Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)

Migration of Cell under Couette Type Shear Flow Field between Parallel Disks:After and Before Proliferation
Shigehiro HASHIMOTO, Kosuke SHIMADA, Yuji ENDO
Biomedical Engineering, Department of Mechanical Engineering,
Kogakuin University, Tokyo, 163-8677, Japan
shashimoto@cc.kogakuin.ac.jp
http://www.mech.kogakuin.ac.jp/labs/bio/

ABSTRACT

along the streamline of the flow [15].

The effect of shear stress on the migration of each cell has been
investigated at proliferation under the constant shear flow fieldin vitro. The culture medium was sandwiched with a constant
gap between a lower stationary culture plate and an upper
rotating parallel plate to make a Couette type of shear flow.
Two types of cells were used in the test: C2C12 (mouse
myoblast cell line), and HUVEC (Human Umbilical Vein
Endothelial Cells). The shear stress (< 2 Pa) was continuously
applied on cells for 24 hours in the incubator. The behavior ofeach cell was traced at the time-lapse images observed by aninverted phase contrast microscope placed in an incubator.
The experiments show following results. HUVEC tends tomigrate downstream.
The tendency is remarkable after
proliferation. Migration tends to be enhanced, when theadhesion area decreased at proliferation. Under the shear
stress field (> 1 Pa), C2C12 tend to migrate to the lower shear
stress area. The velocity of the migration is higher at HUVEC
than C2C12. The experimental system is useful to study thequantitative relationships between the shear stress and the cell
migration.

In the Poiseuille type of flow [16–18], the shear rate depends onthe distance from the wall: highest at the wall. In the Couette
type of flow, on the other hand, the shear rate is constantregardless of the distance from the wall [10, 19–23].
In the present study, an experimental system of the Couette typeflow in the constant gap with a rotating disk [20, 21] has beenused to apply the shear stress quantitatively on the cell during
incubation at the microscopic observation in vitro. The effectof the shear stress field (< 2 Pa) on the cell has been studied
about migration.

2.

Couette Type of Shear Flow Device
A Couette type of shear flow device has been designed: between
a rotating disk and a stationary dish (Fig. 1). The medium issheared between a rotating wall and a stationary wall. The
stationary wall is the bottom of the culture dish (diameter 60mm). In the device, the shear rate (γ) in the medium is
calculated by Eq. (1).

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

γ=rω/d1.

METHODS(1)

In Eq. (1), ω is the angular velocity [rad s－1], and d is the
distance [m] between the wall of the moving disk and the wallof stationary plate. Between the parallel walls, d is constant.
The shear rate (γ [s－1]) in the gap between walls increases inproportion to the distance (r [m]) from the rotating axis. The
angular velocity ω (< 22 rad s－1) was controlled by the stepping
motor. In the observation area of the microscope, r varies
between 17 mm and 18 mm. The distance d, which wasmeasured by the positions of the focus of the walls at the
microscope, was between 0.28 mm and 0.56 mm. Variations
on the shear rates (γ) between 0.6×103 s－1 and 1.3×103 s－1 aremade in the present experiment by adjustment of theseparameters. The shear stress (τ [Pa]) is calculated by theviscosity (η [Pa s]) of the medium.

INTRODUCTION

A biological cell migrates on the scaffold. The adsorption
state affects the migration behavior. It is not easy tostandardize the condition, after seeding cells. In the present
study, the behavior of each cell is traced before and after
proliferation. After proliferation, each cell newly initiates
adhesion to the scaffold.
In several cases, the cell is exposed to the shear stress both invivo and in vitro. The direction of the shear stress field canaffect the direction of the migration [1, 2]. In the present study,
the migration of each cell is traced in the shear stress field of
the medium. The effect of the shear flow on the endothelial
cells [3–10], which are exposed to the blood flow on the innersurface of the vessel wall [11–14], were investigated in manystudies. In the previous study with the vortex flow [15] by theswinging plate in vitro, C2C12 made orientation perpendicular
to the direction of the flow, although HUVEC made orientation

τ=ηγ

(2)

Using the viscosity of the medium of 1.5×10－3 Pa s (measured
by a cone and plate viscometer at 310 K), the variations of theshear stress τ have been calculated as the value between 0.9 Pa

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Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)

and 2.0 Pa.

ω

The rotating disk device is mounted on the stage of the inverted
phase contrast microscope placed in the incubator. The device
allows the microscopic observation of cells cultured on thestationary wall during exposure to the shear flow.

rωrv

Cell Culture
Two types of cells were used in the test: C2C12 (mouse
myoblast cell line originated with cross-striated muscle of C3Hmouse, passage between eight and ten), and HUVEC (Human
Umbilical Vein Endothelial Cells). Cells were cultured in
D-MEM (Dulbecco’s Modified Eagle’s Medium): containing
10% decomplemented FBS (fetal bovine serum), and 1%
penicillin/ streptomycin.

x
y

d
τ

Cell

Cell

Fig. 1: Couette flow velocity distribution (v) between rotating(angular velocity ω) wall and stationary wall at r (radius)(distance d; left): shear stress (τ) on stationary wall (right).

The cells were seeded on the dish at the density of 3000
cells/cm2. To make adhesion of cells to the bottom of theculture dish, the cells were cultured for 24 hours in the
incubator without flow stimulation (without rotation of the disk).
After the pre-incubation for 24 hours without shear, the cells
were continuously exposed to the shear flow field with therotating disk for 24 hours in the incubator by the constantrotating speed of the disk. The constant speed was preset foreach test to keep the designed constant shear stress field.
0.01 mmFig. 2: Contour of each cell (left) was approximated to ellipsoid(right).

Measurement of Cell
The time-lapse microscopic image was taken every ten minutes
during the cultivation. The contour of each cell adhered on thestationary plate of the scaffold was traced, and the projected
two-dimensional area (S) at the image of each cell was
calculated. The contour of each cell was approximated toellipsoid (Fig. 2), and the centroid of each cell was used to track
the migration of the cell. The flow direction was defined as x
axis. The direction to the rotating axis was defined as y axis
(Fig. 1). The migration velocity of each direction (vx and vy)
was calculated using the time-lapse images. From theseimages, cells with the proliferation were picked up. At eachcell, data (S, vx, and vy) were traced before and after two hours
from the proliferation.
The behavior of cells adhering to the stationary wall surface
under the shear stress is observed with a microscope. The
experimental system allows continuous observation of cells
during exposure to the shear flow in the incubator.

3.

Fig. 3a: Tracings of area (S) before proliferation of C2C12
under shear stress field of 1 Pa.

RESULTSIn Figs. 3−6, each mark corresponds to the traced area (S) of
each cell. Fig. 3 shows the tracings of the area (S) of each cell
before (Fig. 3a) and after (Fig. 3b) proliferation of C2C12 under
the shear stress field of 1 Pa. Fig. 4 shows the tracings of thearea (S) of each cell before (Fig. 4a) and after (Fig. 4b)
proliferation of C2C12 under the shear stress field of 1.5 Pa.
Fig. 5 shows the tracings of the area (S) of each cell before (Fig.
5a) and after (Fig. 5b) proliferation of HUVEC under the shear
stress field of 0.9 Pa. Fig. 6 shows the tracings of the area (S)of each cell before (Fig. 6a) and after (Fig. 6b) proliferation of
HUVEC under the shear stress field of 2 Pa. The area S
decreases in forty minutes before proliferation, and increases inforty minutes after proliferation. For two hours before andafter proliferation, the area S before proliferation is larger thanthat after proliferation. The area S tends to decrease under the
shear stress field higher than 1 Pa.

Fig. 3b: Tracings of area (S) after proliferation of C2C12 undershear stress field of 1 Pa.

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Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)(Fig. 10a) and after (Fig. 10b) proliferation of HUVEC undershear stress field of 2 Pa were collected in Fig. 10. The
velocity of the migration tends to be biased downstream after
proliferation.
The tendency is remarkable in HUVEC,
especially after proliferation (Figs. 9b & 10b). Under thehigher shear stress field, C2C12 tend to migrate to the center ofthe rotating axis, which correspond to the lower shear stressarea. The velocity of the migration tends to be higher at
HUVEC than C2C12.

Fig. 4a: Tracings of area (S) before proliferation of C2C12
under shear stress field of 1.5 Pa.

Fig. 5b: Tracings of area (S) after proliferation of HUVEC
under shear stress field of 0.9 Pa.

Fig. 4b: Tracings of area (S) after proliferation of C2C12 undershear stress field of 1.5 Pa.

Fig. 6a: Tracings of area (S) before proliferation of HUVEC
under shear stress field of 2 Pa.

Fig. 5a: Tracings of area (S) before proliferation of HUVEC
under shear stress field of 0.9 Pa.

Data of the migration velocities before (Fig. 7a) and after (Fig.
7b) proliferation of C2C12 under shear stress field of 1 Pa werecollected in Fig. 7. Data of the migration velocities before(Fig. 8a) and after (Fig. 8b) proliferation of C2C12 under shear
stress field of 1.5 Pa were collected in Fig. 8. Data of the
migration velocities before (Fig. 9a) and after (Fig. 9b)
proliferation of HUVEC under shear stress field of 0.9 Pa werecollected in Fig. 9. Data of the migration velocities before

Fig. 6b: Tracings of area (S) after proliferation of HUVEC
under shear stress field of 2 Pa.

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Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)

the cell migration downstream, a cell migrates to adapt to theshear field. While the strong stimulation above the thresholddamages the cell, the stimulation below the threshold remains in
the cell as a memory for the response in the next step [14].
The hysteresis effect governs the active response of the cell.

Fig. 7a: Migration velocity before proliferation of C2C12 undershear stress field of 1 Pa.

Fig. 8b: Migration velocity after proliferation of C2C12 undershear stress field of 1.5 Pa.

Fig. 7b: Migration velocity after proliferation of C2C12 undershear stress field of 1 Pa.

Fig. 9a: Migration velocity before proliferation of HUVEC
under shear stress field of 0.9 Pa.

Fig. 8a: Migration velocity before proliferation of C2C12 undershear stress field of 1.5 Pa.

4.

DISCUSSION

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 [3−10]. Cells are
exfoliated under the shear flow at the wall shear stress higher
than 2 Pa [16, 19]. A biological cell shows passive and active
responses in an environment [14]. While the flow enhancesFig. 9b: Migration velocity after proliferation of HUVEC undershear stress field of 0.9 Pa.

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Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)stability of the rotating motion of the disk, stability of the
optical path for the microscopic observation, morphologic
preciseness of the plane of the disks, and simultaneous
observation over the range of variation of the shear rate
proportional to the radius from the rotational axis. The
behavior of cells under the gradient of the shear stress field canbe observed [9,11−13]. The floating erythrocyte deformation
was observed between counter rotating parallel discs [23].
In the present study, the rotating parallel disk system is selected
to make Couette type of flow instead of the cone and platesystem. The rotating flow can induce the secondary flow by
the centrifugal effect. The rotational speed of the disk issmaller than 0.4 m s－1 in the present system. The microscopic
video image of the moving cells between the rotating disk andthe stationary disk shows the steady flow in the present
experiment. Reynolds number (Re) is calculated by Eq. (3).

Fig. 10a: Migration velocity before proliferation of HUVEC
under shear stress field of 2 Pa.

Re = ρ v d / η = ρ r ω d / η(3)

In Eq. (3), ρ is density of the fluid, v is the circumferential
velocity, r is the distance from the rotating axis, ω is the angularvelocity, d is the distance between the moving wall and thestationary wall, and η is the viscosity of the fluid. Re is
1.5×102, when ρ, r, ω, d, and η are 1×103 kg m－3, 18 mm, 22
rad s－1, 0.56 mm, and 1.5×10－3 Pa s, respectively. Generationof the turbulent flow is suppressed in the flow at the small valueof Reynolds number.
The interaction between cells also governs the behavior of eachcell. The migration of each cell depends also on the positionof the neighbor cell. Cells are sparsely seeded in the present
study. Myoblasts tend to migrate to the oblique direction of
the lower shear stress field at 1 Pa. The effect of shear flow oncells depends on the cell types [24, 25]. The dependency canbe applied to the cell sorting technology. The quantitative
relationships between the shear stress and the cell orientation
can be applied to tissue technology to control of cells in vitro.

Fig. 10b: Migration velocity after proliferation of HUVEC
under shear stress field of 2 Pa.

The migration of a biological cell relates to adhesion to thescaffold [1−3]. Cell tends to be rounded at proliferation. In
the present experiment in vitro, the area (S) of the attachment tothe scaffold is small during proliferation.

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 [15, 24]. When theflow has an open surface, it is difficult to estimate the shear
stress value in the fluid. Between two parallel walls, on theother hand, the velocity profile is estimated to be parabolic in
the laminar flow. In the previous studies, several preparations
were designed to study the effect of mechanical flow
stimulations on biological cells: the tilting parallel-walls
channel [16], the rhombus channel [17], the cross flow channel[18], and the rotating disk type [20, 21].

5.

CONCLUSION

The effect of shear stress on cell migration has been
investigated under Couette type shear flow between paralleldisks in vitro. HUVEC tends to migrate downstream. The
tendency is remarkable after proliferation. Migration tends tobe enhanced, when the adhesion area decreased at proliferation.
Under the shear stress field (> 1 Pa), C2C12 tend to migrate to
the lower shear stress area. The velocity of the migration
tends to be higher at HUVEC than C2C12. The experimental
system is useful to study the quantitative relationships between
the shear stress and the cell migration.

The Couette type of flow is convenient to estimate the shear
stress in the flow with the constant shear rate between themoving wall and the stationary wall, which is also available tonon-Newtonian fluid. The cone-and -plate type device has theuniform shear field in the entire space between the rotating cone
and the stationary plate [10, 19]. The shear stress is constant
independent of the distance from the rotating axis. The
combination of the rotating concave cone and the stationary
convex cone is effective to reduce the inertial secondary flow
[22].

ACKNOWLEDGMENT
The authors thank to Mr. Hiromi Sugimoto for his assistance ofthe experiment.

A parallel disks system between rotating disk and the stationary
disk [20, 21], on the other hand, has several advantages:

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Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)

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