Skin Electroporation: Modeling Perspectives - Porous Media: Applications in Biological Systems and Biotechnology - page 354

These are the primary observed phenomena that the thermodynamic
approach focuses on in its theoretical development. The preceding descrip-
tions of SC electroporation have either neglected these points entirely or
they rely entirely on empirical evidence. Thus, these do not capture the local
thermal kinetics of the creation of the LTR. A recent publication from the
group that helped introduce the description and the underlying physics of
LTR formation in long-pulse skin electroporation builds a hypothesis based
on experimental observations in which the development of the LTR is explic-
itly linked to local temperature rises associated with Joule heating (Pliquett
et al. 2008). This study makes the thermal connection to increased SC elec-
troporation based on the experimental observation that the minimum trans-
dermal potential required to initiate electroporation is inversely related to
local temperature rise: at 4 ◦ C the required voltage to induce electropora-
tion is 80-100 V, while at 60 ◦ C the required transdermal potential drop
is in the range 10-20 V. A numerical model is presented in which a step
function method is used to define the SC behavior: once the condition for
electroporation for one element is reached, the element is classified as elec-
troporated, and its properties are switched from that of lipid to that of
saline.
9.8.1 Fully Thermodynamic Approach
As the electroporation pulses cause local Joule heating within the SC , nearby
lipid architecture experiences a transition from being a highly organized lamel-
lar structure to a highly disorganized one. As the lipid structure is destroyed,
the SC experiences dramatic increases in mass permeability and electrical
conductivity. On the basis of the key points of the experimentally observed
phenomena, a thermodynamic model of skin electroporation, which seeks to
capture the evolution of the LTR, must provide a logical connection between
temperature rise and permeability (both ionic and molecular.) With this in
mind Becker and Kuznetsov (2008a,b) propose a thermally based function that
seeks to capture the degree of SC lipid disorder. Recalling the heat versus tem-
perature curve of Figure 9.6, the thermally influenced disorder is attributed to
phase change E, which lies in the temperature range (65 ◦ C-75 ◦ C). To describe
the degree of disorder, these studies borrow from methods that have been tra-
ditionally designed to model melting and solidification processes occurring
over a temperature range (Voller and Brent 1989; Ozisik 1993), the analogy
being that the thermally influenced transition from structured to disordered
is represented by the solid structure transitioning from solid to liquid.
9.8.2 LTR Lipid Thermal Phase Change
In light of the previously discussed SC lipid thermal behavior and permeability
studies, this model uses phase transition E to model SC lipid melting, during
which the lipid melt fraction is used to describe the degree of lipid disorder