Proceedings of the2nd International Forum on Heat Transfer
September 17-19, 2008, Tokyo, Japan

MEASUREMENT OF DEFORMABILITY OF A SINGLE RED BLOOD CELLIN MICRO-CHANNELS WITH HIGH SHEAR FLOWSUSING AN I-V METHOD
Yoichi KATSUMOTO*, Tatsuki DOI*, Kazuya TATSUMI* and Kazuyoshi NAKABE** Kyoto University, Kyoto 606-8501, Japan
E-mail : yoichi.katsumoto@fy7.ecs.kyoto-u.ac.jp
Keywords : Micro-channel, Red Blood Cell, Deformability, Micro Electric Resistance Sensor.
ABSTRACT
Deformability of a single red blood cell (RBC) flowing in amicro-channel is measured by analyzing the electric resistancedetected between the membrane-type counter-electrodes of
micro sensors mounted onto the channel bottom wall, whererelatively large deformation of RBC is expected due to the highshear flow layers. In the first half of this work, the electric field
and resistance between the electrodes under the conditions ofwith and without RBC were evaluated by numerical simulation
to design the channel geometry and sensor arrangement. In thelater part, the experiment was made in which the deformabilityof RBC was measured by analyzing the time series of theelectric resistance obtained by the sensors using an I-V methodwith a frequency of 10kHz.
1. INTRODUCTION
Micro-channels are one of the useful tools to produce highshear flows and to deform RBCs. In combination withmicroscopic image acquisition, the RBC deformation can bevisualized directly (Korin, 2007). This kind of image-based
analyzing systems, however, has a disadvantage in practical use
considering their throughput and compactness. On the contrary,electrically analyzing systems, such as a coulter counter for cellcounting (Tang, 2005) and a dielectric spectroscopy for physicalquantification of individual cells (Gawad, 2004), can monitor
RBCs’ behaviors with a fast succession of quantitative signals.
In the present method, the RBC deformability is evaluatedfrom the electric resistances of RBCs passing between the
counter-electrodes-type membrane sensors attached to thebottom wall of a micro-channel (see Fig. 1). High shear rate
flows are applied to the RBC where the RBC changes its shape
into ellipsoidal body, depending on its elastic modulus. The
pattern of the resistance signal is believed to be unique to theshape of the RBC, and, therefore, the pattern is analyzed torepresent the deformability of each RBC.

2. SIMULATION
Three-dimensional FEM simulation was conducted for the
3D harmonic electric field under the conditions of with/without
RBC using ANSYS (ANSYS Inc.). RBC solution is aheterogeneous system consisting of solvent and cytoplasm of
micro-scale and cell membrane of nano-scale. In order to avoid
the difficulties of handling such a discrepancy of the scales in
the computation, RBC was treated as a spherical or ellipsoidal
solid having frequency-dependent uniform complex permittivity,
which was analytically derived from Maxwell-Wagner equation.
Under the above assumptions, the frequency dependent
impedance between the electrodes was calculated with highaccuracy. The numerical conditions are tabulated in Table 1 andalso Fig. 2.
Figure 2 shows how the deformation index, DI, affects therelation between the resistance variation, R, and thestreamwise position of the RBC center, xRBC. DI is defined as(a-b)/(a+b), where a and b are the major and minor axes ofRBC, respectively. The case without the guard electrodes, which
was placed to increase the sensor sensitivity, is also plotted in
the figure for comparison. R takes a maximum peak at xRBC =0 and decreases as xRBC increases. The maximum value and thewidth of the R distribution increase as DI increases. This is
ascribable to the increase of a and streamwise-cross-sectional
area of the RBC obtained under the conditions of larger DI
indicating larger deformation of RBC.
The relation between DI and the integrated area of R, Apeak,is plotted in Fig. 3. Apeak increases linearly with an increase inDI. These results indicate the validity of evaluating thedeformability of a single RBC by measuring the pattern of R.
Further discussions on the effects of other parameters, suchas H2, h, and ws will be shown in the poster.

Flow direction

Shear flow

R

CaseA : Normal RBC

τA

ΔR A
Shear stress

Tim eτ
BR

CaseB : Disordered RBC

ΔR BSensor electrodes
Tim eFig. 1 Concept of the measurement for the RBC deformability.

Fig. 2 Relation between the resistance and the cell streamwise
displacement from the center of sensor electrodes.

Proceedings of the2nd International Forum on Heat Transfer
September 17-19, 2008, Tokyo, Japan
Table 1 Parameters employed in the simulation & experiment.

Fig.3 Correlation between the area of R/R, Apeak, and DI.
3. EXPERIMENT
Figure 4 shows the schematic view of the channel used in
the experiment. The geometrical conditions of channel are
specified in Table 1, whose dimensions are same as employed in
the numerical simulation. A forward step and side-flows were
installed in the channel to control the position of RBC to closely
pass the sensing area. RBC from human blood was suspended inthe solvent (phosphate-buffered saline with poly-vinylpyrrolidone), and then this RBC solution was supplied to thecentral channel, while only solvent to the side-flows.
Figure 5 shows the temporal profiles of R obtained by theelectric sensors in the preliminary experiments. Each major
peak in the distributions indicates the period when an individual
RBC crosses the sensor. Apeak was estimated using R, thedifference from the baseline of the signals for each RBC. The
images of RBCs are measured simultaneously by a high-speed
camera, and the DI of individual RBCs are obtained from theseresults. The correlation function between Apeak and DI is thencalculated and applied to the final validation experiment. Moredetails on the present method will be discussed in the poster.
Side flows

OutletBlood

Pt Electrodes
PDMS
Glass Plate(a) A bird’s eye vieww g d ws
Side flows
D

H1
H2

BloodhW
Main sensor

GuardSensor( b ) Top view( c ) Side viewFig.4 Schematic view of the micro-channel and Pt electrodes.

Fig.5 Time series of the resistance between the electrodes.

Parameter

Dimensions

Channel width, WChannel height, H1
Channel height at the sensor, H2
Height of the RBC’s center, hVolume of deformed RBC, V

1000m50m
15m
5m
34 3 3  m
3Distance between the electrodes, DDist. between the sensor and guard, dWidth of the sensor electrodes, ws
Width of the guard electrodes, wg

10m
10m
15m
10m

REFERENCES
Korin, N., Bransky, A., and Dinnar, U., Theoretical model andexperimental study of red blood cell deformation inmicrochannels, J. Biomech., vol. 40, no. 9, pp. 2088 – 2095,
2007.
Tang, H. and Gao, Y., An impedance microsensor with coplanarelectrodes and vertical sensing apertures, IEEE Sensors J., vol.
5, no. 6, pp. 1346 – 1352, 2005.
Gawad, S., Cheung, K., Seger, U., Betsch, A., and Renaud, P.,
Dielectric spectroscopy in a micromachined flow cytometer:
theoretical and practical considerations, Lab Chip, vol. 4, pp.
241 – 251, 2004.
Y. Katsumoto received M.E. (2001) inKyoto Univ. Dept. Mech. Eng. He is now aPhD course student of Dept. of Mech.
Engineering and Science, Kyoto Univ. Hisinterests include nondestructive sensing of
biological cells and biopolymer, andthermo-fluid dynamics involved in them.
T. Doi received the B.E. (2007) in Kyoto
Univ. and is now in the 2nd-year of Mastercourse of Dept. of Mechanical Engineeringand Science, Kyoto Univ.
His
current
interests
includemeasurements of fluid flow and blood cells
in micro channels.
xxxxx
K. Tatsumi received M.E. (1999) and PhD(2003) in Kyoto Univ. Dept. Mech. Eng. He
is now an Assistant Professor of Dept. ofMech. Eng. and Science, Kyoto Univ. His
current interests include measurements andsimulations of micro biological flows,multi-jets and compact heat exchangers.
K. Nakabe received M.E. (1983) in Kyoto
Univ. Dept. Mech. Eng. and PhD (1991) inOsaka Univ. Dept. Mech. Eng. He is now aProf. of Dept. Mech. Eng. & Science, Kyoto
Univ. His current interests are in the fieldsof turbulent mixing, micro fluidics, heattransfer and combustion.