Effect of Couette Type of Shear Flow by Rotating Disk on
Migration of Cell
Hiromi SUGIMOTO, Haruka HINO, Shigehiro HASHIMOTO, Yusuke TAKAHASHI
Biomedical Engineering, Department of Mechanical Engineering,
Kogakuin University, Tokyo, 163-8677, Japan
http://www.mech.kogakuin.ac.jp/labs/bio/
ABSTRACTAn experimental system with a rotating disk has been designed
to apply wall shear stresses on the cell during incubation in
Couette type of flow at the microscopic observation in vitro.
The rotating disk system is mounted on the stage of an inverted
phase contrast microscope to observe cells adhered on the plate
under the shear flow (shear stress lower than 1.5 Pa). The
migration of cells was evaluated at the time lapse images (every
five minutes for 24 hours). The experiments on four kinds ofcells show the following results. Under the shear flow (shear
stress < 1.0 Pa), C2C12 (mouse myoblast cell line) migrates tothe diagonal direction of the stream-line at 1.0 Pa, HUVEC(human umbilical vein endothelial cells) actively migrates at
random at 1 Pa, 3T3-L1 (mouse fat precursor cells) migrates tothe random direction, and L929 (fibroblast connective tissue)
migrates in short distance. At 1.5 Pa, both C2C12 and
HUVEC migrate to the downstream. The effect of shear flowon migration of the cell depends on kinds of cells. The
designed system is useful to trace cells under the quantitatively
controlled wall shear stresses.

formation. The mild shear flow with the wall shear stress < 1
Pa, on the other hand, might accelerate migration, proliferation,and secretion of materials, which make the extracellular matrix.
In the previous study, cells were exposed to the shear flow in adonut-shaped open channel, and the effect of flow stimulation
on cultured cells has been studied in vitro [6, 11]. When theflow has an open surface, it is difficult to estimate the shear
stress in the fluid.
Between two parallel walls, on the other hand, the velocity
profile is easily estimated in the laminar flow. In the previous
studies, several preparations were designed to study the effectof mechanical stimulations on biological cells: rhombus [7],cross [8], and rotating disks types [5, 12].
In the present study, an experimental system of the Couette typeflow with a rotating disk has been designed to apply wall shear
stress quantitatively on the cell during incubation at the
microscopic observation in vitro, and the effect of the shear
flow on the migration of the cell has been studied.

Keywords: Biomedical Engineering, Cell Culture, Shear Stress,
C2C12, Couette Flow and Migration.

1. INTRODUCTION
The mechanical stimulation is one of the interested points in theenvironment of cells, because they receive mechanical forces invivo. The mechanical stimulation on cells might induce
various responses: deformation, migration, proliferation, anddifferentiation. Several methods have been designed to apply
the mechanical stimulation to cells in vitro [1-23].

2. METHODS
Rotating Parallel Disk System
In the present study, a rotating parallel disk system is selected tomake Couette type of flow (Fig. 1). The fluid is sheared
between a rotating disk and a stationary disk. The stationary
disk is the bottom of the culture dish (diameter 60 mm, Iwaki,
Japan) (Fig. 2).
In the system, the shear rate (γ) is calculated by Eq. 1.
γ=rω/dA transmission point of the stress to a specimen is important.
In many studies, the stress is applied to a scaffold [1, 2].
When fixation between the cell and the scaffold is not enough,the stress is not transmitted to the cell. A field, on the other
hand, is effective to transmit stimulation to the cell placed in thefield: the electric field [24], the magnetic field [25], thegravitational field [3], or the flow field [5-23]. The flow canbe used to apply a stress field to a specimen. The cells
exposed to the flow directly receive the shear stress in the shear
flow.
The high shear flow might deform a cell, peel off a cell from thescaffold [6-10], and inhibit proliferation as well as tissue(1)

In Eq. 1, ω is the angular velocity [rad s－1], and d is the
distance [m] between the moving wall and the stationary wall(Fig. 1). In the rotating parallel disk system, the shear rate (γ[s－1]) increases in proportion to the distance (r [m]) from therotating axis.
The rotating speed is controlled by the stepping motor between
50 rpm and 300 rpm, which makes variation of angular velocity
ω between 5.2 rad s－1 and 31 rad s－1. The position for theobservation has the variation on r (the distance from the rotatingaxis) between 12 mm and 18 mm.

system allows observation of cells during exposure to the shear
flow.
Cell Culture
Four kinds of cells were used in the experiment: C2C12 (mouse
myoblast cell line originated with cross-striated muscle of C3Hmouse), L929 (fibroblast connective tissue of C3H mouse),
3T3-L1 (mouse fat precursor cells, a cell line derived from cellsof mouse 3T3), and HUVEC (human umbilical vein endothelial
cells).

Fig. 1: Couette flow between rotating disk and stationary disk.
Motor

C2C12 of the passage between three and nine was cultured in
D-MEM (Dulbecco’s Modified Eagle’s Medium) containing
10% decomplemented FBS (fetal bovine serum) and 1%
penicillin/ streptomycin.
HUVEC of the passage between three and eight was cultured in
EBM-2 (Endothelial Cell Basal Medium) containing 2%
decomplemented FBS (fetal bovine serum).

Bearing
Pulley3T3-L1 of the fifth passage was used for the cell culture.
D-MEM (Dulbecco’s Modified Eagle Medium) containing 10%
decomplemented FBS (Fetal Bovine Serum) and 1% penicillin/
streptomycin was used for the medium.
Culture dishMediumRotating disk

Fig. 2: Cell culture device with rotating disk.

L929 of the passage between three and nine was cultured in
D-MEM (Dulbecco’s Modified Eagle’s Medium) containing
10% decomplemented FBS (fetal bovine serum) and 1%
penicillin/ streptomycin.
A hemocytometer (Burker-Turk) was used to count number ofcells. The cells were seeded on the dish coated with collagenat the density of 2000 cells/cm2. The dish was placed in therotating parallel disk system mounted in the incubator(LCV-110SK). To make adhesion of cells to the bottom of thedish, the cells were cultured for 24 hours in the incubator
without flow stimulation (without rotation of the disk).
After the incubation for 24 hours, the cells were sheared withthe rotating disk for 24 hours in the incubator (Fig. 4).
Variation was made in the rotational speed of the disk: 100, 200,
and 300 rpm.

Fig. 3: Couette flow device in incubator.

The distance d is estimated to 0.5 mm from the positions of the
focus of the walls at the microscope. These variations makethe shear rates (γ) between 0.12×103 s－1 and 1.1×103 s－1 (seeEq. 1).
The shear rate (γ) generates the shear stress (τ [Pa]) in a viscous
fluid.
τ=ηγ
In Eq. 2, η is the viscosity of the fluid [Pa s].
medium of cell culture in the present study.

(2)
The fluid is theMicroscopic Observation
The several positions are marked by grooves on the outside
surface of the culture dish to trace the same position of thescaffold.
The time-lapse image was taken every five minutes during therotation for 24 hours.
The direction of the flow adjacent to the culture plate is tracedby the floating particle in the medium at the video image, anddefined as the x axis in Figs. 7-10.

When the viscosity of the fluid η is 0.0015 Pa s (at 310 K), theshear stress τ varies between 0.18 Pa and 1.7 Pa.
The rotating disk system is mounted on the stage of the inverted
phase contrast microscope mounted in the incubator(LCV-110SK, Olympus Co., Ltd., Tokyo) (Fig. 3). In the
incubator, both the temperature and the partial pressure ofcarbon dioxide are maintained at 310 K and 5 percent,respectively. The behavior of cells adhered on the stationary
wall under shear stress is observed with the microscope. The

24 hour 24 hour

24 hour
48 hour

Control
Experimental
Seeding
Fig. 4: Experimental protocol.

Rest
Stimulation

Both at 0.5 Pa and at 1 Pa, HUVEC actively migrates to every
direction including the perpendicular and the counter directionof the flow (Figs. 7b & 7c). HUVEC migrates to the down
stream at the wall shear stress of 1.5 Pa (Fig. 7d). 3T3-L1
migrates to the random direction at the wall shear stress of 1 Pa
(Fig. 8).
L929 migrates within the short distance toperpendicular direction of the stream line at the wall shear stressof 1 Pa (Fig. 9).

Fig. 5: Migration of C2C12: cell contour of red, shear for 3
hours; cell contour of yellow, shear for 12 hours.

At the microscopic image, the contour of each cell wasapproximated to ellipsoid. The centroid of each cell was used
to trace the migration of the cell (Fig. 5).

3. RESULTSIn Figs. 6-9, the direction of the flow is from left to right along
the x axis. The y axis shows the direction of the center of therotation. The wall shear stress is proportional to the wall shear
rate, so that the wall shear stress decreases with y cordinate.
The coordinate of the origin shows the original position of eachcell. To tarce the migration of each cell, the image of cellevery one hour has been selected from the time lapse image
every five minutes. Each polygonal line in Figs. 6-9 shows theconnected line segments of the centroid of each cell traced
every hour.

Fig. 6b: Migration of ten cells (C2C12) under shear flow: wall
shear stress of 0.5 Pa. Micrometer.

Each cell migrates on the cuture plate (on the scaffold) torandom direction without flow (Fig. 6a). At the wall shear
stress of 0.5 Pa, C2C12 migrates to every direction including
the counter direction (to the left in Fig. 6b) of the flow. At thewall shear stress of 1 Pa, C2C12 migrates to the oblique
direction: along the flow direction, and to the center (to thelower wall shear stress area). At the wall shear stress of 1.5 Pa,
C2C12 migrates to the down stream.
Fig. 6c: Migration of ten cells (C2C12) under shear flow: wall
shear stress of 1 Pa. Micrometer.

Fig. 6a: Migration of ten cells (C2C12) without flow.
Micrometer.

Fig. 6d: Migration of ten cells (C2C12) under shear flow: wall
shear stress of 1.5 Pa. Micrometer.

Fig. 7a: Migration of ten cells (HUVEC) without flow

Fig. 7b: Migration of ten cells (HUVEC) under shear flow: wall
shear stress of 0.5 Pa. Micrometer.

Fig. 7c: Migration of ten cells (HUVEC) under shear flow: wall
shear stress of 1 Pa. Micrometer.

Fig. 7d: Migration of ten cells (HUVEC) under shear flow: wall
shear stress of 1.5 Pa. Micrometer.

Fig. 8: Migration of ten cells (3T3-L1) under shear flow: wall
shear stress of 1 Pa.

Fig. 9: Migration of ten cells (L929) under shear flow: wall
shear stress of 1 Pa.

4. DISCUSSION
In the previous study, myotubes make orientation perpendicular
to the stream line in the donut-shaped flow system. The
donut-shaped open channel is convenient to study the effect offlow direction on the cell culture [6, 11], but it is not easy toestimate quantitatively the shear stress in the fluid because of
the free surface.
Hagen-Poiseulle type of flow is convenient to estimate the shear
stress on the wall with the parabolic velocity distribution for
Newtonian fluid. The flow in the cylindrical pipe, and theflow between the parallel plates are typical preparations forHagen-Poiseulle flow. The rhombus (variation of wall shearrate) [7], the cross (variation of flow direction) [8], and thetilting (flow and gravity) [9] types are variations to study theeffect of mechanical stimulations on biological cells.
The Couette type of flow is also convenient to estimate theshear stress in the flow with the uniform shear rate between themoving wall and the stationary wall, which is also available tonon-Newtonian fluid. Many kinds of the devices of Couette
type flow were designed for quantitative experiments ofbiological fluid in the previous studies [5, 12]. The cone andplate type device has the uniform shear field in the entire space
between the rotating cone and the stationary plate. The clot
formation was quantitatively studied between the rotating cone
and the stationary plate [26], and between the rotating concave
cone and the stationary convex cone [27]. The erythrocyte
destruction was studied between the rotating concave cone andthe stationary convex cone [17].
A parallel disks system does not have the uniform shear field in
the entire space between rotating disk and the stationary disk.
The parallel disks system, on the other hand, has several
advantages: stability of the rotating motion of the disk, stabilityof the optical path for the microscopic observation,
morphologic preciseness of the plane of the disks, andsimultaneous observation over the range of variation of shear
rate proportional to the radius from the rotational axis. The
erythrocyte deformation was observed between counter rotating
parallel discs [18, 19]. In the present study, the rotating
parallel disk system is selected to make Couette type of flow
instead of the cone and plate system.
At the constant angular velocity of 31 rad s－1 (d = 0.5 mm), theshear rate (γ) increases from 0.73×103 s－1 to 1.12×103 s－1,
when the distance from the axis (r) increases from 12 mm to 18
mm in the observation area (Eq. 1). The gradient of shear
stress (0.6 Pa / 0.006 m = 102 Pa m－1) enables the simultaneous
observation of the behavior of cells related to variation of theshear stress (1.1 Pa - 1.7 Pa) in the same view [5, 12]. The
migration speed is slower than 1 mm / 24 hour = 10 －8 m/s.
The rotating flow induces the secondary flow by the centrifugal
effect. The effect is smaller in the system with the rotation ofouter concave cone than with that of inner convex cone. The
effect decreases with the decrease of the rotational speed. The
rotational speed of the disk is smaller than 0.7 m s-1 in thepresent system. The microscopic image of the flowing cells
between the rotating disk and the stationary disk does not show
turbulent flow. Reynolds number (Re) is calculated by Eq. 3.

In Eq. 3, ρ is density of the fluid [kg m － 3], v is thecircumferential velocity [m s－1], ω is the angular velocity [rad s－1], r is the distance [m] from the rotating axis, d is the distance[m] between the moving wall and the stationary wall, and η isthe viscosity of the fluid [Pa s]. Re is 1.4×102, when ρ, r, ω, d,and η are 1×103 kg m－3, 0.018 m, 300 rpm=31 rad s－1, 0.0005
m, and 0.002 Pa s, respectively. The turbulent flow may notoccur in the flow of small value of Reynolds number. The
steady actual flow direction adjacent to the scaffold surface ofcell culture has been confirmed by the stream line traced by the
direction of exfoliation of the cell and of the moving particle
adjacent to the surface.
Endothelial cells are exposed to the shear flow in the bloodvessels in vivo. The effect of shear flow on endothelial cells
was investigated in the previous studies [11, 20-23]. Cells are
not exfoliated under the shear flow at the wall shear stress lower
than 1.5 Pa. Cells were exfoliated at the higher wall shear
stress in the previous studies [6-10].
A biological cell shows passive and active behaviors in anenvironment. While the flow might enhance the cell migration
to the downstream, a cell migrates to adapt the shear field.
While the strong stimulation above the threshold damages thecell, the stimulation below the threshold remains in the cell as amemory for the response in the next step. The hysteresis
effect governs the active behavior of the cell. The interaction
between cells also governs the behaviou of each cell. The
seeding density is selected not so high to trace the image ofeach cell in the present study. The migration of the cell mightalso depends on the morphology and the mechanical property ofthe scaffold [28-30]. At the cell division, migration of twosegments to the counter direction each other is observed in thepresent study.
The temperature in the medium after
stimulation of the shear flow for 24 hours was measured by thethermocouple. The result shows the temperature is the samelevel of 310 K and is not elevated by the heating effect of theshear flow.
In the present study, each cell migrates independently to every
direction includes the counter direction of the flow. The mostof myoblasts tend to migrate to the oblique direction of thelower shear stress field at 1 Pa. The effect of shear flow on
migration of the cell depends on the kind of cells, which might
be applied to the cell sorting technology.

5. CONCLUSION
An experimental system with a rotating disk has been designed
to apply shear stresses on the cell during incubation in Couette
type of flow at the microscopic observation in vitro. The
experiments show the following results. Under the shear flowat the constant shear stress of 1 Pa for 24 hours, C2C12
migrates to the diagonal direction of the stream-line, HUVEC
migrates along the stream-line, 3T3-L1 migrates to the random
direction, and L929 migrates in short distance. The effect ofshear flow on migration of the cell depends on kinds of cells.
The designed system is useful to trace cells under thequantitatively controlled wall shear stresses.

6. ACKNOWLEDGMENT
Re = ρ v d / η = ρ r ω d / η(3)This work was supported by a Grant-in-Aid for Strategic

Research Foundation at Private Universities from the Japanese
Ministry of Education, Culture, Sports and Technology.

REFERENCES[1] J.H.-C. Wang, E.S. Grood, J. Florer and R. Wenstrup,“Alignment and Proliferation of MC3T3-E1 Osteoblasts in
Microgrooved Silicone Substrata Subjected to Cyclic
Stretching”, Journal of Biomechanics, Vol. 33, No. 6, 2000,
pp.729-735.
[2] G. Yourek, S.M. McCormick, J.J Mao and G.C. Reilly,“Shear Stress Induces Osteogenic Differentiation of Human
Mesenchymal Stem Cells”, Regenerative Medicine, Vol. 5,
No. 5, 2010, pp. 713-724.
[3] S. Hashimoto, H. Hino and T. Iwagawa, “Effect of Excess
Gravitational Force on Cultured Myotubes in Vitro”,
Journal of Systemics, Cybernetics and Informatics, Vol.
11, No. 3, 2013, pp. 50-57.
[4] H. Hino, S. Hashimoto, Y. Takahashi and H. Nakajima,“Effect of Ultrasonic Vibration on Proliferation and
Differentiation of Cells”, Journal of Systemics,
Cybernetics and Informatics, Vol. 14, No. 6, pp. 1-7, 2016.
[5] H. Hino, S. Hashimoto, Y. Takahashi and M. Ochiai, “Effectof Shear Stress in Flow on Cultured Cell: Using Rotating
Disk at Microscope”, Journal of Systemics, Cybernetics
and Informatics, Vol. 14, No. 4, 2016, pp. 6-12.
[6] S. Hashimoto, F. Sato, H. Hino, H. Fujie, H. Iwata and Y.
Sakatani, “Responses of Cells to Flow in Vitro”, Journal of
Systemics Cybernetics and Informatics, Vol. 11, No. 5,
2013, pp. 20-27.
[7] F. Sato, S. Hashimoto, T. Yasuda and H. Fujie, “Observationof Biological Cells in Rhombus Parallelepiped Flow
Channel”, Proc. 17th World Multi-Conference on
Systemics Cybernetics and Informatics, Vol. 1, 2013, pp.
25-30.
[8] H. Hino, S. Hashimoto, Y. Takahashi and S. Nakano,“Design of Cross Type of Flow Channel to Control
Orientation of Cell”, Proc. 20th World Multi-Conference
on Systemics Cybernetics and Informatics, Vol. 2, 2016,
pp. 117-122.
[9] H. Iwata, S. Hashimoto, S. Okuda and H. Nakaoka, “Effectof Medium Flow on Cultured Cells”, Proc. 14th World
Multi-Conference on Systemics Cybernetics andInformatics, Vol. 2, 2010, pp. 265-268.
[10] H. Hino, M. Ochiai, S. Hashimoto, K. Kimura, Y.
Takahashi and T. Yasuda, “Effect of Wall Shear Stress in
Flow on Myoblast”, Proc. 19th World Multi-Conference
on Systemics Cybernetics and Informatics, Vol. 2, 2015,
pp. 246-251.
[11] S. Hashimoto and M. Okada, “Orientation of Cells Cultured
in Vortex Flow with Swinging Plate in Vitro”, Journal of
Systemics Cybernetics and Informatics, Vol. 9, No. 3,
2011, pp. 1-7.
[12] M. Ochiai, H. Hino, S. Hashimoto and Y. Takahashi,“Rotating Disk to Apply Wall Shear Stress on Cell Culture at
Microscopic
Observation”,
Proc.
19th
World
Multi-Conference on Systemics Cybernetics andInformatics, Vol. 2, 2015, pp. 288-291.
[13] M.L.C. Albuquerque, C.M. Waters, U. Savla, H.W.
Schnaper and S.A. Flozak, “Shear Stress Enhances Human
Endothelial Cell Wound Closure in Vitro”, American
Journal of Physiology - Heart and Circulatory
Physiology, Vol. 279, No. 1, 2000, pp. H293-H302.
[14] M. Ochiai, S. Hashimoto and Y. Takahashi, “Effect of Flow

Stimulation on Cultured Osteoblast”, Proc. 18th World
Multi-Conference on Systemics Cybernetics andInformatics, Vol. 2, 2014, pp. 156-161.
[15] S.D. Tan, T.J. deVries, A.M. Kuijpers-Jagtman, C.M.
Semeins, V. Everts and J. Klein-Nulend, “Osteocytes
Subjected to Fluid Flow Inhibit Osteoclast Formation andBone Resorption”, Bone, Vol. 41, No. 5, 2007, pp. 745-751.
[16] W. Yu, H. Qu, G. Hu, Q. Zhang, K. Song, H. Guan, T. Liu
and J. Qin, “A Microfluidic-Based Multi-Shear Device forInvestigating the Effects of Low Fluid-Induced Stresses on
Osteoblasts”, PLoS ONE, Vol. 9, No. 2, 2014, pp. 1-7.
[17] S. Hashimoto, “Erythrocyte Destruction under Periodically
Fluctuating Shear Rate; Comparative Study with Constant
Shear Rate”, Artificial Organs, Vol. 13, No. 5, 1989, pp.
458-463.
[18] S. Hashimoto, et al., “Effect of Aging on Deformability ofErythrocytes in Shear Flow”, Journal of Systemics
Cybernetics and Informatics, Vol. 3, No. 1, 2005, pp.
90-93.
[19] S. Hashimoto, “Detect of Sublethal Damage with Cyclic
Deformation of Erythrocyte in Shear Flow”, Journal of
Systemics Cybernetics and Informatics, Vol. 12, No. 3,
2014, pp. 41-46.
[20] R.H.W. Lam, Y. Sun, W. Chen and J. Fu, “Elastomeric
Microposts Integrated into Microfluidics for Flow-MediatedEndothelial Mechanotransduction Analysis”, Lab on Chip,
Vol. 12, No. 10, 2012, pp. 1865-1873.
[21] M.J. Levesque and R.M. Nerem, “The Elongation andOrientation of Cultured Endothelial Cells in Response to
Shear Stress”, Journal of Biomechanical Engineering, Vol.
107, No. 4, 1985, pp. 341-347.
[22] M. Gouverneur, B. Van den Berg, M. Nieuwdorp, E. Stroes
and H.Vink, “Vasculoprotective Properties of the Endothelial
Glycocalyx: Effects of Fluid Shear Stress”, Journal ofInternal Medicine, Vol. 259, No. 4, 2006, pp. 393-400.
[23] T.D. Oblak, P. Root and D.M. Spence, “Fluorescence
Monitoring of ATP-Stimulated, Endothelium-Derived Nitric
Oxide
ProductioninChannelsofaPoly(dimethylsiloxane)-Based
Microfluidic
Device”,
Analytical Chemistry, Vol. 78, No. 9, 2006, pp. 3193-3197.
[24] S. Hashimoto, F. Sato, R. Uemura and A. Nakajima, “Effectof Pulsatile Electric Field on Cultured Muscle Cells in Vitro”,
Journal of Systemics Cybernetics and Informatics, Vol.
10, No. 1, 2012, pp. 1-6.
[25] S. Hashimoto and K. Tachibana, “Effect of Magnetic Field
on Adhesion of Muscle Cells to Culture Plate”, Journal of
Systemics Cybernetics and Informatics, Vol. 11, No. 4,
2013, pp. 7-12.
[26] S. Hashimoto, H. Maeda and T. Sasada, “Effect of Shear
Rate on Clot Growth at Foreign Surfaces”, Artificial
Organs, Vol. 9, No. 4, 1985, pp. 345-350.
[27] S. Hashimoto, “Clot Growth under Periodically Fluctuating
Shear Rate”, Biorheology, Vol.31, No. 5, 1994, pp. 521-532.
[28] H. Hino, S. Hashimoto and F. Sato, “Effect of Micro
Ridges on Orientation of Cultured Cell”, Journal of
Systemics Cybernetics and Informatics, Vol. 12, No. 3,
2014, pp. 47-53.
[29] B.C. Isenberg, P.A. DiMilla, M. Walker, S. Kim and J.Y.
Wong, “Vascular Smooth Muscle Cell Durotaxis Depends on
Substrate Stiffness Gradient Strength”, Biophysical Journal,
Vol. 97, No. 5, 2009, pp. 1313-1322.
[30] C.M. Lo, H.B. Wang, M. Dembo and Y.I. Wang, “Cell
Movement Is Guided by the Rigidity of the Substrate”,
Biophysical Journal, Vol. 79, No. 1, 2000, pp. 144-152.