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To unravel the diffusion mechanisms of percutaneous drug delivery, suitable numerical analysis of stratum corneum structure is essential. In this research paper, we accounted for the permeable envelope layer in the brick-and-mortar finite element models of human stratum corneum. Both penetration and desorption experiments for tritiated water were simulated by transient finite element analysis. Rivet-shaped corneodesmosomes were included in the brick and mortar model. Results showed that cornified lipid permeability (P env ) is a determinant in desorption of the solute, while lipid transverse diffusion coefficient (D lip-trans ) is prominent during penetration. These two major unknowns (P env and D lip-trans ) were obtained by extensive fitting of the finite element model to the experimental water data. P env and D lip-trans were determined to be 1×10 -2 cm/s and 5.7×10 -10 cm 2 /s, respectively., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Crown Copyright © 2023. Published by Elsevier Inc. All rights reserved.)

Many drugs are presently delivered through the skin from products developed for topical and transdermal applications. Underpinning these technologies are the interactions between the drug, product and skin that define drug penetration, distribution, and elimination in and through the skin. Most work has been focused on modeling transport of drugs through the stratum corneum, the outermost skin layer widely recognized as presenting the rate-determining step for the penetration of most compounds. However, a growing body of literature is dedicated to considering the influence of the rest of the skin on drug penetration and distribution. In this article we review how our understanding of skin physiology and the experimentally observed mechanisms of transdermal drug transport inform the current models of drug penetration and distribution in the skin. Our focus is on models that have been developed to describe particular phenomena observed at particular sites of the skin, reflecting the most recent directions of investigation., (Copyright © 2012 Elsevier B.V. All rights reserved.)

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., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Objective and Design: A mathematical analysis of leukocytes accumulating in experimental autoimmune uveitis (EAU), using ordinary differential equations (ODEs) and incorporating a barrier to cell traffic., Materials and Subjects: Data from an analysis of the kinetics of cell accumulation within the eye during EAU., Methods: We applied a well-established mathematical approach that uses ODEs to describe the behaviour of cells on both sides of the blood-retinal barrier and compared data from the mathematical model with experimental data from animals with EAU., Results: The presence of the barrier is critical to the ability of the model to qualitatively reproduce the experimental data. However, barrier breakdown is not sufficient to produce a surge of cells into the eye, which depends also on asymmetry in the rates at which cells can penetrate the barrier. Antigen-presenting cell (APC) generation also plays a critical role and we can derive from the model the ratio for APC production under inflammatory conditions relative to production in the resting state, which has a value that agrees closely with that found by experiment., Conclusions: Asymmetric trafficking and the dynamics of APC production play an important role in the dynamics of cell accumulation in EAU.

What Is Already Known About This Subject: Many products are applied to human skin for local effects in deeper tissues. Animal studies suggest that deep dermal and/or subcutaneous delivery may be facilitated by both dermal diffusion and transport via the cutaneous vasculature. However, the relationship between the extent and pathways of penetration, drug physicochemical properties and deeper tissue physiology is not well understood., What This Study Adds: We have used a physiologically based pharmacokinetic model to analyze published human cutaneous microdialysis data, complemented by our own in vitro skin penetration studies. We found that convective blood, lymphatic and interstitial flow led to significant deep tissue concentrations for drugs that are highly plasma protein bound. In such cases, deeper tissue concentrations will occur earlier and may be several orders of magnitude greater than predicted by passive dermal diffusion alone., Aims: To relate the varying dermal, subcutaneous and muscle microdialysate concentrations found in man after topical application to the nature of the drug applied and to the underlying physiology., Methods: We developed a physiologically based pharmacokinetic model in which transport to deeper tissues was determined by tissue diffusion, blood, lymphatic and intersitial flow transport and drug properties. The model was applied to interpret published human microdialysis data, estimated in vitro dermal diffusion and protein binding affinity of drugs that have been previously applied topically in vivo and measured in deep cutaneous tissues over time., Results: Deeper tissue microdialysis concentrations for various drugs in vivo vary widely. Here, we show that carriage by the blood to the deeper tissues below topical application sites facilitates the transport of highly plasma protein bound drugs that penetrate the skin, leading to rapid and significant concentrations in those tissues. Hence, the fractional concentration for the highly plasma protein bound diclofenac in deeper tissues is 0.79 times that in a probe 4.5 mm below a superficial probe whereas the corresponding fractional concentration for the poorly protein bound nicotine is 0.02. Their corresponding estimated in vivo lag times for appearance of the drugs in the deeper probes were 1.1 min for diclofenac and 30 min for nicotine., Conclusions: Poorly plasma protein bound drugs are mainly transported to deeper tissues after topical application by tissue diffusion whereas the transport of highly plasma protein bound drugs is additionally facilitated by convective blood, lymphatic and interstitial transport to deep tissues., (© 2011 Commonwealth of Australia. British Journal of Clinical Pharmacology © 2011 The British Pharmacological Society.)

Purpose: The maximum flux of solutes penetrating the epidermis has been known to depend predominantly on solute molecular weight. Here we sought to establish the mechanistic dependence of maximum flux on other solute physicochemical parameters., Methods: Maximum fluxes, stratum corneum solubilities and estimated diffusivities through human epidermis were therefore determined for 10 phenols with similar molecular weights and hydrogen bonding but varying in lipophilicity., Results: Maximum flux and stratum corneum solubilities of the phenolic compounds both showed a bilinear dependence on octanol-water partition coefficient (P), with solutes having a maximum solubility in the stratum corneum when 2.7

We investigate the onset of diffusive behavior in polygonal channels for disks of finite size, modeling simple microporous membranes. It is well established that the point-particle case displays anomalous transport, because of slow correlation decay in the absence of defocusing collisions. We investigate which features of point-particle transport survive in the case of finite-sized particles (which undergo defocusing collisions). A similar question was investigated by Lansel, Porter, and Bunimovich [Chaos 16, 013129 (2006)], who found that certain integrals of motion and multiple ergodic components, characteristic of the point-particle case, remain in "mushroom"-like systems with few finite-sized particles. We quantify the time scales over which the transport of disks shows features typical of the point particles, or is driven toward diffusive behavior. In particular, we find that interparticle collisions drive the system toward diffusive behavior more strongly than defocusing boundary collisions. We illustrate how, and at what stage, typical thermodynamic behavior (consistent with kinetic theory) is observed, as particle numbers grow and mean free paths diminish. These results have both applied (e.g., nanotechnological) and theoretical interest.

It is a common approximation in the modeling of adsorption in microporous carbons to treat the pores as slit pores, whose walls are considered to consist of an infinite number of graphitic layers. In practice, such an approximation is appropriate as long as the number of graphitic layers in the wall is greater than three. However, it is understood that pore walls in microporous carbons commonly consist of three or fewer layers. As well as affecting the solid--fluid interaction within a pore, such narrow walls permit the interaction of fluid molecules through the wall, with consequences for the adsorption characteristics. We consider the effect that a distributed pore-wall thickness model can have on transport properties. At low density we find that the only significant deviation in the transport properties from the infinite pore-wall thickness model occurs in pores with single-layer walls. For a model of activated carbons with a distribution of pore widths and pore-wall thicknesses, the transport properties are generally insensitive to the effects of finite walls, in terms of both the solid-fluid interaction within a pore and fluid-fluid interaction through the pore walls.

We examine the transport of methane in microporous carbon by performing equilibrium and nonequilibrium molecular dynamics simulations over a range of pore sizes, densities, and temperatures. We interpret these simulation results using two models of the transport process. At low densities, we consider a molecular flow model, in which intermolecular interactions are neglected, and find excellent agreement between transport diffusion coefficients determined from simulation, and those predicted by the model. Simulation results indicate that the model can be applied up to fluid densities of the order to 0.1-1 nm(-3). Above these densities, we consider a slip flow model, combining hydrodynamic theory with a slip condition at the solid-fluid interface. As the diffusion coefficient at low densities can be accurately determined by the molecular flow model, we also consider a model where the slip condition is supplied by the molecular flow model. We find that both density-dependent models provide a useful means of estimating the transport coefficient that compares well with simulation., ((c) 2004 American Institute of Physics.)

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed., (Copyright 2004 American Institute of Physics)

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory.

We develop a method for determining the elements of the pressure tensor at a radius r in a cylindrically symmetric system, analogous to the so-called "method of planes" used in planar systems [B. D. Todd, Denis J. Evans, and Peter J. Daivis, Phys. Rev. E 52, 1627 (1995)]. We demonstrate its application in determining the radial shear stress dependence during molecular dynamics simulations of the forced flow of methane in cylindrical silica mesopores. Such expressions are useful for the examination of constitutive relations in the context of transport in confined systems.

Recently, a solution for collision-free trajectories in an N particle thermostatted hard-sphere system undergoing homogeneous shear (the so-called "Sllod" equations of motion) led to a kinetic theory of dilute hard-sphere gases under shear. However, a solution for collisions, necessary for a complete theory at higher densities, has been missing. We present an analytic solution to this problem, which provides surprising insights into the mechanical aspects of thermostatting a system in an external field. The equivalence of constant temperature and constant energy ensembles in the thermodynamic limit in equilibrium, the conditions for the nature of heat exchange with the environment (entropy creation and reduction) in the system, and the condition for appearance of the artificial string phase follow from our solution.