Skin Electroporation: Modeling Perspectives - Porous Media: Applications in Biological Systems and Biotechnology - page 351

by Pliquett et al. (1995), Prausnitz (1996), and Pliquett and Gusbeth (2000)
in which it is shown that when exposed to a high-voltage electric field the
electrical resistance of the skin drops dramatically in a time period of

sec.
To model the breakdown of the SC electrical resistance, the conductivity of
the SC is prescribed as follows:
σ SC ( t )= t

µ

σ SC =10 − 5 S / m ≤ 5m s :

(9.25)

σ SC =10 − 3 ,σ SC =10 − 2 S / m

t> 5m s :

The increase in electrical conductivity represents the permeation of the
SC : basically during the first 5 msec of pulsing the SC is treated as com-
pletely unperturbed, and after the first 5 msec the SC is treated as fully per-
meabilized. This method takes advantage of the short time period required
to electroporate the SC at high-intensity applied voltages. This description is
fully empirical, neglecting SC thermal and voltage dependencies.
Recalling that the current understanding of single-membrane electropora-
tion relies on V m to determine the degree of electroporation, it follows that
a macroscale model perhaps should also make use of this dependency. The
idea here is to use experimental data in which degree of electroporation is
represented by directly measured electrical current and local potential drop.
The increase in transdermal current that is associated with electroporation is
represented by an increase in electrical conductivity. It follows that the degree
of electroporation may be similarly represented by an increase in electrical
conductivity.
A novel empirical approach that takes into account the local electric field
influence on the increased permeability is presented by Pavselj et al. (2005,
2007). In these studies the degree of permeability, as represented by the
electrical conductivity, is related to the local electric. The electric field is
defined as

E = ∇ φ (9.26)

The study (Pavselj et al. 2007) conducts a finite element analysis of a
skin fold undergoing electropermeabilization. This is a parametric study that
uses experimentally determined electrical conductivity relation to magnitude
of electric field for three tissue types: subcutaneous, SC , and the combined
dermis and epidermis (excluding SC ). This article uses experimental data
of skin electroporation of electrical conductivity change of the skin composite
layers. The drop in conductivity is modeled as a step function of the magnitude
of the electric field consisting of four different steps. For instance, the SC
conductivity is represented as

⎧
⎨

E (V/m) < 600: σ SC =0 . 0005
600 <E< 800: σ SC =0 . 0165
800 <E< 1000: σ SC (S/m) = σ SC =0 . 06 (9.27)

⎩

1000 <E< 1200: σ SC =0 . 178

1000 <E : σ SC =0 . 5