Finite dose percutaneous drug absorption: theory and its application to in vitro timolol permeation

Development and Characterization of a Microemulsion Containing a Cannabidiol Oil and a Hydrophilic Extract from Sambucus ebulus for Topical Administration

Cannabidiol (CBD) is a safe and non-psychotropic phytocannabinoid with a wide range of potential therapeutic anti-inflamatory and antioxidant activities. Due to its lipophilicity, it is normally available dissolved in oily phases. The main aim of this work was to develop and characterize a new formulation of a microemulsion with potential anti-inflammatory and antioxidant activity for the topical treatment of inflammatory skin disorders. The microemulsion system was composed of a 20% CBD oil, which served as the hydrophobic phase; Labrasol/Plurol Oleique (1:1), which served as surfactant and cosurfactant (S/CoS), respectively; and an aqueous vegetal extract obtained from Sambucus ebulus L. (S. ebulus) ripe fruits, which has potential anti-oxidant and anti-inflammatory activity and which served as the aqueous phase. A pseudo-ternary phase diagram was generated, leading to the selection of an optimal proportion of 62% (S/CoS), 27% CBD oil and 11% water and, after its reproducibility was tested, the aqueous phases were replaced by the vegetal hydrophilic extract. The defined systems were characterized in terms of conductivity, droplet size (by laser scattering), compatibility of components (by differential scanning calorimetry) and rheological properties (using a rotational rheometer). The designed microemulsion showed good stability and slight pseudo-plastic behavior. The release properties of CBD from the oil phase and caffeic acid from the aqueous phase of the microemulsion were studied via in vitro diffusion experiments using flow-through diffusion cells and were compared to those of a CBD oil and a microemulsion containing only CBD as an active substance. It was found that the inclusion of the original oil in microemulsions did not result in a significant modification of the release of CBD, suggesting the possibility of including hydrophilic active compounds in the formulation and establishing an interesting strategy for the development of future formulations.

Finite dose skin mass balance including the lateral part: comparison between experiment, pharmacokinetic modeling and diffusion models

This work investigates in vitro finite dose skin absorption of the model compounds flufenamic acid and caffeine experimentally and mathematically. The mass balance in different skin compartments (donor, stratum corneum (SC), deeper skin layers (DSL), lateral skin parts and acceptor) is analyzed as a function of time. For both substances high amounts were found in the lateral skin compartment after 6h of incubation, which emphasizes not to elide these parts in the modeling. Here, three different mathematical models were investigated and tested with the experimental data: a pharmacokinetic model (PK), a detailed microscopic two-dimensional diffusion model (MICRO) and a macroscopic homogenized diffusion model (MACRO). While the PK model was fitted to the experimental data, the MICRO and the MACRO models employed input parameters derived from infinite dose studies to predict the underlying diffusion process. All models could satisfyingly predict or describe the experimental data. The PK model and MACRO model also feature the lateral parts.

The transient dermal exposure: theory and experimental examples using skin and silicone membranes

A diffusion model is presented to account for the disposition of chemicals applied to skin as transient exposures. Two conditions are considered that apply to the skin surface following the exposure period, which are applicable to chemicals exhibiting two extremes of chemical volatility. For one case, representing highly volatile compounds, the solution is generalized to apply to multiple transient exposures. For both cases, algebraic expressions are derived to calculate the total amount of chemical that penetrates the skin. The theory is applied to experimental measurements of the in vitro penetration of diethyl phthalate applied to hairless guinea pig (HGP) skin and silicone rubber membranes (SRMs) as transient exposures. The transient exposure theory ably models the experimental data, with coefficients of determination greater than 0.97 (HGP) and greater than 0.99 (SRM). The ability of parameters derived from concurrent infinite dose experiments to predict the time course of absorption from transient exposures is explored. Discrepancies were found between measured cumulative penetration of chemical from transient exposure experiments and penetration predicted from parameters derived from infinite dose experiments, particularly for HGP. Possible reasons are explored. The current model may provide a realistic framework for estimating absorption from occupational, environmental and pharmaceutical dermal exposures.

An analytical solution for percutaneous drug absorption: Application and removal of the vehicle

The methods of Laplace transform were used to solve a mathematical model developed for percutaneous drug absorption. This model includes application and removal of the vehicle from the skin. A system of two linear partial differential equations was solved for the application period. The concentration of the medicinal agent in the skin at the end of the application period was used as the initial condition to determine the distribution of the drug in the skin following instantaneous removal of the vehicle. The influences of the diffusion and partition coefficients, clearance factor and vehicle layer thickness on the amount of drug in the vehicle and the skin were discussed.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations.

Kinetics of finite dose absorption through skin 1. Vanillylnonanamide

Despite the considerable success in predicting the steady-state dermal absorption rates of chemical compounds from large reservoirs applied to skin, correspondingly little progress has been made in predicting the absorption rate and extent for small doses of topically applied compounds. In the latter case, steady-state absorption rates are generally not obtained, and rapid evaporation or penetration of the dose solvent makes application of permeability coefficient models problematic. This report presents a new analysis of the finite dose problem in terms of a diffusion model with three parameters-a characteristic time for diffusion, h2/D; a skin solubility factor, S(m)h; and a capacity factor for absorption of the dose during the dry down period, M*. These parameters can be related to the molecular weight and oil and water solubilities of the permeant in a manner similar to models describing steady-state absorption from saturated solutions. Some variation of the parameter values based on the chemical nature and volume of the dose solvent is anticipated. The applicability of the model is demonstrated by analyzing the in vitro absorption rates of varying doses of vanillylnonamide (VN, synthetic capsaicin) applied to excised human skin from propylene glycol. The analysis shows that a three-parameter model that assigns all of the resistance to transport to diffusion through the stratum corneum is able to explain most of the significant features of VN absorption through skin.

Validation protocol of an automated in-line flow-through diffusion equipment for in vitro permeation studies

Transdermal drug delivery experiments are often tedious and time consuming in terms of sampling, labor, etc. In this way, the automation of such experiments has increased in the last few years. A protocol suitable to validate an automated diffusion equipment with seven in-line flow-through cells is described. The proposed protocol was divided into two parts. First, validation of each component which makes up the whole equipment, including the study of the statistical variability of the internal volumes between the cells, the temperature into the different chambers, the time and sample volumes, etc. In the second part, a series of permeation studies were carried out comparing the performance of the system against a classical Franz-type diffusion cell. Ketoprofen was used as a model drug. It was proved the low variability of the replicates obtained with the automated flow-through diffusion cells. The best work conditions as flow rate into the receptor chamber, temperature, etc., as well as the best mathematical approach for the diffusion data, were determined. The advantages in terms of time saved and easiness of validation of the flow-through cell design in comparison to the Franz-type cell were evidenced.

A sequential algorithm for the non-linear dual-sorption model of percutaneous drug absorption

A sequential algorithm is developed for the non-linear dual-sorption model developed by Chandrasekaran et al. [1,2] which monitors pharmacokinetic profiles in percutaneous drug absorption. In the experimental study of percutaneous absorption, it is often observed that the lag-time decreases with the increase in the donor concentration when two or more donor concentrations of the same compound are used. The dual-sorption model has sometimes been employed to explain such experimental results. In this paper, it is shown that another feature observed after vehicle removal may also characterize the dual-sorption model. Soon after vehicle removal, the plots of the drug flux versus time become straight lines on a semilogarithmic scale as in the linear model, but the half-life is prolonged thereafter when the dual-sorption model prevails. The initial half-life after vehicle removal with a low donor concentration is longer than that with a higher donor concentration. These features, if observed in experiments, may be used as evidence to confirm that the dual-sorption model gives an explanation to the non-linear kinetic behaviour of a permeant.

Significance of viable skin layers in percutaneous permeation and its implication in mathematical models: theoretical consideration based on parameters for betamethasone 17-valerate

The role of viable skin layers (viable epidermis and dermis) is examined by the three-layer model using parameter values for betamethasone 17-valerate. The mathematical three-layer diffusion model indicates that the lag time and half-life after vehicle removal in epidermis and split-thickness skin are longer than those in stratum corneum without viable layers, even if drug flux at steady-state is minimally altered. The theoretical values of the lag time and half-life predicted for epidermis and split-thickness-skin samples are compatible with the values observed in another in vitro study. The results predicted by the three-layer model indicate that the simplified model (single-layer or compartment model), which regards the whole skin as one diffusion layer or one compartment, may be warranted because all three skin layers have the same half-life after vehicle removal. The parameters used in the simplified model are estimated from some of the following values directly obtainable in the experiment: flux from skin and amount in the whole skin at steady-state, lag time, and drug concentration or amount maintained to be unchanged in the donor site. However, the simplified model often cannot resolve some discrepancy between the data and model (e.g., the ratio of the half-life to lag time) even if the data may be explained by the three-layer model.

Lag time in the dual sorption model for percutaneous absorption with finite skin-receptor boundary clearance

The lag time in the dual sorption model for percutaneous drug absorption with finite skin-receptor boundary clearance is examined. The effect of the change in the perfusional resistance on the lag time in the dual sorption model is found to be similar to, but a little less prominent than, that in the linear model. It is suggested that the lag time is roughly proportional to the amount in the skin at the steady state. Two numerical methods are used in predictor-corrector combination to obtain a numerical solution of the parabolic partial differential equation, together with the associated initial and boundary conditions, which arise in a nonlinear mathematical model of percutaneous drug absorption. Numerical estimates are obtained for the drug concentration profiles, the cumulative amount of drug excreted into the blood, the flux in the transient and steady states, the lag time, and the amount of drug in the skin per unit area in the steady state.

A linear theory of transdermal transport phenomena

A theory of charge, fluid-mass, and solute (including macromolecular) transport through porous media is applied to describe transport phenomena across the external layer of mammalian skin. Linear relationships are derived between transport fluxes and applied fields. These relationships introduce six effective transdermal transport coefficients. Formulas for each of these coefficients are provided. The practical relevance of these parameters is emphasized in the specific context of transdermal drug delivery. By employing typical physiological values for the various geometrical and physicochemical parameters that appear in the formulas for the transdermal transport coefficients, predictions are made for transport rates of charge, fluid mass, and solute species across a uniform-thickness skin sample contained within a diffusion-cell apparatus. These results are used to explore transdermal phenomena involving forced convection, current flow, electroosmosis, iontophoresis, and molecular diffusion (including convective dispersion). Comparisons with existing transdermal drug delivery data are made. On the basis of these comparisons, the theory suggests that transdermal transport in the presence of an electrical field may occur through corneocytes of the stratum corneum. The theory confirms the importance of a shunt route for small ion transport, as well as an intercellular route of transport for passive diffusion of noncharged substances. These latter conclusions, also based on comparisons with experimental data, are consistent with previous statements in the literature. A new form of solute transport enhancement, termed transdermal convective dispersion, is included in the theory, and methods for its measurement are described. Generalizations and future applications of the theory are discussed.

Dual sorption model for the nonlinear percutaneous permeation kinetics of timolol

The nonlinear percutaneous permeation kinetics of timolol were studied in vitro with human cadaver skin. In the sorption isotherm (equilibrium) study, the plots of the amount of timolol per unit area of epidermis versus aqueous timolol concentration in equilibrium were curvilinear as the dual sorption model predicts. In the penetration study, several aqueous timolol concentrations were maintained in the donor cell for 25 h. The lag-time was prolonged as the timolol concentration in the donor cell was decreased. The change in the lag time was analyzed by a newly proposed method with the lag-time prolongation factor that is calculated from the parameter values obtained in the sorption isotherm study. The ratio of the lag-time to lag-time prolongation factor was of the same magnitude, indicating that the dual sorption model explains the nonlinear percutaneous permeation kinetics of timolol. Finally, the diffusion parameter for the mobile solute was estimated by fitting the data of the cumulative amount excreted into receptor cell versus time to the numerical solution of the dual sorption model. The observed data were roughly compatible with the values predicted by the dual sorption model.

Pharmacokinetics and beta-blocking effects of transdermal timolol

The pharmacokinetic profiles of transdermal timolol 6 and 24 mg (as 5 and 20% w/v patches) was studied in four healthy young volunteers. To assess its bioavailability, the pharmacokinetics of an IV infusion of timolol maleate 5 mg was also determined in the same subjects. When the 20% (w/v) timolol patch was applied, the mean bioavailability was 74.4%. Plasma timolol concentrations were below the detection limit when a 5% patch was applied to the same skin area in all four subjects, except for one in whom the bioavailability was 23.6%. Weak erythema developed at the application site in all of the volunteers after application of the 20% (w/v) patch. However, erythema did not develop in any volunteer when the 5% patch was applied. The beta-blocking effect was determined by exercise testing. Similar plasma levels generated similar changes in exercise-induced heart rate after the transdermal and intravenous administration of timolol.

Percutaneous absorption: a single-layer model

In vitro percutaneous permeation of betamethasone 17-valerate through excised human skin was studied. Pressure-sensitive silicone adhesive containing betamethasone 17-valerate in suspension was used as a vehicle. Steady-state flux through the split-thickness skin was similar to that through the isolated epidermis. However, the lag-time and half-life after removal of the vehicle were longer for the split-thickness skin than from epidermis. At steady state, 37% of the drug in the split-thickness skin was partitioned in dermis. When the kinetic parameters of a simple single-layer model are defined to specify the permeability coefficient and the drug amount in skin at steady state, this model can predict the longer half-life observed for the split-thickness skin sample compared with that for epidermis. The difference between the observed and theoretical values of the half-life after removal of the vehicle was within 23%. On the other hand, the lag-time had a large variation and the simple diffusion model failed to be predictive. A single-layer model described by two or three kinetic parameters may be able to describe percutaneous permeation kinetics even when the processes after the compound permeation through stratum corneum are not negligible. However, it is stressed that none of the kinetic parameters inherent in this simple model directly represents one of the single physicochemical parameters, such as diffusion and partition coefficients and path length of each skin layer.

A nonlinear numerical model of percutaneous drug absorption

A nonlinear mathematical model developed by Chandrasekaran et al. is examined to monitor pharmacokinetic profiles in percutaneous drug absorption and is addressed to several associated problems that could occur in the data analysis of in vitro experiments. The formulation of the model gives rise to a nonlinear partial differential equation (PDE) of parabolic type, and a family of finite-difference methods is developed for the numerical solution of the associated initial/boundary-value problem. The value given to a parameter in this family determines the stability properties of the resulting method and whether the solution is obtained explicitly or implicitly. In the case of implicit members of the family it is seen that the solution of the nonlinear PDE is obtained by solving a linear algebraic system, the coefficient matrix of which is tridiagonal. The behaviors of two methods of the family are examined in a series of numerical experiments. Numerical differentiation and integration procedures are combined to monitor the cumulative amount of drug eliminated into the receptor cell per unit area as time increases. It is found that the use of the equation for the simple membrane model to estimate the permeability coefficient and lag time is warranted even if the system should be described by the dual-sorption model, provided cumulative amount versus time data collected for a sufficiently long time are used. However, being different from the behavior in the simple membrane model, the lag time, which can be estimated in this way, is dose-dependent and decreases with increasing donor cell concentration. On the other hand, the permeability coefficient in the dual-sorption model remains constant irrespective of the donor cell concentrations as in the simple membrane model.

A random walk method for percutaneous drug absorption pharmacokinetics: application to repeated administration of a therapeutic timolol patch

A random walk method for predicting percutaneous drug absorption pharmacokinetics was proposed. The profiles predicted by this method were compatible with those predicted by the analytical method. The random walk method is particularly useful for predicting complex processes such as repeated topical application of a drug. The amount of a drug released into skin from four therapeutic timolol patches was measured when the patches were serially applied for 2.5 h each on the same site of six healthy male volunteers. On the average, 33.2, 23.4, 15.1, and 16.5% of the applied dose was released into skin from the first, second, third, and fourth patches, respectively. This pattern was comparable with the predicted profiles (43.9, 30.2, 24.4, and 21.1%) of amounts of drug which were expected to be released from the first to fourth patches into skin, respectively. The estimation method for the normalized skin-capillary boundary clearance is also described and applied in examining the percutaneous absorption of timolol. The estimated value for this parameter was much greater than the diffusion parameter, indicating that the removal process of timolol by the local circulation is much faster than the diffusion process through skin.

Skin irritation induced by topically applied timolol

1. Erythema induced by topically applied timolol, a non-selective beta-adrenoceptor blocker, was assessed in six male volunteers. Intensity of erythema developed on the inner surface of the left forearm where timolol free base was applied for 10 h was measured by a visual score, laser doppler flowmeter and reflectance spectrophotometry. Plasma timolol concentrations collected from the left and right arms were also measured. 2. The mean values for blood volume and blood flow per unit volume of tissue both of which were assessed by a laser doppler flowmeter, haemoglobin index measured by reflectance spectrophotometry, and magnitude of erythema graded by a visual score significantly increased after the application of an acrylic co-polymer adhesive patch containing 20% (w/v) timolol free base. 3. Plasma timolol concentrations collected from the left antecubital vein were 2.4 to 10.7 times greater than those from the right arm and had significant correlations (rs = 0.55 to 0.76) with the parameters indicating the extent of erythema developed where a patch containing timolol was applied. 4. The inter-individual variation of timolol was attributed to that of the diffusivity of timolol through skin rather than that of the skin reactivity to topically applied timolol because the plasma timolol concentrations drawn from the left arm in the subjects who did not develop erythema were very low.(ABSTRACT TRUNCATED AT 250 WORDS)