Skin Electroporation: Modeling Perspectives - Porous Media: Applications in Biological Systems and Biotechnology - page 350

by the transient circuit representation:

K

+ R − m + R − 1 · C dV m

dt

V m
R i + R P

V O
R P

V m + = (9.23)

j =1

Clearly this is a simplified representation of the potential distribution and
does not account for any lateral variations within the membrane. It should be
noted that in single-cell electroporation studies, the spatial variation of trans-
membrane potential and pore evolution have been captured by calculating
the electrical potential of the solution domain on both sides of the membrane
(Stewart et al. 2004; Krassowska and Filev 2007).
Perhaps the most important conclusion that should be drawn from the
current models of single-membrane electroporation is that there exists a strong
tie between the transmembrane electric potential and the degree of permeation
(as seen in concentration of pores, N ; and pore size, r ). It is important to note
that even if a study were to account for lateral variations (not represented in
equation [9.23]), this theoretical method may become quite involved as the
total number of different pore sizes, K , must be accounted for within each
of the up to 100 SC bilayers at each lateral location. Thus modeling individ-
ual pore creation, while informative, is not practical for skin electroporation
modeling.

9.7.2 Empirical Models
Empirical models allow the researcher to model skin electroporation without
keeping track of the permeability of each of the 100 bilayers by incorporating
experimental observations that monitor the increase in electrical permeability
as the SC undergoes electroporation. The local SC permeability is captured
by the local SC electrical conductivity value, σ SC . The capacitive charging
time associated with non-Ohmic behavior of the SC is very short and may be
neglected at pulsing times greater than 1 msec (Chizmandzhev et al. 1998).
This behavior is typically neglected in studies that are less concerned with
individual electropores but focus on describing the behavior of the SC as a
whole. The electric potential distribution is usually solved from the Laplace
equation:

∇· ( σ SC ∇ φ ) = 0 (9.24)

where φ is the electric potential.
The simplest representation of the increase in electrical conductivity with
electroporation is a time-dependant step function. In (Becker and Kuznetsov
2007a,b) numerical studies focusing on thermal damage assessment are con-
ducted to represent a section of living skin clamped between two electrodes
and exposed to a series of electroporation pulses. These studies provide a very
crude, but simple relation between SC electrical conductivity and degree of
electroporation. The concept is based on the experimental results reported