84
Electromagnetic Fields in Biological Systems
the plasma membrane and subcellular membranes was compared for pulses of 7 μs and
60-ns duration. The electric field of the pulses was adjusted such that the energy density
in both cases was identical. For 60-ns long pulses (left), the cell membranes, plasma
and internal, are fully exposed to the applied 60 kV/cm pulse, clearly demonstrating
that nanosecond pulses allow us to affect subcellular membrane potentials. When the
cell was exposed to a long pulse (7-μs duration) at 1.1 kV/cm, only effects on the plasma
membrane were seen. Thus, the cell interior is shown to be shielded for longer pulsing.
Long pulses cause the creation of membrane pores large enough for large molecules
to pass, whereas the application of short, nanosecond pulses was found to cause the
creation of a high-density “nanopores” with radii in the range 0.8–1.5 nm (Schoenbach
et al. 2007; Vasilkoski et al. 2006; Joshi, Song, and Sridhara 2009). This effect has been
termed supraporation. As an example, we focus on membrane electroporation in
response to a trapezoidal 560 kV/cm pulse with an ON time of 1 ns and rise and fall
times of 0.1 ns, in keeping with typical experimental waveforms generated in our laboratory. The pore distribution n(r) per unit area was evaluated as a function of radius r using
the Smoluchowski equation.
Figure 2.6 illustrates some of the characteristics associated with the intense, nanosecond pulsing. Pore distributions as a result of the electroporation process with and
without a constant surface tension are shown. Conventionally, a constant tension Γ 0 of
10 −3 J/m 2 has been used, while a heuristic model (Isambert 1998) described the tension
2
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
0.5
0.55
Radius (nm)
−3
)
Pore distribution (10
28
· m
Pore area independent (1 pulse)
Pore area independent (2 pulses)
Pore area dependent (1 pulse)
Pore area dependent (2 pulses)
0.6
0.65
0.7
0.75
Figure 2.6 Simulation results of the pore distribution function n(r) for one and two pulses
using constant and pore area-dependent tension. A 560 kV/cm average external field was
used. (After Joshi, R. P., J. Song, and V. Sridhara. 2009. IEEE Trans Dielectr and Electr Insula
16:1243–50.)
Electromagnetic Fields in Biological Systems
the plasma membrane and subcellular membranes was compared for pulses of 7 μs and
60-ns duration. The electric field of the pulses was adjusted such that the energy density
in both cases was identical. For 60-ns long pulses (left), the cell membranes, plasma
and internal, are fully exposed to the applied 60 kV/cm pulse, clearly demonstrating
that nanosecond pulses allow us to affect subcellular membrane potentials. When the
cell was exposed to a long pulse (7-μs duration) at 1.1 kV/cm, only effects on the plasma
membrane were seen. Thus, the cell interior is shown to be shielded for longer pulsing.
Long pulses cause the creation of membrane pores large enough for large molecules
to pass, whereas the application of short, nanosecond pulses was found to cause the
creation of a high-density “nanopores” with radii in the range 0.8–1.5 nm (Schoenbach
et al. 2007; Vasilkoski et al. 2006; Joshi, Song, and Sridhara 2009). This effect has been
termed supraporation. As an example, we focus on membrane electroporation in
response to a trapezoidal 560 kV/cm pulse with an ON time of 1 ns and rise and fall
times of 0.1 ns, in keeping with typical experimental waveforms generated in our laboratory. The pore distribution n(r) per unit area was evaluated as a function of radius r using
the Smoluchowski equation.
Figure 2.6 illustrates some of the characteristics associated with the intense, nanosecond pulsing. Pore distributions as a result of the electroporation process with and
without a constant surface tension are shown. Conventionally, a constant tension Γ 0 of
10 −3 J/m 2 has been used, while a heuristic model (Isambert 1998) described the tension
2
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
0.5
0.55
Radius (nm)
−3
)
Pore distribution (10
28
· m
Pore area independent (1 pulse)
Pore area independent (2 pulses)
Pore area dependent (1 pulse)
Pore area dependent (2 pulses)
0.6
0.65
0.7
0.75
Figure 2.6 Simulation results of the pore distribution function n(r) for one and two pulses
using constant and pore area-dependent tension. A 560 kV/cm average external field was
used. (After Joshi, R. P., J. Song, and V. Sridhara. 2009. IEEE Trans Dielectr and Electr Insula
16:1243–50.)