Biomedical Engineering Reference
In-Depth Information
E is the electric field in the external homogenous
medium, K ¼ s 0 /3 rC m , and q the angle between the
E-field and the cell radius r (cell center is origin).
For electroporation a threshold voltage of about 1V
across the cell membrane has been found. The relation-
ship between the cell membrane potential difference
(corresponding to the order of 2-20 kV/cm in the sus-
pension according to cell size, type, etc.), and electro-
poration may still be a reversible one as long as the latter is
caused by a single pulse of a short time duration (e.g. of the
order of 20 m s). If a train of such pulses is applied, the cell
is killed because of the excessive material exchange. It is
believed that a large part of thematerial exchange (lysis) is
an after-field effect lasting up to 0.1 seconds or more. If
the electroporation is reversible, the pores or cracks then
reseal. Electrofusion is certainly an irreversible after-field
effect.
The primary field effect shows threshold behavior, of
about the same value for poration and fusion: The elec-
tric field effect in the cell membrane lipid bilayer is
a molecular rearrangement with both hydrophobic or
hydrophilic pore formation. Hydrophilic pores are con-
sidered to be water filled, with pore walls which may
comprise embedded lipids. The threshold field strength
has been found to be inversely proportional to the cell
diameter. At the time of pulse application cell fusion may
occur if two cells are in contact with each other, DNA
uptake may occur if DNA is adsorbed to the cell surface.
Cells may be brought in contact with each other by
means of the pearl chain effect (see below). The elec-
troporative cell transformation probability due to DNA
entrance is low, typically 10 -5 . Field values above
threshold are believed to increase the pores in number
and size, until a critical value is reached where complete
membrane rupture occurs (irreversible non-thermal
breakdown). The difference between the threshold level
and the critical level is not large, so overdoses easily kill
the cells. It is interesting to speculate whether electro-
poration is a mechanism in defibrillator chock treatment.
The field strength used is lower (of the order of
500 V/cm), however the pulse duration is longer, of the
order of some milliseconds.
The usual source for the electric field pulse is to dis-
charge a charged capacitor (e.g. a 25 m F capacitor charged
to 1500 V). The charge voltage and the distance between
the capacitor plates determine the E-field strength, and
the capacitance together with the system resistance de-
termines the time constant of the discharge current
waveform. The circuitry is very similar to the de-
fibrillator circuit shown in Fig. 4.1-16 , except that the
inductor extending the time constant into the millisec-
ond range, is not necessarily used. The pulse is accord-
ingly a single exponentially decaying DC pulse, and the
time constant is dependent on the liquid conductivity.
With more complicated circuitry it is possible to make
35
30
25
20
0
10
20
30
40
50
E (kV/cm)
Figure 4.1-21 Measured conductance versus the field strength
for a suspension of Jurkat-cells. The dashed line indicates the
conductance at 30 MHz Source: From Pliquett et al. (2007).
is due to the liberation of ions from the counter-ion
cloud around charged particles like proteins while the
second one describes the creation of new charge carriers
by field dissociation of week electrolytes. Both of these
effects together can explain a conductivity increase by
several percent but not by 140% as seen in Fig. 4.1-21 .
Moreover this dramatic conductivity increase is only
found in solution containing aggregated amphiphiles like
lipids.
The creation of very dense electropores (supra elec-
troporation) is probably the initial step to a complete
disintegration of the membrane. If the electric field is
sufficiently high, micelles instead of membrane struc-
tures become stable. Because of the higher mobility of
ions in the vicinity of the membrane, a significant in-
crease in conductivity happens.
Electrofusion is the connection of two separate cell
membranes into one by a similar pulse. It is believed that
the process is based on the same field-induced restruc-
turing of the bilayer lipid membranes (BLMs), a process
which may be reversible or irreversible.
It is known that an ordinary cell membrane cannot
withstand a prolonged DC potential difference DV m
more than about 150-300 mV without irreversible
damage. For short pulses in the m s range, it has been
found that at a threshold voltage D y m of about 1 V, the
cell membrane becomes leaky and rather large macro-
molecules pass in and out of the cell (lysis). The fol-
lowing expression for the electric field in the membrane
E m is valid if the membrane thickness d is much less than
cell radius r , and that the conductivity of the membrane
material is much less than both the internal and external
(s 0 ) electrolyte conductivity:
E m ¼ 1 : 5 ðr=dÞ Eð 1 e Kt Þ cos q
(4.1.15)
 
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