Periodic electric field enhanced transport through membranes

Abstract

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.

Alternating Current (AC) Iontophoretic Transport across Human Epidermal Membrane: Effects of AC Frequency and Amplitude

“…This multibarrier heterogeneous SC model is supported by the observation of water reservoirs in the SC intercellular space after skin hydration (26,27), in which the interconnected aqueous reservoirs become part of the barrier structure in fully hydrated HEM (3). Another possible explanation is that the homogenous membrane model is not applicable for the case when intrinsic membrane properties are altered due to transmembrane electrical potential (19), and therefore does not adequately describe AC iontophoresis at 2.5 V. Transdermal iontophoretic transport could deviate from the homogenous membrane model at 2.5 V due to the latter two explanations alone or a combination of all three explanations. It is clear from the present study that the iontophoretic transport pathways at 2.5 V, which can involve electric field induced-pores, can be more complicated than the conventional mechanism of iontophoretic transport across either the appendages or intercellular pathways.…”

“…Although a homogenous membrane model does not explain all aspects of the 2.5 V experimental data, such a model (19) is still useful in the analysis of the SC iontophoresis transport pathway situation as a heterogeneous membrane might be viewed as a combination of two or more pathways in series and/or in parallel. In the 2.5 V AC study, the enhancement factors of 23 and 49 for TEA at 0.01 and 0.001 Hz, respectively, would suggest long transport path-length (thickness) barriers in HEM SC.…”

“…For DC iontophoresis transport at 37°C when the applied electric field across the membrane is 1 V, K=37. For a neutral permeant, the enhancement factor (E Δψ ) becomes: (4) Transdermal flux enhancement due to electroosmosis during DC iontophoresis is generally less than 20% of that of electrophoresis for a small permeant (19,23), and the average value of Pe is approximately one-tenth of the K value. From Eqs.…”

“…For AC iontophoresis, a previously described homogenous membrane model (19) was used as a first approximation in analyzing AC flux data. This model assumes Nernst-Planck flux behavior with time variable electric potential.…”

“…Flux enhancement due to electroosmosis and that of electrophoresis was studied with the neutral permeant ARA and charged permeant TEA. The data were interpreted using the models developed based on the Nernst-Planck theory in previous studies (2,3,19), and the effective length of the iontophoretic transport pathway were determined. AC frequency for maximum AC iontophoretic flux enhancement was identified.…”