Finite dose percutaneous drug absorption: a BASIC program for the solution of the diffusion equation

Finite Element Analysis for Predicting Skin Pharmacokinetics of Nano Transdermal Drug Delivery System Based on the Multilayer Geometry Model

Background

Skin pharmacokinetics is an indispensable indication for studying the drug fate after administration of transdermal drug delivery systems (TDDS). However, the heterogeneity and complex skin structured with stratum corneum, viable epidermis, dermis, and subcutaneous tissue inevitably leads the drug diffusion coefficient (Kp) to vary depending on the skin depth, which seriously limits the development of TDDS pharmacokinetics in full thickness skin.

Methods

A multilayer geometry skin model was established and the Kp of drug in SC, viable epidermis, and dermis was obtained using the technologies of molecular dynamics simulation, in vitro permeation experiments, and in vivo microdialysis, respectively. Besides, finite element analysis (FEA) based on drug Kps in different skin layers was applied to simulate the paeonol nanoemulsion (PAE-NEs) percutaneous dynamic penetration process in two and three dimensions. In addition, PAE-NEs skin pharmacokinetics profile obtained by the simulation was verified by in vivo experiment.

Results

Coarse-grained modeling of molecular dynamic simulation was successfully established and the Kp of PAE in SC was 2.00×10⁻⁶ cm²/h. The Kp of PAE-NE in viable epidermis and in dermis detected using penetration test and microdialysis probe technology, was 1.58×10⁻⁵ cm²/h and 3.20×10⁻⁵ cm²/h, respectively. In addition, the results of verification indicated that PAE-NEs skin pharmacokinetics profile obtained by the simulation was consistent with that by in vivo experiment.

Discussion

This study demonstrated that the FEA combined with the established multilayer geometry skin model could accurately predict the skin pharmacokinetics of TDDS.

Modeling of Drug Diffusion Based on Concentration Profiles in Healthy and Damaged Human Skin

Based on experimental drug concentration profiles in healthy as well as tape-stripped ex vivo human skin, we model the penetration of the antiinflammatory drug dexamethasone into the skin layers by the one-dimensional generalized diffusion equation. We estimate the position-dependent free-energy and diffusivity profiles by solving the conjugated minimization problem, in which the only inputs are concentration profiles of dexamethasone in skin at three consecutive penetration times. The resulting free-energy profiles for damaged and healthy skin show only minor differences. In contrast, the drug diffusivity in the first 10 μm of the upper skin layer of damaged skin is 200-fold increased compared to healthy skin, which reflects the corrupted barrier function of tape-stripped skin. For the case of healthy skin, we examine the robustness of our method by analyzing the behavior of the extracted skin parameters when the number of input and output parameters are reduced. We also discuss techniques for the regularization of our parameter extraction method.

Data-based modeling of drug penetration relates human skin barrier function to the interplay of diffusivity and free-energy profiles

Based on experimental concentration depth profiles of the antiinflammatory drug dexamethasone in human skin, we model the time-dependent drug penetration by the 1D general diffusion equation that accounts for spatial variations in the diffusivity and free energy. For this, we numerically invert the diffusion equation and thereby obtain the diffusivity and the free-energy profiles of the drug as a function of skin depth without further model assumptions. As the only input, drug concentration profiles derived from X-ray microscopy at three consecutive times are used. For dexamethasone, skin barrier function is shown to rely on the combination of a substantially reduced drug diffusivity in the stratum corneum (the outermost epidermal layer), dominant at short times, and a pronounced free-energy barrier at the transition from the epidermis to the dermis underneath, which determines the drug distribution in the long-time limit. Our modeling approach, which is generally applicable to all kinds of barriers and diffusors, allows us to disentangle diffusivity from free-energetic effects. Thereby we can predict short-time drug penetration, where experimental measurements are not feasible, as well as long-time permeation, where ex vivo samples deteriorate, and thus span the entire timescales of biological barrier functioning.

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.

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.

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.

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.