Skin Electroporation: Modeling Perspectives - Porous Media: Applications in Biological Systems and Biotechnology - page 357

of large molecules (Bureau et al. 2000; Satkauskas et al. 2005). In skin elec-
troporation the pulse parameters are short (compared to iontophoresis); thus
electroosmosis plays a negligible role, while electrophoresis effects are the pri-
mary effects in transdermal delivery of charged molecules (Regnier et al. 1999;
Denet et al. 2004).
The transport of solute through the SC and into the underlying domain
is formulated from the Nernst-Planck equation (Planck, 1890) as follows:

∂C
∂t

= ∇· ( m i C ∇ φ )+ ∇· ( D i ∇ C ) (9.39)

where D is the diffusion coecient; m is the electromobility; and the subscript
i refers to one of the composite layers g , SC , ED , DERM ,or FAT; and C is
the solute concentration.
Similar to the electrical conductivity the enhanced electrokinetic mobility
of the SC is related to lipid melt fraction by the relation

m SC = m SC + ϕ ( m SC ,MELT −

m SC ) (9.40)

where m SC is the unperturbed mobility of the SC and m SC ,MELT is the mobil-
ity associated with the SC after full lipid melting. In the studies by Becker
and Kuznetsov, (2008a) the values m SC =10 − 17 m 2 /Vs and m SC , MELT

=

10 − 11 m 2 /V s are used.
The SC diffusion coecient is related to the lipid melt fraction by

5 ×

D SC = D SC + ϕ ( D SC ,MELT −

D SC ) (9.41)

where D SC corresponds to the initial diffusion coecient of the solute in the
SC and D SC ,MELT is the diffusion coecient associated with the SC after
full lipid melting. In the studies by Becker and Kuznetsov (2008a) The values
D SC =10 − 17 m 2 / sec and D SC ,MELT =10 − 13 m 2 / sec are used.
The values used to represent the mass transport coecients associated
with the fully thermally altered SC have been chosen to approximate the
very resistive conditions a large DNA molecule would experience within the
tortuous route between the unaltered corneocytes of the SC : the approximated
diffusion and electrophoretic mobility coecients used are much lower than
those associated with those of even the high collagen content tissue of the
epidermis. These are the coecients that should be modeled using porous
media perspectives. As yet, however, this has not been accomplished.

9.8.4 Thermal Energy
The lipid melt fraction of equation (9.37) and associated electrical and mass
permeability rises of equations (9.38), (9.40), and (9.41) require an accurate
description of the temperature distribution within the SC. Should the study
attempt to reflect a skin fold it is important to consider that the process of
skin electroporation involves additional tissues and materials to the SC that
are exposed to electric fields. In the studies by Becker and Kuznetsov (2008a)