The development of a computation / mathematical model to predict drug absorption across the skin
The ability to predict accurately the dermal permeation of a chemical is important for the development of new therapeutic formulations in transdermal drug delivery and also for the assessment of the potential risks of environmental chemicals and agents used in cosmetics industry. There have been a large number of studies investigating skin permeability, both experimentally- and theoretically-based. The experimental measurement of skin permeability is a time-consuming and difficu process and, when put in the context of the great numbers of chemicals that may come into contact with the skin, it is also cosdy. /ls a consequence, there has been a great interest over the past years to 'predict' the ability of a compound to cross the skin using its physicochemical characteristics and a number of mathematical models have been reported. Most models are based on experimental data, with skin permeability linearly correlated to the physicochemical properties and I or molecular structure parameters of the chemical compounds. A mu ilinear regression method is often used to fit available experimental data and such empirical models are referred to as quantitative structure-property relationships (QSPRs). Many QSPR models relate skin permeability to the physicochemical properties of the solutes while others use molecular structure properties. Successful application of such models can realise a marked reduction in the number of potentially therapeutic molecules requiring synthesis and validation since they can be precluded from study on the basis of their predicted lack of skin permeability. In terms of skin permeability data with respect to QSPR analysis, the science has not been developed significanijy since the publication of what is now universally known as the Flynn dataset (Flynn 1990). The most widely cited model that was developed on the basis of the Flynn dataset was the Potts and Guy (1992) model and since then a number of a emative models have been developed using the Flynn and other subsequendy assembled datasets. The aim of this study was to determine the limitations of the existing models and to address any deficiencies by the development of new mathematical models. Databases containing measured and well-defined skin absorption data are a key first step in the development of QSPR models, which might improve the understanding of the dermal absorption process for chemicals. Therefore the first objective was to develop a more stringendy controlled database that induded parameters derived under more strictly defined experimental conditions. These data oould then enable the current models to be re-evaluated and accordingly a detailed analysis of all the available in vitro dermal absorption data to be conducted with a view to dassifying the data according to the corresponding experimental conditions employed so as to produce a number of data subsets. Subsequendy, advanced computational regression modelling methods, such as the Gaussian method, were applied to develop the most efficient model in terms of statistical fit. The Gaussian process (GP) has not been applied previously to skin permeability data. The potential of induding additional descriptors such as molecular weight, lipophilicity, Fedors' solubility parameter, hydrogen bond acceptor and donor capacity into any developed equations with a view to improving accuracy was investigated. For comparison reasons, a new linear regression model was also developed based on the above-mentioned 5 addttional descriptors (Sf linear regression model). The GP model yielded a predictive model that provided a significandy more accurate estimate of skin absorption than previous models across a wider range of molecular properties. It proved to be particularly capable of providing excellent predictions where previous studies have shown QSPRs to fail: at high log P and MW of penetrants. The results indicate that, in terms of statistical performance, the Gaussian model was better than the Sf model. This suggested that, statistically, a nonlinear approach, as employed herein, is more appropriate for analysis than linear techniques. The relative accuracy of the GP, Sf linear regression and Potts and Guy (1992) models were also compared. Permeation data were obtained under carefully controlled conditions and these were correlated to values calculated from the application of various models. Apart from comparing the experimental values with those predicted from each model, all deviations were recorded and the performance of each model was assessed. The flux values of t'M> drug candidates, ibuprofen and furosemide, determined using the GP and Sf models, agreed well INith those obtained experimentally. However, procaine hydrochloride diffused at a rate that was slower than that predicted by all models and paracetamol diffused at a much higher rate than was predicted from the GP model. The latter results could possibly be due to the relatively small degree of paracetamol ionisation. Ps a resutt, the effect of ionisation on permeability was measured by determining the flux of a single ionisable drug at three different pH values. The experimental results obtained were compared INith the linear ionisation model, in which log D values were incorporated into the equation instead of log P values. n was concluded that ionisation, together with nonlinearity, were t'M> of the most important factors that require further consideration when designing new models to predict dermal absorption. A series of more strictly defined databases was successfully assembled during the course of this study and used to propose novel computational models for dermal absorption. Such models showed satisfactory predictive capacity but do require further development, particularly in the case of ionisable compounds. However, the development of such databases alone is of great use for future model development.
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