Axial electric field (kV/cm)
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Time (ns)
93
Pulsed Electric Fields in Biological Cells and Membranes
Figure 2.11 (See color insert.) Calculated axial electric fields at the center of the 2.5-μm
radius neuron for the trapezoidal external pulse at locations of 5, 10, 15, and 20 mm downstream.
The excitation source was taken to be 1 mm from the nerve axis.
begin to decrease and the distributed voltages are progressively governed by the resistive
conduction currents. Electric fields as high as 160 kV/cm are predicted, corresponding
to the transmembrane voltage shifts on the order of 80 mV within 1 μs for a 5-nm-thick
membrane. In this nanosecond pulsing context, it has already been reported that electric
fields of about 20–80 kV/cm are sufficient to cause calcium release from internal stores
within cells (Beebe et al. 2004; Vernier et al. 2008). Thus, the 160 kV/cm fields threading
the internal organelles can be expected to cause similar bioeffects. A quick train of multiple pulses would add tunability based on the number within a short burst.
The higher electric fields predicted in Figure 2.11, slightly further along the nerve axis
(e.g., at 10 mm vs. 5 mm), emerge from the stronger role of conduction currents at later
times. This is easily visualized in terms of a simple distributed circuit representation consisting of a ladder network for the nerve. More current paths from the vicinity of the excitation source merge on to the axial corridor with increasing distance. Consequently, the
longitudinal current increases. For a given resistivity, the axial potential drop and the electric field are also enhanced. It might be mentioned that internal electric fields and TMP
changes within the cell can be expected to remain in effect beyond the 1-μs timescales
shown in Figure 2.11. A longer time estimate of ∼1 ms for internal current flows and electrical membrane discharging is based on typical time constants for nerves.
Finally, it may be mentioned that the results of Figure 2.11 seem roughly consistent with two recent reports. In one experiment, both muscle twitch facilitation
and inhibition were demonstrated in rat experiments by using nanosecond pulsing
180
160
140
120
100
80
60
40
20
0 0
500
600
700
800
900
5 mm
10 mm
15 mm
20 mm
100
200
300
400
Time (ns)
93
Pulsed Electric Fields in Biological Cells and Membranes
Figure 2.11 (See color insert.) Calculated axial electric fields at the center of the 2.5-μm
radius neuron for the trapezoidal external pulse at locations of 5, 10, 15, and 20 mm downstream.
The excitation source was taken to be 1 mm from the nerve axis.
begin to decrease and the distributed voltages are progressively governed by the resistive
conduction currents. Electric fields as high as 160 kV/cm are predicted, corresponding
to the transmembrane voltage shifts on the order of 80 mV within 1 μs for a 5-nm-thick
membrane. In this nanosecond pulsing context, it has already been reported that electric
fields of about 20–80 kV/cm are sufficient to cause calcium release from internal stores
within cells (Beebe et al. 2004; Vernier et al. 2008). Thus, the 160 kV/cm fields threading
the internal organelles can be expected to cause similar bioeffects. A quick train of multiple pulses would add tunability based on the number within a short burst.
The higher electric fields predicted in Figure 2.11, slightly further along the nerve axis
(e.g., at 10 mm vs. 5 mm), emerge from the stronger role of conduction currents at later
times. This is easily visualized in terms of a simple distributed circuit representation consisting of a ladder network for the nerve. More current paths from the vicinity of the excitation source merge on to the axial corridor with increasing distance. Consequently, the
longitudinal current increases. For a given resistivity, the axial potential drop and the electric field are also enhanced. It might be mentioned that internal electric fields and TMP
changes within the cell can be expected to remain in effect beyond the 1-μs timescales
shown in Figure 2.11. A longer time estimate of ∼1 ms for internal current flows and electrical membrane discharging is based on typical time constants for nerves.
Finally, it may be mentioned that the results of Figure 2.11 seem roughly consistent with two recent reports. In one experiment, both muscle twitch facilitation
and inhibition were demonstrated in rat experiments by using nanosecond pulsing