Electrodiffusion of molecules in aqueous media: a robust, discretized
description for electroporation and other transport phenomena
K. C. Smith, J. C. Weaver IEEE Trans Biomed Eng. 59(6):1514-22. 2012.
Electrically driven transport of molecules and ions within
aqueous electrolytes is of long-standing interest, with direct
relevance to applications that include the delivery/release of
biologically active solutes to/from cells and tissues. Examples
include iontophoretic and electroporation-mediated drug delivery.
Here, we describe a robust method for characterizing electrodiffusive
transport in physiologic aqueous media. Specifically, we treat the
case of solute present in sufficiently low concentration as to
negligibly contribute to the total ionic current within the system.
In this limiting case, which applies to many systems of interest,
the predominant electrical behavior due to small ions is decoupled
from solute transport. Thus, electrical behavior may be characterized
using existing methods and treated as known in characterizing
electrodiffusive molecular transport. First, we present traditional
continuum equations governing electrodiffusion of charged solutes
within aqueous electrolytes and then adapt them to discretized systems.
Second, we examine the time-dependent and steady-state interfacial
concentration gradients that result from the combination of diffusion
and electrical drift. Third, we show how interfacial concentration
gradients are related to electric field strength and duration.
Finally, we examine how discretization size affects the accuracy of
these methods. Overall these methods are motivated by and well suited
to addressing an outstanding goal: estimation of the net ionic and
molecular transport facilitated by electroporation in biological systems.