BS-3

ExHFT-7
28 June – 03 July 2009, Krakow, Poland

ELECTRICAL CLASSIFICATION OF SINGLE RED BLOOD CELL
DEFORMABILITY IN HIGH SHEAR MICRO-CHANNEL FLOWS
Y. Katsumoto, K. Tatsumi*, T. Doi, K. Nakabe
Kyoto University, Kyoto, Japan

ABSTRACT. Measurement of human red blood cell (RBC) deformability in a micro-channel using
electric micro-sensors is proposed and carried out in this study. The time series of the electric
resistance is measured using an alternative current vs. voltage (I-V) method as the RBCs deformed byhigh shear flows individually pass between the electrodes. The resistance distributions vary in relation
with the RBC shape, which depends on the cell deformability under the condition of a constant shear
stress produced by the flow. Experiment is carried out with the samples of normal and glutaraldehyde
treated (rigidized) RBC to evaluate the feasibility of the present method.
Keywords: Micro-channel, Red blood cell, Deformability, Micro electric resistance sensor
INTRODUCTION
Measurement of the deformability of a red blood cell (RBC) is an important issue in terms of not only
investigating the hydrodynamic characteristics of the blood such as fluid viscosity and electricpermeability[1], but also diagnosing initial symptoms of diseases in clinical investigation. For example,
in Plasmodium falciparum, which is one of the most virulent diseases causing severe anaemia in
number of tissues and organs[2], the deformability of the RBC is significantly reduced due to theincrease of the internal viscosity and rigidization of the cytomembrane caused by having theplasmcytoskeleton of the RBC bounded with the neoantigens during the parasite, even in the early‘ring’ stage[3]. Therefore, developing a technique which can evaluate the deformability of the RBC
with low cost, short time and simplified procedure would provide a large contribution in the medical
fields particularly in clinical testing[3,4].
There are several typical measuring schemes to evaluate the RBC deformability. The one using
viscometer[5] evaluates the deformability of the bulk RBC solutions from the fluid viscosity. The one
using a rheometer with coaxial rotating cylinder applies shear stress on the RBC and measures thedeformability visually[6]. Measurement using optical tweezers[7] or micro-glass pipettes[8] stretches
single RBC and evaluates the extension rate. However, the accuracy of the former two measuring
schemes is low especially when the number density of infected RBC is small. This is not preferable forclinical test of diseases in the early stages. On the other hand, the latter two can evaluate thedeformability of each single RBC whereas the available sampling number of RBC is limited.
The motivation of the present study is to develop a micro sensor which can measure thedeformability of a single RBC using hydrodynamic stresses and electrical sensors applied in a
micro-channel. Recently, Korin et al.[9] visualized the behaviour of RBCs in a micro-channel andmeasured the cell deformation by analysing the images of the cells stretched by the high shear flow.
The usage of the micro-channel has the advantage in reducing the cost, measuring time, and sample
volumes. Their method, however, requires high spatial resolution image recording equipment,
which may increase the cost and impair the compactness of the application. In contrast, the sensor
proposed in the present study is based on an electrical measurement to evaluate the RBC
deformation. Namely, micro platinum membrane electrodes are attached to the channel bottom wall
* Corresponding author: Dr. K. Tatsumi
Phone: + (81)-75-7535209, Fax: + (81)-75-7535209
E-mail address: tatsumi@mbox.kudpc.kyoto-u.ac.jp201

7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June – 03 July 2009, Krakow, Poland
Flow direction

Shear stress

Shear flow
Channel bottom wall

Sensor electrodes
Normal RBC case
Flow

Rigidized RBC case
Flow

τA
R

R

τB
ΔR A

t

ΔR B

t

Figure 1. Concept of the measuring method of RBC deformability.
of the sensor, and the time-sequential signals of electric resistance are measured as the RBC crosses
the electrodes. Compared with the aforementioned optical measurements, the present method candecrease the size and cost of the device markedly. A higher affinity to the existing RBC counting
equipments is also another advantage. In this paper, experiment is carried out to evaluate thefeasibility of the sensor proposed in this study. Micro-channel with the micro membrane electrodes
is fabricated, and the electric resistances of the RBC crossing the electrodes are measured andanalysed using the samples of normal human RBC and glutaraldehyde-treated rigidized RBC.
MEASUREMENT PHYSICSThe electric conductivity of the RBC cytomembrane is approximately 1×10-6S/m, which is smallenough to be considered as an insulating material compared with the cytoplasm and normal saline
solution. When a low frequency AC electric field is applied around the RBC suspended in asolution, the current is interfered mainly by the cytomembrane. In this case, the cell shape also
affects the distribution of the current density, in other words, the electric resistance monitored
between the electrodes changes depending on the cell shape.
Figure 1 shows the schematic of the measuring method proposed in this study. A pair of platinum
membrane electrodes is attached to the bottom wall of a micro-channel, and the time-sequential
signals of the electric resistance between the electrodes are measured. When RBCs are suspended in
the micro-channel flow, the resistance between the electrodes increases significantly as the RBC
passes between them due to its high electric insulating property. While the RBCs flow in thechannel, they are stretched and deformed attributed to the high shear stress provided by the steep
velocity gradient of the flow. The profile of the measured resistance is affected not only by the fluid
properties but also by the size, position and shape of the RBC. If the position of the RBC passing
between the electrodes can be precisely controlled, then the shape of the RBC, which also
represents the deformability of the RBC, can be evaluated by analysing the resistance signals.
When an electric field is, thus, applied to the RBC by using the sensor shown in Fig. 1, the parallel
circuit between the electrodes consists of cytoplasm, cytomembrane, solvent, and the electric
double layer formed at the electrode surface as shown in Fig. 2(a). This circuit can also be
simplified as parallel components of variable resistance and capacitance connected in series withthe component of the electric double layer, presenting the change in the electric characteristics as
the RBC passes between the electrodes.
As one can see, the accuracy of the measurement largely relies on how large the difference between
the resistances of the buffer solution and the RBC membrane is. If a solution of high ionicconcentration, such as isotonic sodium chloride solution, is used, however, the effect of the electric
double layer cannot be neglected. This problem can be solved by applying a high frequency ACelectric field to the electrodes and reducing the capacitance of the electric double layer. In contrast,
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7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June – 03 July 2009, Krakow, Poland
Solvent
Rs

Cell membrane
ε cm , κ cm

Cs

t cm
C p’

R p’

C p’

d RBC

R p’

Electric
double layer

Cytoplasm
ε cp, κ cp

Electrode

Cell

d RBC

Solventεs, κsSolvent
ε s, κ s
Equivalent sphere
εRBC, κ RBC

Electrode(a) Equivalent circuit(b) Cell model
Figure 2. (a) Equivalent circuit model of the sensor with an RBC suspended in a solvent, (b) Cell
model simplified as a sphere in the numerical simulation.

400

1.60
εsus

κsus

εsus

300
200

1.58

7

10

Bare Pt electrodePt-plated electrode

6

10

R (Ω)

1.62

κsus (S/m)

500

5

10

1.56

4

10

100
0
3
10

fc

1.54
3

5

10

7

f (Hz)

10

10

2

10

3

10

4

10

5

10

6

f (Hz)10710(a) Effects of f on ε and κ (sim.)(b) Effects of f on R (exp.)
Figure 3. AC frequency effects on (a) permittivity ε and conductivity κ of RBCs suspended in
PBS (simulation), and (b) the resistance of the PBS without RBC (experiment).
since the cell membrane has electrically insulation properties, an increase in the frequency of theelectric field can incur a decrease of the cell resistance. Therefore, there is a trade-off problem indetermining the frequency range to be applied on the electrodes.
The maximum limit of the frequency is obtained from the numerical simulation calculating theimpedance characteristic of RBCs suspended in the solution using the model proposed by
Katsumoto et al.[10]. This model treats the RBC as a 6μm diameter sphere shown in Fig. 2(b)having the frequency-dependent complex permittivity derived form from the Maxwell-Wagner
equation.
Figure 3(a) depicts the results of the computation showing the effects of the frequency, f , on ε andκ , respectively. κ increases with f in the area above several MHz in the figure showing therelaxation behaviour of the solution. This indicates that the cytomembrane acts as an insulator when
the frequency is low, while the cytoplasm is directly measured when the frequency is high. As
mentioned above, the present sensor shows a higher performance with larger difference in thesolution and RBC. Therefore frequency of several tens of kHz is suitable for the sensors. The lower
limit of the frequency to be applied will be discussed shortly.
EXPERIMENTAL SETUP
Figure 4 and Table 1 show the schematic and dimensions of the channel and sensor electrodes usedin this study, respectively. The channel width is 1mm and is much larger than the channel heights
H1 and H2. Therefore, the channel flow can be considered as two-dimensional flow, and the RBC isdeformed receiving the shear stress in the streamwise direction.
The channel has three inlets, and RBCs suspended in phosphate buffer saline (PBS: Amresco)
solution are supplied from the center inlet while PBS solution only is supplied from the side ones.
Due to the low Reynolds number of the flow in the micro-channel, the flow is in laminar regime
and the molecular diffusion of the flow supplied from the center inlet becomes small. Therefore, by203

7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June – 03 July 2009, Krakow, Poland

H1

H1
H2

h

H2

Electrode

RBC

wg Lg ws

( a ) Side view

z
Step
Blood
solution

Electrodes
Flow

Ls
O

W

Sensor electrodex
Guard electrodes

Side flows( b ) Top view( c ) Magnified view of electrodes

Figure 4. Schematic of the micro-channel and sensor electrodes.
W
1000

Table 1. Parameters of the micro-channel and electrodes (μm).
H1
H2
Ls
Lg
ws
52
10
5.2
2.3
14.8

wg
14.6

changing the flow rate of each side flow, the spanwise position of the RBC passage can becontrolled to pass the center of the electrodes. These fluids are supplied by syringe pumps (Nihon
Kohden: CFV-3200, Harvard Apparatus: econoflo) with flow rates of 0.01 and 1.0μl/min.
When the RBC is placed in the channel shear flow, the RBC receives a lift force attributed to the socalled Fåhraeus effect[11]. This lift force moves the RBC away from the channel wall on which thesensor electrodes are embedded. Apparently, this leads to a decrease of the measuring resistanceand the sensor S/N ratio. To tackle this problem, the channel heights at the center inlet and at theelectrodes are smaller than the other parts of the channel, i.e. backward-facing and forward-facing
steps are installed in the downstream of the center inlet and immediately upstream of the electrodes,
respectively. The RBC is, thus, supplied from the inlet in a lower position, and the downwash flowat the forward-facing step carries the RBC toward the bottom wall. This spanwise and downward
positioning of the RBC passage can control the relative distance between the RBC and electrodes.
The micro-channel illustrated in Fig. 4 is made of poly-dimethylsiloxane (PDMS) and is fabricatedby using SU-8 (MicroChem) as a casting mold. To fabricate the SU-8 mold, an optical mask, on
which the channel pattern is printed, is prepared first. Then, SU-8 layer spincoated on a slide glass
is exposed to the UV light through the mask. After the post baking and etching processes, an SU-8
mold is obtained. PDMS in liquid phase is then poured over the SU-8 mold, and is rigidized andripped off. The PDMS channel is then attached to a slide glass, on which the platinum membrane
patterns of electrodes are formed. These electrodes are fabricated through a sputtering and lift-off
processes using a sputtering equipment (ULVAC KIKO: SCOTT-C3) and ZPN (ZEON) resist.
The electrodes are serially connected to the shunt resistance for detection. Sinusoidal wave of AC
voltage is applied to these resistances under the condition of 10kHz using a function generator (NF:
WF-1973). By measuring the phases of the shunt resistance and applied voltages, the resistancemeasurement accuracy is enhanced.
As shown in Fig. 4, guard electrodes are placed on both sides of the sensor electrode (the one used
for detection). Voltage is charged to these guard electrodes through an FET input Op-amp
possessing the same electric potential with the sensor electrode. The electric fluxes from the guard
electrodes will suppress the fringe effect of the fluxes from the sensor electrode. This leads to anarrow distribution of the current density in the streamwise direction and enhances the sensitivity.
To evaluate the impedance characteristic of the electrodes, the electric resistance between theelectrodes embedded in the channel filled with PBS solution is first measured by using animpedance analyser (Agilent: 4294A). Figure 3(b) shows how the frequency of the applied AC
voltage, f , affects the resistance, R. The open and solid circles in the figure present the results using
platinum bare electrodes and platinum black plated ones, respectively. The Pt-plated electrodes
represent those with Pt nano particles attached on the surface using the following plating process.
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7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June – 03 July 2009, Krakow, Poland

Namely, first filling the channel with a solution of hexachloroplatinic (H2PtCl6) 30mg/mL and lead
acetate (CH3COO)2Pb 0.3mg/mL, and then applying 2V DC voltage between the electrodes.
As shown in Fig. 2(a), when f is not sufficiently high, an electrical double layer is formed at theelectrode surfaces, which leads to a reduction in the resistance measurement performance. This canbe observed in Fig. 3(b), where the resistance R plotted with the open circles decreases as fincreases and then becomes constant. As mentioned above, 10kHz AC electric field is applied inthis study. This is, however, not large enough to suppress the appearance of the electric double layer
as can be found in Fig. 3(b), i.e. R measured under the condition of f = 10kHz is larger than thevalues in higher frequency region. To tackle this problem, the aforementioned Pt-black plating is
conducted on the electrode surface in this study. A layer of Pt nano-particles will be formed on thesurface as a porous media, and the surface area is increased by this structure resulting in the
reduction of the electric double layer effect. In this case, the frequency range from which R begins
to increase is shifted toward the lower f side and R is small and uniform under the condition of f =10kHz compared with the case of bared electrodes. It should be noted that the reason why theresistance in the plated case are lower than those of the bare electrodes is attributed to the fact thatthe plate is formed uniformly on the surface and the distance between the electrodes is decreased.
Along with the above electric measurements, optical measurement is carried out using a microscope(Olympus: IX-71) and halogen lamp as the light source for the purpose of verifying the position andshape of the RBC when passing between the electrodes. An objective lens (Olympus:
LMPLFLN100X, ×100 magnification and NA = 0.8) and a high speed camera (Vision Research:
Phantom V7.3) are used to record the images. The frame rate of the camera is 1000 frames/s and the
CCD resolution is 800×650 pixels. The optical resolution of the image is 0.21μm/pixel. The
focusing depth of the image Δz is 1.669μm calculated from the following equation:nλn(1)Δz = 0 2 +eMNANAe and M are the smallest distance that can be resolved by the detector, and lateral magnification,
respectively. λ0 and n are the wave length of light in air and refraction index.
Korin et al. [13] reported that shear stress required to deform an RBC with a deformation index
DI=0.5 in a micro-channel is approximately 15Pa. Here, DI is defined as DI = (a−b)/(a+ b), wherea and b are the long and short axes of the RBC, respectively. When water is used as the working
fluid, it is not suitable to obtain this value of shear stress by increasing the flow rate because of thetime resolution of the measurement using the high-speed camera and electric sensors.
Polyvinylpyrrolidone (PVP: MW 3.6×105, Nacalai tesque) is, therefore, mixed with the working
fluid to increase the viscosity, by which sufficient shear stress is achieved to deform the RBC.
RBC treatment is carried out by the following procedure. 10μl sample blood is collected from ahealthy human volunteer. The blood is first suspended in 1ml PBS, and then centrifuged during
10min with 1000G to separate the RBC from other substances, i.e. plasma, plaque and leucocytes.
Supernatant solution is removed, and 0.1ml PBS is added to the collected RBC. 0.4ml PBS with
10wt% PVP is added to the solution, and RBC suspended solution of PBS with 8wt% PVP is
prepared and used as the normal RBC suspended working fluid.
Rigidized RBCs are prepared by treating the cells with glutaraldehyde. Glutaraldehyde (Nakalaitesque: 25% solution) is first diluted with PBS by 0.025wt%. The RBC separated from othersubstances in the same way shown above is then added to this solution and settled for 30min underroom temperature. The solution is, then, centrifuged during 10min with 1000G. After removing thesupernatant solution, 1ml PBS is added. Once again the solution is centrifuged and the supernatantsolution is removed. Finally, 0.1ml PBS and 0.4ml PBS with 10wt% PVP are respectively added tothe solution, and, thus, PBS solution of 8wt% PVP with rigidized RBC is prepared.
EXPERIMENTAL RESULTS
Figures 5(a) and (b) show the snapshots presenting the behaviour of the normal and rigidized RBCs
passing between the electrodes, respectively. The flow direction is from the left to the right, and the205

7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June – 03 July 2009, Krakow, Poland(a) Normal RBC case(b) Rigidized RBC case
Figure 5. Snapshots of RBCs passing between the electrodes.
Table 2. Averaged value of the major and minor axes of the RBC and deformation index, DI.
Normal RBC
Rigidized RBC
14.54
7.37
a [μm]
4.65
7.35
b [μm]
0.52
0.00
DI
arrow indicates the location of the forward-facing step. Although not shown here, the height of the
RBC passage, h, was obtained visually by measuring the distance between the points focused on the
RBC and bottom wall. h was nearly constant for all RBC measured as h=5μm. It should be noted thatthe degree of the error in h is approximately equal to the aforementioned focusing depth Δz.
In the figure, the RBC is deformed and stretched in the streamwise direction owing to the twodimensional shear flow in the channel. In Fig. 5(a), the RBC deforms most when passing the forwardstep. This is due to downward flow generated at the step by which not only the shear stress is increased,
but also the RBC is carried to the area of larger shear stress located close to the bottom wall. The
deformation rate gradually decreases as the RBC flows to the downstream. This can be attributed to theFåhraeus effect[11], namely, a lift force works on the RBC and the RBC moves toward the channel
center resulting in a reduction of the shear stress.
In contrast with the normal RBC case, the rigidized RBC shown in Fig. 5(b) maintains a biconcave
surface and no deformation of the cell is observed. The RBC rotates as it flows, which is a motion socalled ‘flipping’. When a normal RBC is suspended in a shear flow, the cytomembrane not only
deforms but also rotates together with the cytoplasm. This is called ‘tank treading motion’ of the cell,which prevents the cell to flip[12]. Since the shape of the cytomembrane in the rigidized RBC case isfixed, the tank treading motion cannot be generated and the flipping motion takes place.
Table 2 shows the averaged value of the long and short axes of the RBC, a and b, and the deformationindex, DI , obtained from the visualization results. As mentioned above, rigidized RBCs show no
deformation and have a circle projection shape. Therefore a and b are identical in this case. On theother hand, since the normal RBC is deformed, a is almost three times larger than b. DI isapproximately 0.5 in the normal RBC case.
Figure 6 shows the distributions of ΔRmax and δ of the normal and rigidized RBCs. ΔRmax and δ are themaximum value and half bandwidth of the resistance peak distributions obtained when each RBC
passes the electrodes, respectively. During the experiment, variation in the RBC spanwise position
when passing the electrodes is observed. This is attributed to the width of the center inlet of the channel,
which is 50μm and is much larger than the gap between the electrodes, Lg =5μm . To discuss this effect,
the spanwise position of the cell, yRBC, is taken as the abscissa in the figure. The lines in the figure
present the results obtained by using the least-square method (L.S.M.) in each RBC case.

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7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June – 03 July 2009, Krakow, Poland

200
180
160
140

Normal RBC
Rigidized RBC

δ (μm)

ΔRmax (μm)(a) Relation between ΔRmax and yRBC(b) Relation between δ and yRBC
Figure 6. Distributions of peak resistance ΔRmax and half bandwidth δ against spanwise locationof RBC, yRBC.

120
100
80
60
-0.1

0.0

0.1

0.2

0.3

0.4

0.5

DI

0.6

27
26
25
24
23
22
21
20
19
18
-0.1

Normal RBC
Rigidized RBC

0.0

0.1

0.2

0.3

0.4

0.5

0.6

DI

(a) Relation between ΔRmax and DI(b) Relation between δ and DI
Figure 7. Distributions of modified ΔRmax and δ against deformation index DI.
In Fig. 6 (a), ΔRmax decreases as the RBC position yRBC is closer to the ground electrode. On the other
hand, δ increases as yRBC decreases as shown in Fig. 6(b). This can be attributed to the following
reason: As seen in Figs. 4 and 5, the sensor side consists of three electrodes, the sensor and guard
electrodes, while the ground side has a single electrode. The effect of the guard electrodes reducing thefringe components of the electric flux deteriorates in the ground side. Namely, the current density
distribution becomes wide and the value decreases in the position close to the ground electrode. The
amount of electric flux blocked by the RBC, therefore, decreases, which leads to a decrease in theresistance particularly the maximum value, ΔRmax. On the other hand, since the current density
distribution is wider at the location close to the ground electrode, δ increases.
As shown in Fig. 6, yRBC appears to affect ΔRmax and δ linearly. Therefore, the linear component using
the L.S.M. line in the figure is subtracted from each value, and is shown in Fig. 7 in relation with DI.
Since only two kinds of RBCs, normal and glutaraldehyde-treated ones, are measured in theexperiment, two large groups are found in the area close to DI = 0.0 and 0.5.
To evaluate the variation of the samples in each RBC case, coefficient of variance, Cv=σ /m×100, isshown in Table 3. σ and m are the standard deviation and arithmetic average of the distributions,
respectively.
In Fig. 7(a), ΔRmax of both RBCs show similar values and overlap with each other. Furthermore, Cv of
ΔRmax shown in Table 3 is relatively large in both RBC cases, indicating that the variation of thesamples is large.
On the other hand, a difference in the groups of δ for the normal and rigidized RBCs is recognizable inFig. 7(b) indicating the fact that there is a correlation between δ and DI. Furthermore, Cv shown in
Table 3 is small compared with those of ΔRmax . These results point out that the half bandwidth δ ismore reasonable as an index to evaluate the shape, i.e. deformability of the RBC, than ΔRmax.
The reason why δ shows a better characteristic than ΔRmax is due to current density distribution
between the electrodes. ΔR can be more sensitive with the RBC height position h. Therefore, evenwhen the RBC height position is controlled by the step flow, small variation in h can vary ΔRmax
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7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June – 03 July 2009, Krakow, Poland

Cv (%)

Table 3. Coefficient of variance for ΔRmax and δ
ΔRmax
δNormal RBC
Rigidized RBC
Normal RBC
Rigidized RBC
12.1
15.4
3.42
7.39

largely enough to make the difference of the RBC shape ambiguous. δ , however, depends more on thecurrent density distribution in the streamwise direction, which is less affected by other parameters.
CONCLUSIONS
A micro sensor consisted of micro-channel and electric sensors, which can measure thedeformability of a single RBC was proposed and evaluated in this study. The sensor was fabricatedand its feasibility was examined using normal and rigidized human red blood cells. The major
results are stated as follows:
1. The frequency of the sensor AC voltage was determined numerically and experimentally.
Together with the Pt-black plated on the electrodes, frequency specification of 10kHz reduced
the influences of the electric double layer formed on the electrodes and dielectric relaxation
appearing around the cell membrane, which led to the increase of the sensor sensitivity.
2. The backward- and forward facing steps, and the side flows applied in the micro-channel wereeffective to control the height and spanwise positions of the RBC in order to closely pass thearea between the sensor electrodes.
3. A good correlation was observed between the half bandwidth of the time-sequential signals of
the resistance and the deformation index. In contrast, the correlation between the peak value ofthe resistance and deformation index was considerably small. This characteristic was strongly
attributed to the current density distribution formed between the electrodes. Consequently, thefeasibility of the present sensor was verified from the results.
ACKNOWLEDGEMENT
This study was financially supported by The Japanese Ministry of Education, Culture, Sports, Science.

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