Skin Electroporation: Modeling Perspectives - Porous Media: Applications in Biological Systems and Biotechnology - page 358

A physical model is developed of a skin fold which includes the electrode,
applicator gel, and skin composite layers (see Figure 9.4[a]). Figure 9.4(b)
shows the composite representation of this configuration consisting of elec-
trodes ( e ), gel ( g ), and skin. The skin model consists of four sections: SC ,
epidermis ( ED ), dermis ( DERM ), and subcutaneous fat ( FAT ).
The Pennes' bioheat equation (Pennes 1948) is used along with an addi-
tional source term to describe thermal energy:

ρ i c i ∂T
∂t

T a )+ q i + Q J

= ∇· ( k i ∇ T ) − ω i c b ( T − (9.42)

where ρ is the density, c is the specific heat, k is the thermal conductivity,
T is the temperature, T a is the arterial temperature, q is the metabolic
volumetric heat generation, ω m is the nondirectional blood flow associated
with perfusion, and t is the time. The parameter c b in the perfusion term is
the specific heat of blood, which is assigned a value of c b =3 , 800J/kgK (Duck
1990). The subscript i refers to the gel, electrode, or one of the four composite
skin layers SC , ED , DERM ,or FAT .
The second and third terms on the right-hand side (RHS) of equation
(9.42), which denote perfusion and metabolic heat generation are not present
in the nonbiological electrode and gel layers. The term, Q J , on the RHS of
equation (9.42) is the Joule heat generated from the induced electric field.
Joule heating occurs during the applied electric pulse in the gel and tissue
composite layers, and it is defined as

2

Q J = σ i |∇ φ | (9.43)

where φ is the electric potential from the applied electric field, which is solved
from the Laplace equation

∇· ( σ i ∇ φ ) = 0 (9.44)

where φ is the electric potential and σ i is the composite electrical conductivity,
and the subscript i refers to one of the composite layers g , SC , ED , DERM ,
or FAT .
Equation (9.44) neglects non-Ohmic behavior as well as the minor influence
of the charged molecules of the solute on the electrical distribution of the large
magnitude pulse.