Modelling skin permeability in risk assessment––the future

Abstract

The modelling of skin permeability is important for transdermal drug delivery, in the cosmetic industry and for risk assessment attendant on dermal exposure to toxic substances. The two principal methods currently used are quantitative structure–activity relationships (QSARs), used in the main to predict permeability coefficients, and mathematical modelling based on analytical or numerical solutions to the relevant partition and transport equations and used to predict the amount of a substance permeating through the skin. This paper will assess recent progress in this area and suggest what will be needed for future advancements. The considerable effort invested in the development of QSARs during the past decade has resulted in only rather modest progress. Further significant improvement in our ability to predict percutaneous permeability is likely to require the measurement of new data under carefully controlled conditions and its fitting to new QSAR equations. Reliable assessments of risks following dermal exposures will demand new integrated mathematical models that include the variables associated with the exposure and penetration processes as well as the factors that control the subsequent passage of the penetrant into the systemic system.

Introduction

The advantages in being able to make accurate predictions of the extent to which substances penetrate through human skin are very evident in estimating the potential for transdermal drug delivery, in assessing the risk associated with dermal contacts with toxic substances and in the cosmetics industry. Modelling such dermal exposures has as its ultimate objective the development of expert systems capable of reliably predicting the extent to which a molecule will be percutaneously absorbed, without the need to make experimental measurements. The need to limit and, if possible, to completely dispense with in vivo experimental measurements is obvious. There are also difficulties in obtaining excised human skin, which is the best membrane to use for in vitro measurements. As a consequence there has been considerable interest, particularly during the past two decades, in developing methods to model dermal penetration. Because of the relative complexity of human skin and of many of the penetrant molecules of interest it is not yet possible to calculate the relevant diffusion barriers from first principles as has now been done for simpler systems (Watson et al., 2001; Rurali et al., 2003). Neither is it possible to use simulation methods, such as molecular dynamics, that rely on interatomic potentials to represent the molecular forces acting between the species in the system. Two principal approaches have emerged. The first is the use of quantitative structure–activity relationships (QSARs) that are used mainly to predict steady-state permeabilities: the second utilises mathematical models to simulate the sequence of partition and transport processes involved in the absorption and can predict the extent and rate of chemical permeation through the skin.

QSARs are widely used in science to statistically correlate selected relevant physicochemical properties of compounds with their biological activities (Martin, 1978). Quite a number have now been developed specifically to model skin permeation and this field has been the subject of comprehensive reviews (Moss et al., 2002; Vecchia and Bunge, 2002a, Vecchia and Bunge, 2002b). These algorithms typically predict the permeability, K_p, of the substance through the Stratum corneum, where:

$$\text{K}{}_{\mathrm{<mtext>p</mtext>}}\text{=K}{}_{\mathrm{<mtext>m</mtext>}}\text{·D}{}_{\mathrm{<mtext>m</mtext>}}\text{/h}$$

Here h is the thickness of the S. corneum, D_m is the permeant diffusivity in the membrane and K_m is its partition coefficient between the S. corneum and the vehicle. In calculations, K_m is often substituted for by the octanol–water partition coefficient, K_ow. Ideally, the experimental data analysed to develop and evaluate QSARs should be measured in a single laboratory using designated protocols and with uniform skin samples taken from the same source. In reality, however this has not been possible and the permeability data used have been drawn from the literature and so from experiments in which they have usually been measured for other purposes.

Uncertainties may also arise in the values used for K_ow. Hadgraft and Valenta (2000) have detailed the importance of pH in the transport of ionisable substances across S. corneum and the values of K_ow used must therefore refer to appropriate conditions. Ideally also, the structure–activity relationship that is employed in the algorithm should be related to the mechanism of the process that it seeks to model. Because the passage of a molecule through the S. corneum involves a lipophilic pathway most QSARs contain descriptors of hydrophobicity. Since it is also a diffusion process descriptors of molecular size, such as molecular weight (MW) or volume, are also commonly included. More recently, with the advent of readily available programmes to quickly calculate other molecular descriptors, some QSARs have been made to scan a wide range of these and include those found to be most significant in improving the algorithms (Patel et al., 2002).

QSARs for skin permeation are of two types. The first are `general' where the algorithm is intended to encompass a wide range of substances without reference to their chemical nature e.g., Potts and Guy (1992). The second are `specific' and have been developed to cover a smaller number of homologous chemical molecules or to investigate the influence of a particular physicochemical property common to a group of molecules. In this latter category, Lien and Gao (1995) included the number of hydrogen bonds that may be formed by a compound, H_b, in their algorithm. Abraham et al. (1999) confirmed the importance of the inclusion of terms relating to hydrogen bonding, particularly in the absence of a direct descriptor of hydrophobicity. Flynn (1990) published a set of permeability coefficients for 97 compounds, which many authors have subsequently used so that it has had a significant impact on studies of this type. Table 1 sets out a selection of the QSARs developed over the past 10 years to predict skin permeability: the influence of the Flynn dataset is obvious.

The general QSAR based on the Flynn (1990) dataset and reported by Potts and Guy (1992) established the use of a combination of the octanol–water partition coefficient, K_ow, and the MW or molecular volume as physicochemical descriptors as being both mechanistically relevant and capable of providing an adequate interpretation of these data. This QSAR has the form

$$\text{Log}\text{K}{}_{\mathrm{<mtext>p</mtext>}}\text{=0.71}\text{log}\text{K}{}_{\mathrm{<mtext>ow</mtext>}}\text{−0.0061}\text{MW}\text{−6.3}$$

It has received considerable attention since its publication and is also of additional interest because it is used to estimate parameters for the steady-state permeability from water in what is perhaps the best-known mathematical model of both steady-state and non-steady-state percutaneous absorption (Cleek and Bunge, 1992; Bunge and Cleek, 1995; Bunge et al., 1995). The Potts and Guy (1992) QSAR is also used to estimate parameters in the more modern and versatile mathematical model developed by Kruse and Verberk (2001).

Roberts et al. (1999) and McCarley and Bunge (2001) have recently reviewed mathematical pharmacokinetic models of percutaneous penetration. In such models the algebraic equations that accurately represent the partition processes and diffusion migration of a molecule through the different layers of the S. corneum, are written down and solved within certain chosen simplifying assumptions. Cleek and Bunge (1992) solved such a set of equations analytically for both steady- and non-steady-state transport through a two-membrane composite representing the lipophilic S. corneum and the hydrophilic viable epidermis layers. Kruse and Verberk (2001) have also developed a model that treats the skin as a two-layer membrane with the possibility for a parallel route to circumvent this barrier. It is very versatile and can be used for vapours, liquid solutions and solids in contact with the skin with the appropriate differential equations being numerically integrated using the ACSL––advanced continuous simulation language––(www.acslsim.com) software package. After its passage through the skin the clearance of the diffusant by blood perfusion can also be simulated. This model therefore presents the type of integrated treatment of exposure, penetration and subsequent removal of the penetrant in the systemic circulation that is essential if predictive data useful for risk assessment under realistic conditions such are experienced in the workplace are to be generated. Models of this kind can then easily be further extended by making use of existing PK models of the body that are solved using standard software packages.

The very considerable current interest in occupational risk assessment carries with it, as an integral part of the procedure, the need to make a reliable estimate of the risks ensuing from dermal exposure. For this, and also because of the importance to pharmaceutical and cosmetic sciences of developing a predictive capacity for the percutaneous penetration of molecules, this paper will assess the progress made with this task to date. It will also make some suggestions as to the future needs and to the directions in which further improvements are likely to be made. Specifically the performances of the Potts and Guy (1992) QSAR will be compared with that of the QSAR published recently by Patel et al. (2002) for a very comprehensive dataset containing 186 permeability coefficients for some 158 structurally diverse compounds that had not been considered in toto before. In developing their best QSAR the authors removed a number of compounds for which the permeability data were considered as outliers from the dataset and developed a QSAR that gave a value of r²=0.90 for the remaining 143 compounds. This contained a term for hydrophobicity (the octanol–water partition coefficient, K_ow), a term for molecular size (the MW) and two additional calculated descriptors. These terms were the sum of absolute charges on oxygen and nitrogen atoms (ABSQon) and the sum of E-state indices for all methyl groups (SsssCH). The final QSAR had the form:

$$\text{Log}\text{K}{}_{\mathrm{<mtext>p</mtext>}}\text{=0.652}\text{log}\text{K}{}_{\mathrm{<mtext>ow</mtext>}}\text{−0.00603}\text{MW}\text{−0.623}\text{ABSQon}\text{−0.313}\text{SsssCH}\text{−2.30}$$

The additional descriptors were identified, using stepwise regression, to be the most significant in a total of 169 physicochemical descriptors that were calculated for all 158 compounds in the dataset using a range of software. The authors also fitted these data with a QSAR of the general form:

$$\text{Log}\text{K}{}_{\mathrm{<mtext>p</mtext>}}\text{=a(}\text{hydrobhobicity}\text{)−b(}\text{molecular}\text{size}\text{)+c}$$

i.e., the form used by Potts and Guy (1992), which they reported fitted well to the data but for which they gave no details of the a, b and c parameters.