Skin Electroporation: Modeling Perspectives - Porous Media: Applications in Biological Systems and Biotechnology - page 335

associated with solutes of low molecular weight. The basic equations governing
the transport of solute through the skin are for pure diffusion:

∂C
∂t

= ∇· ( D eff ∇ C ) (9.1)

and, for nondestructive electrically enhanced diffusion:

∂C
∂t

= ∇· ( D eff ∇ C )+ ∇· ( m eff C ∇ φ ) − U eff ·∇ C (9.2)

where C is the solute concentration, D eff is the effective diffusion coecient,
φ is the electric potential resulting from the applied electric field, m eff is the
effective electrophoretic mobility coecient, which describes the ability of the
field to move the solute, and U eff is the effective electroosmotic flow.
The challenge to researchers has been the way to use the porous medium
approach to define the effective coecients (diffusion, electrophoretic mobil-
ity, and electroosmotic flow) within the skin based on the architecture and
the physics of the skin. This section describes some of the methods that are
currently being used to describe these coecients—primarily with respect to
pure diffusion within the SC .
It is important to note that the following examples are almost exclusively
modeled as in vitro situations in which the skin acts as a barrier membrane
between a donor and receiver reservoir. Although these do not necessarily
closely resemble transport through living skin into the subcutaneous tissue,
important information can be extracted from these types of models and exper-
iments. The permeability, P , is defined as the steady dimensionless flux of
solute transported though the SC :

1
C I

C I − C O

P = D eff (9.3)

L

where C I is the concentration of solute on the donor side of the SC , C O is the
concentration of solute on the receiver side of the SC , and L is the thickness
of the SC .
A particular solute's permeability within the SC is often described by a
dependency on chemical and geometric parameters, and it is these parameter
values that are used to validate a model's accuracy by comparing the results
with those of the experiment (often a Franz diffusion cell).
There are two mechanistic approaches used to describe the permeability
within the SC architecture. One takes into account the known structure of the
lipid-corneocyte matrix, while the other incorporates more traditional mem-
brane modeling strategies by a representation of the SC, which is permeated
by microscopic tortuous pores.

9.5.1 Brick and Mortar Models
The underlying concept behind the brick and mortar model is that the lipid-
filled space is permeable, while the corneocytes are either completely or highly