Modeling Techniques – Novel Approach to Skin Permeability Measurement

Mohit Soni^*, Daisy Sharma, Tejvir Kaur, Sandeep Kumar, GD Gupta

Department of Pharmaceutics, ASBASJSM College of Pharmacy, Bela, Ropar, (Punjab) 140111 INDIA.

ABSTRACT

The stratum corneum, possess a formidable challenge to formulators of drug delivery systems. In this review, various aspects of penetration through the stratum corneum have been highlighted with use of new mathematical models. These models are useful for enhancement strategies of drugs through dermal penetration and are also use in predicting pharmacological and toxicological point of view. These techniques are used to control the penetration rate through stratum corneum.

KEYWORDS: Stratum corneum, mathematical models, pharmacological, toxicological

INTRODUCTION

Skin is the largest organ of the body with a surface area ~1.8– 2.0 m² and a weight of almost 9 kg. An average square centimeter of skin contains 10 hair follicles, 15 sebaceous glands, 12 nerves, 100 sweat glands, 360 cm of nerves, and three blood vessels. It forms a unique and flexible interface between our internal milieu and the external environment and possesses sensory, thermoregulatory, metabolic and immunological functions. It is flexible enough to resist permanent distortion from movement and thin enough to allow stimulation. It also performs many ancillary functions, such as metabolism, and the production of sweat enables temperature control and excretion of waste products^1-3. The skin is composed of three layers- subcutaneous tissue, dermis and epidermis. The discontinuous layer of sebum, a complex lipophilic fluid secreted by the sebaceous glands, is sometimes considered to be a fourth, outermost layer. The stratum corneum is the outermost layer of the epidermis and considered as the rate limiting barrier in transdermal permeation of most molecules. In humans, it consists of 10 and 25 layers of dead, elongated, fully keratinised corneocytes that are embedded in a matrix of lipid bilayers. This layer is only 6–10 mm thick in most of the regions of the body but 0.4–0.6 mm thick in the palms of the hands and soles of the feet. The stratum corneum consists of ~40% protein of which 80% is keratin. Keratin is a group of α-helical polypeptides ranging in size from 40,000–68,000 daltons. The type and amount of lipid in the stratum corneum depends on body-site and, currently, it is generally accepted that skin permeability is affected by stratum corneum lipids^4-7.

Skin permeability is an important parameter in the assesment of potential toxicity of environmental agents or the feasibility of a drug for transdermal delivery. Although skin penetration can be determined experimentally, a simple model that can predict this descriptors, based on few inputs is valuable as compared to high risk assessment and drug delivery investigations. A number of algorithm and predictive models have been used to estimate the skin permeability coefficients these are: empirical and theoretical. Theoretical models are based on the contributions of the possible routes of percutaneous penetration and the interaction of elements of these routes with the penetrants. Empirical models rely on measured experimental permeability coefficients of series of chemicals and correlate them with the physicochemical properties^8,9.

Penetration from Skin:

Although the skin has the barrier function, some chemicals are able to penetrate through it. Penetrations routes exist for passive transport of xenobiotics through the skin include the following:

(1) Intercellular diffusion through lipid lamellae

(2) Transcellular diffusion through both the keratinocytes and lipid lamellae

(3) Diffusion through appendages (hair follicles and sweat ducts) ^7,9-11.

Techniques for Predicting Skin Permeability

Earlier Models Newer Models

Linear Free Energy Principal Components

Relationship Analysis,

Quantitative Structure Probabilistic

Activity Analyses,

Relationship Artificial Neural Network Modeling,

Probabilistic Analyses,

Fuzzy Modeling,

Biopartitioning Micellar Chromatography Considering Lateral Free- Volume

Diffusion and Diffusion through Pores and Shunts

EARLIER MODELS:

Human stratum corneum permeability coefficient (K_p, often expressed as log K_p) to predict skin permeability and they have examined the effect structural parameters of penetrants have on permeability led to the development of models. Using molecular descriptors that explain variations in physicochemical properties or biological activity of penetrants has resulted in the development of linear free-energy relationships (LFER) and quantitative SAR (QSAR). Quantitative structure-activity relationship method is used to statistically relate the skin permeation of compounds with their structural descriptors or physicochemical parameters. QSARs are useful in predicting behaviour of novel compounds and provide insights into mechanisms of activity. The stratum corneum being a two-phase region consisting of ‘bricks and mortar’, where the aqueous protein phase in the keratinocytes represents the bricks and the intercellular lipid phase represents the continuous mortar⁷. The transport of the compound through the stratum corneum was assumed to be the sum of the diffusion through the lipid and protein. It was then concluded that diffusion through the lipid phase was ~500 times slower than diffusion through the protein phase⁹. The density and compactness of the intracellular protein in the keratinocytes of the stratum corneum make it almost thermodynamically and kinetically impossible for compounds to cross. Intercellular diffusion through the lipid lamellae is the predominant mode of transport.

Log K_P = -6.3 + 0.71 Log P_oct/w – 0.0061 MW -----------Eq 1

Where, Log K_P is the human skin permeability coefficient; Log P_oct/w is the octanol-water partition coefficient; and MW is the molecular weight. Flynn interpreted the data from the literature in terms of a risk assessment and he concluded that penetration through the skin is related to the octanol–water partition coefficient (K_oct, often expressed as log K_oct). He proposed that a rough prediction of the skin permeability coefficient is sufficient to estimate the risk factor^6,8,12-17.

NEWER MODELS:

Considering Lateral Free-Volume Diffusion and Diffusion Through Pores and Shunts:

Solute permeation through four possible routes in the stratum corneum, including free-volume permeability through lipid bilayers (K_p^fv) lateral permeability along lipid bilayers (K_p^lateral), permeability through pores (K_p^pore) and permeability through shunts (K_p^shunt). Mathematically, skin permeability of hydrophobic or hydrophilic solutes is described by following equation.

K_p = K_p^fv + K_p^lateral + K_p^pore + K_p^shunt ----------------------Eq 2

Where, K_p^fv shows permeability associated with free-volume type of diffusion through lipid bilayers, K_p^lateral corresponds to permeability of hydrophobic solutes due to lateral diffusion of lipids, K_p^pore corresponds to solute permeability through pores, and K_p^shunt corresponds to solute permeability through shunts (hair follicles and sweat ducts). Hydrophilic solutes permeates the skin through imperfections in the lipid bilayers, modelled as pores.

The most important finding of this model is that solute permeation can take place through four different pathways (i.e free-volume permeability through lipid bilayers, lateral permeability along lipid bilayers and permeability through shunts) and also that the contribution of each pathway can be estimated in a consistent manner. The predominant pathway used by a solute was determined by a combination of the molecular radius and hydrophilicity. It was found that permeation of low MW hydrophilic solutes (e.g. water) can entirely be explained by diffusion through intercellular lipid bilayers. However, larger hydrophilic solutes, such as sucrose, permeate by diffusion through pores. Diffusion of macromolecules, such as dextran, was consistent with diffusion through shunts^9,10,15.

Probabilistic Analyses:

A probabilistic, transient three-phase model of percutaneous absorption of chemicals was developed to assess the relative importance of uncertain parameters and processes of the penetration that might be important for the dermal risk-based exposure assessments. Penetration routes through the skin were modelled including the following (1) intercellular diffusion through the stratum corneum comprised of an immobile protein phase, a mobile aqueous (water) phase, and a mobile oil (lipid) phase; (2) aqueous-phase diffusion through sweat ducts; and (3) oil-phase diffusion through hair follicles. Sensitivity analyses, using stepwise linear regression, were also performed to identify model parameters that were most important for the simulated mass fluxes at different times. This Probabilistic Analysis of Percutaneous Absorption (PAPA) method has been developed to improve risk-based exposure assessments and transdermal drug delivery analysis where parameters and processes can be highly uncertain (Uncertainty distributions were assigned to model parameters and a probabilistic Monte Carlo analysis was performed to simulate a distribution of mass fluxes through each of the routes). The result indicated at early time points before steady-state conditions had been established, transport through the sweat ducts provided a significant amount of drug flux into the bloodstream. Because of the uncertainty in the input parameters, a large range of permeant fluxes were simulated through each of the three routes at this early time. After one hour, when system had reached the steady state the uncertainty was reportedly reduced, and the relative importance of the pathways had changed. The most important parameters for the simulated mass flux were identified and the relative importance of each parameter was quantified through the incremental coefficients of determination and semipartial correlations. Diffusion through the stratum corneum became important because of the relatively large surface area. Similarly, despite the lower oil-phase molecular diffusion coefficient of the hair follicles, diffusion through the hair follicles was more significant than diffusion through the sweat ducts at later time because of the larger simulated porosity of hair follicles. These model analysis were found to be extremely useful in not only quantifying the uncertainty in the simulated output variables, but also in identifying the input parameters that greatly influenced simulated results. These probabilistic methods can provide more meaningful interpretations of exposure assessments and risk regarding dermal uptake of contaminants^9,11.

Principal Components Analysis:

Principal components analysis (PCA) has been used to determine the permeant diffusion across the human stratum corneum. Log (D/h) values were used instead of log K_p values, considering the diffusion coefficient (D, cm²/h), diffusional path length (h, cm), permeability coefficient (K_p, cm/h) and K_oct. MWs with scaled H-bonding parameters (α and β) or a summed modulus of partial charge from molecular modelling (sum of oxygen charges, sum of hydrogen charges on the molecule, etc.) were tested as predictors of (D/h). PCA detects relationships called Principal Components (PCs) among the variables in a table (matrix) that account for the data variation. PCA was considered to be related to the log (D/h), MW, α and β and sum of eigenvalues¹⁸. Contribution of log (D/h) and it was found to have an important role in the PC (or mechanism). PCA analyses were performed considering log(D/h), MW, α and β. The sum of eigenvalues is the number of PCs. The eigenvalue of a PC shows the proportion of the total variation in the matrix attributable to that PC. Thus if log (D/h) were completely determined by a single process involving MW, α and β then PC1 would have an eigenvalue of 4 and PCs 2, 3, 4 would all be zero. This proportion for PC1 is 0.82 (i.e. 3.27/4). Within PC1 the eigenvector of a variable indicates how much of the variation in data is attributable to that variable. It was defined as the sum of the squares of the eigenvectors.

(0.54²) + (-0.54²) + (-0.44²) + (-0.48²) = 1 ---------------Eq 3

The contribution of log (D/h) is thus 0.29 (i.e. 0.54²) which means that it plays an important role in the PC (or mechanism). Eigenvector sign is significant, so that PC1 suggests a mechanism involving log (D/h) inversely with MW and H-bonding. PCA thus enables us:

(1) To identify relationships between groups of variables

(2) To estimate the importance of each relationship in determining the overall process

(3) To estimate the importance of each variable within a relationship

The eigen value of a PC shows the proportion of the total variation in the matrix attributable to that PC^9,16,19-20.

Artificial Neural Network Modeling (ANN):

It is also used to predict skin permeability and biologically inspired computer algorithm designed to gather information from data in a manner emulating the learning pattern in the brain. ANN systems are highly complex, multidimensional, nonlinear, information processing systems. The input layer neurons obtain data and the output neurons produce the ANN response. Hidden neurons communicate with other neurons. The weighted sum of the inputs simulates the activation of the neuron. Thus, what is learned in a hidden neuron is based on all the inputs taken together. The activation signal is passed through an activation function (transfer function) to produce a single output of the neuron. The behaviour of a neural network is determined by the transfer functions of its neurons, by the learning rule and by the architecture itself. It is based on use of partial charge, logK_oct and MW data, predicting skin permeability using these factors as inputs into an ANN (Fig. 1)^13,21-23.

Fuzzy Modeling:

All the modelling schemes, whether based on traditional mathematical principles or developed through fuzzy techniques, represents a mapping of set of inputs to a set of outputs. It has been successfully used for modelling, control systems, pattern recognition, image processing, among other applications and proposed to predict skin permeability coefficients. For predicting chemical penetration through the skin, the output is the skin permeability coefficient and inputs include a variety of descriptors, such as molecular weight (MW), molecular volume (MV), log octanol/water partition coefficients and hydrogen bonding activity⁹. Fuzzy models were developed by Pannier et al. using the adaptive neural Fuzzy inference system (ANFIS), the MatLab computer software, as well as Flynn’s, Potts and Guy’s and Abraham’s databases that include MW, log K_oct and molecular parameters for the compounds, such as H-bond donor activity (solute summation H-bond acidity, ∑α^H₂), H-bond acceptor activity (solute summation H-bond basicity, ∑β^H₂) and dipolarity or polarizability (p). Three Fuzzy inference models were developed using subtractive clustering to define natural structures within the data and assign subsequent rules. The numeric parameters describing the rules were refined through the use of an ANFIS implemented in the MatLab program. Each model was evaluated using the dataset. The data were divided into two subsets, defined as the training and checking sets, which were used to train the model and then to prevent over-fitting the data. If it is over-trained, the program can memorize data. The model was then evaluated by running the entire dataset through it and the output data were compared with the published experimental data. All databases produced Fuzzy inference models that successfully predicted skin permeability coefficients. Fuzzy rule-based models are a realistic and promising tool that can be used to model and predict skin permeability coefficients as well as (or better than) previous algorithms with fewer inputs^24,25.

Biopartitioning Micellar Chromatography (BMC):

BMC is very useful technique for predicting the effect pH on the skin permeability of drugs. By using this approach, it is easy to estimate the permeability constants of the ionized and neutral forms of drugs. It was reported that the ionized forms of the compounds contribute to the overall permeability, although the contribution of the neutral forms²⁶. This technique has advantages like fast, reproducible, simple and economical, and provides similar results to the conventional in vivo approaches that use human skin in compound studies. This is of great interest for the pharmaceutical industry, particularly when the effect of these variables have on the permeability of compounds needs to be determined to optimize the vehicle features. Several QRPRs for predicting skin permeability have been reported in the literature, including the use of Immobilized Artificial Membrane (IAM) columns and immobilized keratin stationary phases²⁷. The success of Biopartitioning Micellar Chromatography (BMC) in constructing these models could be attributed to the similarities between the BMC system and biological barrier and extracellular fluid interphases. The biomicellar partition coefficient is given in Equation

k_BMC = k_HAKh + k_{A -------------------------------------------------------------------}Eq 4

1 + Kh

In this h represents the retention and the proton concentrations at each pH values and k_HA and k_A are fitting parameters representing the BMC retention of the protonated and deprotonated forms of the compound, respectively. K is the fitting parameter corresponding to the protonation constant in this experimental condition. For acidic compounds k_HA and k_A correspond to the retention of the neutral and anionic form, respectively, whereas for basic compounds these parameters represent the retention of the cationic protonated and neutral deprotonated base. Finally, a successful model was obtained by using the three significant variables, log k_BMC, melting points and molecular weights, as predictor variables. The model demonstrated to be useful in describing the biological behaviour of different kinds of drugs and to predict human oral drug absorption, skin permeability, and ocular tissue permeability of drugs. The success of BMC in constructing these models could be attributed to the fact that the characteristics of the BMC systems show similarities with the biological barriers and extracellular fluids^9,28-32.

Fig. 1: Schematic representation of a three-layered feed-forward neural network (taken from 23)

CONCLUSION:

Looking into the wide range of efficiency and predictability of modelling approaches in skin permeation, these models covers wide range of structurally diverse compounds. The findings of various researchers suggest that penetration process through skin is extremely complicated and influenced by several steps. Thereby, a particular model cannot be regarded as the best model. Therefore, use of more than one model is recommended, so that maximum benefit from pharmacological and toxicological point of view can be drawn.

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Received on 08.04.2009

Accepted on 12.05.2009

© A&V Publication all right reserved

Research Journal . of Pharmaceutical Dosage Forms and Technology. 1(1): July.-Aug. 2009, 13-17