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Pulsed Electric Fields in Biological Cells and Membranes
(Song, Joshi, and Beebe 2010; Bagci et al. 2006; Budihardjo et al. 1999; Li, P. et al. 1997).
The other apoptosis route (known as the intrinsic pathway) involves cytochrome c
release from another membrane—the mitochondria, which is an intracellular organelle
(Zoratti and Szabo 1995; Marzo et al. 1998).
The classical theory of transmembrane voltage induction was developed in the 1950s
by H. P. Schwan and coworkers (Schwan 1957; Pauly and Schwan 1959). Discussions on
the increase in permeability (Neumann and Rosenheck 1972) of the plasma membrane
of a biological cell—an effect that was termed electroporation—appeared in 1972. The
electric fields required to achieve electroporation depend on the duration of the applied
pulse because this process involves the gradual charging of the capacitive sheath followed by the molecular rearrangement of the lipids. Typical pulses range from tens of
milliseconds with amplitudes of several hundred V/cm to pulses of a few microseconds
or smaller but requiring fields of several kV/cm.
More recently, the electrical pulse duration range has been shortened into the
nanosecond range. Pulse durations as brief as several nanoseconds and pulse amplitudes as
high as 300 kV/cm are being used (Schoenbach et al. 2008). Conceptually, such short pulse
durations offer the possibility of triggering purely electrically driven responses without any
thermal heating. In principle, fast processes such as electron transfers between molecules
(Kranich et al. 2008), electrophoretic separation and self-organization (Groves, Boxer, and
McConnell 1997), or field induced changes in reaction kinetics (De Biase et al. 2009) could
also be fashioned. An even newer field of research opens up when the pulse duration is
decreased further into the subnanosecond range. This push toward further pulse shortening is driven in part by the possibility of using wideband antennas, rather than direct
contact electrodes, to deliver electrical energy and create fields in tissues as discussed in
the literature (Kumar et al. 2011). Also conceptually, because the dielectric permittivity of
membranes (and the aqueous media) has a nonlocal, time-dependent polarization, ultrafast
excitation can effectively sample transient permittivities that are different from the steadystate values. This provides for electrical-based value selection of the dielectric parameters.
The influence of short pulses has been shown to reach into the cell interior (Schoenbach,
Beebe, and Buescher 2001). This can perhaps be better understood through the following
simple argument. Consider a spherical shell with a concentric inner organelle as shown
in Figure 2.1. We assume for simplicity that the conductivities of both membranes are
zero and that current continuity applies across line ABCDE shown in Figure 2.1. For
long-duration, slow-rising pulses, a near quasisteady state prevails, and the current density, J, is nearly given by J = σE + εdE/dt ∼ σE, where E, σ, and ε refer to the local electric
field, conductivity, and permittivity, respectively. Because σ for the membranes is nearly
zero, there is virtually no current through them. Choosing the cell center as the reference
voltage, the node potentials are then roughly as follows: V D ∼ 0 and V B ∼ V C . Also, the
negligible membrane current, under the quasisteady state forces is V CD ∼ V FG ∼ 0. Thus,
the potential across the inner membrane can be expected to be very modest, at best. This
implies that membrane poration and other electrical effects would not be strong across
cellular substructures and inner organelles, and the outer membrane would shield the
cell at almost all times. Fast-rising, ultrashort pulses, on the other hand, would force
a large nonequilibrium transient and create substantially large values of V CD and V FG
across the inner membranes. This would allow fairly large potentials (∼1 V or so, a value