Model fitting for small skin permeability data sets: hyperparameter optimisation in Gaussian Process Regression

OBJECTIVES

The aim of this study was to investigate how to improve predictions from Gaussian Process models by optimising the model hyperparameters.

METHODS

Optimisation methods, including Grid Search, Conjugate Gradient, Random Search, Evolutionary Algorithm and Hyper-prior, were evaluated and applied to previously published data. Data sets were also altered in a structured manner to reduce their size, which retained the range, or 'chemical space' of the key descriptors to assess the effect of the data range on model quality.

KEY FINDINGS

The Hyper-prior Smoothbox kernel results in the best models for the majority of data sets, and they exhibited significantly better performance than benchmark quantitative structure-permeability relationship (QSPR) models. When the data sets were systematically reduced in size, the different optimisation methods generally retained their statistical quality, whereas benchmark QSPR models performed poorly.

CONCLUSIONS

The design of the data set, and possibly also the approach to validation of the model, is critical in the development of improved models. The size of the data set, if carefully controlled, was not generally a significant factor for these models and that models of excellent statistical quality could be produced from substantially smaller data sets.

The application of machine learning to the modelling of percutaneous absorption: an overview and guide

Machine learning (ML) methods have been applied to the analysis of a range of biological systems. This paper reviews the application of these methods to the problem domain of skin permeability and addresses critically some of the key issues. Specifically, ML methods offer great potential in both predictive ability and their ability to provide mechanistic insight to, in this case, the phenomena of skin permeation. However, they are beset by perceptions of a lack of transparency and, often, once a ML or related method has been published there is little impetus from other researchers to adopt such methods. This is usually due to the lack of transparency in some methods and the lack of availability of specific coding for running advanced ML methods. This paper reviews critically the application of ML methods to percutaneous absorption and addresses the key issue of transparency by describing in detail - and providing the detailed coding for - the process of running a ML method (in this case, a Gaussian process regression method). Although this method is applied here to the field of percutaneous absorption, it may be applied more broadly to any biological system.

Discriminant analysis as a tool to identify compounds with potential as transdermal enhancers

Structure-activity relationships were sought for 73 enhancers of hydrocortisone permeation from propylene glycol across hairless mouse skin. Enhancers had chain lengths (CC) from 0 to 16 carbon atoms, 1 to 8 H-bonding atoms (HB), molecular weight 60 to 450, log P (calculated) −1.7 to 9.7 and log S (calculated) −7.8 to 0.7. These predictive properties were chosen because of their ready availability. Enhancement ratio (ER) was defined as hydrocortisone transferred after 24 h relative to control. Values for the ER ranged from 0.2 to 25.3. Multiple regression analysis failed to predict activity; ER values for the ‘good’ enhancers (ER>10) were underestimated. Simple guidelines suggested that high ER was associated with CC>12 and HB 2–5. This was refined by multivariate analysis to identify significant predictors. Discriminant analysis using CC, HB, and molecular weight correctly assigned 11 of the 12 ‘good’ enhancers (92%). The incorrectly assigned compound was a known, idiosyncratic Br compound. Seventeen of the 61 ‘poor’ enhancers (28%) were incorrectly assigned but four could be considered marginal (ER>8). The success of this simple approach in identifying potent enhancers suggested its potential in predicting novel enhancer activity.

Mechanical characterization and drug permeation properties of tetracaine-loaded bioadhesive films for percutaneous local anesthesia

In the development of bioadhesive patch devices for percutaneous local anesthesia, the tensile properties of the films produced after the casting of the gel intermediates is of key importance to the clinical compliance of the product, and its effective delivery of the local anesthetic agent. A range of bioadhesive patches were formulated and their mechanical and in vitro permeation properties determined. Altering formulation significantly altered the mechanical properties of films. The tensile properties of the films could be modified to allow concomitant benefits in the mechanical and drug permeation properties of the films, ensuring that patches not only exerted clinically beneficial effects, but are also mechanically robust. Tetracaine was found to plasticize films and while this effect was weak, it was significant both statistically and potentially also in the effect it has on the clinical use of these devices. Drug release from tetracaine patches demonstrate the same trends as found previously across polydimethylsiloxane films. By altering the formulation of the patch device, the drug release from the device to the skin is readily and accurately controlled, and was not solely a function of the stratum corneum barrier properties but additionally of the formulation.

Quantitative structure-permeability relationships (QSPRs) for percutaneous absorption

Quantitative structure-permeability relationships (QSPRs) have been derived by many researchers to model the passive, diffusion-controlled, percutaneous penetration of exogenous chemicals. Most of these relationships are based on experimental data from the published literature. They indicate that molecular size (as molecular weight) and hydrophobicity (as the logarithm of the octanol-water partition coefficient; log k(ow)) are the main determinants of transdermal penetration. This article reviews the current state of the art in QSPRs for absorption of chemicals through the skin, and where this technology can be exploited in future research. The main shortfalls in QSPR models result from inconsistency and error of the experimental values used to derive them. This is probably caused by the manner in which they employ data from a variety of sources and, in some cases, slightly different experimental protocols. Further, most current models are based on data generated from either aqueous or ethanolic solution, where each penetrant is present at its saturated solubility or a fraction of its saturated solubility. No models currently account for the influences of formulation upon percutaneous penetration. Current QSPR models provide a significant tool for assessing the percutaneous penetration of chemicals. They may be important in determining the bioavailability of a range of topically applied exogenous chemicals, and in issues of dermal toxicology and risk assessment. However, their current use may be limited by their lack of applicability across different formulation types. As a consequence, their true value may be to make predictions within specific formulation types, as opposed to a general model based on a range of formulation types. In addition, the endpoint of models may be inappropriate for specific applications other than the systemic delivery of topically applied chemicals.

Novel bioadhesive delivery system for percutaneous local anaesthesia

We have assessed the efficacy of a novel bioadhesive amethocaine patch device, compared to Ametop gel, in a randomized, double-blinded trial. Patch and gel formulations, including placebos, were applied to the forearms of volunteers (n = 30) for 40 min. Once the formulations were removed from the skin, anaesthesia was assessed by volunteers using a conventional pinprick test. Pain scores were recorded for 4 h after removal of gels and patches. Statistical analysis of the results indicated that both amethocaine gel and patch preparations were superior to placebo (P < 0.05). No significant difference was observed between amethocaine gel and patch formulations (P > 0.05) in either onset time or duration of action for percutaneous local anaesthesia. The results of this study indicate therefore that the novel bioadhesive patch provides clinically comparable anaesthesia to the established gel formulation in a more defined dosage form.

In vivo ac impedance spectroscopy of human skin. Theory and problems in monitoring of passive percutaneous drug delivery

The use of impedance spectroscopy to evaluate transdermal drug delivery is discussed and new techniques and protocols are suggested to avoid or minimize potential problems. A novel multichannel impedance analyzer, exploiting the advantages of the "three-electrode" configuration, was employed to measure the effects of differing topically applied concentrations of the percutaneous local anesthetic amethocaine on the electrical properties of the treated skin sites. Each measured impedance spectrum was modeled by an equivalent circuit consisting of a resistor in series with the parallel combination of a pseudocapacitance and a resistor. Due to differences in skin sites and to the finite times taken to apply each electrode, it was difficult to satisfactorily compare and contrast the results obtained from adjacent skin sites. Normalization of data highlighted differences in relative impedance changes and aided the meaningful comparison of treated skin sites.

Investigation of the mechanism of flux across human skin in vitro by quantitative structure-permeability relationships

Permeability coefficients for 114 compounds across excised human skin in vitro were taken from Kirchner et al. Forty-seven descriptors were calculated encompassing the relevant physicochemical parameters of the compounds. Quantitative structure-permeability relationships (QSPRs) were developed using least-squares regression analysis. A two-parameter QSPR, describing the permeability coefficients (Kp) across excised skin, was obtained: log Kp=0.772 log P -0.0103 Mr - 2.33 where log P is the logarithm of the octanol-water partition coefficient and Mr is molecular mass. This equation indicates that percutaneous absorption is mediated by the hydrophobicity and the molecular size of the penetrant. Comparison with a QSPR based on penetration across a synthetic (polydimethylsiloxane) membrane suggests that the mechanisms of drug flux across polydimethylsiloxane membranes and excised human skin are significantly different.

An investigation of the mechanism of flux across polydimethylsiloxane membranes by use of quantitative structure-permeability relationships

Quantitative structure-permeability relationships (QSPRs) based on readily calculated parameters have been developed to study penetration across a polydimethylsiloxane membrane. Maximum steady-state flux values for 256 compounds through a polydimethylsiloxane membrane were taken from previous studies. Forty-three physicochemical parameters were calculated for each compound and their significance to flux determined. Removal of fourteen outliers enabled derivation of a significant three-parameter QSPR based on the number of hydrogen-bond acceptor and donor groups and sixth-order path molecular connectivity. Models based on parameters important for penetration across human skin (log P and molecular weight) were comparatively poor. This model suggests that the mechanism of flux across a polydimethylsiloxane membrane is based mainly on hydrogen-bonding effects; as such it occurs via a mechanism of action different from that of penetration of the skin in man.