Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

Targeted drug delivery to the skin and deeper tissues: Role of physiology, solute structure and disease

1. Drug delivery through the skin has been used to target the epidermis, dermis and deeper tissues and for systemic delivery, The major barrier for the transport of drugs through the skin is the stratum corneum, with most transport occurring through the intercellular region, The polarity of the intercellular region appears to be similar to butanol, with the diffusion of solutes being hindered by saturable hydrogen bonding to the polar head groups of the ceramides, fatty acids and other intercellular lipids, Accordingly, the permeability of the more lipophilic solutes is greatest from aqueous solutions, whereas polar solute permeability is favoured by hydrocarbon-based vehicles. 2. The skin is capable of metabolizing many substances and, through its microvasculature, limits the transport of most substances into regions below the dermis. 3. Although the flux of solutes through the skin should be identical for different vehicles when the solute exists as a saturated solution, the fluxes vary in accordance with the skin penetration enhancement properties of the vehicle. It is therefore desirable that the regulatory standards required for the bioequivalence of topical products include skin studies. 4. Deep tissue penetration can be related to solute protein binding, solute molecular size and dermal blood flow. 5. Iontophoresis is a promising area of skin drug delivery, especially for ionized solutes and when a rapid effect is required. 6. In general, psoriasis and other skin diseases facilitate drug delivery through the skin. 7. It is concluded that the variability in skin permeability remains an obstacle in optimizing drug delivery by this route.

In vitro human epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 from a range of solvents

Purpose. To study epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 (BP) from a range of single solvent vehicles and evaluate solvent effects on permeability parameters. Methods. The solubility of BP was measured in a number of solvents. Penetration of BP across human epidermis and high density polyethylene (HDPE) membranes was studied from 50% saturated solutions in each solvent. Results. Maximal BP fluxes from the solvents across the two membranes varied widely. Highest fluxes were observed from 90% ethanol (EtOH) for epidermis and from isopropyl myristate (IPM) and C12-15 benzoate alcohols (C12-15 BA) for HDPE membrane. Both the flux and estimated permeability coefficient and skin-vehicle partitioning of BP appeared to be related to the vehicle solubility parameter (delta(v)). The major effects of solvents on BP flux appear to be via changes in BP diffusivity through the membranes. Conclusions. Minimal penetration of sunscreens such as BP is best achieved by choosing vehicles with a delta(v) substantially different to the solubility parameter of the membrane.

Supersaturated solutions evaluated with an in vitro stratum corneum tape stripping technique

The flux of a compound across a membrane from any formulation, whether it contains penetration enhancers or not, is limited by its saturated solubility in the vehicle. Under such conditions the concentration of the permeant in the outer layers of the stratum corneum is also saturated. Consequently, when the permeation of a drug from a supersaturated solution leads to enhanced penetration, the concentration of the drug in the outer layers of the membrane is also supersaturated. Therefore, the stratum corneum may possess antinucleant properties which inhibit or retard the crystallisation process. In this study, the enhanced in vitro permeation of supersaturated solutions of piroxicam across human skin in diffusion cells was demonstrated. The amount of permeant in the stratum corneum was determined using a tape stripping technique. Supersaturated solutions up to four degrees of saturation were investigated which produced a linear relationship between the degree of saturation and the amount of piroxicam in the stratum corneum (R-2 = 0.970). Furthermore, the amount of piroxicam in the viable layers of the skin also increased with increasing degree of saturation. An analysis of the results suggested that enhanced penetration across human skin from supersaturated solutions of piroxicam may occur as a result of the antinucleating ability of the intercellular lipids of the stratum corneum. (C) 1997 Elsevier Science B.V.

Probing the effect of vehicles on topical delivery: Understanding the basic relationship between solvent and solute penetration using silicone membranes

Purpose. In the present study we examined the relationship between solvent uptake into a model membrane (silicone) with the physical properties of the solvents (e.g., solubility parameter, melting point, molecular weight) and its potential predictability. We then assessed the subsequent topical penetration and retention kinetics of hydrocortisone from various solvents to define whether modifications to either solute diffusivity or partitioning were dominant in increasing permeability through solvent-modified membranes. Methods. Membrane sorption of solvents was determined from weight differences following immersion in individual solvents, corrected for differences in density. Permeability and retention kinetics of H-3-hydrocortisone, applied as saturated solutions in the various solvents, were determined over 48 h in horizontal Franz-type glass diffusion cells. Results. Solvent sorption into the membrane could be related to differences in solubility parameters, MW and hydrogen bonding (r(2) = 0.76). The actual and predicted volume of solvent sorbed into the membrane was also found to be linearly related to Log hydrocortisone flux, with changes in both diffusivity and partitioning of hydrocortisone observed for the different solvent vehicles. Conclusions. A simple structure-based predictive model can be applied to the sorption of solvents into silicone membranes. Changes in solute diffusivity and partitioning appeared to contribute to the increased hydrocortisone flux observed with the various solvent vehicles. The application of this predictive model to the more complex skin membrane remains to be determined.

Influence of natural polymer derived from starch as a sensory modifier in sunscreen formulations

Background: Nowadays, there has been increased incidence of skin cancer, which is mainly related to increased sun exposure. Although sunscreen products may prevent the appearing of this disease, consumers may not use them due to some factors, including the sensory properties. The Aluminum Starch Octenylsuccinate (Dry-Flo® Pure, Akzo Nobel), an aluminum salt produced by the reaction of anhydride octenylsuccinic with starch, is able to improve the spreadability on the skin and reduce the oiliness of the formulation. Objective: To verify volunteers' acceptance for sunscreen formulation with natural polymer, compared with a control formulation (without polymer). Methods: To carry out the sensory analysis a formulation with or without 2. 0% Aluminum Starch Octenylsuccinate was prepared. Formulations had FPS 15, with critical wavelength of 353 nm, determined by testing in silico using the BASF® Sunscreen Simulator. Sensory analysis was performed on 60 students of both sexes, aged between 18 and 25 years, regular users of sunscreen products. Results: The results suggested that the polymer was able to promote a very soft and velvety feel on the skin when used in a sunscreen formulation, and it was able to mitigate and noticeably reduce the oiliness of the skin. Of the 60 volunteers who participated in the study, 45 volunteers (75%) considered that the polymer formulation provides little brightness or did not notice the difference in brightness of the skin after application. Conclusions: It was able to improve the sensory of the product, contributing to greater volunteers' acceptance.

Absorption of sunscreens across human skin: an evaluation of commercial products for children and adults

Aims Topical sunscreens are routinely applied to the skin by a large percentage of the population. This study assessed the extent of absorption of a number of common chemical sunscreen agents into and through human skin following application of commercially available products. Methods Sunscreen products were applied to excised human epidermis in Franz diffusion cells with the amount penetrating into and across the epidermis assessed by h.p.l.c. for 8 h following application. Results All sunscreen agents investigated penetrated into the skin (0.25 g m(-2) or 14% of applied dose), but only benzophenone-3 passed through the skin in significant amounts (0.08 g m(-2) or 10% of the applied dose). With one exception, suncreen agents in corresponding products marketed for adults and children had similar skin penetration profiles. Conclusions Whilst limited absorption across the skin was observed for the majority of the sunscreens tested, benzophenone-3 demonstrated sufficiently high penetration to warrant further investigation of its continued application.

Percutaneous absorption of sunscreen agents from liquid paraffin: Self-association of octyl salicylate and effects on skin flux

This study provides an investigation of the availability of octyl salicylate (OS), a common sunscreen agent, from liquid paraffin and the effect of OS on skin permeability. A model membrane system to isolate the vehicle effect from membrane permeability has been developed. Partitioning of OS between liquid paraffin and aqueous receptor phases was conducted. Partition coefficients increased with increase in OS concentration. A range of OS concentrations in liquid paraffin was diffused across human epidermis and synthetic membranes into 4% bovine serum albumin in phosphate-buffered saline and 50% ethanol. Absorption profiles of OS obtained from silicone and low-density polyethylene (LDPE) membranes were similar to each other but higher than for the high-density polyethylene [HDPE (3 times)] membrane and human epidermis (15 times). The steady state fluxes and apparent permeability coefficients (K-p') obtained from the diffusion studies showed the same trends with all membranes, except for the HDPE membrane which showed greater increase in flux and K-p' at concentrations above 30%. IR spectra showed that several bands of OS were shifted with concentrations, and the molecular models further suggested that the main contribution to the self-association is from non-1,4 van der Waals interactions.

Investigation of in vitro transdermal absorption of fentanyl from patches placed on skin samples obtained from various anatomic regions of dogs

Objective-To investigate in vitro transdermal absorption of fentanyl from patches through skin samples obtained from various anatomic regions of dogs. Sample Population-Skin samples from 5 Greyhounds. Procedure-Skin samples from the dogs' thoracic, neck, and groin regions were collected postmortem and frozen. After samples were thawed, circular sections were cut and placed in Franz-type diffusion cells in a water bath (32degreesC). A commercial fentanyl patch, attached to an acetate strip with a circular hole, was applied to each skin sample. Cellulose strips were used as control membranes. Samples of receptor fluid in the diffusion cells were collected at intervals for 48 hours, and fentanyl concentrations were analyzed by use of high-performance liquid chromatography. Results-Mean +/- SD release rate of fentanyl from the patch, defined by its absorption rate through the non-rate-limiting cellulose membrane, was linear during the first 8 hours (2.01 +/- 0.05 pg/cm(2) of cellulose membrane/h) and then decreased. Fentanyl passed through skin from the groin region at a faster rate and with a significantly shorter lag time, compared with findings in neck or thoracic skin samples. Conclusions and Clinical Relevance-In vitro, fentanyl from a patch was absorbed more quickly and to a greater extent through skin collected from the groin region of dogs, compared with skin samples from the thoracic and neck regions. Placement of fentanyl patches in the groin region of dogs may decrease the lag time to achieve analgesia perioperatively; however, in vivo studies are necessary to confirm these findings.

The effect of region of application on absorption of ethanol and hexanol through canine skin

The effect of region of application on the percutaneous penetration of solutes with differing lipophilicity was investigated in canine skin. Skin from the thorax, neck, back, groin, and axilla regions was harvested from Greyhound dogs and placed in Franz-type diffusion cells. Radiolabelled (C-14) ethanol (Log P 0.19) or hexanol (Log P 1.94) was applied to each skin section for a total of 5 h. The permeability coefficient (k(P), cm h(-1)) and residue of alcohol remaining in the skin were significantly (P = 0.001) higher for hexanol compared to ethanol. In contrast, ethanol had a far greater maximum flux (J(max), mol (cm(2))(-1) h(-1)) than hexanol (P = 0.001). A comparison of regional differences shows the k(P) and Jmax for ethanol in the groin was significantly lower (P = 0.035) than the back. The k(P) and Jmax for hexanol were significantly higher (P = 0.001) in the axilla than the other four skin sites. An understanding of factors influencing percutaneous drug movement is important when formulating topical preparations for the dog. (C) 2003 Elsevier Ltd. All rights reserved.

Effects of vehicle and region of application on absorption of hydrocortisone through canine skin

Objective-To determine the effects of various vehicles on the penetration and retention of hydrocortisone applied to canine skin. Sample Population-20 canine skin samples obtained from the thorax, neck, and groin regions of 5 Greyhounds. Procedure-Skin was harvested from dogs after euthanasia and stored at -20 degrees C until required. The skin was then defrosted and placed into diffusion cells, which were maintained at approximately 32 degrees C by a water bath. Saturated solutions of hydrocortisone that contained trace amounts of radiolabelled [C-14]-hydrocortisone in each vehicle (ie, PBS solution [PBSS] alone, 50% ethanol [EtOH] in PBSS [wt/wt], and 50% propylene glycol in PBSS [wt/wt]) were applied to the outer (stratum corneum) surface of each skin sample, and aliquots of receptor fluid were collected for 24 hours and analyzed for hydrocortisone. Results-The maximum flux of hydrocortisone was significantly higher for all sites when dissolved in a vehicle containing 50% EtOH, compared with PBSS alone or 50% propylene glycol, with differences more prominent in skin from the neck region. In contrast, higher residues of hydrocortisone were found remaining within the skin when PBSS alone was used as a vehicle, particularly in skin from the thorax and neck. Conclusions and Clinical Relevance-Penetration of topically applied hydrocortisone is enhanced when EtOH is used in vehicle formulation. Significant regional differences (ie, among the thorax, neck, and groin areas) are also found in the transdermal penetration and skin retention of hydrocortisone. Variability in clinical response to hydrocortisone can be expected in relation to formulation design and site of application.

Percutaneous absorption of steroids: Determination of in vitro permeability and tissue reservoir characteristics in human skin layers

The skin localization of steroids following topical application is largely unknown. We determined the distribution of five steroids in human skin using excised epidermal, dermal, and full-thickness membranes in vitro. There was no significant difference in steroid maximum flux through epidermal and full-thickness membranes, other than significantly lower fluxes for the most polar steroid, aldosterone. Hydrocortisone had the highest dermal diffusivity and dermal penetration, and the accumulation of hydrocortisone and corticosterone was higher than that of the other steroids. Slower penetration and higher accumulation in the viable epidermis of progesterone in full-thickness skin were consistent with dermal penetration limitation effects associated with high lipophilicity. Copyright (c) 2006 S. Karger AG, Basel

In vitro safety assessment of papain on human skin: A qualitative Light and Transmission Electron Microscopy (TEM) study

Papain is a thiol proteolytic enzyme widely used in dermatology that found applications in wound treatment. Recently, papain was also used as absorption enhancer which can modify the peptide/ protein material in the bilayer domain. We investigated papain safety using human skin that was exposed to papain in vitro at different times: 4, 24 and 48 hours. The samples were examined using Light and Transmission Electron Microscopy (TEM) to study of the mechanisms involved in enhancer-skin interaction. After 24 hours, changes occurred in corneosomes. However, samples of 48 hours did not show major changes in agreement with the control. These findings indicated that papain could be used safely onto the skin.

Penetration of Quantum Dot Particles Through Human Skin

The skin is a large and accessible area of the body, offering the possibility to be used as an alternative route for drug delivery. In the last few years strong progress has been made on the developing of nanoparticulate systems for specific applications. The interaction of such small particles with human skin and their possible penetration attracted some interest from toxicological as well as from drug delivery perspectives. As size is assumed to play a key role, the aim of the present work was to investigate the penetration profile of very small model particles (similar to 4 nm) into excised human skin under conditions chosen to mimic the in vivo situation. Possible application procedures such as massaging the formulation (5 to 10 minutes) were analyzed by non-invasive multiphoton- and confocal laser scanning microscopy (MPM, CLSM). Furthermore, the application on damaged skin was taken into account by deliberately removing parts of the stratum corneum. Although it was clearly observed that the mechanical actions affected the distribution pattern of the QDs on the skin surface, there was no evidence of penetration into the skin in all cases tested. QDs could be found in deeper layers only after massaging of damaged skin for 10 min. Taking these data into account, obtained on the gold standard human skin, the potential applications of nanoparticulate systems to act as carrier delivering drugs into intact skin might be limited and are only of interest for partly damaged skin.