Predicting Human Dermal Drug Concentrations Using PBPK Modeling and Simulation: Clobetasol Propionate Case Study.

Quantitative in silico tools may be leveraged to mechanistically predict the dermato-pharmacokinetics of compounds delivered from topical and transdermal formulations by integrating systems of rate equations that describe permeation through the formulation and layers of skin and pilo-sebaceous unit, and exchange with systemic circulation via local blood flow. Delivery of clobetasol-17 propionate (CP) from DermovateTM cream was simulated using the Transdermal Compartmental Absorption & Transit (TCATTM) Model in GastroPlus®. The cream was treated as an oil-in-water emulsion, with model input parameters estimated from publicly available information and quantitative structure-permeation relationships. From the ranges of values available for model input parameters, a set of parameters was selected by comparing model outputs to CP dermis concentration-time profiles measured by dermal open-flow microperfusion (Bodenlenz et al. Pharm Res. 33(9):2229-38, 2016). Predictions of unbound dermis CP concentrations were reasonably accurate with respect to time and skin depth. Parameter sensitivity analyses revealed considerable dependence of dermis CP concentration profiles on drug solubility in the emulsion, relatively less dependence on dispersed phase volume fraction and CP effective diffusivity in the continuous phase of the emulsion, and negligible dependence on dispersed phase droplet size. Effects of evaporative water loss from the cream and corticosteroid-induced vasoconstriction were also assessed. This work illustrates the applicability of computational modeling to predict sensitivity of dermato-pharmacokinetics to changes in thermodynamic and transport properties of a compound in a topical formulation, particularly in relation to rate-limiting steps in skin permeation. Where these properties can be related to formulation composition and processing, such a computational approach may support the design of topically applied formulations.

Multiscale modeling framework of transdermal drug delivery.

This study addresses the modeling of transdermal diffusion of drugs to better understand the permeation of molecules through the skin, especially the stratum corneum, which forms the main permeation barrier to percutaneous permeation. In order to ensure reproducibility and predictability of drug permeation through the skin and into the body, a quantitative understanding of the permeation barrier properties of the stratum corneum (SC) is crucial. We propose a multiscale framework of modeling the multicomponent transdermal diffusion of molecules. The problem is divided into subproblems of increasing length scale: microscopic, mesoscopic, and macroscopic. First, the microscopic diffusion coefficient in the lipid bilayers of the SC is found through molecular dynamics (MD) simulations. Then, a homogenization procedure is performed over a model unit cell of the heterogeneous SC, resulting in effective diffusion parameters. These effective parameters are the macroscopic diffusion coefficients for the homogeneous medium that is "equivalent" to the heterogeneous SC, and thus can be used in finite element simulations of the macroscopic diffusion process. The resulting drug flux through the skin shows very reasonable agreement to experimental data.

Using the method of homogenization to calculate the effective diffusivity of the stratum corneum with permeable corneocytes.

The stratum corneum is the outermost layer of the skin, which acts as a barrier membrane against the penetration of molecules into and out of the body. It has a biphasic structure consisting of keratinized cells (corneocytes) that are embedded in a lipid matrix. The macroscopic transport properties of the stratum corneum are functions of its microstructure and the transport properties of the corneocytes and the lipid matrix, and are of considerable interest in the context of transdermal drug delivery and quantifying exposure to toxins, as well as for determining the relation of skin disorders to disruption of the stratum corneum barrier. Due to the complexity of the tissue and the difference in length scales involved in its microstructure, a direct analysis of the mass transport properties of the stratum corneum is not feasible. In this study, we undertake an approach where the macroscopic diffusion tensor of the stratum corneum is obtained through homogenization using the method of asymptotic expansions. The biphasic structure of the stratum corneum is fully accounted for by allowing the corneocytes to be permeable and considering the partitioning between the corneocytes and the lipid phases. By systematically exploring the effect of permeable corneocytes on the macroscopic transport properties of the stratum corneum, we show that solute properties such as lipophilicity and relative permeabilities in the two phases have large effects on its transdermal diffusion behavior.

Mechanical properties of human stratum corneum: effects of temperature, hydration, and chemical treatment.

An in vitro mechanics approach to quantify the intercellular delamination energy and mechanical behavior of isolated human stratum corneum (SC) in a direction perpendicular to the skin surface is presented. The effects of temperature, hydration, and a chloroform-methanol treatment to remove intercellular lipids were explored. The delamination energy for debonding of cells within the SC layer was found to be sensitive to the moisture content of the tissue and to the test temperature. Delamination energies for untreated stratum corneum were measured in the range of 1-8J/m(2) depending on test temperature. Fully hydrated specimen energies decreased with increasing temperature, while room-humidity-hydrated specimens exhibited more constant values of 2-4J/m(2). Lipid-extracted specimens exhibited higher delamination energies of approximately 12J/m(2), with values decreasing to approximately 4J/m(2) with increasing test temperature. The peak separation stress decreased with increasing temperature and hydration, but lipid-extracted specimens exhibited higher peak stresses than untreated controls. The delaminated surfaces revealed an intercellular failure path with no evidence of tearing or fracture of cells. The highly anisotropic mechanical behavior of the SC is discussed in relation to the underlying SC structure.

Finite element modeling of coupled diffusion with partitioning in transdermal drug delivery.

The finite element method is employed to simulate two-dimensional (axisymmetric) drug diffusion from a finite drug reservoir into the skin. The numerical formulation is based on a general mathematical model for multicomponent nonlinear diffusion that takes into account the coupling effects between the different components. The presence of several diffusing components is crucial, as many transdermal drug delivery formulations contain one or more permeation enhancers in addition to the drug. The coupling between the drug and permeation enhancer(s) results in nonlinear diffusion with concentration-dependent diffusivities of the various components. The framework is suitable for modeling both linear and nonlinear, single- and multicomponent diffusions, however, as it reduces to the correct formulation simply by setting the relevant parameters to zero. In addition, we show that partitioning of the penetrants from the reservoir into the skin can be treated in a straightforward manner in this framework using the mixed method. Partitioning at interface boundaries poses some difficulty with the standard finite element method as it creates a discontinuity in the concentration variable at the interface. To our knowledge, nonlinear (concentration-dependent) partitioning in diffusion problems has not been treated numerically before, and we demonstrate that nonlinear partitioning may have an important role in the effect of permeation enhancers. The mixed method that we adopt includes the flux at the interface explicitly in the formulation, allowing the modeling of concentration-dependent partitioning of the permeants between the reservoir and the skin as well as constant (linear) partitioning. The result is a versatile finite element framework suitable for modeling both linear and nonlinear diffusions in heterogeneous media where the diffusivities and partition coefficients may vary in each subregion.

Antibody penetration into a spherical prevascular tumor nodule embedded in normal tissue.

A finite-element (FE) method is used to numerically solve a pharmacokinetic model that describes the uptake of systemically administered antibody (mAb) in a prevascular spherical tumor nodule embedded in normal tissue. The model incorporates plasma kinetics, transcapillary transport, lymphatic clearance, interstitial diffusion in both the normal tissue and tumor, and binding reactions. We use results from the FE analysis to assess previous predictions that employed either a Dirichlet boundary condition (b.c.), or an approximate, composite (Dirichlet and Neumann) b.c. at the tumor surface. We find that the Dirichlet b.c. significantly overpredicted the mean total tumor mAb concentration. In contrast, the composite b.c. yielded good agreement with FE predictions, except at early times. We also used the FE model to investigate the influence of the approximately 30-fold difference in the values of mAb diffusion coefficient measured by Clauss and Jain (Cancer Res. 50:3487-3492, 1990) and Berk et al. (Proc. Natl. Acad. Sci. U.S.A. 94:1785-1790, 1997). For low diffusivity, diffusional resistance slows both mAb uptake by and efflux from the tumor. For high diffusivity at the same mAb dose, more rapid uptake produces earlier and higher peak mAb levels in the tumor, while the efflux rate is limited by the dissociation of the mAb-tumor antigen complex. The differences in spatial and temporal variation in mAb concentration between low and high diffusivities are of sufficient magnitude to be experimentally observable, particularly at short times after antibody administration.