Hughes M.P., Hoettges K.F. (Eds.) Microengineering in Biotechnology

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In this case, the detection area is directly defined by the electrode

geometry within the capillary channel. This approach reduces

stray capacitances and thus increases the device operating band-

width toward higher frequencies. Measurements at the higher

end of the b-dispersion (see below) are then possible. Small

channel cross-sections permit sequential tracking of cells along

the channel and the integration of features such as sorting by

partitioning the channel length for successive operations. Small

microelectrodes result in an apparent dilemma; on the one hand,

a higher sensitivity results from the higher field line concentra-

tion around the cell. On the other hand, the high interface

impedance (due to the electrical double layer) makes measure-

ment at low frequency more difficult. To alleviate this problem

there are some techniques to increase the effective surface area of

microelectrodes based on nanoporous films such as platinum

black, iridium oxide, or titanium nitride (27, 28).

Nanoporous films can be deposited on a seed electrode through

an additional fabrication step. For platinum black, which uses

electro-deposition, the effective surface area increase can reach

100- to 1,000-fold, but in practice it is particularly difficult to

obtain a high reproducibility of the final interface impedance.

Alternatively, the use of a sputtered iridium oxide film (IrOx)

demonstrates reproducible results and large effective surface area

increase following activation (29). The activation is simply per-

formed by applying a cyclic voltametry step of 10–20 cycles of 3 V

at 0.1 Hz to the microelectrodes with the microfluidic channel

filled with NaCl. It can be seen in Fig. 7.3 that after activation the

low frequency cut-off point (taken at a 45 phase) is decreased

from 100 kHz down to the 1 kHz range. The electrodes phy-

sical dimensions are in this case 20  40 mm.

Another issue arises from the inhomogeneous current density,

be it either within the channel constriction (i.e., aperture) or if

small electrodes are used between the closely placed electrode pair.

Fig. 7.3. Frequency response analysis showing impedance amplitude and phase of a pair of IrOx microelectrodes

as measured before and after the activation procedure.

156 Gawad et al.

This inhomogeneity can bias the detection signal peak, as a func-

tion of the particle’s trajectory, as it passes through the measure-

ment volume. In traditional Coulter systems, the length and shape

of the aperture plays an important role in controlling the unifor-

mity of the signal shape and this has been extensively studied (30).

Similar studies may be performed for the integrated chip approach

with embedded microelectrodes. A complex dielectric model is

used to determine the change in electric current between a pair of

electrodes due to passage of a biological cell. The influence on the

dielectric spectrum of different cell properties, such as membrane

capacitance and cytoplasm conductivity is of particular interest.

The measurement volume is located between a pair of facing

microelectrodes in a microchannel filled with a saline solution. A

3D finite element model is used to determine the electric field in

the channel and the resultant changes in charge densities at the

measurement electrode boundaries as a cell flows through the

measurement volume. The charge density is integrated on the

electrode surface to compute the displacement current and the

channel impedance for a given applied alternating electrode vol-

tage and frequency. The excitation signals are taken to be of

suitably low frequency and low applied voltage, allowing the

quasi-static approximation and linear behavior of the system to

be assumed. In the present example, the measurement volume

geometry details are for the specific case of a sensor with a channel

of 20  20 mm

cross-section and two facing electrodes, 20 

20 mm

in area, on opposite walls of the channel (Fig. 7.4). These

channel dimensions are chosen in order to determine the sensitiv-

ity of a sensor, which could accommodate cell diameters up to

15 mm without clogging the channel.

Fig. 7.4. Diagram of flow cytometry measurement in a microchannel with integrated

microelectrodes. The modeled cell passes between the electrode pair, altering the

electric field distribution for different excitation frequencies, thus giving rise to a change

in the measured channel impedance spectrum. The electric field density in the channel

represented here by isosurfaces shows typical polarization effects of the Maxwell-

Wagner type (caps on the top and bottom of the modeled cell) and the inhomogeneous

field due to the electrode pair. (From Gawad et al. (31) – Reproduced by permission of

The Royal Society of Chemistry)

Impedance Spectroscopy, Optical Analysis of Single Biological Cells 157

A dielectric sphere of equivalent complex permittivity is used

as a simplified model to describe a biological cell. The model

includes various geometrical parameters of the cell, such as size

and position in the channel. Using such a model it is shown that

given a reasonable size and placement of the cell along the center

line of the channel, a good signal reproducibility can be obtained.

Also using analytical methods, such as conformal mapping, com-

pensation factors can be found, depending on the sensor geome-

try, to account for the fringing effect and non-uniformity of the

electric field. Numerical approaches have been used to determine

the practical limits of this compensation method (31).

4.1.3. Cell Detection Area

and Differential

Measurement

In practice, the measurement area of the chips contains two mea-

surement volumes (pairs of electrodes) in close proximity. In the

measurement area the channel width is reduced in order to

decrease the detection volume and thus increase the electrical

sensitivity of the system to the passage of the cell. This restriction

also decreases the chance of having two cells entering the measure-

ment area simultaneously. The electrode areas are typically 20 

40 mm

and channel cross-section 20  40 mm

. The distance

between the two electrode pairs is 60 mm.

The particle or cell moving under pressure-driven flow succes-

sively pass through the two electric field regions, thus consecu-

tively modifying the current through each detection volume. The

use of a differential measurement scheme significantly reduces

the measurement noise; small thermal fluctuations or variations

in the composition of the suspending fluid are thus cancelled out.

The chip is connected to a circuit which uses differential electro-

nics to amplify the small difference of current passing through the

two sensors. This approach allows rejection of the common mode

signal early on, avoiding saturation of the amplifiers. A double

peak (one positive and one negative) electrical signal shape is

thus obtained for each passing cell (Fig. 7.5). This approach offers

many advantages compared to a non-referenced measurement

technique in terms of ground level stability and signal amplifica-

tion. The cell speed within the detection channel is obtained by

dividing the center-to-center distance between the detection

volumes by the transit time t

separating the two measured

peaks. This method also presents some advantages in terms of

robustness compared to a single peak width measurement, as it is

less sensitive to the cell size or shape.

4.1.4. Further Techniques

4.1.4.1. Guard Ring

The addition of a guard ring in order to straighten the electric field

lines around the current sensing electrodes is a practical approach

that addresses the issue of the electric field uniformity and permits

simplification of the calculation of the cell geometric factor. The

use of grounded guard electrodes in conjunction with current

sensing electrodes connected to a virtual ground in auto-balanced

158 Gawad et al.

bridge configuration is preferred (Fig. 7.6). This is because at

higher frequencies (MHz and greater) it is difficult to implement

non-phase lagging followers to drive active guard electrodes, as

would be required by a traditional bridge electrical circuits. This

amplification approach also reduces the effect of the stray capaci-

tances as there is no current leakage from the current sensing leads,

at a virtual ground potential, to the ground shielding or guard

electrodes leads.

Fig. 7.5. Cell detection principle and expected electrical differential current signal for a

passing cell. The detection and reference volumes switch as the cell passes through

each. The cell speed in the measurement channel is computed by measuring the transit

time t

separating the two peaks. The bottom electrodes are kept at a virtual ground

potential.

Fig. 7.6. Principle and geometrical approach to implement guard electrodes in a

differential auto-balanced amplification scheme.

Impedance Spectroscopy, Optical Analysis of Single Biological Cells 159

4.1.4.2. 4 Point Differential

Electrodes

An alternative method to that of nanoporous modification of

electrodes surfaces, to increase the effective charge density of the

electrodes, is the use of a 4-point differential electrode configura-

tion (32). In this configuration an alternating voltage is applied

between two large microelectrodes placed at either end of the

channel and the injection current is measured. Three pickup elec-

trodes are placed symmetrically in the channel. The differential

voltage drops between the pickup electrodes are then amplified

and compared yielding the impedance variation due to the pre-

sence of the cell. This technique has been shown to work well up to

10 kHz using the geometry shown in Fig. 7.7a.InFig. 7.7b the

impedance variation measured at 1 kHz is represented for a passing

cell as a function of its position in the channel.

The pickup electrodes surface capacitance, due to the double

layer, still subsists in the tetrapolar measurement scheme. But since

the input impedances used in the amplification is high only negli-

gible amounts of current flow through those electrodes. The

measured transient changes in voltage at the electrode thus corre-

spond to those taking place in the liquid bulk with minimal voltage

drops due the double layer capacitance.

4.2. Optical Detection The chip substrate consist of optical quality glass, it is therefore

possible to perform optical measurements on the cells as they pass

through the channel. Details of such an optical system are shown

in Fig. 7.8. This system was designed to measure fluorescence

from single cells at three different wavelength ranges. To opti-

cally excite the cells light from a 532 nm (solid state YAG) and a

633 nm (HeNe) laser is coupled into the channel using a free-

space optics setup and a standard microscope objective. The laser

beams are combined and pass through a beam expander into an

infinity corrected objective lens ( 20, 0.5 N.A. Nikon). For

Fig. 7.7. (a) 4-point differential measurement principle. (b) Measured impedance signal.

(Figure courtesy of T. Braschler)

160 Gawad et al.

detection the fluorescent light emitted from the cells is collected

by the same objective lens is spectrally and spatially filtered by

passing through dichroic mirrors, band pass filters, and lens and

pinholes positioned in front of photomultiplier tubes (Hama-

matsu). The intensity of the light at the focal point of the objec-

tive (optical detection zone in the channel) is typically 600 mW.

The emission filters have center wavelengths of 585 nm and

675 nm and a longpass filter with cutoff at 710 nm (Chroma,

Rockingham, VT, USA).

4.3. Sample Preparation

and Chip Maintenance

Sample preparation is certainly one of the most time consuming

and critical aspect of the system operation. The quality of the

sourced sample is important as is proper lab technique for cell

harvesting, filtering, labeling, and washing. The large amount of

cell debris, DNA fragments or other substances, which accumu-

lates on the channel walls necessitates regular cleaning of the

microchannel.

Fig. 7.8. Schematic of the single-cell optical detection system using two excitation lasers

and up to three emission detectors.

Impedance Spectroscopy, Optical Analysis of Single Biological Cells 161

For cultured cells, trypsin is generally used to re-suspend cells

adherent to the petri dish wall. For cells grown in suspension

mechanical action using a pipette or gentle vibration is sufficient

to separate large cluster of cells into single units. Mesh filters of 50

microns are used to avoid clogging of the capillary channel with

large debris.

Another issue is due to the time taken for the measurement,

generally over 1 min to measure a few hundreds of cells. With the flow

speed being rather low in the larger parts of the channel sedimenta-

tion and cell adhesion to the bottom glass surface of the channel or

tubing can occur. To reduce sedimentation a small percentage of

Ficoll 400 a long chain poly-sucrose molecule can be used to obtain

the condition of neutral buoyancy as suggested by Holmes et al. (33).

Ficoll400 is useful in that is does not effect the osmotic balance of the

cells. In general, a temporary flow speed increase between measure-

ments is sufficient to resuspend cells that have sedimented and tem-

porarily adhered to the walls. A cell dilution of up to 10

cells ml

–1

was found to be suitable to reduce the occurrence of doublet events

(two separated cells flowing simultaneously through the detection

zone) while still achieving a steady stream of cells.

4.4. Dielectric

Properties of a

Suspension of Cells

The determination of the equivalent dielectric properties of a

randomly distributed suspension of homogeneous particles started

with the work of Maxwell, who originally considered conductivity,

and was extended to complex permittivity by Wagner. In deriving

the model Maxwell considered a number N

of non-interacting

particles of radius R, placed in the spherical volume of radius R

The sum p

sum

of their effective dipole moment p

eff

contributions is

simply obtained by

sum

¼ N

eff

[2]

Considering a sphere filled with a homogeneous material with a

complex permittivity

, suspended in a liquid of complex permit-

tivity

, the effective dipole moment of the sphere p

sphere

is then

given by

sphere

¼ 4pR



þ 2



[3]

A complex permittivity

" is defined as

" ¼ "



i

[4]

 is the conductivity of the material, "

is the relative permittivity,

the permittivity of free space, and ! the angular frequency.

By equating the relations [2] and [3], the complex form of

Maxwell’s expression gives an expression for the equivalent com-

plex permittivity of the suspension

equ

162 Gawad et al.

equ



equ

þ 2

¼ 



þ 2

[5]

The volume fraction ’ is defined by  ¼ N



. An elegant

formulation of the equivalent complex permittivity

" is given by

Jones

equ

1 þ 2

Kð

;

1  

Kð

;

[6]

where

K is the complex Clausius–Mossotti factor which contains

the magnitude and phase information of the dipole representing

the cell defined as

K ¼



þ 2

[7]

An expression for more complex particle models including multi-

ple shells is obtained by substituting the corresponding Clausius–

Mossotti factor to account for additional relaxations in the dielec-

tric properties of the cell (Fig. 7.9).

Fig. 7.9. Frequency dependence of the real and imaginary part of the Clausius–Mossotti

factor for a shell-covered sphere in suspending media of different conductivity, with

parameters 

¼1.2

–3

–1.2 Sm

–1

, 

¼1

–8

Sm

–1

, 

¼0.5 Sm

–1

, "

¼78"

¼ 10"

, "

¼ 60"

, R ¼ 2 mm, d ¼ 10 nm.

Impedance Spectroscopy, Optical Analysis of Single Biological Cells 163

The number of theoretical relaxations (drops in permittivity

with increasing frequency) is equal to the number of interfaces in

the cell model. In particular, the single-shell model displays two

relaxations: one for the interface between the external medium and

the membrane and the second for the membrane internal interface

with the cytoplasm.

Even in the simple case of a sphere covered by a single shell, the

expression can get rather intricate and can become impractical for

studying experimental data. Pauly and Schwan were the first to

publish a convenient set of equations detailing the dispersion

parameters for such a model (34). Although the single-shell

model theoretically gives two separate relaxations when consider-

ing the full Pauly and Schwan expressions, permittivity measure-

ments in physiological saline solution show only one relaxation

in practice. Its characteristic frequency is located in the MHz

range and is related to the time needed to charge the membrane

(subscript 2) through the intra-(subscript 3) and extracellular

(subscript 1) media. The simplified expressions describing this

dispersion are



¼ 

ð1  Þ

1 þ =2

; [8]



¼ 

1 þ 2ð

 

Þ=ð

þ 2

1  ð

 

Þ=ð

þ 2

; [9]

¼ "

ð1  =2Þ

ð1 þ Þ

þ " with " ¼



2 þ ðÞ

[10]

¼ "

ð1 þ 2Þ"

þ 2ð1 Þ"

ð1  Þ"

þð2 þ Þ"

; [11]

and

T ¼

2pf

¼ RC



1  ðÞ

2 þ ðÞ



: [12]

Subscript s relates to the dielectric properties of the suspension at

low frequencies while subscript 1 relates to the values at high

frequency. T is the characteristic time constant and is related to the

characteristic frequency f

of the dispersion. The membrane capa-

citance C

¼ "

=d is a function of the membrane thickness d and

permittivity "

. The approximations involved here are small shell

thickness d  R, low shell conductivity 

 

;

, and the

assumption that 

 !"

and 

 !"

The second dispersion is observed with a suspending medium

of low conductivity at a higher frequency range. The membrane

capacitance is considered short-circuited and the observed relaxa-

tion is due to the Maxwell-Wagner dispersion resulting from the

164 Gawad et al.

difference in permittivity between the relatively conductive cyto-

plasm and the insulating suspending solution. The permittivity and

conductivity of a suspension of shell-covered particles is plotted in

Fig. 7.10 for suspending media of different conductivities.

Determining the optimum suspending medium conductivity in

terms of device sensitivity is an important question. For practical

operation, it would be convenient to pass cells through the mea-

surement system using standard culture medium or buffered saline.

Nevertheless, as it represents an important adjustable parameter it is

essential to determine whether the measurement sensitivity would

benefit from resuspension of the sample in a medium of different

conductivity. With this in mind the different approaches of AC

electrokinetics and AC dielectric spectroscopy are compared below.

4.4.1. AC Electrokinetics In AC electrokinetic techniques such as DEP and ROT, the move-

ment of a cell under the influence of an applied electric field is used

to obtain information about the complex electrical properties of

the cell. The magnitude of the observed displacement and related

forces are a function to the cell’s dielectric properties. For DEP and

ROT experiments, sucrose is generally added to the solution (to

control the osmolarity of the solution) when working at decreased

conductivities (1.210

–2

–1

). From the observation of the

Clausius–Mossotti factor frequency dependence for the single-

shell cell model in Fig. 7.9, it is clear that separation and measure-

ment techniques based on AC electrokinetics benefit from a low

conductivity of the suspending medium:

Fig. 7.10. Permittivity and conductivity spectrum for a shell covered sphere in different

suspending media conductivities, with ’ ¼0.2, 

¼1.210

–3

–1.2 Sm

–1

, 

¼110

–8

Sm

–1

, 

¼ 0.5 Sm

–1

, "

¼ 78"

, "

¼ 10"

, "

¼ 60"

, R ¼ 2 mm, d ¼ 10 nm.

Impedance Spectroscopy, Optical Analysis of Single Biological Cells 165