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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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J. Phys. D: Appl. Phys.41(2008) 175502 M S Jaegeret al

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).

5


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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

6


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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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