Until the early 1960s, theory suggested that cosmetic ingredients rarely penetrated the skin. However, many experts today suspect that penetration occurs with most ingredients. As consumers and health care professionals have become educated about safety, the percutaneous penetration of cosmetic and fragrance ingredients has gained interest. Therefore, the industry has sought means to estimate the penetration of chemical structures through human skin.

While previous algorithms for predicting the skin absorption of permeants was based on in vitro data, the present article proposes a quantitative structure-activity relationship (QSAR) model based on in vivo human data. Here, a set of human in vivo data is described that provides entry into predicting the penetration of cosmetic ingredients.

## Assessing Delivery

Due to skin barrier properties, a chemical must exhibit specific physicochemical traits in order to be a candidate for passive transdermal delivery. For example, its molecules should be small (MW < 500) and have a low melting point (< 200°C). However, detailed analysis of the pharmacokinetics of transdermal drug delivery and its correlation with physicochemical characteristics of the delivered drugs is minimal. Predictive equations for skin permeability coefficients of chemicals are made based on in vitro static cell experiments using animal or human skin. Moreover, there is considerable interindividual variation in transdermal penetration and pharmacokinetics, which could be one reason for imprecision in predicting dermatopharmacokinetic parameters of transdermally delivered drugs based on their molecular properties.

Therefore, the dermatopharmacokinetic parameters of transdermal drugs are reviewed here. In addition, the interindividual variations in pharmacokinetic parameters such as maximal plasma concentration (C_{max}) are assessed and the in vivo data and physicochemical characteristics of the drugs are correlated. For the present work, patches were chosen since they minimize variance by removing three forces that affect penetration: rub-off, exfoliation and wash.^{ }

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**Revised with permission from Elsevier from: S Farahmand and HI Maibach, Transdermal drug pharmacokinetics in man: Interindividual variability and partial prediction, Int J Pharm 367 1–15 (2008)*

Until the early 1960s, theory suggested that cosmetic ingredients rarely penetrated the skin. However, many experts today suspect that penetration occurs with most ingredients. As consumers and health care professionals have become educated about safety, the percutaneous penetration of cosmetic and fragrance ingredients has gained interest. Therefore, the industry has sought means to estimate the penetration of chemical structures through human skin.

While previous algorithms for predicting the skin absorption of permeants was based on in vitro data, the present article proposes a quantitative structure-activity relationship (QSAR) model based on in vivo human data. Here, a set of human in vivo data is described that provides entry into predicting the penetration of cosmetic ingredients.

## Assessing Delivery

Due to skin barrier properties, a chemical must exhibit specific physicochemical traits in order to be a candidate for passive transdermal delivery. For example, its molecules should be small (MW < 500) and have a low melting point (< 200°C).^{1} However, detailed analysis of the pharmacokinetics of transdermal drug delivery and its correlation with physicochemical characteristics of the delivered drugs is minimal. Predictive equations for skin permeability coefficients of chemicals are made based on in vitro static cell experiments using animal or human skin.^{2, 3} Moreover, there is considerable interindividual variation in transdermal penetration and pharmacokinetics,^{4} which could be one reason for imprecision in predicting dermatopharmacokinetic parameters of transdermally delivered drugs based on their molecular properties.

Therefore, the dermatopharmacokinetic parameters of transdermal drugs are reviewed here. In addition, the interindividual variations in pharmacokinetic parameters such as maximal plasma concentration (C_{max}) are assessed and the in vivo data and physicochemical characteristics of the drugs are correlated. For the present work, patches were chosen since they minimize variance by removing three forces that affect penetration: rub-off, exfoliation and wash.^{5 }

## Pharmacokinetic Parameters for Delivery

The single dose pharmacokinetic profile for transdermal delivery includes three periods: the time until plasma concentrations are achieved (the lag time), the plateau at constant steady-state plasma concentrations and a declining phase, post-patch removal. The last phase may be prolonged due to a drug’s pharmacokinetic characteristics and the presence of a skin depot, where chemicals remain in the skin after the delivery system is removed; these materials may therefore enter the circulation.^{6, 7}

The pharmacokinetic evaluation of a transdermal therapeutic system (TTS) is often accomplished through randomized crossover studies that compare either the pharmacokinetic profile of a transdermal system with that of an intravenous or oral dose or different products for bioequivalence studies. The pharmacokinetic data of transdermal patches after single dose treatment was recently summarized.^{8 }

## Models for Permeability

In relation to a material’s delivery is its penetration. Scheuplein and Blank proposed that epidermal penetration depends on the structural features of the penetrant.^{9} The epidermal transport of most solutes is restricted to passive diffusion across the stratum corneum (SC) and studies have evaluated the role of molecular structure and physicochemistry in this process. Most attempts to develop predictive equations for permeability have focused on the contributions of molecular size and the solubility in SC lipids.

The data availability and relative success in addressing the wide range of biophysical processes involved in skin permeation make molecular weight (MW) and logarithmically transformed octanol-water partition coefficient (log K_{oct}) the most widely used parameters for predicting skin penetration.^{1} Melting point may also be considered an important predictor of skin permeability coefficient since it correlates strongly with the oil solubility of drugs.

Two types of structure-activity models have been used to estimate the skin permeability coefficients of chemicals: empirical and theoretical. Theoretical models are based on the contributions of the possible routes of percutaneous penetration and the interactions of the elements of these routes with the penetrants. Empirical models rely on the measured experimental permeability coefficients of series of chemicals and correlate them with physicochemical properties.

The Guy and Hadgraft theoretical model^{10} is based on a linear pharmacokinetic model. The rate constants in this model have been chosen so that they may be related to the penetrant’s physicochemical properties. Equations have been derived that may be used to estimate the concentration of drug in the plasma following transdermal application. A database of in vitro skin permeability coefficient values has been consolidated, and more than 20 empirical equations have been published estimating the permeability coefficients for chemicals penetrating the human skin from aqueous vehicles.^{1}

**Eq. 1** is an empirical model developed by Potts and Guy that is widely used to predict the permeability coefficient (Kp) based on octanol-water partition coefficient (log K_{oct}) and MW.

Log Kp = −2.72 + 0.71 log K_{oct} − 0.0061 MW

** Eq. 1 **

Variability in the proposed models is partly due to the experimental uncertainties and individual skin variations, which limit the prediction of skin permeability coefficients. However, the correlation of in vivo skin permeation descriptors such as plasma concentration and molecular characteristics has not been evaluated in the literature.

According to **Eq. 2**, where *A* is the patch area and *Ke* is the elimination rate constant,^{11} after transdermal drug delivery, plasma concentration depends on steady-state flux (Css) of the drug per unit area (J) and is inversely related to the drug’s volume of distribution (Vd ).

Css = A*J/Ke* Vd

** Eq. 2 **

Fick’s first law of diffusion describes steady-state diffusion through a membrane, as seen in **Eq. 3**.

J = K*D/h * C0

** Eq. 3 **

In **Eq. 3**, *K* is the SC/formulation partition coefficient of the drug, *D* is its diffusion coefficient in the SC of path length *h*, and *C0* is the concentration of the drug applied. Therefore, the dependency of plasma concentration on flux (J) allows a relation to the drug’s physicochemical properties. Meanwhile, as a component of drug clearance, volume of distribution is also related to a drug’s solubility characteristics, which emphasizes the correlation of plasma concentration with the structural features of drug molecules.

Here, using multiple regression analysis, an empirical model has been adapted for predicting the C_{max} of transdermally administered drugs based on their physicochemical properties such as log k_{oct}, MW or molecular volume (MV) and hydrogen bonding descriptors.

## Methods and Results

As with most transdermal study techniques, the proposed model was based on multiple regression analysis^{2, 8, 12} of the C_{max} of 10 drugs, excluding fentanyl and clonidine, against physicochemical parameters,^{8} which yielded **Eq. 4** as the best-fitted model.

C_{max} (ng/mL) = 8.625 e^{−}07 HA + 8.231 e^{−}07 log K_{oct} −

1.22e^{−}06HD − 2.58e^{−}06

** Eq. 4 **

In **Eq. 4**, *n* = 10, *r* = 0.974, *F* = 37.45, *SD* = 0.82 and *p* < 0.001. In this equation and elsewhere, HA is the total number of hydrogen bond acceptor groups on the molecule, log K_{oct} is logarithmically transformed octanol-water partition coefficient, and HD is the total number of hydrogen bond donor groups on the molecule. All predictors had significant (p < 0.05) partial effects in the full model. The inclusion of molecular weight failed to significantly improve the statistics of this equation. Furthermore, no linear correlation could be established between C_{max} and MW. The further inclusion of Abraham’s descriptors led to the model in **Eq. 5**.

C_{max} = 6.055 e^{−}07 log K_{oct} + 8.691 e^{−}07 HA + 1.075 e^{−}06 V −

1.91 e^{−}06 E – 2.84 e^{−}06

** Eq. 5**

In **Eq. 5**, *n* = 10, *r* = 0.989, *F* = 56.49,* SD* = 0.75 and *p* < 0.001. In this equation, *V* is the McGown characteristic volume in units of (cm^{3}mol^{-1})/100, and *E* is the solute excess molar refractivity in units of (cm^{3}mol^{-1})/10. No collinearity was found between the variables in the model (VIF < 2 for all the variables in both models).

Studentized residuals showed a normal distribution according to Kolmogrov-Smirnov test of normality (p > 0.05); the residual is the difference between the observed and predicted values of C_{max}. Its normality has been tested to assure that the standard errors of regression coefficients are not biased and unusual leverage values were not found, which confirms there is no serious outlier influence in the model.

## Interindividual Variations

The main advantage that transdermal drug delivery possesses over oral dose regimens is that it avoids the variability associated with the gastrointestinal tract, which can be affected by pH, motility, transit time and food intake. Nevertheless, drug permeation through human skin at a selected skin site can vary from 46–66% among individuals.^{7} To study the variations, transdermal patches were chosen over volatile solvent vehicles such as acetone or semi-solids such as cream or ointment since transdermal patches offer a fixed dose and an abrupt removal, except for skin reservoirs. In addition, transdermal patches do not entail other penetration steps such as volatility (i.e., evaporation of the active) and rub removal. Further, these systems are near or at maximum thermodynamic activity (saturation).

In transdermal pharmacokinetic literature, data measured from different individuals were reported in means and standard deviation. In this study, the mean coefficient of variation (CV) of C_{max} was calculated for transdermal drugs. The mean CV of values reported from several resources ranged from 26% (for nicotine) to 53% (for nitroglycerin).^{8 }The mean CV of C_{max} also was calculated for the oral dosage form of these drugs.

In **Figure 1**, the CV of C_{max} for nicotine after smoking and for fentanyl after intravenous infusion is shown. The CV values from non-transdermal routes of administration range from 12.3% (for clonidine) to 202% (for testosterone), as seen in **Figure 1**. The main factors controlling the interindividual variation in transdermal drug delivery can be categorized in four groups: study design and methodology, general subject factors, TTS system design and kinetic variations of drug molecules.

* Age:* Among the drugs administered transdermally, the pharmacokinetics of fentanyl have been studied extensively in subjects ages 6–75 years.

^{7}The plasma profile at steady state was similar between children ages 7–18 years and adults, although the interindividual variability in kinetics was less in children. There were no marked differences found in C

_{max}and the area under the time concentration curve in the elderly and adult group. However, the data suggests a longer delay and decay of fentanyl in elderly patients.

^{7}

Although the effects of aging on barrier qualities of skin affect drug permeation, the variability could also be explained by differences in cytochrome P_{450} 3A4 activity in a population of patients covering a wide age range. Cytochrome P_{450} 3A4 is one of the most important enzymes involved in the metabolism of xenobiotics in the body. In addition, renal function decreases with age, which could also increase interindividual variation, as was shown for some topically applied lipophilic drugs.^{13}

* Gender:* Although there are significant differences in the general appearance of skin and distribution of hair follicles between males and females, there is no convincing evidence to suggest major differences in barrier function. A pharmacokinetic study of nicotine demonstrated the higher values for apparent nicotine elimination rate constants in women. Greater subcutaneous lipid in women compared with men could be hypothesized to affect transdermal drug delivery but this has not been confirmed. In general, bioavailability and protein binding do not appear to be significantly affected by gender.

^{14}Further studies are needed to address the gender effect on the efficiency of transdermal drug delivery.

* Other:* Formation of skin depots and the duration of effects varies in different subjects. This is known to cause interindividual variations in the plasma concentration profiles of clonidine after the delivery system’s removal. In some subjects the plasma concentration rises and in others, it declines.

^{15}Local blood flow is considered as a limiting factor for the exchange rate of transdermally applied nicotine. This explains the increased drug release from the TTS during exercise.

## Plasma Concentration and Molecule Properties

The models obtained here suggest the possibility of a determinant correlation between C_{max} of transdermally administered drugs and their molecular properties. These models were developed based on the available data for all the pharmacokinetically studied marketed drugs except fentanyl and clonidine, which showed exceptionally high C_{max} values. Since this trial evaluates the relationship of in vivo absorption data of transdermally applied drugs with their structural features, only a small data set was available. Although this may reduce the predictive power of the model for further molecules, correlations are evaluated for a relevant data set that corresponds to a group of drugs with proven clinical efficacy after transdermal absorption.

According to the standardized partial regression coefficients, the number of hydrogen bond acceptor groups (HA) has the largest contribution in predicting C_{max }in both equations, in the context of the other predictor variables in the model. This finding is in accordance with the previous studies, where HA was determined to be a main parameter in predicting permeability coefficient.^{3}

**Eq. 4** and **5** disclose that the C_{max} is positively correlated to the HA. Lipinski et al. proposed that a large number of hydrogen bond acceptor sites may potentially delay skin permeation. Poor absorption or permeation is more likely when there are more than five hydrogen bond donors or ten hydrogen bond acceptors present on the molecule.^{16}

The issue is complicated further if the composite nature of log K_{oct} is considered, because it contains a degree of information regarding hydrogen bonding. Although no proven collinearity of variables was detected in the adopted models in the present study, a poor insignificant correlation between log K_{oct} and HA (r: −0.361, p > 0.05) was found. The poor correlation coefficient does not demonstrate that log K_{oct} and HA are independent. If C_{max} was an indication of drug permeation rate, a negative correlation between C_{max} and HA could be expected.

The positive correlation of HA and Cmax from **Eq. 4 **and **5** suggests considering C_{max} as a complex parameter composed of absorption and elimination. If a high number of hydrogen bonding acceptor groups can impede the skin permeation, its effect on the clearance process also should be noted. The affinity of the drugs to body fluids, which affects the volume of distribution, is partly related to their molecular properties, such as hydrogen bonding.

Assuming a linear single compartment model, the total amount of drug in the blood may be expressed as **Eq. 6**.

dS/dt = −k*S + A*J

**Eq. 6 **

In **Eq. 6**, *k* is the sum of the various elimination rate constants, *A* is the patch area, and *J* is the flux of drug across the skin.^{11} An increased number of hydrogen bond acceptor groups may decrease *J*, but also may increase* k*. Therefore its net effect on blood concentration should be noted. Moreover, the effects of hydrogen bonding capacity on protein binding and metabolism may also interfere with plasma concentration.

Predictivity of the permeation models based on physicochemical properties of molecules such as MW and log K_{oct} has been questioned by the fact that they give little information as to the actual structural features of solutes that influence skin permeability. ^{13}

**Eq. 7** was suggested for the prediction of log k_{oct} from molecular properties.

Log K_{oct} = 0.088 + 0.562 R_{2} − 1.054 π_{2}^{H} + 0.034 Σ α_{2}^{H} −

3.46 Σ β_{2}^{H} + 3.814V_{x}

**Eq. 7**

In **Eq. 7**, *R _{2}* is an excess molar refraction,

*π*is the solute dipolarity/polarizability,

_{2}^{H}*Σ α*and

_{2}^{H}*Σ β*are the overall hydrogen bond acidity and basicity, respectively, and

_{2}^{H}*V*is the McGown characteristic volume. Therefore, a criticism of

_{x}**Eq. 5**could be that log K

_{oct}, as a predictive variable in this equation, may be collinear with the other equation variables.

Although **Eq. 5** could show the effect of molecular size on the C_{max}, the inclusion of MW in **Eq. 4** failed to result in a significant correlation. Again, the complexity of C_{max} as an indicator of absorption and elimination, and/or narrow range of MW of studied compounds (162–357) could explain this finding.

When C_{max} was plotted against log K_{oct}, there is a two-segment linear correlation of C_{max} and log K_{oct} (r^{2} = 0.984, p < 0.05) (see **Figure 2**). The outliers were clonidine, fentanyl and nitroglycerin, with high C_{max} values, and estradiol with a low C_{max} value. This significant pattern of correlation suggests that log K_{oct} = 3 is an inflection point below which log K_{oct} is negatively correlated with C_{max}, and above that, there is a positive correlation between C_{max} and log K_{oct}.

If the skin permeability coefficient (log Kp) was considered as the only parameter determining C_{max}, then according to **Eq. 1**, which is applicable in the range of −3 < log K_{oct} < 6 , there should be a direct linear correlation between C_{max} and log K_{oct}. This contrast supports that the effects of physicochemical parameters on C_{max} are expressed through different in vivo processes such as absorption, clearance metabolist, etc., which are responsible for observed plasma concentration profiles.

## Conclusion

Interindividual variation in pharmacokinetics remains an important challenge in transdermal drug delivery. The present results suggest an increased interindividual variability by decreased MW and log K_{oct} values, in the range of 200 < MW < 400 and 1.6 < log K_{oct} < 4.3. This could be explained by augmented vulnerability of smaller and more hydrophilic molecules in this range to permeation and elimination, the main sources of intersubject variability.

In an attempt to develop a predictive model for C_{max} based on physicochemical characteristics of drugs, two statistically significant empirical equations were established for 10 molecules. The results demonstrated that the number of HA has the largest contribution in predicting C_{max} in both of the equations, in the context of the other predictor variables in the model.

This data analysis provides entry into predicting the penetration of cosmetic ingredients based on an in vivo human data set. Such an approach might be helpful when the systemic absorption of a cosmetic active or formulation ingredient is of specific concern.^{17-19} A validated QSAR model for predicting the fate of a cosmetic ingredient in the human body would eliminate the need for in vivo experiments and aid in predicting the permeation of novel cosmetic compounds before their synthesis.

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