Mathematical Models of Mass Transfer in Tissue for Molecular Medicine Reversible Electroporation - Porous Media: Applications in Biological Systems and Biotechnology - page 56

45

1
3
4
5
6
8

40

35

30

25

20

15

10

5

0 0

200 400 600 800 1000

Electric field [V/cm]

1200 1400 1600 1800 2000

FIGURE 2.6
Change in tissue conductivity as a function of the electrical field. A simple
piecewise linear model is used to interpolate the changes in conductivity of
rat liver tissue for various electric fields. Results are shown after each elec-
troporation pulse, which are represented here by different lines numbered 1
through 8.

since the electric field and the conductivity have a mutual effect. An electric
field above the electroporation threshold for some minimal duration will cre-
ate pores in the membranes of cells in that part of the tissue and cause the
tissue conductivity to increase. The increase in conductivity will have a neg-
ative effect on the local electric field, which will decrease, thus changing the
electroporation process. To accurately solve this iterative process we require
a reliable model of electroporation mechanism that will precisely describe the
time evolution of pores as a function of the changing electric field. For many
purposes, the first order solution without additional iterations will suce.
In general, those regions of the tissue where the electric field during the
electroporation pulses was high will display an increased conductivity over
areas of lower electrical fields. Imaging these regions using EIT will enable real
time monitoring and control of the electroporation process. Using additional
electrodes and possibly the electroporation electrodes as well (Granot and
Rubinsky 2007) we can reconstruct the conductivity map of the electroporated
tissue. We rely again on the Laplace equation and use FEM to solve it albeit
this time the solution is much more dicult. In the simulation part we have
calculated the electric potential u with known conductivity and boundary