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Bioelectrics Publications Frank Reidy Research Center for Bioelectrics
2007
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Repository Citation
Schoenbach, Karl H.; Hargrave, Barbara Y.; Joshi, Ravindra P.; Kolb, Juergen F.; Nuccitelli, Richard; Osgood, Christopher J.;
Pakhomov, Andrei G.; Stacey, Michael W.; Swanson, James R.; White, Jody A.; Xiao, Shu; Zhang, Jue; Beebe, Stephen J.; Blackmore,
Peter F.; and Buescher, E. Stephen, "Bioelectric E=ects of Intense Nanosecond Pulses" (2007). Bioelectrics Publications. 67.
h?ps://digitalcommons.odu.edu/bioelectrics_pubs/67
Authors
Karl H. Schoenbach, Barbara Y. Hargrave, Ravindra P. Joshi, Juergen F. Kolb, Richard Nuccitelli, Christopher
J. Osgood, Andrei G. Pakhomov, Michael W. Stacey, James R. Swanson, Jody A. White, Shu Xiao, Jue Zhang,
Stephen J. Beebe, Peter F. Blackmore, and E. Stephen Buescher
>is article is available at ODU Digital Commons: h?ps://digitalcommons.odu.edu/bioelectrics_pubs/67
Bioelectric Effects of Nanosecond Pulses
Karl H. Schoenbach, Barbara Hargrave, Ravindra P. Joshi, Juergen F. Kolb, Christopher
Osgood, Richard Nuccitelli, Andrei Pakhomov, James Swanson, Michael Stacey, Jody A.
White, Shu Xiao, Jue Zhang
Frank Reidy Research Center for Bioelectrics
Old Dominion University
830 Southampton Avenue, #5100
Norfolk, VA 23510, USA
and
Stephen J. Beebe, Peter F. Blackmore, E. Stephen Buescher
Eastern Virginia Medical School
825 Fairfax Avenue
Norfolk, VA 23507, USA
ABSTRACT
Electrical models for biological cells predict that reducing the duration of applied
electrical pulses to values below the charging time of the outer cell membrane (which is
on the order of 100 ns for mammalian cells) causes a strong increase in the probability
of electric field interactions with intracellular structures due to displacement currents.
For electric field amplitudes exceeding MV/m, such pulses are also expected to allow
access to the cell interior through conduction currents flowing through the
permeabilized plasma membrane. In both cases, limiting the duration of the electrical
pulses to nanoseconds ensures only nonthermal interactions of the electric field with
subcellular structures. This intracellular access allows the manipulation of cell
functions. Experimental studies, in which human cells were exposed to pulsed electric
fields of up to 30 MV/m amplitude with durations as short as 3 ns, have confirmed this
hypothesis and have shown that it is possible to selectively alter the behavior and/or
survival of cells. Observed nanosecond pulsed effects at moderate electric fields include
intracellular release of calcium and enhanced gene expression, which could have long
term implications on cell behavior and function. At increased electric fields, the
application of nanosecond pulses induces a type of programmed cell death, apoptosis, in
biological cells. Cell survival studies with 10 ns pulses have shown that the viability of
the cells scales inversely with the electrical energy density, which is similar to the
“dose” effect caused by ionizing radiation. On the other hand, there is experimental
evidence that, for pulses of varying durations, the onset of a range of observed
biological effects is determined by the electrical charge that is transferred to the cell
membrane during pulsing. This leads to a similarity law for nanosecond pulse effects,
with the product of electric field intensity, pulse duration, and the square root of the
number of pulses as the similarity parameter. The similarity law allows one not only to
predict cell viability based on pulse parameters, but has also been shown to be
applicable for inducing platelet aggregation, an effect which is triggered by internal
calcium release. Applications for nanosecond pulse effects cover a wide range: from a
rather simple use as preventing biofouling in cooling water systems, to advanced
medical applications, such as gene therapy and tumor treatment. Results of this
continuing research are leading to the development of wound healing and skin cancer
treatments, which are discussed in some detail.
Index Terms — Bioelectrics, nanosecond pulsed electric fields, apoptosis, pulse
power, subcellular effects, platelet aggregation, tumor treatment, wound healing.
1 INTRODUCTION
The effect of intense pulsed electric fields on biological
cells and tissues has been the topic of research since the late
1950’s. Intense means that the electric field is of sufficient
magnitude to cause nonlinear changes in cell membranes. The
first paper reporting the reversible breakdown of cell
membranes when electric fields are applied was published in
1985 [1]. The first report on the increase in permeability of
the plasma membrane of a biological cell, an effect
subsequently named “electroporation” appeared in 1972 [2].
The electric fields that are required to achieve electroporation
depend on the duration of the applied pulse. Typical pulses
range from tens of milliseconds with amplitudes of several
100 V/cm to pulses of a few microseconds and several kV/cm.
More recently, the pulse duration range has been shortened
into the nanosecond range. The effects of such short pulses
have been shown to reach into the cell interior [3]. Pulse
durations are as brief as several nanoseconds, with pulse
amplitudes as high as 300 kV/cm for short pulses. A new field
of research opens, when the pulse duration is decreased even
further, into the subnanosecond range. With electric fields
reaching values of almost 1 MV/cm, it will be possible to
directly affect the structure of macromolecules, such as DNA,
in cells and tissue.
This field of research, which, until recently, was a subarea of
bioelectromagnetics or bioelectrochemical effects, and
recognized by professional societies such the
Bioelectromagnetics Society and the Bioelectrochemistry
Society, has found acceptance in the pulse power community
and dielectric community under the new name “Bioelectrics”.
There were, and are, special sessions and workshops on this
topic at the Modulator Symposium and the Dielectric and
Electrical Insulation conference.
This review will provide a brief overview of the state of the
research on the biological effects of intense nanosecond
pulses. Information on electroporation, where orders of
magnitude longer pulses are used, can be found in references
[4,5,6,7].
2 MODELING OF THE INTERACTION OF
PULSED ELECTRIC FIELDS WITH CELLS
Modeling of pulsed electric field effects on the charge
distribution in biological cells ranges from simple analytical
models to those generated using molecular dynamics.
Molecular dynamics simulations provide the most basic and
fundamental approaches for modeling the effect of electric
fields on cells. The part of the cell that is to be modeled is
considered as a collection of interacting particles. In the case
of a cell membrane, which is a lipid bilayer, these particles are
DPPC (Dioleoyl-phosphatidyl-choline) molecules that are
characterized by charged subgroups. Thus, the structural
details on the nanoscale can be included into the simulation for
maximum accuracy and relevant physics. For each of the
molecules the equation of motion (Newton’s equation) is
solved, with the force on each charge and dipole within the
molecular structure generated by the surrounding charges and
dipoles. In spite of its simplicity, this modeling method has
only recently [8,9] been used to model cellular membranes
under electrical stress [8,9,10,11]. The simulation difficulties
include the immense number of particles that need to be
considered, and also the small time steps, both requiring the
use of high-speed computer clusters. This makes molecular
dynamics a computationally intensive approach. As an
example, Joshi has used 164,000 particles to model a patch of
membrane, with time steps on the order of one femtosecond.
This means that modeling small parts of a cell and following
the membrane changes numerically can only be done for times
on the order of 10-20 ns. Therefore, molecular dynamics, at
this point in time, is restricted to modeling small parts of a cell
and to ultrashort (ns) pulse effects. The importance of this
method is in the visualization of membrane effects on this
timescale, the inclusion of complex underlying physics, and
the determination of critical electrical fields for membrane
changes on the nanoscale, e.g. for pore formation.
This information can be used in less computer intensive,
but more comprehensive models (i.e., for describing larger
systems, such as an entire cell). In these models the cells are
represented as micro resistor-capacitor (RC) units, with the
resistive parts being time-dependent. The information from
the molecular dynamics can then be used to determine the
dynamic resistance for such simpler models and will be
discussed in more detail in section 2b. They allow us to
determine the response of electric fields on the entire cell,
including the plasma and subcellular membranes. However,
these models still call for extensive numerical efforts when
high spatial resolution is required. So, for quick and simple
estimates of the pulsed field effects on cells, molecular
dynamics can be used to describe the critical electric fields for
pore formation. Although such models will not provide
complete information for complicated structures, they can
provide guidance to the experimentalist in choosing an
appropriate electric field-pulse duration range for bioelectric
effects.
2.1 AN ANALYTICAL APPROACH
We will initially focus on a simple analytical, passive, and
linear model of the cell. By passive and linear, we mean that
changes in the properties of the cell structures, such as
electroporation, are not considered. The assumption holds,
therefore, only for electric field amplitudes below those
required for electroporation or nanoporation. However, it
provides useful information on the threshold for the onset of
nonlinear effects. After introducing the concept of
electroeffects that depend on pulse duration, we will discuss
advanced models that include changes in cell structures.
Figure 1a shows a cross-section of a mammalian cell, with
the only membrane-bound substructure shown being the
nucleus. The cytoplasm, which fills much of the cell, contains
dissolved proteins, electrolytes and forms of glucose, and is
moderately conductive, as are the nucleoplasm and the
contents of other organelles. On the other hand, the
membranes that surround the cell and subcellular structures
have a low conductivity. We can, therefore, think of the cell
as a conductor surrounded by a lossy, insulating envelope, and
containing substructures with similar properties. Data on the
dielectric constants and conductivities of cell membranes and
cytoplasm, as well as nuclear membranes and nucleoplasm,
have been obtained using dielectric spectroscopy of cells [12,
13]. Typical values for the plasma membrane of mammalian
cells, e.g. B- or T-cells, are: relative permittivities on the order
of 10, and conductivities of approximately 10
5
S/m. For the
cytoplasm, the relative permittivity is approximately that of
water, 80, and the conductivity is typically one-fifth that of
seawater, 1 S/m.
In the equivalent circuit shown in Figure 2, the
conductance of the plasma membrane is assumed to be zero,
and the capacitive components of cytoplasm (interior of cell)
are neglected. These are assumptions that limit the
applicability of the model to a temporal range that is
determined by the dielectric relaxation times of membrane and
cytoplasm. The dielectric relaxation time, τ
r
, provides
information on the importance of the resistive or capacitive
component of the membrane and cytoplasm, respectively, with
respect to the duration of an applied electric field, τ. τ
r
is given
as:
τ
r
= ε/σ [1]
where ε is the permittivity, and σ the conductivity. For a pulse
duration, τ, long compared to τ
r
, the
resistive component
dominates, for the opposite case it is the capacitive
component.
In order to describe the effect of electrical pulses on cells
over a wide range of pulse duration, we need to consider the
equivalent circuit of a cell where these additional circuit
elements are taken into account. For simplicity, in the
following discussion we will focus on the relevant part of the
equivalent circuit only, which includes a section of the plasma
membrane and cytoplasm. The equivalent circuit for this case
is shown in Figure 3. Although we focus here only on the
plasma membrane, it will be shown that the conclusions that
are drawn from the discussion of this simple model can easily
Fig. 1 Cross-section of a cell with nucleus as would be
observed with a light microscope. The typical dimension of
a mammalian cell (diameter) is on the order of 10 µm.
Figure 2 Electrical equivalent circuit of a cell between
two electrodes. The cell membrane is described by a
capacitance, C
m
, the entire cell interior by a resistance, Rc.
R
0
, R
1
, C
0
, and C
1
, are dependent on the electrical
properties of the medium, in which the cell is embedded,
and the geometry of the system.
(a)
(b)
(c)
Figure 3 Equivalent circuit of membrane and cytoplasm
section of a biological cell. Figure 3a Equivalent circuit
used to describe charging of the plasma membrane in the
temporal range between the dielectric relaxation time of the
membrane and that of the cytoplasm. Figure 3b. Equivalent
circuit of a section of a biological cell for long pulses
(pulse duration > dielectric relaxation time of the plasma
membrane).Figure 3c. Equivalent circuit of a biological cell
for extremely short pulses (pulse duration < relaxation time
of cytoplasm), generally less than 1 ns for mammalian cells.
