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.

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.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

An optimized reverse-phase high performance liquid chromatographic method for evaluating percutaneous absorption of glucosamine hydrochloride

A relatively simple, selective, precise and accurate high performance liquid chromatography (HPLC) method based on a reaction of phenylisothiocyanate (PITC) with glucosamine (GL) in alkaline media was developed and validated to determine glucosamine hydrochloride permeating through human skin in vitro. It is usually problematic to develop an accurate assay for chemicals traversing skin because the excellent barrier properties of the tissue ensure that only low amounts of the material pass through the membrane and skin components may leach out of the tissue to interfere with the analysis. In addition, in the case of glucosamine hydrochloride, chemical instability adds further complexity to assay development. The assay, utilising the PITC-GL reaction was refined by optimizing the reaction temperature, reaction time and PITC concentration. The reaction produces a phenylthiocarbarnyl-glucosamine (PTC-GL) adduct which was separated on a reverse-phase (RP) column packed with 5 mu m ODS (C-18) Hypersil particles using a diode array detector (DAD) at 245 nm. The mobile phase was methanol-water-glacial acetic acid (10:89.96:0.04 v/v/v, pH 3.5) delivered to the column at 1 ml min(-1) and the column temperature was maintained at 30 degrees C Using a saturated aqueous solution of glucosamine hydrochloride, in vitro permeation studies were performed at 32 +/- 1 degrees C over 48 h using human epidermal membranes prepared by a heat separation method and mounted in Franz-type diffusion cells with a diffusional area 2.15 +/- 0.1 cm(2). The optimum derivatisation reaction conditions for reaction temperature, reaction time and PITC concentration were found to be 80 degrees C, 30 min and 1 % v/v, respectively. PTC-Gal and GL adducts eluted at 8.9 and 9.7 min, respectively. The detector response was found to be linear in the concentration range 0-1000 mu g ml(-1). The assay was robust with intra- and inter-day precisions (described as a percentage of relative standard deviation, %R.S.D.) < 12. Intra- and inter-day accuracy (as a percentage of the relative error, %RE) was <=-5.60 and <=-8.00, respectively. Using this assay, it was found that GL-HCI permeates through human skin with a flux 1.497 +/- 0.42 mu g cm(-2) h(-1), a permeability coefficient of 5.66 +/- 1.6 x 10(-6) cm h(-1) and with a lag time of 10.9 +/- 4.6 h. (c) 2005 Elsevier B.V. All rights reserved.

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC. (C) 2004 Wiley-Liss, Inc.

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

Chemical and physical methods of enhancing the percutaneous absorption of antimicrobial agents

Contrary to previously held beliefs, it is now known that bacteria exist not only on the surface of the skin but they are also distributed at varying depths beneath the skin surface. Hence, in order to sterilise the skin, antimicrobial agents are required to penetrate across the skin and eliminate the bacteria residing at all depths. Chlorhexidine is an antimicrobial agent with the widest use for skin sterilisation. However, due to its poor permeation rate across the skin, sterilisation of the skin cannot be achieved and, therefore, the remaining bacteria can act as a source of infection during an operation or insertion of catheters. The underlying theme of this study is to enhance the permeation of this antimicrobial agent in the skin by employing chemical (enhancers and supersaturated systems) or physical (iontophoresis) techniques. The hydrochloride salt of chlorhexidine (CHX), a poorly soluble salt, was used throughout this study. The effect of ionisation on in vitro permeation rate across the excised human epidennis was investigated using Franz-type diffusion cells. Saturated solutions of CHX were used as donor and the variable studied was vehicle pH. Permeation rate was increased with increasing vehicle pH. The pH effect was not related to the level of ionisation of the drug. The effect of donor vehicle was also studied using saturated solutions of CHX in 10% and 20% ethanol as the donor solutions. Permeation of CHX was enhanced by increasing the concentration of ethanol which could be due to the higher concentration of CHX in the donor phase and the effect of ethanol itself on the membrane. The interplay between drug diffusion and enhancer pretreatment of the epidennis was studied. Pretreatment of the membrane with 10% Azone/PG demonstrated the highest diffusion rate followed by 10% olcic acid/PG pretreatment compared to other pretreatment regimens (ethanol, dimethyl sulfoxide (DMSO), propylene glycol (PG), sodium dodecyl sulphate (SDS) and dodecyl trimethyl ammonium bromide (DT AB). Differential Scanning Calorimetry (DSC) was also employed to study the mode of action of these enhancers. The potential of supersaturated solutions in enhancing percutaneous absorption of CHX was investigated. Various anti-nucleating polymers were screened in order to establish the most effective agent. Polyvinylpyrrolidone (PVP, K30) was found to be a better candidate than its lower molecular weight counterpart (K25) and hydroxypropyl methyleellulose (HPMC). The permeation studies showed an increase in diffusion rate by increasing the degree of saturation. Iontophoresis is a physical means of transdemal drug delivery enhancement that causes an increased penetration of molecules into or through the skin by the application of an electric field. This technique was employed in conjunction with chemical enhancers to assess the effect on CHX permeation across the human epidermis. An improved transport of CHX, which was pH dependant was observed upon application of the current. Combined use of iontophoresis and chemical enhancers further increased the CHX transport indicating a synergistic effect. Pretreatment of the membrane with 10% Azone/PG demonstrated the greatest effect.

The percutaneous absorption of ionisable compounds

The effects of ionisation on transdermal drug delivery using excised human epidermis (HS) and silastic rubber (SR) as model permeation barriers were investigated in vitro using Franz-type absorption cells. Suspensions and solutions of salicylic acid (SA), the model ionogenic permeant, were used as donors and the variables studied were vehicle pH and trans-membrane pH-gradients. For solutions, the pH effect was related to the level of ionisation of the drug and the degree of saturation of the solution. With suspensions, the observed permeation rate was unaffected by pH. The penetration profiles through HS and SR were similar, although the overall flux through HS was about 70% of that observed through SR. Pretreatment of the membranes with various enhancer regimens, including oleic acid, Azone and N, N-dimethylamides in propylene glycol (PG) and isopropyl myristate (IPM) promoted the penetration of SA. SR was not a suitable model for enhancer pretreatment using IPM as a vehicle as the membrane was significantly disrupted by this vehicle. The results from comparable experiments with and without a trans-membrane pH-gradient did not have a significant effect upon flux or flux enhancement after pretreatment with the above enhancers. A theoretical model for the extraction coefficients of weak acids was derived using the partition coefficients of the ionised and unionised species, pH and pKa. This model was shown to account for the variation in overall partition of salicylic acid dependent upon pH and pKa. This model was shown to account for the variation in overall partition of salicylic acid dependent upon pH and pKa. The distribution of this solute between aqueous and oily phases, with and without added enhancer, was measured as a function of pH. The extraction coefficients determined were consistent with the model and showed that the behaviour of the system can be explained without referral to ion-pair mechanisms. Phosphonoacetate is an effective antiviral agent. However, as it is charged at physiological pH, its permeation across cell membranes is limited. To assess the improvement of the transport properties of this molecule, mono-, di- and tri-ester prodrugs were examined. These were assessed for stability and subsequent breakdown with respect to pH by HPLC. In vitro percutaneous absorption was observed using the triester, but not the ionic mono- or di-esters. The triester absorption could be potentiated using a range of enhancers with oleic acid being the most effective. Cyclodextrins (CD) have a role as absorption enhancers for peptide compounds across nasal epithelium. One potential mode of action is that CDs include these compounds, protect them from enzymic attack and thereby increase their residence time in the nasal epithelium. This study investigated the potential of CDs to protect ester prodrugs from enzymatic breakdown and prevent production of poorly transportable ionic species. Using a range of CD to ester molar ratios (10:1 to 2500:1) a small, but measurable, protection for the model esters (parabens) against esterase attack was observed. Possible mechanisms for this phenomenon are that CDs include the ester, making it unavailable for hydrolysis, the CDs may also affect the esterase in some way preventing access for the ester into the active site.

Bovine-serum-albumin-containing receptor phase better predicts transdermal absorption parameters for lipophilic compounds

Based on the hypothesis that limited receptor solubility of lipophilic compounds may result in lower observed permeability parameters, the aim of this study was to determine the in vitro human epidermal permeability coefficients and membrane retention of a series of aliphatic alcohols (C1-C10, log p -0.72 to 4.06) using two different receptor solutions (water and 4% bovine serum albumin in phosphate-buffered saline). Aqueous solutions of radiolabeled alcohols were dosed into the stratum corneum side of membranes mounted in side-by-side glass diffusion cells. Appearance of alcohol in the receptor compartment filled with either of the two solutions was monitored over a 7 h period when both stratum corneum (assessed by tape stripping) and the remaining epidermis levels of radioactivity were determined. In a separate study the degree of binding of alcohols to 4% bovine serum albumin was determined. The data showed increased receptor phase solubility in the bovine serum albumin solution and higher permeability coefficients for the more lipophilic alcohols in the series. No changes were seen in the partitioning of the alcohols from the vehicle into either the stratum corneum or tape-stripped epidermis with the two receptor phases; however, a decrease in the amount of the more lipophilic alcohols partitioning into the water receptor phase from the tape-stripped epidermis was observed. We conclude that bovine serum albumin receptor phase allows better estimation of real permeability parameters for lipophilic compounds due to its increased solubility capacity and we question whether permeability parameters for lipophilic solutes from older data sets based on aqueous receptor phases are completely reliable.

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.

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.

Influence of Urea, Isopropanol, and Propylene Glycol on Rutin In Vitro Release from Cosmetic Semisolid Systems Estimated by Factorial Design

Rutin, one of the major flavonoids found in an assortment of plants, was reported to act as a sun protection factor booster with high anti-UVA defense, antioxidant, antiaging, and anticellulite, by improvement of the cutaneous microcirculation. This research work aimed at evaluating the rutin in vitro release from semisolid systems, in vertical diffusion cells, containing urea, isopropanol and propylene glycol, associated or not, according to the factorial design with two levels with center point. Urea (alone and in association with isopropanol and propylene glycol) and isopropanol (alone and in association with propylene glycol) influenced significant and negatively rutin liberation in diverse parameters: flux (g/cm2.h); apparent permeability coefficient (cm/h); rutin amount released (g/cm2); and liberation enhancement factor. In accordance with the results, the presence of propylene glycol 5.0% (wt/wt) presented statistically favorable to promote rutin release from this semisolid system with flux = 105.12 8.59 g/cm2.h; apparent permeability coefficient = 7.01 0.572 cm/h; rutin amount released = 648.80 53.01 g/cm2; and liberation enhancement factor = 1.21 0.07.

Biophysical techniques used to evaluate the stratum corneum

Assortments of biophysical methods are used to the study the stratum corneum morphology and dynamic with the objective to elucidate the correlation between its structure and functions. Among these methods, there are: X-ray diffraction, electron paramagnetic resonance, differential scanning calorimetry, Raman spectroscopy with Fourrier transform, infrared spectroscopy and photoacustic spectroscopy. In this manuscript, methods are presented and discussed in relation to the use indication, interpretation of results and advantages and limitations to the stratum corneum analysis.

Characterization and stability study of a water-in-oil microemulsion incorporating quercetin

Background: The effectiveness of a water/oil (w/o) microemulsion containing quercetin against ultraviolet B radiation (UVB) induced damage was recently demonstrated by our group. However, during the development of new pharmaceutical products, the evaluation of percutaneous absorption and in vivo effectiveness should be accompanied by evaluation of stability parameters as an integral part of the process. Objective: The aim was to investigate the stability of the final microemulsion formulation considering the temperature ranges of storage and application. Methods: The physical, chemical, and functional stability of this formulation under different conditions of storage during 12 months and the photostability of quercetin incorporated into this system over UVB exposure for 7 days were evaluated. Results: Although the results indicated a notable physical stability of the w/o microemulsions during the experimental period under all employed conditions, in both, the chemical and functional studies, a significant loss of quercetin content and antioxidant activity was found after 6 months of storage at 30 degrees C/70% relative humidity and after 2 months at 40 degrees C/70% relative humidity. The photostability study results demonstrated that the incorporation of quercetin into the w/o microemulsion maintained the previously demonstrated photostability of this flavonoid under forced exposure to UVB irradiation. Conclusion: Thus, this work demonstrates that special storage conditions (at 4 +/- 2 degrees C) are necessary to maintain the functionality of the w/o microemulsion containing quercetin and mainly emphasizes the importance of studying physical, chemical, and functional parameters at the same time during stability evaluation of active principles.