Physiologically relevant one-compartment pharmacokinetic models for skin. 1. Development of models

Penetration pathways, influencing factors and predictive models for dermal absorption of exobiotic molecules: A critical review

This review provides a comprehensive summary of the skin penetration pathways of xenobiotics, including metals, organic pollutants, and nanoparticles (NPs), with a particular focus on the methodologies employed to elucidate these penetration routes. The impacts of the physicochemical properties of exogenous substances and the properties of solvent carriers on the penetration efficiencies were discussed. Furthermore, the review outlines the steady-state and transient models for predicting the skin permeability of xenobiotics, emphasizing the models which enable realistic visualization of pharmaco-kinetic phenomena via detailed geometric representations of the skin microstructure, such as stratum corneum (SC) (bricks and mortar) and skin appendages (hair follicles and sebaceous gland units). Limitations of published research, gaps in current knowledge, and recommendations for future research are highlighted, providing insight for a better understanding of the skin penetration behavior of xenobiotics and associated health risks in practical application contexts.

Using Compartments to Model Drug Delivery from Biodegradable Polymers

Polymeric drug delivery systems can improve patient compliance, decrease toxicity and prolong therapeutic effects for a wide range of therapeutic treatments, by controlling drug release. Polymer delivery system development can be facilitated by mathematical models. We present here a new compartmental model that will be more familiar to pharmaceutical professionals and equally as effective as common diffusion equation-based models. The compartmental model considers both polymer degradation and drug diffusion to predict drug release. The model is adapted into three different geometries for different polymer delivery scenarios: membranes, fibres and particles. Model parameters are derived in terms of diffusion coefficients. Polymer-drug binding interactions and distributions of fibre/particle diameters are incorporated to the model. The model is validated by comparison to common diffusion equation-based solutions and fitting to experimental data. It is shown how the model for drug release can be incorporated into existing distribution models to predict plasma concentrations of an in vivo administration. A user-friendly Python implementation of the model is available on Github, at https://github.com/spirt-t/compartments_model.

Compartmental modeling of skin absorption and desorption kinetics: Donor solvent evaporation, variable diffusion/partition coefficients, and slow equilibration process within stratum corneum

This work expands the recently developed compartmental model for skin transport to model variable diffusion and/or partition coefficients, and the presence of slow equilibration/slow binding kinetics within stratum corneum. The model was validated by comparing it with the diffusion model which was solved numerically using the finite element method. It was found that the new compartmental model predictions agreed well with that of the diffusion model, providing a sufficient number of compartments was used. The compartmental model was applied to two previously published experimental data sets: water penetration and desorption data and the finite dose dermal penetration of testosterone. Significant improvement of the fitting quality for all these data sets was achieved using the compartmental model.

Topical drug delivery: History, percutaneous absorption, and product development

Topical products, widely used to manage skin conditions, have evolved from simple potions to sophisticated delivery systems. Their development has been facilitated by advances in percutaneous absorption and product design based on an increasingly mechanistic understanding of drug-product-skin interactions, associated experiments, and a quality-by-design framework. Topical drug delivery involves drug transport from a product on the skin to a local target site and then clearance by diffusion, metabolism, and the dermal circulation to the rest of the body and deeper tissues. Insights have been provided by Quantitative Structure Permeability Relationships (QSPR), molecular dynamics simulations, and dermal Physiologically Based PharmacoKinetics (PBPK). Currently, generic product equivalents of reference-listed products dominate the topical delivery market. There is an increasing regulatory interest in understanding topical product delivery behavior under 'in use' conditions and predicting in vivo response for population variations in skin barrier function and response using in silico and in vitro findings.

Relating transdermal delivery plasma pharmacokinetics with in vitro permeation test (IVPT) findings using diffusion and compartment-in-series models

Increasing emphasis is being placed on using in vitro permeation test (IVPT) results for topical products as a surrogate for their in vivo behaviour. This study sought to relate in vivo plasma concentration - time pharmacokinetic (PK) profiles after topical application of drug products to IVPT findings with mechanistic diffusion and compartment models that are now widely used to describe permeation of solutes across the main skin transport barrier, the stratum corneum. Novel in vivo forms of the diffusion and compartment-in-series models were developed by combining their IVPT model forms with appropriate in vivo disposition functions. Available in vivo and IVPT data were then used with the models in data analyses, including the estimation of prediction intervals for in vivo plasma concentrations derived from IVPT data. The resulting predicted in vivo plasma concentration - time profiles for the full models corresponded closely with the observed results for both nitroglycerin and rivastigmine at all times. In contrast, reduced forms of these in vivo models led to discrepancies between model predictions and observed results at early times. A two-stage deconvolution procedure was also used to estimate the in vivo cumulative amount absorbed and shown to be linearly related to that from IVPT, with an acceptable prediction error. External predictability was also shown using a separate set of in vitro and in vivo data for different nitroglycerin patches. This work suggests that mechanistic and physiologically based pharmacokinetic models can be used to predict in vivo behaviour from IVPT data for topical products.

Using physiologically-based pharmacokinetic-guided "body-on-a-chip" systems to predict mammalian response to drug and chemical exposure

The continued development of in vitro systems that accurately emulate human response to drugs or chemical agents will impact drug development, our understanding of chemical toxicity, and enhance our ability to respond to threats from chemical or biological agents. A promising technology is to build microscale replicas of humans that capture essential elements of physiology, pharmacology, and/or toxicology (microphysiological systems). Here, we review progress on systems for microscale models of mammalian systems that include two or more integrated cellular components. These systems are described as a "body-on-a-chip", and utilize the concept of physiologically-based pharmacokinetic (PBPK) modeling in the design. These microscale systems can also be used as model systems to predict whole-body responses to drugs as well as study the mechanism of action of drugs using PBPK analysis. In this review, we provide examples of various approaches to construct such systems with a focus on their physiological usefulness and various approaches to measure responses (e.g. chemical, electrical, or mechanical force and cellular viability and morphology). While the goal is to predict human response, other mammalian cell types can be utilized with the same principle to predict animal response. These systems will be evaluated on their potential to be physiologically accurate, to provide effective and efficient platform for analytics with accessibility to a wide range of users, for ease of incorporation of analytics, functional for weeks to months, and the ability to replicate previously observed human responses.

Mathematical and pharmacokinetic modelling of epidermal and dermal transport processes

Topical delivery to the various regions of the skin and underlying tissues, transdermal drug delivery and dermal exposure to environmental chemicals are important areas of research. Mathematical models of epidermal and dermal transport, involving penetration of a solute through various layers of the skin, metabolism in the skin and its subsequent distribution and clearance into systemic circulation from underlying tissues, play an essential role in this research area and are reviewed in this work.

In-silico model of skin penetration based on experimentally determined input parameters. Part II: Mathematical modelling of in-vitro diffusion experiments. Identification of critical input parameters

This work describes a framework for in-silico modelling of in-vitro diffusion experiments illustrated in an accompanying paper [S. Hansen, A. Henning, A. Naegel, M. Heisig, G. Wittum, D. Neumann, K.-H. Kostka, J. Zbytovska, C.M. Lehr, U.F. Schaefer, In-silico model of skin penetration based on experimentally determined input parameters. Part I: experimental determination of partition and diffusion coefficients, Eur. J. Pharm. Biopharm. 68 (2008) 352-367 [corrected] A mathematical model of drug permeation through stratum corneum (SC) and viable epidermis/dermis is presented. The underlying geometry for the SC is of brick-and-mortar character, meaning that the corneocytes are completely embedded in the lipid phase. The geometry is extended by an additional compartment for the deeper skin layers (DSL). All phases are modelled with homogeneous diffusivity. Lipid-donor and SC-DSL partition coefficients are determined experimentally, while corneocyte-lipid and DSL-lipid partition coefficients are derived consistently with the model. Together with experimentally determined apparent lipid- and DSL-diffusion coefficients, these data serve as direct input for computational modelling of drug transport through the skin. The apparent corneocyte diffusivity is estimated based on an approximation, which uses the apparent SC- and lipid-diffusion coefficients as well as corneocyte-lipid partition coefficients. The quality of the model is evaluated by a comparison of concentration-SC-depth-profiles of the experiment with those of the simulation. Good agreements are obtained, and by an analysis of the underlying model, critical parameters of the models can be identified more easily.

Estimating contaminant dose for intermittent dermal contact: model development, testing, and application

Assessments of aggregate exposure to pesticides and other surface contamination in residential environments are often driven by assumptions about dermal contacts. Accurately predicting cumulative doses from realistic skin contact scenarios requires characterization of exposure scenarios, skin surface loading and unloading rates, and contaminant movement through the epidermis. In this article we (1) develop and test a finite-difference model of contaminant transport through the epidermis; (2) develop archetypal exposure scenarios based on behavioral data to estimate characteristic loading and unloading rates; and (3) quantify 24-hour accumulation below the epidermis by applying a Monte Carlo simulation of these archetypal exposure scenarios. The numerical model, called Transient Transport through the epiDERMis (TTDERM), allows us to account for variable exposure times and time between exposures, temporal and spatial variations in skin and compound properties, and uncertainty in model parameters. Using TTDERM we investigate the use of a macro-activity parameter (cumulative contact time) for predicting daily (24-hour) integrated uptake of pesticides during complex exposure scenarios. For characteristic child behaviors and hand loading and unloading rates, we find that a power law represents the relationship between cumulative contact time and cumulative mass transport through the skin. With almost no loss of reliability, this simple relationship can be used in place of the more complex micro-activity simulations that require activity data on one- to five-minute intervals. The methods developed in this study can be used to guide dermal exposure model refinements and exposure measurement study design.

Pharmacokinetic models of dermal absorption

Many studies have used pharmacokinetic (compartment) models for skin to predict or analyze dermal absorption of chemicals. Comparing these models is difficult because the relationships between rate constants and the physicochemical parameters were not always defined clearly, simplifying assumptions built into models sometimes were not stated, and which skin layers were included often were not specified. In this paper we review and compare published one- and two-compartment models for which rate constants were expressed in terms of the physicochemical and physical properties of the skin (i.e., diffusion coefficients, partition coefficients and thickness). Nine one-compartment and two two-compartment models are presented with a consistent nomenclature and clearly defined assumptions. In addition, methods used for estimating the physicochemical parameters required by the various are summarized. These eleven compartment models are compared with calculations from a two-membrane skin model that corresponds better with skin function. Many of the compartment models do not predict key characteristics of the two-membrane skin model, especially the effect of blood flow on skin concentration and penetration rates, even when the same input parameters were used. The compartment models developed by Kubota and by McCarley are better predictors of the two-membrane model results, because these models were developed to match characteristics of the membrane model.

Physiologically relevant two-compartment pharmacokinetic models for skin

Pharmacokinetic (compartment) models for skin have been used to predict or analyze absorption of chemical into and through skin. For highly lipophilic chemicals, the stratum corneum (sc) and the viable epidermis (v.e.) both contribute a significant resistance to chemical penetration and thus, both should be included in the model. This paper describes two-compartment models that represent the sc and the ve separately by extending the procedures previously developed for one-compartment models. The two-compartment models described here were developed by matching characteristics of a two-membrane model of skin. These compartment models were compared with membrane representations of the s.c. and v.e. for several different dermal exposure scenarios. When valid, which it is for many chemical exposure scenarios, the two-compartment model developed using characteristic times of the membrane model (model B2) more closely represents the two-membrane model than the model developed with equilibrium conditions of the membrane model (model B1). When model B2 is invalid, then model B1 is recommended. Criteria are provided for choosing from the various one- or two-compartment model options.

Dermal absorption and distribution of topically dosed jet fuels jet-A, JP-8, and JP-8(100)

Dermal exposure to jet fuels has received increased attention with the recent release of newer fuels with novel performance additives. The purpose of these studies was to assess the percutaneous absorption and cutaneous disposition of topically applied (25 microl/5 cm(2)) neat Jet-A, JP-8, and JP-8(100) jet fuels by monitoring the absorptive flux of the marker components 14C naphthalene and (3)H dodecane simultaneously applied nonoccluded to isolated perfused porcine skin flaps (IPPSF) (n = 4). Absorption of 14C hexadecane was estimated from JP-8 fuel. Absorption and disposition of naphthalene and dodecane were also monitored using a nonvolatile JP-8 fraction reflecting exposure to residual fuel that might occur 24 h after a jet fuel spill. In all studies, perfusate, stratum corneum, and skin concentrations were measured over 5 h. Naphthalene absorption had a clear peak absorptive flux at less than 1 h, while dodecane and hexadecane had prolonged, albeit significantly lower, absorption flux profiles. Within JP-8, the rank order of absorption for all marker components was (mean +/- SEM % dose) naphthalene (1.17 +/- 0.07) > dodecane (0.63 +/- 0.04) > hexadecane (0.18 +/- 0.08). In contrast, deposition within dosed skin showed the reverse pattern. Naphthalene absorption into perfusate was similar across all fuel types, however total penetration into and through skin was highest with JP-8(100). Dodecane absorption and total penetration was greatest from JP-8. Absorption of both markers from aged JP-8 was lower than other fuels, yet the ratio of skin deposition to absorption was greatest for this treatment group. In most exposure scenarios, absorption into perfusate did not directly correlate to residual skin concentrations. These studies demonstrated different absorption profiles for the three marker compounds, differential effects of jet fuel types on naphthalene and dodecane absorption, and uncoupling of perfusate absorption from skin disposition.

Physiologically relevant one-compartment pharmacokinetic models for skin. 2. Comparison of models when combined with a systemic pharmacokinetic model

Transport of chemicals through skin is best modeled as passive diffusion through a membrane, but mathematical solutions for realistic conditions are cumbersome. Compartment models, representing skin as a stirred tank, are mathematically simpler but less physiologically relevant. In a previous paper, several different compartment models were developed assuming constant blood and vehicle concentrations. Here, five skin models (four of the previously described compartment models and one membrane model) are combined with a one-compartment systemic pharmacokinetic (PK) model to examine the effects of changing vehicle and blood concentrations and to clarify how differences between skin models affect the predicted systemic response. The skin-PK models were solved with the same input parameters (i.e., permeability coefficients, partition coefficients, skin thickness, and cutaneous blood flow rates) and compared for five different exposure scenarios. Because the models have different underlying assumptions, they do predict different results. For many exposure situations compartment models give acceptable results, with the most pronounced differences from the membrane model during short exposure times. Generally, the compartment model that most closely represents the membrane model was developed by forcing it to match the membrane model for conditions similar to those of the given exposure scenario.