The skin is the main barrier between the internal body environment and the external one. The characteristics of this barrier and its properties are able to modify and affect drug delivery and chemical toxicity parameters. Therefore, it is not surprising that permeability of many different compounds has been measured through several in vitro and in vivo techniques. Moreover, many different in silico approaches have been used to identify the correlation between the structure of the permeants and their permeability, to reproduce the skin behavior, and to predict the ability of specific chemicals to permeate this barrier. A significant number of issues, like interlaboratory variability, experimental conditions, data set building rationales, and skin site of origin and hydration, still prevent us from obtaining a definitive predictive skin permeability model. This review wants to show the main advances and the principal approaches in computational methods used to predict this property, to enlighten the main issues that have arisen, and to address the challenges to develop in future research.

This article is focused on the design of a fuzzy logic-based control system to optimize a drug freeze-drying process. The goal of the system is to keep product temperature as close as possible to the threshold value of the formulation being processed, without trespassing it, in such a way that product quality is not jeopardized and the sublimation flux is maximized. The method involves the measurement of product temperature and a set of rules that have been obtained through process simulation with the goal to obtain a unique set of rules for products with very different characteristics. Input variables are the difference between the temperature of the product and the threshold value, the difference between the temperature of the heating fluid and that of the product, and the rate of change of product temperature. The output variables are the variation of the temperature of the heating fluid and the pressure in the drying chamber. The effect of the starting value of the input variables and of the control interval has been investigated, thus resulting in the optimal configuration of the control system. Experimental investigation carried out in a pilot-scale freeze-dryer has been carried out to validate the proposed system.

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.

Freeze-drying of peptide and protein-based pharmaceuticals is an increasingly important field of research. The diverse nature of these compounds, limited understanding of excipient functionality, and difficult-to-analyze quality attributes together with the increasing importance of the biosimilarity concept complicate the development phase of safe and cost-effective drug products. To streamline the development phase and to make high-throughput formulation screening possible, efficient solutions for analyzing critical quality attributes such as cake quality with minimal material consumption are needed. The aim of this study was to develop a fuzzy logic system based on image analysis (IA) for analyzing cake quality. Freeze-dried samples with different visual quality attributes were prepared in well plates. Imaging solutions together with image analytical routines were developed for extracting critical visual features such as the degree of cake collapse, glassiness, and color uniformity. On the basis of the IA outputs, a fuzzy logic system for analysis of these freeze-dried cakes was constructed. After this development phase, the system was tested with a new screening well plate. The developed fuzzy logic-based system was found to give comparable quality scores with visual evaluation, making high-throughput classification of cake quality possible.

The permeation coefficient characterizes the ability of a chemical to penetrate the dermis, and the current study describes our efforts to develop structure-based models for the permeation coefficient. Specifically, we have integrated nonlinear, quantitative structure-property relationship (QSPR) models, genetic algorithms (GAs), and neural networks to develop a reliable model. Case studies were conducted to investigate the effects of structural attributes on permeation using a carefully characterized database. Upon careful evaluation, a permeation coefficient data set consisting of 333 data points for 258 molecules was identified, and these data were added to our extensive thermophysical database. Of these data, permeation values for 160 molecular structures were deemed suitable for our modeling efforts. We employed established descriptors and constructed new descriptors to aid the development of a reliable QSPR model for the permeation coefficient. Overall, our new nonlinear QSPR model had an absolute-average percentage deviation, root-mean-square error, and correlation coefficient of 8.0%, 0.34, and 0.93, respectively. Cause-and-effect analysis of the structural descriptors obtained in this study indicates that that three size/shape and two polarity descriptors accounted for approximately 70% of the permeation information conveyed by the descriptors.

The skin is a major exposure route for many potentially toxic chemicals. It is, therefore, important to be able to predict the permeability of compounds through skin under a variety of conditions. Available skin permeability databases are often limited in scope and not conducive to developing effective models. This sparseness and ambiguity of available data prompted the use of fuzzy set theory to model and predict skin permeability. Using a previously published database containing 140 compounds, a rule-based Takagi-Sugeno fuzzy model is shown to predict skin permeability of compounds using octanol-water partition coefficient, molecular weight, and temperature as inputs. Model performance was estimated using a cross-validation approach. In addition, 10 data points were removed prior to model development for additional testing with new data. The fuzzy model is compared to a regression model for the same inputs using both R2 and root mean square error measures. The quality of the fuzzy model is also compared with previously published models. The statistical analysis demonstrates that the fuzzy model performs better than the regression model with identical data and validation protocols. The prediction quality for this model is similar to others that were published. The fuzzy model provides insights on the relationships between lipophilicity, molecular weight, and temperature on percutaneous penetration. This model can be used as a tool for rapid determination of initial estimates of skin permeability.

A cubic spline function for describing the verapamil concentration profile, resulting from the verapamil absorption input to be evaluated, has been used. With this method, the knots are taken to be the data points, which has the advantage of being computationally less complex. Because of its inherently low algorhythmic errors, the spline method is less distorted and more suitable for further data analysis than others. The method has been evaluated using simulated verapamil delayed release tablet concentration data containing various degrees of random noise. The accuracy of the method was determined by how well the estimates of input rate and extent represented the true values. It was found that the accuracy of the method was of the same order of magnitude as the noise level of the data. Spline functions in convolutional modeling of verapamil formulation bioavailability and bioequivalence, as shown in the numerical simulation investigation, are very powerful additional tools for assessing the quality of new verapamil formulations in order to ensure that they are of the same quality as already registered formulations of the drug. The development of such models provides the possibility to avoid additional or larger bioequivalence and/or clinical trials and to thus help shorten the investigation time and registration period.

This article reviews some new mathematical models and techniques used to predict and understand percutaneous penetration and transdermal delivery. These models are also useful for various enhancement strategies that can be used in dermal-penetration and formulation development studies. If appropriate, biophysical techniques can be combined with these new mathematical models and statistical analyses and it will be possible to understand the factors affecting penetration of molecules through skin. These factors, or parameters, can then be used to control the penetration rate when effective transdermal delivery or therapy is required or targeted.

The purpose of this study was to evaluate the efficiency of a neuro-fuzzy logic-based methodology to model poorly soluble drug formulations and predict the development of the particle size that has been proven to be an important factor for long-term stability.

An adaptive neuro-fuzzy inference system was used to model the natural structures within the data and construct a set of fuzzy rules that can subsequently used as a predictive tool. The model was implemented in Matlab 6.5 and trained using 75% of an experimental data set. Subsequently, the model was evaluated and tested using the remaining 25%, and the predicted values of the particle size were compared to the ones from the experimental data. The produced adaptive neuro-fuzzy inference system-based model consisted of four inputs, i.e., acetone, propylene glycol, POE-5 phytosterol (BPS-5), and hydroxypropylmethylcellulose 90SH-50, with four membership functions each. Moreover, 256 fuzzy rules were employed in the model structure.

Model training resulted in a root mean square error of 4.5 x 10(-3), whereas model testing proved its highly predictive efficiency, achieving a correlation coefficient of 0.99 between the actual and the predicted values of the particle size (mean diameter).

Neuro-fuzzy modeling has been proven to be a realistic and promising tool for predicting the particle size of drug formulations with an easy and fast way, after proper training and testing.

The prediction of transdermal absorption for arbitrary penetrant structures has several important applications in the pharmaceutical industry. We propose a new data-driven, predictive model for skin permeability coefficients k(p) based on an ensemble model using k-nearest-neighbor models and ridge regression. The model was trained and validated with a newly assembled data set containing experimental data and structures for 110 compounds. On the basis of three purely computational descriptors (molecular weight, calculated octanol/water partition coefficient, and solvation free energy), we have developed a model allowing for the reliable, purely computational prediction of skin permeability coefficients. The model is both accurate and robust, as we showed in an extensive validation (correlation coefficient for leave-one-out cross validation: Q = 0.948, mean standard error: 0.2 for log k(p)).

In recent years, several new methods for the mathematical modeling have gradually emerged in pharmacokinetics, and the development of pharmacokinetic models based on these methods has become one of the most rapidly growing and exciting application-oriented sub-disciplines of the mathematical modeling. The goals of our MiniReview are twofold: i) to briefly outline fundamental ideas of some new modeling methods that have not been widely utilized in pharmacokinetics as yet, i.e. the methods based on the following concepts: linear time-invariant dynamic system, artificial-neural-network, fuzzy-logic, and fractal; ii) to arouse the interest of pharmacological, toxicological, and pharmaceutical scientists in the given methods, by sketching some application examples which indicate the good performance and perspective of these methods in solving pharmacokinetic problems.