The skin concentration of a substance after a topical application or exposure determines both local treatment outcomes and the dermal toxicity assessment of various products. However, quantifying the time course of those concentrations at skin effect sites, such as the viable epidermal, superficial dermis and appendages in humans is especially problematic in vivo, making physiologically based mathematical modelling an essential tool to meet this need. This work further develops our published physiologically based pharmacokinetic and COMSOL based dermal transport modelling by considering the impact of the superficial subpapillary dermal plexus, which we represent as two well stirred compartments. The work also studied the impact on dermal concentrations of subpapillary plexus size, depth, blood velocity and density of subpapillary plexus vessels. Sensitivity analyses are used to define the most important transport determinants of skin concentrations after topical application of a substance, with previously published results used to validate the resulting analyses. This resulting model describes the available experimental data better than previous models, especially at deeper dermal depths.

Viable skin drug transport is an important concept to consider as it can have a significant impact on the local concentration of a drug. The concentration becomes even more critical for toxicological issues when implementing different permeability enhancement techniques. For this reason, it is important to develop models that can predict drug transport in the viable skin. This paper expands upon previous capillary modeling by representing the convective transport of a solute that has permeated into the capillary loops. As a result, convective transport caused the concentration profile to plateau within the deeper dermal layers, effectively matching the trend of previous experimental data. Furthermore, the new model also has a significantly quicker transient profile as the time required to reach steady-state is five-fold faster than predicted in previous homogenous models.

INTRODUCTION:In the past, mathematical modeling of the transport of transdermal drugs has been primarily focused on the stratum corneum. However, the development of pharmaceutical technologies, such as chemical enhancers, iontophoresis, and microneedles, has led to two outcomes; an increase in permeability in the stratum corneum or the ability to negate the layer entirely. As a result, these outcomes have made the transport of a solute in the viable skin far more critical when studying transdermal drug delivery.AREAS COVERED:The review will explicitly show the various attempts to model drug transport within the viable skin. Furthermore, a brief review will be conducted on the different models that explain stratum corneum transport, microneedle dynamics and estimation of the diffusion coefficient.EXPERT OPINION:Future development of mathematical models requires the focus to be changed from traditional diffusion-based tissue models to more sophisticated three-dimensional models that incorporate the physiology of the skin.

The stratum corneum is the main barrier to transdermal drug delivery which has previously resulted in mathematical modelling of solute transport in the skin being primarily directed at this skin layer. However, for topical treatment and skin toxicity studies, the concentration in the epidermis and dermis is important and needs to be modelled mathematically. Hitherto, mathematical models for viable skin layers typically simplified the clearance of solute by blood, either assuming sink condition at the top of the skin capillary loops or assuming a distributed clearance in the dermis. This paper is an attempt to develop a physiologically based mathematical model of drug transport in the viable skin. It incorporates explicit modelling of the capillary loops within the dermis and employs COMSOL Multiphysics® software to model the transport in three dimensions. Previously derived simplified models were compared to the results from this new numerical model. The results of this comparison showed that the simplified model reasonably described the average concentration in the viable skin layers when parameters of the models were chosen appropriately. When the recruitment of the capillary loops in the dermis was full and the top of capillary loops was at a depth of 100μm, the effective depth to place a sink condition in the simpler models was found to be at 150μm. However, when there was only partial recruitment of the capillaries, the effective depth increased to 180μm. The presented modelling is also essential for determining a transdermal flux when the stratum corneum barrier is compromised by such methods as microporation, application of chemical enhancers or microneedles.

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.