Temperature effect on the build-up of exponentially growing polyelectrolyte multilayers. An exponential-to-linear transition point

In this study, the effect of temperature on the build-up of exponentially growing polyelectrolyte multilayer films was investigated. It aims at understanding the multilayer growth mechanism as crucially important for the fabrication of tailor-made multilayer films. Model poly(L-lysine)/hyaluronic acid (PLL/HA) multilayers were assembled in the temperature range of 25–85 1C by layer-by-layer deposition using a dipping method. The film growth switches from the exponential to the linear regime at the transition point as a result of limited polymer diffusion into the film. With the increase of the build-up temperature the film growth rate is enhanced in both regimes; the position of the transition point shifts to a higher number of deposition steps confirming the diffusion-mediated growth mechanism. Not only the faster polymer diffusion into the film but also more porous/permeable film structure are responsible for faster film growth at higher preparation temperature. The latter mechanism is assumed from analysis of the film growth rate upon switching of the preparation temperature during the film growth. Interestingly, the as-prepared films are equilibrated and remain intact (no swelling or shrinking) during temperature variation in the range of 25–45 1C. The average activation energy for complexation between PLL and HA in the multilayers calculated from the Arrhenius plot has been found to be about 0.3 kJ mol 1 for monomers of PLL. Finally, the following processes known to be dependent on temperature are discussed with respect to the multilayer growth: (i) polymer diffusion, (ii) polymer conformational changes, and (iii) inter-polymer interactions

Numerical simulation of skin transport using Parareal

In silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms. This article investigates the applicability of the time-parallel Parareal algorithm to a brick and mortar setup, a precursory problem to skin permeation. The C++ library Lib4PrM implementing Parareal is combined with the UG4 simulation framework, which provides the spatial discretization and parallelization. The combination’s performance is studied with respect to convergence and speedup. It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal’s convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed

Space- and time-resolved investigation on diffusion kinetics of human skin following macromolecule delivery by microneedle arrays

Microscale medical devices are being developed for targeted skin delivery of vaccines and the extraction of biomarkers, with the potential to revolutionise healthcare in both developing and developed countries. The effective clinical development of these devices is dependent on understanding the macro-molecular diffusion properties of skin. We hypothesised that diffusion varied according to specific skin layers. Using three different molecular weights of rhodamine dextran (RD) (MW of 70, 500 and 2000 kDa) relevant to the vaccine and therapeutic scales, we deposited molecules to a range of depths (0–300 µm) in ex vivo human skin using the Nanopatch device. We observed significant dissipation of RD as diffusion with 70 and 500 kDa within the 30 min timeframe, which varied with MW and skin layer. Using multiphoton microscopy, image analysis and a Fick’s law analysis with 2D cartesian and axisymmetric cylindrical coordinates, we reported experimental trends of epidermal and dermal diffusivity values ranging from 1–8 µm2 s-1 to 1–20 µm2 s-1 respectively, with a significant decrease in the dermal-epidermal junction of 0.7–3 µm2 s-1. In breaching the stratum corneum (SC) and dermal-epidermal junction barriers, we have demonstrated practical application, delivery and targeting of macromolecules to both epidermal and dermal antigen presenting cells, providing a sound knowledge base for future development of skin-targeting clinical technologies in humans

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC. (C) 2004 Wiley-Liss, Inc

Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in booth experimental and clinical situations

Lateral iontophoretic solute transport in skin

Purpose, The lateral iontophoretic transport of three solutes (sodium, ethanolamine, lidocaine) from an active electrode through skin and other tissues to an indifferent electrodes was investigated. Methods, Anodal epidermal iontophoresis was carried out on an in vivo rat model using constant direct current of 0.38 mA/cm(2). Cells were fixed on the epidermis of anesthetized rats at distances of adjacent, 3 cm and 7 cm apart. After iontophoresis, tissues were dissected at I cm intervals between the electrodes. Concentrations of the radiolabelled solutes in tissues were determined by liquid scintillation counting or gamma counting. Results. The concentration of each solutes in the epidermis, dermis and other tissues was found to decrease in an exponential manner with lateral distance from the active electrode to the indifferent electrode. The detectable lateral distance for ethanolamine and lidocaine was less than 2 cm from the donor sites, at which distance the concentrations were not significantly different to those found in the corresponding contralateral site. The lateral drift velocities for all solutes in the epidermis and dermis were consistent with diffusivities of the order of 10(-6) cm(2)/s. The drift velocity of sodium was greater than either lidocaine or ethanolamine. Conclusions. The decline in solute concentration with lateral distance is mainly due to clearance from the site of application by the skin's microcirculation and decreases with distance from the active electrode until a baseline concentration, similar to the contralateral tissue concentration is reached

Epidermal iontophoresis: I. Development of the ionic mobility-pore model

Purpose, An integrated ionic mobility-pore model for epidermal iontophoresis is developed from theoretical considerations using both the free volume and pore restriction forms of the model for a range of solute radii (r(j)) approaching the pore radii (r(p)) as well as approximation of the pore restriction form for r(j)/r(p) < 0.4. In this model, we defined the determinants for iontophoresis as solute size (defined by MV, MW or radius), solute mobility, solute shape, solute charge, the Debye layer thickness, total current applied, solute concentration, fraction ionized, presence of extraneous ions (defined by solvent conductivity), epidermal permselectivity, partitioning rates to account for interaction of unionized and ionized lipophilic solutes with the wall of the pore and electroosmosis. Methods, The ionic mobility-pore model was developed from theoretical considerations to include each of the determinants of iontophoretic transport. The model was then used to reexamine iontophoretic flux conductivity and iontophoretic flux-fraction ionized literature data on the determinants of iontophoretic flux. Results. The ionic mobility-pore model was found to be consistent with existing experimental data and determinants defining iontophoretic transport. However, the predicted effects of solute size on iontophoresis are more consistent with the pore-restriction than free volume form of the model. A reanalysis of iontophoretic flux-conductivity data confirmed the model's prediction that, in the absence of significant electroosmosis, the reciprocal of flux is linearly related to either donor or receptor solution conductivity. Significant interaction with the pore walls, as described by the model, accounted for the reported pH dependence of the iontophoretic transport for a range of ionizable solutes. Conclusions. The ionic mobility-pore iontophoretic model developed enables a range of determinants of iontophoresis to be described in a single unifying equation which recognises a range of determinants of iontophoretic flux

Periodic electric field enhanced transport through membranes

We examine the mean flux across a homogeneous membrane of a charged tracer subject to an alternating, symmetric voltage waveform. The analysis is based on the Nernst-Planck flux equation, with electric field subject to time dependence only. For low frequency electric fields the quasi steady-state flux can be approximated using the Goldman model, which has exact analytical solutions for tracer concentration and flux. No such closed form solutions can be found for arbitrary frequencies, however we find approximations for high frequency. An approximation formula for the average flux at all frequencies is also obtained from the two limiting approximations. Numerical integration of the governing equation is accomplished by use of the numerical method of lines and is performed for four different voltage waveforms. For the different voltage profiles, comparisons are made with the approximate analytical solutions which demonstrates their applicability. (c) 2005 Elsevier B.V. All rights reserved