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Contact-free single-cell cultivation by negative dielectrophoresis
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2008 J. Phys. D: Appl. Phys. 41 175502
(http://iopscience.iop.org/0022-3727/41/17/175502)
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IOP PUBLISHING JOURNAL OFPHYSICSD: APPLIEDPHYSICS
J. Phys. D: Appl. Phys.41(2008) 175502 (8pp) doi:10.1088/0022-3727/41/17/175502
Contact-free single-cell cultivation bynegative dielectrophoresis
Magnus S Jaeger1, Katja Uhlig1, Thomas Schnelle2 and Torsten Mueller3
1 Fraunhofer Institute for Biomedical Engineering (IBMT), Am Muehlenberg 13, 14476 Potsdam,
Germany2 Zimmermann and Partner, European Patent Attorneys, Oranienburger Strasse 90, 10178 Berlin,
Germany3 JPK Instruments AG, Aufgang C, Haus 2, Bouchestrasse 12, 12435 Berlin, Germany
E-mail:[email protected]
Received 10 June 2008, in final form 7 July 2008
Published 8 August 2008Online atstacks.iop.org/JPhysD/41/175502
Abstract
In parallel to recent progress of high-content analysis in cell biology, negative
dielectrophoresis (nDEP) has continuously evolved as a potent tool for contact-free
manipulation and investigation of single cells. As such, it can be especially beneficial for the
handling of rare and valuable cells, e.g. in stem cell research, immunology and autologous
therapy. Current nDEP applications are mainly based on flow-through systems where a small
volume or single cells are pumped through microfluidic channels and analysed in seconds to
minutes. Such short-term electric field exposures were repeatedly shown to be physiologically
harmless. Conditions, however, might change in longer experiments when damages may
accumulate. Therefore, we focus on potential limits to long-term nDEP application, with yeast
serving as a model organism. Cells are reported to be successfully cultivated over severalhours while suspended contact-freely in cell medium by nDEP. From comparisons of the cell
division in nDEP structures under different electric conditions, conclusions are drawn with
respect to which parameters govern the possible stress on the cells and how to avoid it. Firstly,
the observed frequency dependence hints at an influence of the membrane polarization.
Secondly, the inhibition of proliferation at high voltages is found to be overcome by external
cooling of the microchips. This implies thermal effects on the cells. The warming is further
examined by infrared (IR) thermometry. Despite its inherent drawbacks, IR provides a quick
and easy method of determining the temperature of microfluidic systems without interfering
local probes or reporter substances.
1. Introduction
Dielectrophoresis (DEP) has become a common method
in biotechnology for a wide range of applications dealing
with low cell counts [15], e.g. sorting of single cells,
centrifugation-free exposure of cells to different media or
candidate drugs, accumulation of bacteria and viruses for
improved detection, transient contact formation between two
cells for signal transduction experiments and controlled fusion
after individual characterization of two cells [6,7]. Due to
the low physiological stress caused by DEP, in all of these
instances the cells remain viable after treatment and can be
cultured for further purposes. The underlying mechanism ofDEP was described decades ago by Debye [8]and Pohl [9]:
an external electric field induces a dipole moment or higher
electric moments [10] in any object that differs in polarizability
from the medium that surrounds it. These induced moments
interact with the generating electric field, resulting in either
an attractive force towards regions of high electric field
strength (positive dielectrophoresis, pDEP) or a repulsive force
(negative dielectrophoresis, nDEP). The decisive advantage
of nDEP is its ability to handle micro- and nano-objects in
a contact-free manner. This is strongly improved by the use
of two microelectrode layers on the ceiling and the floor of
microfluidic channels [11]. Thus, eight microelectrodes may
be arranged so that the tips, where the electric field strength is
highest, form the corners of a cube (figure 1(b)), resulting inan nDEP field cage with four microelectrodes in each layer.
0022-3727/08/175502+08$30.00 1 2008 IOP Publishing Ltd Printed in the UK
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Figure 1. (a) Brightfield microscopy image showing the 700 m wide linear microfluidic channel (white) of the DEP microchips used here.The microfluidic channel is formed by a polymer spacer (grey) between two glass slides. The microelectrodes appear black and are arrangedinto two funnels (F1, F2), three field cages (C1C3) and one resistance sensor (S). (b) Phase shifts of the high-frequency signal at themicroelectrodes on the ceiling and the floor of the microfluidic channel in the case of the ac and the ROT mode.
Particles that are subject to nDEP are repelled from these
corners and stably held in the cube centre.
Earlier studies on DEP identified electromagnetic
field parameters where interference of manipulation with
physiology was lowest. For example, Pethig [12] reported
on the heat shock response of yeast investigated by
electrorotation. Voldman [13] pointed out the beneficial
effect of heating-induced convective flowfor enhanced particle
manipulation. A more technological approach to the Joule
heating in the vicinity of specific nDEP barrier elements,
namely, fluorothermometry, was chosen by Renaud [14].
Gascoyne [15]investigated the growth interruption in murine
leukaemia cells after DEP handling. However, the cells
were not cultivated in the DEP device. Instead, they were
exposed to the electric field and their proliferation and viability
were analysed subsequently. Previous reports on cell growth
in high-frequency electric fields mainly aimed at inhibitoryeffects, e.g. for anti-fouling purposes. Therefore, they
concentrated on adherently growing cells [16]. In contrast,
we use the nDEP field cage to investigate the proliferation
of suspended yeast cells with the intention of finding optimal
physiological conditions. The selection of certain parameter
settings, e.g. voltage, frequency and external temperature,
clearly indicates the limits to the biological compatibility of
DEP. Which adverse effects occur beyond these limits? We
present evidence that thermal effects play a leading role if
stress is created on the cells during electrical radio-frequency
manipulation. At lower frequencies, non-thermal field effects,
presumably induced changes in the transmembrane potentialprevail. To further elucidate the temperature distribution in
DEP microchips, we employed infrared (IR) thermometry.
A thorough comparison of the results gained from IR with
theoretical considerations provides the base for an evaluation
of the suitability of the IR technique. Note that the time scale
we use differs from standard nDEP applications in which cells
usually are subjected to the electric fields for several seconds
or up to a minute only [17]. Here, they are exposed for hours.
We chose yeast instead of mammalian cells for several
reasons: yeast cells are easier to cultivate under conditions
of very low cells numbers while mammalian cells often
exhibit sustained growth only when other cells are present
in their vicinity. Furthermore, our aim lay in investigatingthe influence of a permanent electric field on cells in a 3D
structure and yeast cells do not require a substrate they can
adhere to for an optimum division rate. Finally, they are
usually grown in media with an electric conductivity which is
by a factor of about 2.5 below that of mammalian cell culture
media. Media of high electric conductivity, in contrast, may
cause undesirable electrochemical effects and microelectrode
wear in dielectrophoretic structures. For physical reasons,
pDEP-based assays require low-conductivity media (usually
10200 mS m1 [4, 5,15]), while nDEP can also be performed
in mammalian culture media (1.4 S m1).
2. Materials and methods
2.1. Microchips
All experiments were performed with dielectric field cage
(DFC) microchips (Perkin Elmer, Hamburg, Germany) whichwere driven with high-frequency generators (Cytoman or
Cytocon 400) from the same distributor, partly using the
Switch software module provided with the generator system.
DFC microchips possess a linear microchannel created
by a polymer spacer between two glass slides. One of
the slides has a thickness of 150 m which is compatible
with high-resolution microscopy. The other glass slide
is 500 m thick for stability reasons. The microchannel
has fluidic ports at both its ends and a width of 700 m
(figure 1(a)). In most cases, chips with a channel height
of 40 m were used. For some experiments, the channel
height was 20 m. Identical arrangements of 110 nm thickPt microelectrodes are processed photolithographically on
both glass slides that form the ceiling and the floor of the
microchannel. Three field cages (C1, C2, C3) are formed
by eight microelectrodes each, of which four are mounted
on the ceiling and four on the floor of the microchannel
(figure 1(b)). In addition to the three field cages, DFC
microchips also feature two dielectrophoretic funnels (F1, F2)
consisting of four microelectrodes each and one meander-
shaped resistance sensor (S) for temperature measurements.
The microelectrodes that constitute the nDEP elements are
usually of blank metal. In specific experiments, microchips
were used with microelectrodes which were covered by an
insulating passivation layer of silicon nitride. The sensor (S)is always covered by the 600 nm thick passivation layer.
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2.2. Dielectrophoresis
A cell that is repelled equally from all eight microelectrodes
of a field cage by nDEP forces is stably suspended at the
centre of the cube [17]. For reasons of improved biological
and technical compatibility, DEP is commonly performed with
high-frequency voltages of 104 Hz and above. The use of ac
voltages opens up various possibilities of applying phase shiftsbetween the signals fed to different microelectrodes. Here, we
use two different modes, namely, the ac mode and the ROT
mode. In the ac mode, only phase shifts of are used and no
electric field occurs between two electrodes that are positioned
above each other in the z direction (figure1(b)). In the ROT
mode (used e.g. in electrorotation experiments), signals have
phases shifted by /2 and there is an electric field between any
microelectrode and all its neighbours (figure1(b)).
2.3. Yeast cultivation
Saccharomyces cerevisiaewas cultivated under standard brothand atmospheric conditions (YPD Broth LAB 175, IDG,
Bury, UK, electric conductivity: 0.546 S m1). For the
28 experiments in standard flasks (figure 3(a)), they were
seeded at an initial cell count of (9970 20) ml1, kept in
various incubators and refrigerators at different temperatures,
harvested after (2500 200) min and recounted. From both
cell numbers and the total time interval between seeding and
harvesting, the mean doubling time was calculated. For this,
we assumed that on average the time for each cell doubling
cycle stayed the same over the whole measurement time. In
the chip experiments, the initial cell density was 10 5 ml1.
The chips were first cleaned with pepsin solution, a pH-
neutral detergent and water. Then, the cells were manually
flushed into the chip through a three-way valve. As soon
as a single cell floated by, the field cage was activated to
trap the cell. The channel was fluidically short-circuited by
connecting both its ends. After one day, the video footage
was analysed. Temperature control of the microchips during
time-lapseoptical microscopy was achieved witha home-made
flow-through microscopy table (Gabriele Reinke, Humboldt
University, Berlin, Germany).
2.4. Optical microscopy
Yeast cultivation in dielectrophoretic microchips was recordedin transmission brightfield mode on an inverted microscope
(IX71, Olympus GmbH, Hamburg, Germany) equipped with a
CCD camera (kam Pro 02, EHD imaging GmbH, Damme,
Germany), a monitor (PVM-14N5E, Sony GmbH, Koln,
Germany) and a time-lapse VCR (AG-6730, Panasonic,
Hamburg, Germany). The video footage was subsequently
digitized (VMagic Movie Basic, VMagic GmbH, Falkensee,
Germany).
2.5. IR measurements
For the IR experiments, the microchannel of the chip was filled
with electric conductivity-adjusted aqueous NaCl solutions ofalternately 0.3, 0.6 and 1.2 S m1. No particles were flushed
into the channel. The measurements were performed with a
Pyroview 256 camera (DIAS GmbH, Dresden, Germany).
Its pyroelectric sensor provides a cropped circular image with
a pixel size of about 47 m 47 m (figure4(a)). The chip
was continuously filmed at an acquisition rate of 1.25 s per
frame while the voltage at the microelectrodes was switched
from off to on and then back off again. The maximumtemperature value of each image was extracted. Then, the
resulting data sets on(t ) and off(t ) describing the warming
and the cooling, respectively, were fitted single-exponentially
to fit(t ) = on,off a e
c(bt) , where a to c denote free
fitting parameters and on,offare the asymptotic values while
the voltage is on and off, respectively. Then, the warming
is T = on off (figure 4(b)). Note that
on is an
asymptotic value obtained through the fitting procedure and
not measured directly. Under experimental conditions where
the warming was below the noise level of the measuring
system, the described fitting procedure was inapplicable and,
consequently, noTvalue was calculated.
2.6. Impedance
Frequency-dependent power consumption Pof the field cages
C1C3 was obtained by measuring impedance spectra Z(f )
and phase shift (f) at a given voltage of 10mV with a
Solartron 1260 (Instrumex GmbH, Sauerlach, Germany) and
an integration time per data point of 0.5 s. Then, the effective
power loss P = U2 Z1 cos . In order to facilitate
subsequent comparisons, this powerwas scaledto thesquare of
the voltage:P U2 = Z1 cos . To account for the parasitic
impedanceof thefeed lines,etc, measurementswere taken with
thechannel filled first with airand then with buffer of an electricconductivity of 546.8 mS m1. The differences between both
readings are given below.
3. Theoretical
Application of an electric field E to a medium of electric
conductivity leads to a volume-specific heat production of
P V1 = E2 which yields under conditions of constant
geometry the proportionality P V1 U2 where U is the
voltage applied to the microelectrodes[18]. InnDEPstructures
as used here, the nDEP field cage volume is about 32 pl and the
power Pis on the order of 150 W. This power is dissipatedmainly through heat conduction as described by Fouriers law
P = Ad1T where denotes the heat conductivity [19].
Inside the heated volumeVa stationary temperature rise T
occurs at any given point with distance dfrom the surfaceA.
By combining both expressions, this warming T can be
approximated as T = k U2 where the constantk depends
on geometric parameters and inversely on . However,
itself is also a function of T. In a linear approximation,
(T) = 0(1 + T )where0 is the electric conductivity
at T = 0 and the slope = 0.022K1. Substitution of
= (T) yields T = k0U2(1 k0U
2)1 which
means that the temperature rise Tis expected to be roughly
proportional to the electric conductivityand to the square ofthe voltageU. In addition,and, thus,k is also dependent on
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Figure 2. Example of yeast proliferation in an nDEP field cage. In the brightfield transmission microscopy images the microelectrodesappear black. The time stamps are in hh : mm format. Initially, a single yeast cell is trapped contact-freely in the nDEP field cage (a) whereit undergoes several divisions, finally resulting in a cell agglomerate. Due to the electric field distribution of the ac mode (cf figure1(c)), thetwo cells resulting from the first division (b) orient along thez axis (tip-to-tip distance of opposite microelectrodes: 40 m, channel height:40 m,= 0.546Sm1,Urms = 1.99 V,f= 8 MHz).
T, but the slope of the function (T ) = 0(1 + T )
is by one order of magnitude smaller than and, therefore,neglected here.
How long does it take until a constant Tis reached after
the voltage Uhas been switched on? Derivations proposed
by Ramos [19]yield the approximation= cl 21 where
denotes the density of the medium, c its thermal capacitance
and the time for the diffusion of a temperature front across
a distance l. Under the conditions of the nDEP field cages
used here,is about 0.6 s. This, however, does not take into
account the concomitant warming of the glass components
which form the boundary of the microfluidic channel. In
reality, amounts to several seconds as confirmed by time-
resolved measurements.
4. Results
We performed 91 individual experiments in which we trapped
single living yeast cells in an nDEP field cage under various
conditions and examined their proliferation. Figure2shows a
typical example of continuous cell divisions inside an nDEP
element. Initially, a single yeast cell was held contact free at
the cage centre by means of the repulsive forces exerted by the
high-frequency electric field near the electrodes. Subsequent
cell divisions resulted in a cell cluster which was still stably
positioned by the electric field. Due to the limited channel
height, the cells reached the confining glass slides after severalhours. As described before [20], the mean square electric field
distribution, in the ac phase pattern used here, is not spherical
but elongated along the optical axis, i.e. the z directionin figure 1(b). In the extreme case of all cells arranging
themselves along this direction, they would touch the glass
when there are eight cells i.e. after three divisions, because
each cell has a radius of about 2.5 m. As figure2 however
shows, assuming a close-packed spherical aggregate is more
realistic. This means that the cluster is expected to reach the
channel limits after nine cell divisions. Therefore, it is actually
possible with our set-up to investigate the cultivation of cells
in the absence of any mechanical contact. It should be noted,
that the non-spherical mean square electric field distribution
in this case is caused by the specific phase pattern. This was
chosen for thermal reasons explained below. Other drivingmodes allow, e.g. the orientation of cell agglomerates parallel
to thexyplane [21].
In order to elucidate the response of the yeast strain
used here to thermal stress, we first measured its growth
rate under twelve different temperature conditions outside the
microchips, i.e. in standard flasks. The mean doubling time
was lowest at 25 C and was(131.5 0.6) min. As would be
expected, this time markedly increases at non-physiologically
high (>37.5 C) and low (
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(a)
(b)
Figure 3. (a) The generation timeof yeast, i.e. the intervalbetween two consecutive cell divisions, as a function of thetemperature . The data points were normalized to the minimumvalue ofat 25 C where25 C = (131.5 0.6) min. These datawere acquired in standard cell culture flasks, not inside the
microchips. (b) Percentage of dividing cells inside the nDEP fieldcage under different experimental conditions. First row on theabscissa:Urms, second row:f, third row: ambient temperature of themicrochip, fourth row: number of experiments.
to the microelectrodes, 84% of 19 cells proliferated. When the
cells were dielectrophoretically held with a voltage of about
2.8Vrms at 3 MHz, none out of four cells divided. However,
for the same voltages, the proportion of dividing cells was
71%, when higher frequencies of 8 MHz were used. Voltages
above 2.9 Vrms led to a ratio of dividing cells of only 18%.
Apparently, the higher voltages had a detrimental effect on the
cells. Lowering the ambient temperature of the chips by 5 K
from25 to20
C restored the cell proliferation even at voltagesof up to 4.3 V. Further increases in the voltage resulted in an
inhibition of cell growth even at 20 C.
Apparently, the inhibition of cell growthat higher voltages
isat least in parta thermal effect. To gain further insight
into the extent of warming in these nDEP chips, we performed
IR thermography (figure 4). Voltage-dependent measurements
confirmed the validity of the theoretical approach outlined
above which predicts a near-square relation T(U). The
experimental data obtained were fitted to the derived equation
T(U , ), yielding the parameter k introduced in the
theoretical section as a convenient measure for the warming
under different conditions. Three comparisons were made:
(i) In the ROT mode, kROT = 3.0 7 K m W1 which is by afactor of 2.10 higher than kac = 1.463KmW
1 in the ac
(b)
(a)
Figure 4. (a) Pseudo-colour representation of an exemplary IRimage of the microchip. Red areas denote high temperatures(39 C), blue areas show low temperatures (24 C). The five nDEPelements are marked in accordance with figure1(a). Due to heatdissipation, temperatures at the outermost elements are lowest. Theheat production of the funnels exceeds that of the field cagesbecause of their larger microelectrode area: each funnel makes up36% of the total electrode area, C1 9%, C2 8% and C3 11%(= 1.2 S m1,Urms = 1.72 V,f= 100 kHz, thin glass slide, phasemode: ROT). (b) Calculation of the warming Tfrom the IRmeasurements. The maximum temperature of the microchip wascontinuously monitored while the voltage at the microelectrodeswas transiently switched on (orange box). The resulting data sets ofheating and subsequent cooling were fitted single-exponentially(solid blue and green line, respectively). The warming T wasderived from the plateau values.
(This figure is in colour only in the electronic version)
mode. (ii) Comparing the results from channels of differentheights butwhichotherwiseare under similar conditionsshows
that in the ROT case the heating in the 20 m channel is 7%
above that in the 40 m channel (k20 m = 3.9 7 K m W1,
k40 m = 3.6 9 K m W1). In the ac case, however, the 40 m
channel gets 43% warmer than the 20 m channel (k20 m =
1.129KmW1, k40 m = 1.6 2 K m W1). (iii) Finally,
we investigated the influence of whether the temperature is
detected from the floor of the channel which is formed by a
150 m thick glass slide or from its ceiling where the glass
slide is 500 m thick. In the ac case, the temperature on the
thin glass slide was 22%higher than that on thethick glass slide
(kthin = 1.6 2 K m W1,kthick= 1.328KmW
1). In contrast,
both kvalues did not differ significantly from each other in theROT case (kthin = 3.6 9 K m W
1,kthick= 3.7 0 K m W1).
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(a)
(b)
(c)
Figure 5. (a) Frequency dependence of the warming T. Themeasurements were taken at different voltages and normalized to1 Vrms. Black ROT, grey ac, solid lines 1.2 S m
1, dashed lines0.6Sm1, dotted lines 0.3 S m1. (b) Measurements taken witheither blank microelectrodes (solid lines) or microelectrodes thatwere covered by a passivation silicon nitride layer (dashed lines).
Black ROT, grey AC, 0.3 S m1
. (c)Power consumption inside threeDEP field cages of different sizes (tip-to-tip distances of oppositeelectrodes: light grey 30 m, dark grey 40 m, black 50 m). Thevalues are normalized to a voltage of 1 Vrms. The channel was filledwith a solution of electric conductivity of 0.5468 S m1. The dent at1 MHz is an artefact caused by an internal range switching of themeasurement device.
The theoretical considerations described above do not
imply a dependence of the warming on the applied frequency.
Indeed, the warming is almost constant over a frequency
range of more than two orders of magnitude (figure 5(a)),
although there is a tendency towards an increased warming at
higher frequencies. This effect is enhanced by depositing an
electrically insulating silicon nitride layer of sub-micrometre
thickness on the electrodes (figure 5(b)). At higher
frequencies, the chips with Si3N4-covered electrodes show an
especially pronounced increase in warming. For comparison,
impedance measurements were taken which show that the
powerturnover in thefield cages generallyriseswith increasing
frequencyalbeit to slightly varying degrees depending on the
cage geometry (figure5(c)).
5. Discussion
Unimpeded cell proliferation is a very strict criterion for low
stress levels when working with living cells. Other tests, suchas staining assays, yield information much faster but only
record severe damages, e.g. corrupted membrane integrity or
apoptosis induction. Cultivation experiments, however, also
detect damages that accumulate over one cell cycle or several
generations. Here, we have put the physiological compatibility
of nDEP to this test. To this end, a yeast strain was used
which shows a steep increase in doubling time over a course
of merely 5 K from 37.5 to 42.5
C and which, thus, is clearlyheat-sensitive.
When kept in the chips without electric field (0V), not
every yeast cell divided but only 84% of them. This is
possibly due to spatial restrictions in the diffusional supply
with nutrients in the microchannel and to the continuous
microscope illumination. At about 2.8 Vrms and 3 MHz, no
proliferation was observed, although comparable voltages
were harmless at a frequency of 8 MHz. This frequency
dependence cannot be explained with thermal effects. Instead,
we attribute it to the induced change in the transmembrane
potentialind that a cell experiences in an external electric
field: inddecreases with increasing frequency and at 3 MHz
is more than double of what it is at 8 MHz [22]. This would
imply that using highest possible frequencies is beneficial in
nDEP manipulation. However, the DEP force is frequency-
dependent [1, 5, 12, 13, 15, 19 21]and in the given medium
conductivity, the nDEP holding force at 8 MHz is by a factor
of more than six below that at 3 MHz.
Increasing the voltage while maintaining the frequency at
8 MHz for compatibility with the cells leads to a drop in cell
proliferation (figure3(b)) that is probably due to thermal stress.
As derived above, the Joule heating increases roughly as the
square of the applied voltage. The assumption of a thermally
induced growth inhibition is corroborated by the observation
that an external cooling of the chips allows cell growth at thehigher voltages which act inhibitory without cooling.
To further elucidate the heat generation, we applied
IR thermometry. This choice of method was made for
the following reasons: (i) the experimental effort is low,
(ii) IR gives information on the temperature distribution
of a comparatively large area (cf figure 4(a)) and (iii) it
works without a potentially interfering sensor which has
to be placed close to the microelectrodes of interest: e.g.
ohmic resistors are much larger than typical nDEP elements
and may impede optical accessibility; liquid crystals may
change the electric properties of the liquid between the
electrodes; fluorescent molecules may be subject to DEP-induced concentration inhomogeneities whichmimic a thermal
effect [23]. IR thermometry has two major disadvantages:
firstly, its low spatial resolution (figure 4(a)). Secondly, it
detects the temperature of the outer chip surface and not
inside the channel. To assess this latter effect, we performed
temperature measurements in dependence on the thickness of
the glass slide through which the channel was observed. The
outside of the thin glass slide exhibited a higher temperature
than that of the thick glass slide, since it is by a factor of more
than three closer to the heated volume.
The IR thermometry yielded two major findings: (i) the
higher the electric conductivity of the fluid in the channel, the
stronger the warming. This result confirms the dependence ofthe warming on the voltage and on the electric conductivity
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as deduced theoretically above. (ii) Warming is strongly
influenced by the phase shifts between the electric signals:
in the distribution of the ROT mode, the warming is more than
double of that occurring in the ac case. The explanation is
foundinthefigure 1(b): in theROT case, an electric field occurs
between an electrode and any of its neighbours, whereas in the
ac case, there is no potential difference between an electrodeand its counterpart on the opposite glass slide. As described in
the theoretical section, warming is proportional to the square
of the electric field strength. Numerical evaluation of the ratio
between the heat production in the cage volume Vunder ROT
and ac conditions yields
E2ROTdV /
E2acdV 2.20 which
coincides with our experimental result of 2.10.
If the channel height is reduced by half along the zaxis as
defined in figure1,the heating is reduced in the ac mode while
the effect is negligible in the ROTcase. Under constant voltage
conditions in the ROT case, the lower channel height leads
to a doubling of the electric field strength between opposite
electrodes which should result in a fourfold increase in heat
production between these electrodes (see Theoretical section).However, scaling a microstructure by half its edge length
doubles its surface-to-volume ratio so that there is a stronger
heat dissipation which counteracts the electric field-induced
warming. In contrast, no electric field enhancement occurs in
the ac case, since there is no electric field between opposite
electrodes, irrespective of the channel height (see figure 1(b)).
Therefore, only the improved heat dissipation occurs and a
lowering in heating can be achieved in the ac case by reducing
the channel dimensions.
The results illustrated in figure 5 indicate that the warming
also is a function of thefrequency. Evidently, a higherwarming
occurs at higher frequencies. This means that under theseconditions there is a stronger electric field in the electrically
conductive liquid. Possible explanations comprise, firstly,
a better coupling of the electric field from the electrodes
into the fluid at higher frequencies through capacitive effects
and, secondly, thin non-conductive layers on the electrodes
that may result from the manufacturing process. The
resistance of such layers decreases with increasing frequency
as they become capacitively bridged. The impedance-based
measurements of power consumption in the field cages also
indicate higher losses at higher frequencies (figure5(c)). These
losses are converted into thermal energy. The frequency
dependenceis especially pronouncedin microelectrodeswhich
are covered by a silicon nitride layer of sub-micrometre
thickness (figure 5(b)): since this layer reduces the electric
field in the liquid, it strongly reduces the warming for all
frequencies. However, such electrode coatings are not a viable
method for reducing the thermal influence on particles in
the microchannel because they equally lower the DEP force
available for manipulation [24].
6. Conclusion
Knowing the limits to the application of nDEP is indispensable
for the successful use of the method in biotechnology and
medicine. Here, we have put nDEP to a demanding test ofbiocompatibility, namely, the unhampered growth of living
Table 1. Numerically derived data of the mean temperature of a220 m 220 m area with a nDEP field cage in its centre.Comparison of chips with 40 m channel height made fromdifferent materials forming the top/bottom slide. The temperaturevalues were calculated for the ac mode at 0.7 Vrms in a medium of0.3Sm1 and subsequently normalized to the glass/glass case. Thesimulation volume was sized 250 m 750 m 500 m.
Top/bottom slide Normalized mean temperature
Glass/glass 1.00Corundum/glass 0.11Silicon carbide/glass 0.10Silicon/glass 0.10Corundum/corundum 0.03Silicon carbide/silicon carbide 0.02Silicon/silicon 0.02
cells under conditions as they may occur in normal nDEPexperiments. In summary, two different effects inhibit
growth: one is frequency dependent, occurs at low frequencies
and is overcome by higher frequencies. The other one athigh voltages was identified as being clearly thermal andwas characterized further by IR thermometry. In these
IR experiments, the maximum electric conductivity of thebuffer was more than double of that of yeast broth and,thus, comparable to that of media used in mammalian cell
culture. Our results provide a base for improved experimentaldesigns that reduce the stress on living cells during long-term
manipulation. The appropriate electric conductivity of thefluid, a high frequency, the minimum feasible voltage, the
right phase pattern and the smallest possible nDEP elementare among the most important factors for an optimum survivalrate of living cells inside the microstructure.
Considerable improvements concerning the warminggenerated inside the chip can be achieved by using materials
with higher thermal conductivities such as corundum, siliconcarbide or diamond. These substances have the advantage of
being optically transparent which the cheaper silicon is not.Table 1 gives an outlook as to which reductions in heatingcould be realized in non-glass chips.
Acknowledgments
Heiko Zimmermann and Frank R Ihmig are gratefullyacknowledged for providing their infrared set-up (both
Fraunhofer IBMT, St Ingbert, Germany). We thank Gabriele
Reinke for the temperature-controlled microscopy table,Thomas Buckhout for the yeast strain (both Humboldt
University, Berlin, Germany) and Claus Duschl (FraunhoferIBMT, Berlin, Germany) for helpful discussions and his
careful reading of the manuscript. We are grateful to MariaMatschuk for having performed preparatory experiments. This
work was supported by the European Commission throughthe Integrated Project Cellprom of the sixth FrameworkProgramme (NM P4-CT-20 04-50 00 39).
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