Biomedical Engineering Reference
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phase transition by electroporation show very long recovery times (
>
30 min-
utes)(Pliquett and Gusbeth 2004).
SC
lipid structural changes associated with
localized Joule heating during electroporation remain for some time after cool-
ing of the
SC
(Pliquett et al. 2005). Polarized light thermal microscopy of
SC
and extracted lipid samples heated to 130
◦
C show that, as the
SC
samples
return to room temperature, the restructuring of the lipids shows evidence of
aggregate variation (Silva et al. 2006a). Because of these findings and in light
of the relatively short time periods that transience is modeled (ms to s) upon
cooling it may not be necessary to consider lamellar restructuring of the lipid
bilayers and subsequent electrical recovery. Thus, the lipid melt fraction may
be described as
⎧
⎨
max (
ϕ
t
,
0) :
T<T
E,
1
ϕ
t
+1
=
max(
ϕ
t
,EQ
(
p
17)) :
T
E,
1
<T <T
E,
2
(9.37)
⎩
1:
T
E,
2
<T
where the superscript
t
and
t
+ 1 refer to the previous and current time steps,
respectively.
At this point we have a thermodynamically derived function that repre-
sents the degree of lipid disorder, which is in the range 0
≤
ϕ
≤
1, where
ϕ
= 0 corresponds to the insulative unaltered lipid organization and
ϕ
=1
corresponds to permeable, fully disrupted
SC
lipids architecture.
The next task of the model is to quantify the
SC
permeability based on the
lipid melt fraction. The lamellar structure of the bilayer matrix greatly reduces
ionic permeability, and with the fluidization the lamellar lipid extracellular
sheets of phase transition E comes increased
SC
ionic permeability. Thermal
dependence of electrical resistance has been shown experimentally to drop
by two orders of magnitude in the temperature range of this phase change
(Craane van Hinsberg et al. 1995). To capture this effect, the local
SC
effective
electrical conductivity increase is linearly related to lipid melt fraction by the
relation:
σ
SC
=
σ
SC
+
ϕ
(
σ
SC ,MELT
−
σ
SC
)
(9.38)
where
σ
SC
is the normal electrical conductivity and
σ
SC ,MELT
is the electrical
conductivity associated with the
SC
after full lipid melting. In the studies by
Becker and Kuznetsov (2008a) the values
σ
SC
=10
−
5
S
/
m and
σ
SC ,MELT
=
10
−
3
S
/
m are used.
9.8.3 Transport
Electrically driven transdermal delivery is negotiated by the three modes of
transport: electrophoresis, electroosmosis, and diffusion. Studies focusing on
electrically driven transport of large charged molecules show that especially
for short-duration pulses, electroosmotic effects are negligible compared to
electrophoresis forces (Zaharoff et al. 2002). Homogenous tissue
in vivo
elec-
troporation studies show that electrophoretic forces dominate in the transport
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