Biomedical Engineering Reference
In-Depth Information
Electric field, norm [V/cm]
0.8
0.6
0.4
0.2
0
1500
1500
-0.2
500
-0.4
-
0.6
-0.8
200
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
FIGURE 2.9
Electric field for a 1,000 V pulse with two needle electrodes that are 1 cm
apart. The electrodes are marked by the two black circles at the center part of
the tissue. The contours depict the isopotential lines at 200 V/cm, 500 V/cm,
and 1,500 V/cm.
to verify that the solution for a certain mesh does not depend on the spe-
cific mesh that was chosen. Obtaining two different solutions using different
meshes and comparing them is a simple way of checking that the solution is
stable.
An example of a typical solution to equation (2.1) with a 1,000 V voltage
difference overa1cmgapbetweentheelectrodes is shown in Figure 2.9.
The electric field for this configuration is such that the largest field is around
the electrodes, reaching values well above the ratio of voltage over distance.
When plate electrodes are used, the electric field is more uniform and may be
estimated by dividing the voltage by the distance between the plates. In our
example, the field is not uniform at all so care must be taken to avoid fields that
are too large near the electrodes, or that are too small in the treated region.
The electrodes in such a procedure are usually inserted into the treated tissue
so the field should be adjusted in such a way that the entire area between
the electrodes shall have an electric field above the electroporation threshold.
The example shown in Figure 2.9 may have irreversible electroporation close
to the needles, for example, where the electric field exceeds 1,500 V/cm, but
most of the tissue is expected to experience reversible electroporation. The
reversible electroporated region may include the entire area where the electric
field is above 200 V/cm.
Choosing a specific protocol for electroporation will determine the results
of the process since many more parameters need to be considered except
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