, niacinamide (NIA), in (i) conventional vertical Franz diffusion cells with excised human skin or porcine skin and (ii) a recently developed Parallel Artificial Membrane Permeation Assay (PAMPA) model. Both finite and infinite dose conditions were evaluated in both models using a series of simple NIA solutions and one commercial preparation. The Franz diffusion cell studies were run over 24 h while PAMPA experiments were conducted for 2.5 h. A linear correlation between both models was observed for the cumulative amount of NIA permeated in tested models under finite dose conditions. The corresponding correlation coefficients (r2) were 0.88 for porcine skin and 0.71 for human skin. These results confirm the potential of the PAMPA model as a useful screening tool for topical formulations. Future studies will build on these findings and expand further the range of actives investigated.

Topical delivery of climbazole to mammalian skin

Dandruff is a common condition, affecting up to half the global population of immunocompetent adults at some time during their lives and it has been highly correlated with the over-expression of the fungus Malassezia spp. Climbazole (CBZ) is used as an antifungal and preservative agent in many marketed formulations for the treatment of dandruff. While the efficacy of CBZ in vitro and in vivo has previously been reported, limited information has been published about the uptake and deposition of CBZ in the skin. Hence, our aim was to investigate the skin permeation of CBZ as well as the influence of various solvents on CBZ skin delivery. Four solvents were selected for the permeability studies of CBZ, namely propylene glycol (PG), octyl salicylate (OSal), Transcutol® P (TC) and polyethylene glycol 200 (PEG). The criteria for selection were based on their wide use as excipients in commercial formulations, their potential to act as skin penetration enhancers and their favourable safety profiles. 1% (w/v) solutions of CBZ were applied under infinite and finite dose conditions using Franz type diffusion cells to human and porcine skin. In line with the topical use of CBZ as an antidandruff agent, comparatively low amounts of CBZ penetrated across the skin barrier (<1% of the applied dose of CBZ). Finite dose studies resulted in a higher extraction of CBZ from human skin compared with infinite dose studies (p < 0.05). CBZ was also taken up to a higher extent in porcine skin (>7-fold) compared with human skin (p < 0.05). Nevertheless, no statistical differences were observed in the amounts that permeated across the different membranes. These preliminary results confirm the potential of simple formulations of CBZ to target the outer layers of the epidermis. The PG and OSal formulations appear to be promising vehicles for CBZ in terms of overall skin extraction and penetration. Future work will expand the range of vehicles studied and explore the reasons underlying the retention of CBZ in the outer layers of the skin.

An integrated approach to optimizing skin delivery of cosmetic and pharmaceutical actives

The academic literature on skin delivery provides countless examples of scientific insights into specific aspects of the overall process. For the practical formulator, however, it is difficult to know how to combine such insights in a way that fits into the realities of commercial formulations. In this study, five key principles are combined into an integrated approach that can be applied to real-world formulations. Given the complexities of skin science, the integrated approach cannot be expected to be highly precise. Instead, it is intended as a way for a formulation team to balance the many conflicting issues. The predictions are sufficiently specific to be examined by those with the appropriate analytical resources and data on formulation efficacy. It is hoped that such challenges will allow the approach to be refined for the future.

Effect of γ-cyclodextrin on the in vitro skin permeation of a steroidal drug from nanoemulsions: Impact of experimental setup

Numerous reports on the enhancement effect of cyclodextrins (CDs) on the skin permeation of dermally applied drugs exist, the majority of which is based on in vitro diffusion cell studies. The specific experimental setup of such studies may skew the obtained results, which is rarely discussed in the context of CD studies. Thus, the aim of this work was to conduct a systematic in vitro investigation of the permeation enhancement potential of γ-CD on a steroidal drug from a nanoemulsion. The role of critical diffusion cell parameters such as the dose of application, occlusive conditions, the nature of the receptor medium and the skin thickness were investigated. The results showed that significantly enhanced skin permeation rates of fludrocortisone acetate were indeed caused by 1% (w/w) of γ-CD at both finite and infinite dose conditions. At 0.5% (w/w) of γ-CD, significant enhancement was only achieved at infinite dose application. Additional in vitro tape stripping experiments confirmed these tendencies, but the observed effects did not reach statistical significance. It may be concluded that the full permeation enhancement potential of the CD as observed in the franz-cell setup can only be realised at infinite dose conditions while preserving the formulation structure.

Human skin penetration of a copper tripeptide in vitro as a function of skin layer.

Objective and designSkin retention and penetration by copper applied as glycyl-l-histidyl-l-lysine cuprate diacetate was evaluated in vitro in order to assess its potential for its transdermal delivery as an anti-inflammatory agent.Materials and methodsFlow-through diffusion cells with 1 cm2 exposure area were used under infinite dose conditions. 0.68% aq. copper tripeptide as permeant was applied on isolated stratum corneum, heat-separated epidermis and dermatomed skin and receptor fluid collected over 48 h in 4 h intervals using inductively coupled plasma mass spectrometry to analyze for copper in tissues and receptor fluid.ResultsThe permeability coefficient of the compound through dermatomed skin was 2.43 ± 0.51 × 10−4 cm/h; 136.2 ± 17.5 μg/cm2 copper permeated 1 cm2 of that tissue over 48 h, while 97 ± 6.6 μg/cm2 were retained as depot.ConclusionsCopper as tripeptide was delivered in potentially therapeutically effective amounts for inflammatory disease.

Human skin retention and penetration of a copper tripeptide in vitro as function of skin layer towards anti-inflammatory therapy.

Objective and designThe skin retention and penetration characteristics of copper applied as glycyl-l-histidyl-l-lysine cuprate diacetate were evaluated in vitro in order to assess the potential for its transdermal delivery as anti-inflammatory agent.Materials and methodsFlow-through diffusion cells with 1 cm2 exposure area were used under infinite dose conditions. 0.68% aq. Copper as a tripeptide was applied on isolated stratum corneum, on heat-separated epidermis and on dermatomed skin. Receptor fluid collected over 48 h in 4 h intervals was analyzed by inductively coupled plasma mass spectrometry for copper in tissues and receptor fluid.ResultsThe permeability coefficient of the compound through dermatomed skin was 2.43 ± 0.51 × 10−4 cm/h; 136.2 ± 17.5 μg/cm2 copper permeated 1 cm2 of that tissue over 48 h, while 82 ± 8.1 μg/cm2 of copper were retained there as depot.ConclusionsApplied tansdermally as the tripeptide on human skin ex vivo, copper permeated the skin and was also retained in skin tissue in amounts potentially effective for the treatment of inflammatory diseases.

New in vitro dermal absorption database and the prediction of dermal absorption under finite conditions for risk assessment purposes

Most QSARs for dermal absorption predict the permeability coefficient, Kp, of a molecule, which is valid for infinite dose conditions. In practice, dermal exposure mostly occurs under finite dose conditions. Therefore, a simple model to predict finite dose dermal absorption from infinite dose data (Kp and lag time) and the stratum corneum/water partition coefficient (KSC,W) was developed. To test the model, a series of in vitro dermal absorption experiments was performed under both infinite and finite dose conditions using acetic acid, benzoic acid, bis(2-ethylhexyl)phthalate, butoxyethanol, cortisone, decanol, diazinone, 2,4-dichlorophenol, ethacrynic acid, linolenic acid, octylparaben, oleic acid, propylparaben, salicylic acid and testosterone. For six substances, the predicted relative dermal absorption was not statistically different from the measured value. For all other substances, measured absorption was overpredicted by the model, but most of the overpredictions were still below the European default absorption value. In conclusion, our finite dose prediction model provides a useful and cost-effective estimate of dermal absorption, to be used in risk assessment for non-volatile substances dissolved in water at non-irritating concentrations.

The maximum pharmacodynamic effect as a response parameter: pharmacokinetic considerations.

In previous human in-vivo studies measuring the maximum pharmacodynamic response to characterize cutaneously applied ointment preparations, it was observed that differences between various formulations caused by penetration enhancement led to different enhancement factors depending on the method used for determination of these factors from activity-response curves. To clarify this discrepancy, pharmacokinetic simulations have been performed based on an open one-compartment model with either first- or zero-order drug penetration kinetics and first-order elimination kinetics. Under the assumption that the maximum pharmacodynamic response corresponds to the maximum effective drug concentration in the receptor compartment, which represents the difference between the maximum drug concentration and the threshold concentration, drug concentration vs time profiles and dose-response curves were simulated. In addition, maximum effective concentrations were calculated and plotted against the logarithm of the thermodynamic drug activity to obtain activity-response curves. Relative bioavailability and enhancement factors were determined either from the horizontal distance between the curves of a standard and a test preparation, or as the ratio of the maximum effective concentration of test and standard formulations. A significant difference between the first-order and the zero-order input kinetics with regard to the evaluation of bioavailability and drug penetration enhancement was shown. Under finite dose conditions, i.e. first-order input kinetics from solution-type preparations, a misestimation of the factors usually occurs. Only under infinite dose conditions, i.e. if large preparation volumes are applied to achieve zero-order input kinetics, is the determination of bioavailability and enhancement factors from dose- and activity-response curves accurate.

Time of Erythema Onset after Application of Methyl Nicotinate Ointments as Response Parameter: Influence of Penetration Kinetics and Enhancing Agents

The time of erythema onset may be used as a response parameter for quantification of the cutaneous erythema response induced by methyl nicotinate. The vehicles light mineral oil (LMO; test) and medium chain triglycerides (MCT; standard) were compared with regard to the pharmacodynamic response. Moreover, the influence of penetration enhancers on the time of erythema onset was investigated under zero order penetration kinetics. The enhancers dimethyl sulfoxide, diethylene glycol monoethyl ether and three different glycerides in different concentrations were added to MCT as a standard vehicle. All preparations were applied to the forearms of volunteers under infinite dose conditions at different thermodynamic drug activity levels (0.2–3.2% of the saturation level) and different drug concentrations (0.051–0.816%), respectively. Different penetration kinetics do not influence data of erythema onset, as these data are comparable to those obtained under finite dose conditions (first order penetration kinetics). With regard to the penetration enhancers, a significantly enhanced penetration of methyl nicotinate could be observed only for diethylene glycol monoethyl ether and dimethyl sulfoxide. However, no significant difference between light mineral oil and MCT could be found with regard to penetration enhancement. The time of erythema onset is an easy and efficient parameter for quantification of the pharmacodynamic response caused by nicotinates.

Penetration of Ammonium Perfluorooctanoate Through Rat and Human Skin In Vitro

Rat and human epidermal membranes were mounted onto in vitro diffusion cells with an exposure area of 0.64 cm2, and skin integrity was confirmed using electrical impedance. Following membrane selection, Fluorad FC-118, a 20% aqueous solution of ammonium perfluorooctanoate (AFPO), was applied to the epidermal surface of each skin replicate at approximately 150 µL/cm2 and the donor chamber opening occluded with Parafilm. Serial receptor fluid samples were collected hourly from 1 to 6 h and at 12, 24, 30, and 48 h and analyzed by liquid chromatography–mass spectrometry (LC-MS) for APFO anion (PFO−). For rat skin, the time to steady-state penetration (6500 ± 3000 ng APFO · cm− 2· h− 1) occurred in less than 12 h, which was sustained until termination (48 h). Based on the concentration of the applied test material, the permeability coefficient (Kp) for APFO in rat skin was calculated to be 3.25 ± 1.51 × 10− 5 cm/h. By end of the 48-h exposure period, only a small portion of the total APFO applied (1.44 ± 1.13%) had penetrated through rat skin. For human skin, steady-state penetration of APFO (190 ± 57 ng APFO · cm− 2· h− 1) was reached by 12 h. Based on the concentration of the applied test material, the permeability coefficient for APFO in human skin was calculated to be 9.49 ± 2.86 × 10− 7 cm/h. By the end of the 48-h exposure period, only a negligible amount of the total APFO applied (0.048 ± 0.01%) had penetrated through human skin. Thus, under infinite dose and occlusive conditions, the steady-state penetration of APFO from a 20% solution was approximately 34-fold faster through rat skin than human skin.