Etorphine is an opiate analgesic physicochemically suited to transdermal delivery

The influence of diffusion cell type and experimental temperature on machine learning models of skin permeability

OBJECTIVES

The aim of this study was to use Gaussian process regression (GPR) methods to quantify the effect of experimental temperature (T_exp ) and choice of diffusion cell on model quality and performance.

METHODS

Data were collated from the literature. Static and flow-through diffusion cell data were separated, and a series of GPR experiments was conducted. The effect of T_exp was assessed by comparing a range of datasets where T_exp either remained constant or was varied from 22 to 45 °C.

KEY FINDINGS

Using data from flow-through diffusion cells results in poor model performance. Data from static diffusion cells resulted in significantly greater performance. Inclusion of data from flow-through cell experiments reduces overall model quality. Consideration of T_exp improves model quality when the dataset used exhibits a wide range of experimental temperatures.

CONCLUSIONS

This study highlights the problem of collating literature data into datasets from which models are constructed without consideration of the nature of those data. In order to optimise model quality data from only static, Franz-type, experiments should be used to construct the model and T_exp should either be incorporated as a descriptor in the model if data are collated from a range of studies conducted at different temperatures.

Evaluation on the reliability of the permeability coefficient (Kp) to assess the percutaneous penetration property of chemicals on the basis of Flynn's dataset

PURPOSE

The permeability coefficient (K_p) is often used for prediction of the dermal penetration of chemicals. Mathematical models have mostly been derived on K_p data basis. However, confusing K_p values are reported, questioning the general reliability of this parameter. In this study, we tested the plausibility of K_p values expressing the dermal penetration velocity (cm h^-1) of chemicals on a larger dataset from literature.

METHODS

K_p was applied for the calculation of the time for penetration through skin membranes of defined thickness (t_CrossSkin). K_p values were obtained from Flynn's dataset (1990), containing data determined mostly under similar experimental conditions using diffusion cells. Further skin penetration parameters, e.g., times at which the chemicals were firstly measured in the receptor phase, lag times, steady-state times, and exposure duration, where available, were related to K_p values. The data congruence was tested comparing K_p values from Flynn's dataset with those reported in the EDETOX database. Variables, which could bias the results, such as different experimental protocols and research groups were also considered.

RESULTS

K_p data for 94 chemicals matched the inclusion criteria were evaluated. According to the K_p values, 21 (22%) compounds would require longer than 100 h, and 20 (21%) further compounds longer than 10 h of exposure to penetrate skin membranes of ~ 0.01-2.5 mm thickness. Obviously, erroneous K_p were found in studies of almost all research groups in Flynn's database, indicating that neither the observer nor the experimental conditions alone biased the values.

CONCLUSIONS

Our evaluation demonstrates high implausibility of K_p values to represent the dermal penetration velocity and supports general invalidity of the parameter for implementation in studies using skin membranes. The K_p should not be used to characterize the percutaneous penetration of chemicals or in risk assessment without verification.

The application and limitations of mathematical modelling in the prediction of permeability across mammalian skin and polydimethylsiloxane membranes

OBJECTIVES

Predicting the rate of percutaneous absorption of a drug is an important issue with the increasing use of the skin as a means of moderating and controlling drug delivery. One key feature of this problem domain is that human skin permeability (as K(p)) has been shown to be inherently non-linear when mathematically related to the physicochemical parameters of penetrants. As such, the aims of this study were to apply and evaluate Gaussian process (GP) regression methods to datasets for membranes other than human skin, and to explore how the nature of the dataset may influence its analysis.

METHODS

Permeability data for absorption across rodent and pig skin, and artificial membranes (polydimethylsiloxane, PDMS, i.e. Silastic) membranes was collected from the literature. Two quantitative structure-permeability relationship (QSPR) models were used to compare with the GP models. Further performance metrics were computed in terms of all predictions, and a range of covariance functions were examined: the squared exponential (SE), neural network (NNone) and rational quadratic (QR) covariance functions, along with two simple cases of Matern covariance function (Matern3 and Matern5) where the polynomial order is set to 1 and 2, respectively. As measures of performance, the correlation coefficient (CORR), negative log estimated predictive density (NLL, or negative log loss) and mean squared error (MSE) were employed.

KEY FINDINGS

The results demonstrated that GP models with different covariance functions outperform QSPR models for human, pig and rodent datasets. For the artificial membranes, GPs perform better in one instance, and give similar results in other experiments (where different covariance parameters produce similar results). In some cases, the GP predictions for some of the artificial membrane dataset are poorly correlated, suggesting that the physicochemical parameters employed in this study might not be appropriate for developing models that represent this membrane.

CONCLUSIONS

While the results of this study indicate that permeation across rodent (mouse and rat) and pig skin is, in a statistical sense, similar, and that the artificial membranes are poor replacements of human or animal skin, the overriding issue raised in this study is the nature of the dataset and how it can influence the results, and subsequent interpretation, of any model produced for particular membranes. The size of the datasets, in both absolute and comparative senses, appears to influence model quality. Ideally, to generate viable cross-comparisons the datasets for different mammalian membranes should, wherever possible, exhibit as much commonality as possible.

In vitro studies on transdermal permeation of butorphanol

The influence of the donor vehicles pH and the addition of laurocapram or transkarbam 12 as permeation enhancers on the transdermal permeation of butorphanol through human skin were examined with the aim of finding out about its possible use in the transdermal delivery system. As the pH of the donor vehicles rises, the mean value of butorphanol skin fluxes declines; an exponential relationship of the means of butorphanol flux values against the pH of the buffered aqueous donor vehicles has been demonstrated. The presence of 1% of transkarbam 12 (T12) or 5% of laurocapram (LC), respectively, in an isopropylmyristate (IPM) donor vehicle increased transdermal fluxes of butorphanol almost 2.5 times (58.1+/-5.7 microg cm-2 hr-1) or 1.5 times (36.4+/-7.0 microg cm-2 hr-1), respectively, when compared to blank donors. Considering clinical and pharmacokinetic data on butorphanol, it is possible to expect that a transdermal preparation sized 20 cm2 and possessing flux values ranging between 5.1 and 15.3 microg cm-2 hr-1 should be sufficient to achieve effective butorphanol transdermal fluxes, namely using IPM donors containing T12. In conclusion, butorphanol is a suitable candidate for transdermal administration and T12 is a very a suitable enhancer for it.

Molecular size as the main determinant of solute maximum flux across the skin

One of the most important determinants of dermatological and systemic penetration after topical application is the delivery or flux of solutes into or through the skin. The maximum dose of solute able to be delivered over a given period of time and area of application is defined by its maximum flux (J(max), mol per cm(2) per h) from a given vehicle. In this work, J(max) values from aqueous solution across human skin were acquired or estimated from experimental data and correlated with solute physicochemical properties. Whereas epidermal permeability coefficients (k(p)) are optimally correlated to solute octanol-water partition coefficient (K(ow)) and molecular weight (MW) was found to be the dominant determinant of J(max) for this literature data set: log J(max)=-3.90-0.0190MW (n=87, r(2)=0.847, p<0.001). Estimated solubility in octanol (S(oc)) was also a determinant, but improvement in the regression by the addition of log S(oc) was small (r(2) increased to 0.856). Addition of other physicochemical parameters to MW by forward stepwise regression only marginally improved the regression with a melting point (Mpt) term (r(2)=0.879) and then hydrogen bonding acceptor capability (H(a)) (r(2)=0.917) is significant. Validation of the equation above was carried with a number of other data sets: an aqueous vehicle with full- and split-thickness skin (r(2)=0.784, n=56), some pure solutes (r(2)=0.537, n=34), an aqueous vehicle with ionizable solutes (r(2)=0.282, n=54) and solutes from a propylene glycol vehicle (r(2)=0.484, n=36). An analysis of the entire database gave the equation log J(max)=-4.52-0.0141MW (n=278, r(2)=0.688, p<0.001), with inclusion of Mpt and H(a) increasing r(2) to 0.760 (n=269). Separate analysis of full- and split-thickness skin data confirmed that the dermal resistance term had only a marginal effect on overall J(max). Application of the latter model to an in vivo situation where the dermal capillary bed is slightly below the epidermal-dermal junction revealed that the dermal resistance term was unnecessary for in vivo predictions for most solutes.

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.

Transdermal delivery of the potent analgesic dihydroetorphine: kinetic analysis of skin permeation and analgesic effect in the hairless rat

Dihydroetorphine is an extraordinarily strong opioid analgesic. To assess its effectiveness after topical application in hairless rats we have examined the kinetic analysis of skin permeation through excised skin and the in-vitro reservoir effect of skin, and have investigated the predictability of plasma concentration and analgesic effect following in-vivo transdermal application. Dihydroetorphine was moderately permeable from an aqueous suspension through excised hairless rat skin. Dihydroetorphine flux from drug-dispersed pressure-sensitive adhesive tape was threefold that from the applied aqueous suspension. The fluxes through the abdominal and the dorsal skin during tape application fitted the Fickian diffusion equation well after the tape was removed peeling off the outer layer of the stratum corneum. The relationship between the plasma concentration and the analgesic effect was examined for four different rates of infusion of dihydroetorphine. A non-linear pharmacokinetic disposition was observed. Following abdominal (0.28 cm2, 20 microg) and dorsal (0.50 cm2, 35 microg) applications of the dihydroetorphine tape, plasma concentration (0.2-0.8 ng mL(-1)) and analgesic effect were maintained at a suitable level, for more than 8 h, until removal of the tape. These profiles were predictable using the combined equation for percutaneous absorption, disposition and the analgesic effect, but the analgesic effect was slightly lower than the predicted value. The results show that it was possible to control the plasma concentration and the analgesic effect of dihydroetorphine by topical application of the analgesic using pressure-sensitive adhesive tape in the hairless rat. It was possible to predict the result using mathematical modelling.

Estimating skin permeation. The validation of five mathematical skin permeation models

This study provides an analysis of the reliability of five mathematical models, simulating permeation of substances through the skin from aqueous solutions. An extensive database was generated, containing data on 123 measured permeation coefficients of 99 different chemicals and their physicochemical properties. In addition, in this database all relevant experimental conditions are included. The coefficients of the different skin permeation models were estimated by non-linear multiple regression, using the octanol-water partition coefficient and the molecular weight as independent parameters. The reliability of the models was evaluated by testing variation of regression coefficients and of residual variance for subsets of data, randomly selected from the complete database. Three models were considered to provide reliable estimations of the skin permeation coefficient. These are based on the McKone and Howd model, the Guy and Potts model and the Robinson model. The last-mentioned two models were adaptations, because MW0.5 as independent parameter provided a better fit than MW (MW = molecular weight) in the original models. The McKone and Howd model and the Robinson model have the advantage, that they predict more precisely the skin permeation of highly hydrophilic and highly lipophilic chemicals compared to the Guy and Potts model. The revised Robinson model resulted always in the smallest residual variance.