T HE A SIAN S YMPOSIUM ON C OMPUTATIONAL H EAT T RANSFER AND F LUID F LOW - 2011, 22–26 S EPTEMBER 2011, K YOTO , JAPANPaper ID: #175

Numerical and Experimental Study on Measurement of a Single Red Blood Cell
Deformability Using a Microchannel and Electric Sensors
Ryouji FUJIWARA, Kazuya TATSUMI∗ ,Yoichi KATSUMOTO and Kazuyoshi NAKABE
Department of Mechanical Engineering and Science,
Kyoto University, Kyoto 606-8501, Japan*corresponding author, E-mail: tatsumi@me.kyoto-u.ac.jp

Abstract
An electric micro-resistance sensor that can continuously
measure the deformability of a single red blood cell (RBC)
in a microchannel and a numerical model that can simulate
the resistance and capacitance of the cell membrane andcytoplasm are developed and improved. The resistance signal pattern between the electrodes is measured to evaluate
the feasibility of the present sensor, using the human RBCs
samples of normal RBCs and rigidized ones treated with
Ca2+ and ionophore A23187. Synchronized with the resistance measurement, the behavior of the RBC is visualizedusing a high speed video camera. A correlation between
the resistance signal pattern and the RBC deformation image is observed. Furthermore, in order to examine the influence of the sensor’s parameters, especially the RBC height
position and the sensor electrode arrangement, on the sensor sensitivity, numerical simulations are carried out for the
harmonic electric field formed around a single RBC and theelectrodes of the sensor in the microchannel. A numericalmodel introducing the equivalent electric circuit of the RBC
successfully simulated the current density distributions byconsidering the potential drops produced by the resistanceand capacitance of the membrane. The numerical results
show that the variation of the RBC height position greatly
influences the sensitivity and uncertainty of the sensor output signal. Rearrangement of the sensor electrode following these results, effectively suppresses the height influenceand improves the sensor performance.

1. Introduction
Measurement of the red blood cell (RBC) deformability
is an important issue from the viewpoint not only to clarify the hydrodynamic characteristics of the blood as fluid
viscosity, but also to diagnose the initial symptoms of diseases during clinical investigation. For example, Plasmodium falciparum, a highly infectious parasite that causes severe anemia in a number of tissues and organs [1], considerably reduces the deformability of RBCs by producing
cytoadherence-related neoantigens [2], [3]. Therefore, if atechnique that can measure the deformability of these RBCs
through a cheap, fast, simple and accurate procedure is de-veloped, it would make a large contribution to the field of
medicine, particularly in the area of clinical testing [4].
The microsensor proposed in this study evaluates the
RBC deformability by measuring and analyzing the electric
resistance of RBCs as they pass between a pair of electrodes
embedded in the microchannel. Compared with the conventional optical measurements [5], [6], the present sensor
offers the advantages of decreasing the size, cost and measuring time, and also showing greater compatibility withexisting RBC counting equipment.
In this study, a microsensor consisting of microchannel and micro-electrodes was fabricated and the resistancemeasurement was made to demonstrate the feasibility of thepresent sensor. Samples of normal RBCs, and rigidified
ones prepared by controlling the Ca2+ concentration in thecytoplasm with ionophore that was similar to those in vivo
were used in the measurement.
The results were compared with the visualization results
to determine the relation between the resistance distribution
and the deformation rate of individual RBC, and to evaluate
the performance of the proposed sensor. Additionally, numerical simulations were carried out to examine the effects
of several parameters representing the sensor geometry on
the sensor’s sensitivity for the purpose of gaining insightsthat would ensure the design of an improved sensor.
In order to conduct accurate computations on the resistance distribution obtained as the RBCs passed between
the electrodes, a new model that could simulate the resistance and capacitance of the cell membrane and cytoplasm
was developed in this study. Attentions were particularly
paid on the RBC height location and the sensor electrodearrangement that were considered to greatly influence themeasurement sensitivity and uncertainty.

2. Measurement physics
Figure 1 illustrates the schematic of the measurement technique of this study. When the RBC flows through the highshear flow produced in the microchannel, it is stretched in
the flow direction. If the applied shear stress is constant foreach RBC, the deformation degree, in other words shapeof the RBC, corresponds to the deformability of the RBC.

Channel bottom wall

Flow direction

H1
RBC

Sensor electrodes

R

RBC

H2
( a ) Side view

Channelbottom wall

z

H2

Shear
flow

R

H1

Step

Sensorelectrodes

Bloodsolution

Electrodes

ElectrodesWrWt( a ) Normal RBC case

Side flowst( b ) Rigidized RBC case( b )Bird ' s eye view

Figure 1: Concept of the present measurement system.

l g l sg l s

Table 1: Dimensions of the channel and electrodes (Experiment).
W [µm] W r [µm] H1 [µm] H2 [µm]
1000
50
52
10
ws [µm]5.4

lsg [µm]
4.3

ls [µm]
12.7

G

S

y

G

w s S : Sensor

Flowelectrodexlg [µm]18.5

GS

G : Guard
electrodeG( c ) Magnified top view of the electrodes

Therefore, the RBC deformability can be evaluated by measuring the deformation degree of the RBC accurately. In
this study, we will employ the electric resistance measurement technique using a micro-resistance sensor of countertype electrodes to evaluate the deformation degree of the
RBC suspended in the microchannel flow.
The micro-resistance sensor is made of counter-type
membrane electrodes that are attached to the bottom wallof the microchannel. The electric resistance between thesesensor electrodes is continuously monitored as each RBC
passes between the electrodes. Since the RBC membrane
has the electric conductivity of approximately 1 × 10−6 S/mthat is much smaller than those of cytoplasm 1.67S/m andsolvents, the RBC membranes can be regarded as electric
insulators in the electric field. Therefore, the measured resistance increases only while a RBC passes between theelectrodes. Since the membrane is the major factor that influences the electric resistance, the value and distributionof the resistance will vary depending on the shape of the
RBC as shown in Fig. 1(a) and (b). This characteristic ofresistance is used to evaluate the deformation degree in thisstudy.

Figure 2: Schematic of RBC-detecting microchannel.
value are specified in Table 1. The microchannel is madefrom polydimethylsiloxane (PDMS) and is bonded with aslide-glass. Platinum counter-type electrodes are attachedto the bottom wall. This channel has three inlets as shown in
Fig. 2(b); central-flow inlet and two side-flow inlets. RBC
suspension is supplied from the central-flow inlet. The twoside-flows produce a sheath flow that can control the spanwise positions of RBCs precisely by independently controlling the flow rate of side-flows. Further, backward-facing
and forward-facing steps are installed in the microchannel(cf. Fig. 2(a)) in order to control the height position of RBC
to be located close to the electrodes. This will enhance thesensitivity of the sensor because a high current density ofthe electric field is obtained in the area close to the electrodes.
As shown in Fig. 2(c), the electrodes are placed perpendicular to the flow. These electrodes consist of the sensor
and guard electrodes. The sensor electrodes used to measure the resistance are placed in the middle. The electrodes
located at both sides of the sensor electrodes are guard electrodes to which electric potential equal to the sensor electrodes is applied for the purpose of reducing the fringe effect of the electric field. Platinum black coating is appliedon all the electrodes to reduce the potential drop due to theelectric double layer formed on the electrode surfaces.

3. Experiment
Before discussing the numerical procedure and results ofthis study, the results of the measurement using the microsensor developed by the authors group are described in thissection to provide some information on the measurement
technology.

3.2. Experimental procedure and conditions
3.1. Microchannel and electrodes geometry

RBC solution and solvent are supplied to central-flow inlet and side-flow ones of the microchannel using syringes
and syringe pumps (Harvard Apparatus Co.; econoflo,

Figure 2 illustrates the schematic view of the microchannel and electrodes of micro-sensor. The dimensions of each2

Nihon-Kohden Co.; CFV-3200) with flow rates of 0.02 and
1.0µL/min, respectively. The complex impedance between
the sensor electrodes is measured as the RBC passes between them at 10kHz AC frequency, and the resistance isderived from the real part of this complex impedance.
Synchronized with the resistance measurement, thebehavior of the RBC is visualized using a microscope(OLYMPUS Co.; IX-71), ×100 objective lens (OLYMPUS
Co.; LMPLFLN100X), and a high speed video camera (Vision Research; Phantom V7.3). Flame rate and exposure
time of the camera are 1000fps and 99µs, respectively. The
spatial resolution and the focal depth of the video images
are 0.21µm/pixel and 1.7µm, respectively. Detail information on the apparatus and measurement method are described in the authors’ previous publication [7].
The deformation degree of the RBC is evaluated withthe video images to be compared with the resistance distribution. The deformation degree of the RBC is presented by
the deformation index, DI as defined by Eq. (1) [6]. a andb are the RBC’s lengths in x and y directions, respectively.
a−b
DI =
a+b

(a) Normal RBC(DI = 0.58)(b) Rigidized RBC(DI = 0.31)(c) Spherocyte(DI = 0.02)

Figure 3: Photographs of RBC with various DI passing
between the electrodes.

(1)

Table 2: Average values of the size and shape parameters.

Small amount of sample blood is collected from a single healthy human donor (one of the present authors). In
order to obtain RBCs with different deformability, three
types of RBCs are prepared in the experiment. The
first one is referred to as normal RBCs: The RBCs are
separated from other suspended materials by centrifugation (1000G) for 10 minutes. After removing the supernatant liquid, the deposit is suspended to 0.5mL phosphatebuffered saline (PBS) to which 10wt% polyvinylpyrrolidone (PVP) is added. The second sample is referred toas rigidized RBCs [8]: RBCs are separated by centrifugation (1000G) for 10 minutes. After removing the supernatant, the rest is suspended to buffer solution of A23187
ionophore (1µmol/L A23187, 1µmol/L CaCl2 , 10mmol/L
KCl, 130mmol/L NaCl, 2mmol/L MgCl2 , 15mmol/L tris,
pH=7.4). The buffer solution with RBCs is incubated at
37◦ C for 40 minutes. Then, the solution is centrifuged(1000G) for 10 minutes, and RBCs are suspended to 0.5mL
PBS with 10wt% PVP. The third RBC sample is the spherocyte: RBCs are separated by centrifugation (1000G) for 10
minutes, and are suspended in buffer solution of A23187
ionophore (1µmol/L A23187, 2µmol/L CaCl2 , 10mmol/L
KCl, 130mmol/L NaCl, 2mmol/L MgCl2 , 15mmol/L tris,
pH=7.4). This solution is incubated at 37◦ C for 40 minutes.
Then the RBCs are centrifuged (1000G) for 10 minutes, andare suspended to 0.5mL PBS with 10wt% PVP.
It should be noted here that PVP is added to the solutions in order to increase the fluid viscosity. This increases
the flow shear stress applied to the RBC under the same
flow rate condition, and increases the deformation degreeof the RBC. The viscosity of the solution measured by therheometer is 1.84 × 10−1 Pa·s.

Normal RBC
Rigidized RBC
Spherocyte

Samples
57
30
8

a [µm]
13.93
13.72
5.00

b [µm]
3.86
4.66
4.81

DI
0.56
0.48
0.02

3.3. Visualization results of RBCs
Figure 3 shows the photographs of the RBCs at time t = 0
that is the moment the RBC passes the center of the sensor electrodes. The photographs (a), (b) and (c) show theresults of the normal RBC (DI = 0.58), rigidized RBC(DI = 0.31), and spherocyte (DI = 0.02), respectively.
As shown in Fig. 3(a), the normal RBC is stretched in thestreamwise direction due to the shear stress of the flow. The
rigidized RBC shown in Fig. 3(b) is also deformed in xdirection similar to normal RBC, however, the deformation
degree is relatively smaller. Therefore, it is confirmed thatthe deformability of the rigidized RBC is decreased by therigidizing treatment. As for the spherocyte shown in Fig.
3(c), the RBC keeps its spherical shape in spite of the applied shear stress.
The average deformability index, DI, measured fromthe images is shown in Table 2 together with the averagevalues of a, b, and the sample number.
3.4. Electric resistance measurement
Figure 4 shows the distribution of the resistance variation,∆Rx , as the RBC passes between the electrodes in the casesof the typical results of the normal RBC, rigidized RBC andspherocyte. Note that the data is smoothed for analysis by
averaging adjacent 15 points. ∆Rx is defined as Eq. (2),3

flow the electric resistance will increase. Considering thenthat a RBC with larger DI has a longer streamwise length a,the RBC will start to interrupt the current flow at a streamwise position located further upstream compared with the
RBC with smaller DI. As a result, the width of the resistance distribution increases as DI increases. As one can see
in the figure and table, positive correlation between δ and
DI is observed; DI becomes larger as δ increases. These
results show that the deformation degree can be measured
by measuring the resistance distribution, and the feasibilityof this sensor is confirmed.
However, Figure 5 also shows relatively large variationin the δ distribution for each DI. One of the reasons of thisuncertainty is that the current density distribution is densein the area adjacent to the bottom wall and gradually decreases in the height direction. Even if RBCs passing between the sensor electrodes have the same DI, the amountof the current density interrupted by each RBC can change
when the RBC height position varies. It has been found inexperiments that the variation of the RBC height position isapproximately 1.7µm, and can influence the resistance distributions. Other reasons for the data uncertainty are: thedifference of individual RBC size with the same DI, thevariation of the RBC spanwise position and S/N ratio of
the resistance measurement. Among these influences, the
RBC height position and the electrode arrangement will be
discussed further in Section 4.

1.2
Normal RBC

1.0

Rigidized RBC

Rx / R 0

Spherocyte

0.8

0.6

0.4

0.2

0.0
-40

-20

0
x

RBC

20
[

40

m]

Figure 4: Relationship between the normalized resistancevariation and RBC streamwise position.

34
Normal RBC

32

Rigidized RBC

[ m]

30

Spherocyte

28
26
24
22
20
18
16
-0.1

0.0

0.1

0.2

0.3

DI

0.4

0.5

0.6

0.7

4. Numerical simulation

Figure 5: Relation between δ and DI.

As mentioned in Section 3.4, relatively large variation of δin each DI is considered to be attributed particularly to the
RBC height position and S/N ratio of the resistance measurement. It is, however, difficult to precisely evaluate theinfluences of these factors, and to suggest the improved design of the micro-sensor experimentally. It is, therefore, important to develop a numerical model that can simulate theresistance measured by the electrodes as the RBC passes
between them. In the following sections, the numericalmodel will be examined, and the results evaluating the influences of the RBC shape, RBC height position, and theelectrode arrangement on the resistance distribution will be
discussed.

Table 3: Average half-width δ for each type of RBC.
Normal RBC
Rigidized RBC
Spherocyte

Samples
57
30
8

δ[µm]
26.25
24.74
20.30

where R(xRBC ) and R(∞) are the resistances measured
at the moment when the RBC is located at xRBC and infinitely far from the electrodes, respectively. xRBC is thestreamwise position of the center of RBC and ∆R0 is ∆Rxof xRBC = 0.
∆Rx = R(xRBC ) − R(∞)

4.1. Numerical procedure and RBC model(2)

Three-dimensional finite element method (3D-FEM) simulation is carried out for the harmonic electric field formed
around the RBC and the electrodes placed in the microchannel using a commercially available 3D-FEM software COMSOL (COMSOL Multiphysics Co.). In the simulation, the governing equation shown in Eq. (3) is solved,
where V is the electric potential. ²0 and κ are relative permittivity and electric conductivity, respectively. ²0 is thevacuum permittivity, and f is the frequency of the supplied
potential.

Figure 4 shows the typical resistance distribution ofeach type of RBC. The bottom width of each peak is longer
in the order of, normal RBC, rigidized RBC and spherocyte.
Next, by analyzing the resistance distributions and comparing them with the visualization results, the relation between
the half-width of the ∆Rx peak height, δ, and DI for every
sample are obtained and plotted in Fig. 5. Further, the average half-width δ of each type of RBC is shown in Table 3.
The electric current flows from one side to the other side of
the sensor electrodes. When a RBC interrupts this current

5 · ((²0 − i4κ)5V)=02πf ²0

(3)

1.65

500

sus

analytical

400
sus
sus

numerical

analytical

1.60

sus

300
sus

numerical

Cytoplasm
Cellmembrane

sus

'

'

200

Cell
membrane

Red blood cell

1.55

100

0

3

10

Figure 6: Equivalent circuit model for an RBC.

4

10

5

6

10

²0cm
5

κcm [S/m]
1 × 10−7

tcm [nm]5dRBC [µm]
6.7

²0PBS
78.3

κPBS [S/m]1.67²0Glass
3.4

κGlass [S/m]
1 × 10−12²0PDMS
2.5

κPDMS [S/m]
1 × 10−122(1 − ν)²∗cm + (1 + 2ν)²∗cp(2 + ν)²∗cm + (1 − ν)²∗cp

ν=(dRBC − 2tcm 3
)
dRBC

κ
2πf ²0

9

10

[Hz]

0

(κcm + i2πf ²0 ²cm )(V out − Vin )J~ · ~n =tcm(7)

J~ [A/m2 ] is a current density that passes through the cellboundary. ~n is an unit normal vector of the RBC surface.
Vout [V] and Vin [V] are, respectively, the voltages at theapparent boundaries between the membrane and fluid, andbetween the membrane and cytoplasm. Obviously, thisboundary condition can be applied to the membranes of
RBCs with arbitrary shapes, and is effective for the present
computation.

(4)

(5)

4.2. Validation of the numerical model
In order to validate the model, the frequency dependenceof relative permittivity ²0sus and conductivity κsus of a domain filled with solvent is examined in the case that a single
RBC is suspended. The domain is a cubic with the lengthof 14.7µm, and the volume fraction of the RBC is 0.05.

dRBC and tcm are the diameter of the RBC and the membrane thickness, respectively. The complex relative permittivity ²∗ is defined as Eq. (6) in terms of the relative permittivity ²0 and the electrical conductivity κ. Table 4 indicates
relevant physical properties.
²∗ ≡ ²0 − i

810much smaller than the diameter of the cytoplasm, and directly solving this part in the computation is extremely difficult. Instead of using the composite complex permittivity
represented in Eq. (4), the boundary condition at the surface of the RBC is modified in the new model. In this case,the potential drop produced by the resistance and capacitance of the membrane is considered as Eq. (7) and applied
to the boundary between the cell and fluid.

The complex impedance Z ∗ that would be measured by
the sensor electrodes, is obtained from the complex electric
current passing through the electrode surfaces. The equivalent circuit of the RBC that consists of the cell membrane
and cytoplasm can be described as a parallel circuit of resistor and capacitor as shown in Fig. 6. Katsumoto [9] suggested a model that considered the cell as a sphere with uniform complex relative permittivity ²∗RBC . ²∗RBC was definedas Eq. (4) derived by Hanai using the relative permittivitiesof the cell membrane ²∗cm and cytoplasm ²∗cp .
²∗RBC = ²∗cm

10

Figure 7: ²∗sus (f ) of spherical RBCs suspended in PBS.

Table 4: Each parameter of RBC, PBS, Glass and PDMS.
κcp [S/m]
0.67

7

10

f

²0cp
50

[S/m]

'

The results are compared with analytical ones obtained
from Eq. (4), and are shown in Fig. 7. In the figure, the results obtained by the present model excellently correspondwith the analytical ones. This assures the validity of themodel. Further, conductivity of the suspension κsus sharply
increases approximately at f = 106 Hz showing the relaxation for high frequency AC electric field. This indicatesthat the RBC membrane acts as an insulating film in therange of relatively low frequency below 100kHz, and themeasuring frequency should be kept below this value in order to detect the resistance variation caused by the RBC
passing.

(6)This model has shown a good performance and amarked reduction of computational load by decreasing thegrid number. This model is, however, limited only to spherical cells and is not fully applicable for the present computation that should evaluate the influences of the RBC shape(deformation degree) on the electric field. In order to tackle
this problem, the following model is proposed in this study.
As mentioned previously, the RBC consists of cytoplasm and membrane. The thickness of the membrane is
51.0

Ellipsoidal shape (zGuard electrodeSpherical shape (z

= 4

m)

m)

RBC

0.5

HP D M S

PDMS

H2

RBC

z

HG l a s s

W/ 2

y

z RBC

R

x

/

R

0

Sensor electrode

= 4

RBC

x

w s /2
WC D

Glass

0.0

l s l sg l g

0

5

10

15

x

LC D

RBC

20

[

25

30

m]

Figure 9: Normalized resistance distributions of the RBC
streamwise position (RBC shape effect).

Figure 8: Computational domain of counter-type electrodes.

1.0

Ellipsoidal shape (z

= 4

m)

Ellipsoidal shape (z

= 5

m)

RBC

Table 5: Dimensions of the computational domain.
W [µm]
1000

HPDMS [µm]100

HGlass [µm]100

H2 [µm]10ls [µm]12lg [µm]20

lsg [µm]
4

ws [µm]
6

R

WCD [µm]
700

0.5

R

x

/

LCD [µm]
800

0

RBC

0.0

0

5

10

Ellipsoidal shape
Spherical shapea [µm]
14
6.7

b [µm]
4
6.7

15

x

Table 6: Values of size and shape parameter.

RBC

20

[

25

30

m]

Figure 10: Normalized resistance distributions of the RBC
streamwise position (height effect in ellipsoidal RBC case).

DI
0.55
0.00

1.0

Spherical shape (z

= 4

m)

Spherical shape (z

= 5

m)

15

25

RBC

RBC

/

R

0

4.3. The influence of the RBC height position on the resistance distribution

0.5

R

x

Numerical simulations on the resistance measurement using the present sensor will be conducted now. As discussed
in Section 3.4, the measurement variation against each DI
is relatively large, and the sensitivity of the half-width δfor DI is small. It is, therefore, required to improve thesensitivity of the present sensor considering the practicaluse in the medical field. The major factors that influence
the sensitivity and measurement variation are believed tobe the height position of the RBC, and electrode width andarrangement. Among these parameters, the effects of the
RBC height position zRBC and the electrode arrangement
will be discussed in the present computation.
The computational domain is shown in Fig. 8 with thecoordinates and parameters. The dimensions are tabulated
in Table 5. The domain includes the channel top wall madeof PDMS and the bottom wall made of glass. Relative permittivity ²0cp and conductivity κcp of the RBC, PDMS, andglass employed in the computation are listed in Table 4.
The electrode thickness is set as zero. Symmetric boundary conditions are applied in the x-z plane at y = 0, and 0V
conditions are applied to the streamwise boundaries. 0.5V
is applied to the surface of the electrodes with a frequency

0.0

0

5

10

x

RBC

20

[

30

m]

Figure 11: Normalized resistance distributions of the RBC
streamwise position (height effect in spherical RBC case).
Table 7: zRBC and RBC shape effects on δ and ∆R0 .
δ

6zRBC [µm]4.05.0Ellipsoidal shape [µm]
16.5
17.5

zRBC [µm]
4.0
5.0

∆R0
Ellipsoidal shape [Ω]Spherical shape [Ω]
4.46×103
6.64×103
3.93×103
4.86×103

Spherical shape [µm]
14.7
15.6

of 10kHz. In order to obtain the complex admittance andthe resistances of the region located between the oppositefacing sensor electrodes, complex currents distributed on
the surface of the sensor electrode are integrated and divided by the applied voltage 1V.
The streamwise position of the RBC is varied fixing the
spanwise position at y = 0 to simulate the resistance distribution as the RBC passes the electrodes. Two different
RBC shapes, ellipsoid and sphere, are considered in thecomputation in order to discuss the influence of the RBC
deformation degree on the resistance distribution. In thiscase, the RBC shape is changed keeping the surface area of
the RBC constant. The streamwise and spanwise lengths aand b, and the DI of these RBCs are shown in Table 6.
The influence of the RBC shape on the resistance distribution is first discussed here setting the height positionsof both RBC shapes as zRBC = 4µm. Figure 9 shows the∆Rx /∆R0 distributions against the streamwise position of
the RBC, xRBC . The distribution shows that the ellipsoidal
RBC produces a wider distribution and half-width δ of the
distribution is greater than the one observed in the spherical
RBC case. This trend corresponds well with the experimentshown in Fig. 4.
Next, the influence of the RBC height position zRBC
on the resistance distribution is discussed. Figures 10 and
11 show the relationship between the ∆Rx /∆R0 and xRBC
in the cases of ellipsoidal and spherical RBCs. Table 7
shows the half-width δ of the ∆Rx /∆R0 distribution and∆R0 that presents the maximum value of ∆Rx . It should
be noted that the height zRBC = 5µm is considered in thiscomputation on basis of the fact that the variation of zRBC
was approximately ±0.85µm in the experiment.
As shown in Table 7, the maximum value ∆R0 increases as zRBC decreases. As mentioned previously, thecurrent density distribution of the region located between
the electrodes increases with a decrease in zRBC which iscorrelated with the distance of the RBC center from the sensor surface. Therefore, in the case of smaller zRBC , theRBC will pass close to the sensor electrodes in the area ofmuch higher current density distribution leading to a greater
value of the measured resistance. The ∆Rx /∆R0 distributions shown in Figs. 10 and 11, differ comparing the casesof zRBC = 4 and 5µm. The decrease of ∆Rx depending onzRBC will decrease the S/N ratio of the measured signal anddeteriorate the sensor sensitivity. This results in the variation in the half-width δ as shown in Table 7. The variationof δ due to the change of the RBC height position will becomparable with the difference of δ caused by the change
in the RBC shape (= DI) shown in Fig. 9. Thus, the variation of the RBC height position can greatly influence themeasurement sensitivity and uncertainty.

Guard electrodeSensor electrode

HP D M S

W1

PDMS
z

H2
HG l a s s

W2

y
x

WC D

Glass

l s l sg l g
LC DFigure 12: Computational domain of the cross-over typeelectrodes.
1.0

Spherical shape (z

= 4

m)

Spherical shape (z

= 5

m)

RBC

0.5

R

x

/

R

0

RBC

0.0

0

5

10

15

x

RBC

20

[

25

30

m]

Figure 13: Normalized resistance distributions of the RBC
streamwise position (height effect in spherical RBC case).

Table 8: Numerical result of the cross-over type sensor.
zRBC [µm]4.05.0δ [µm]
13.9
14.0∆R0 [Ω]
7.55×103
7.32×103

trode width and increase the S/N ratio of the measurement.
Another solution is to change the electrode arrangementthat will be discussed in this section.
Figure 12 shows the electrode arrangement consideredin this study. The electrodes are attached to the channel top
and bottom walls to form an electric field mainly along thez-axis in the area between the electrodes. The current density in the area becomes relatively uniform in the height direction which indicates that the measured resistance is lessinfluenced by zRBC . It should be noted that it is importantto carefully design the overlapping area of the upper andlower electrodes. If the area becomes too larger than thesize of the RBC, the resistance variation ∆Rx decreases.
On the other hand, if the area becomes too small, it will bedifficult to control the spanwise position of the RBC.
To evaluate the suggested electrode arrangement, thenumerical computation on the domain shown in Fig. 12
is carried out. The additional dimensions of the domain are
specified in the following; W1 = 497µm, W2 = 5µm. Other
dimensions of channel and electrodes are the same as Fig.

4.4. Electrode arrangement to increase the sensor sensitivity
As shown in the previous section, it was found that the RBC
height position zRBC influences the sensor sensitivity. Oneof the solutions to tackle this problem is to change the elec7

Acknowledgement

8. The boundary conditions and computational methods arealso the same as those shown in Section 4.3.
Figure 13 shows the normalized resistance ∆Rx /∆R0
distributions in the case of the spherical RBC. Table 8shows δ and ∆R0 values. The results of zRBC = 4 and 5µm
are shown in the figure and table. The results shown in Fig.
13 indicate that the influence of zRBC on the ∆Rx /∆R0
distribution is much smaller compared with the case of theelectrodes attached to the channel bottom wall. Actually,
the half-width δ of both cases shown by the line in the figure
are almost identical. Further, the ∆R0 values show greater
values compared with those shown in Table 7. These results show that the sensor sensitivity and accuracy can bemarkedly improved by attaching the electrodes to the top
and bottom walls providing a more uniform current density
distribution.

This work was financially supported by the Ministry of Education, Culture, Sports and Science and Technology ofJapan.

References

5. Conclusions
An electric micro-resistance sensor that could measure thedeformability of RBC in a microchannel was fabricatedand the feasibility of micro-sensor was evaluated using normal, rigidized RBCs and spherocytes. Further, a numericalmodel that considers the resistor and capacitor of the cell
membrane as boundary specific conditions was developed.
Using this model, the influences of the RBC height position and sensor electrode arrangement were discussed. The
major results are as follows:• Rigidized RBCs and spherocytes could be preparedusing Ca2+ and A23187.
• A correlation between the half-width δ of the measured resistance distribution and the deformability index DI of RBC was observed. The feasibility of thepresent sensor was confirmed from these measurements.
• The proposed numerical model introducing theequivalent electric circuit of the RBC by considering
the potential drops produced by the resistance and capacitance of the membrane was validated comparing
the results of electric characteristics of a suspended
RBC with the analytical ones.
• The variation of δ due to the RBC height position
was comparable with the difference of δ by changing the RBC shape. The results showed that one of
the reasons was attributed to the fact that both of thesensor electrodes were attached to the bottom wall.
This electrode arrangement resulted in the decay ofthe electric field in the height direction. The uniform
electric field which was formed by a new arrangement of electrodes attached to the top and bottom
wall decreased the variation of δ and improved thesensor sensitivity.

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