Proceedings of The 24th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2020)

Hysteresis Effect of Shear Flow Field on Migration Velocity of Cell: After and
Before Division of L929 and 3T3-L1
Shigehiro HASHIMOTO, Kosuke SHIMADA, Yuji ENDO, Hiroki YONEZAWA
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/
Kiyoshi YOSHINAKA
Health and Medical Research Institute, National Institute of Advanced Industrial Science & Technology
Tsukuba, 305-8564, Japan
ABSTRACT

were investigated in many studies [4–8]. In the previous study
with the vortex flow by the swinging plate in vitro, C2C12
made orientation perpendicular to the direction of the flow,
although HUVEC made orientation along the streamline of theflow [9]. The orientation of each cell in the tissue depends onthat of neighbor cell [3].

The effect of shear flow field on the migration of each cell has
been investigated under Couette type shear flow field in 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. The wall
shear stress (τ) on the lower culture disk was controlled by therotating speed of the upper disk. Two types of cells were usedin the test: L929 (mouse fibroblast connective tissue), and
3T3-L1 (mouse fat precursor cells). After cultivation without
flow for 24 hours for adhesion of cells on the lower plate, τ = 1
Pa was continuously applied on cells for 7 days in the incubator.
The behavior of each cell (before and after division) was traced
at the time lapse image observed by an inverted phase contrast
microscope placed in an incubator. The experimental results
show that cells make division under shear stress of 1 Pa. Eachcell makes wider variation of adhesion area (before and after
division) in L929 than in 3T3-L1. Migration to perpendicular
direction is more frequently at L929 than at 3T3-L1. Somecells of 3T3-L1 migrate downstream after division.

At the wall shear stress, a cell might show the following
responses: elongation [6], tilting to the streamline [9], migration[7, 10], deformation to be rounded [10], proliferation [8], andexfoliation from the wall of the scaffold [11].
In the Poiseuille type of flow, the shear rate depends on the
distance from the wall: highest at the wall. In the Couette typeof flow, on the other hand, the shear rate is constant regardlessof the distance from the wall [12, 13].
In the present study, an experimental system of the Couette typeflow in the constant gap with a rotating disk has been designed
to apply the shear stress quantitatively on the cell during
incubation at the microscopic observation in vitro, and the effectof the shear stress field (1 Pa) on each cell at division has beenstudied about migration.

Keywords: Biomedical Engineering, Shear Stress, Division,
Migration, L929, 3T3-L1 and Couette Flow.

2.
1.

METHODSINTRODUCTION
Couette Type of Shear Flow Device
A Couette type of shear flow device has been used: between arotating 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).

A biological cell migrates on the scaffold. In several cases,
cells are exposed to the shear stress both in vivo and in vitro.
The direction of the shear stress field might affect the directionof the migration [1]. The hysteresis also might affect thedirection of the migration [2]. The behavior of each cell might
depend on the initial state. In the most of tests in vitro, cells
are incubated for several hours for adhesion to the scaffold
before flow stimulation. Each cell can make division under
the wall shear stress field [3]. Is the effect maintained in eachcell after division? The adhesion status of the cell is
controlled by itself after division. In the present study, themigration of each cell is traced at the division in the shear stressfield of the medium.

In the device, the shear rate (γ) in the medium is calculated by
Eq. (1).
γ=rω/d(1)

In Eq. (1), ω is the angular velocity [rad s㸫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㸫1]) in the gap between walls increases inproportion to the distance (r [m]) from the rotating axis.
The angular velocity ω (< 22 rad s㸫1) was controlled by the

The effect of the shear flow on the endothelial cells, which areexposed to the blood flow on the inner surface of the vessel wall,37

Proceedings of The 24th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2020)

Fig. 5 shows tracings of area (S) before (Fig. 5a) and after (Fig.
5b) division of 3T3-L1 under shear stress field of 1 Pa. The
decrease of the area of 3T3-L1 before division is slower thanthat of L929. The increase of the area of 3T3-L1 before
division is also slower than that of L929.

stepping motor. In the observation area of the microscope, rvaries between 17 mm and 18 mm. The distance d, which wasmeasured by the positions of the focus of the walls at the
microscope, was around 0.6 mm. The shear rates (γ) of
6.7×102 s㸫1 are made in the present experiment by adjustmentof these parameters.

Fig. 6 shows the velocity of the migration before (Fig. 6a) andafter (Fig. 6b) division of L929 under shear stress field of 1 Pa.
Several cells migrate upstream. Some cells migrate to thedirection of the rotating axis, where the wall shear stress islower (Fig. 3). The migration velocity is lower after division(data concentrate to origin) than before division.
The
distribution of migration direction is random (symmetrical
distribution of data) after division.

The shear stress (τ [Pa]) is calculated by the viscosity (η [Pa s])of the medium.
τ=ηγ

(2)

Using the viscosity of the medium of 1.5×10㸫3 Pa s (measured
by a cone and plate viscometer at 310 K), the shear stress τ havebeen calculated as the value of 1 Pa.
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.

ωCell Culture
Two types of cells were used in the test: L929 (fibroblast
connective tissue of C3H mouse), and 3T3-L1 (mouse fat
precursor cells, a cell line derived from cells of mouse 3T3).
Cells were cultured in D-MEM (Dulbecco’s Modified Eagle’s
Medium): containing 10% decomplemented FBS (fetal bovine
serum), and 1% penicillin/ streptomycin.

V

d
vy

S

τ

vx

Cell

Fig. 1: Couette flow (velocity (V) distribution) between rotating(angular velocity ω) wall and stationary wall at r (radius)(distance d): migration velocity (vx, vy) of cell on stationary
wall: wall shear stress (τ).

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 thedisk).
After the pre-incubation for 24 hours without shear, the cells
were continuously sheared with the rotating disk for 24 hours in
the incubator at the constant rotating speed. The constant
speed was preset for each test to keep the designed shear stressfield.

S1

S’1

S2
Rounding

S’2

S’’1
Division

S’’2

Fig. 2: Area (S) change of cell before (from S1 to S2) and after
division (from S’1 to S’2, and from S’’1 to S’’2).

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 (Fig. 2).
The contour of each cell wasapproximated to ellipsoid, and the centroid of each cell wasused to track the migration of the cell (Fig. 3). The flow
direction was defined as x axis. The direction to the rotating
axis was defined as y axis.

3.

r

y

Approximated ellipsoid

x

Flow

Distribution of τv

Centroidvx

vy

RESULTS

Fig. 4 shows tracings of area (S) before (Fig. 4a) and after (Fig.
4b) division of L929 under shear stress field of 1 Pa. The time
zero correspond to the timing of division of the cell. The
decrease of the area (S) before division correspond to therounding of the cell before division. The same kind of line
shows the tracings of the same cell in both Fig. 4a and Fig. 4b.
The same lines of different color after division show the same
origin of cell. After division, the area of each cell tends toreturn to that of before division.

Cell
Fig. 3: Centroid of approximated ellipsoid of cell is traced:migration velocity (vx, vy) of cell: wall shear stress (τ)
distribution; x, parallel to flow; y, perpendicular to flow.

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Proceedings of The 24th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2020)

Fig. 5b: Tracings of area (S) after division of 3T3-L1 undershear stress field of 1 Pa.

Fig. 4a: Tracings of area (S) before division of L929 undershear stress field of 1 Pa.

Fig. 6a: Velocity of the migration before division of L929 undershear stress field of 1 Pa.

Fig. 4b: Tracings of area (S) after division of L929 under shear
stress field of 1 Pa.

Fig. 6b: Velocity of the migration after division of L929 undershear stress field of 1 Pa.

Fig. 5a: Tracings of area (S) before division of 3T3-L1 undershear stress field of 1 Pa.

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Proceedings of The 24th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2020)

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 [9]. When the flow
has an open surface, it is difficult to estimate the shear stressvalue in the fluid. Between two parallel walls, on the other
hand, the velocity profile is estimated to be parabolic in thelaminar flow. In the previous studies, several preparations
were designed to study the effect of mechanical flow
stimulations on biological cells: the tilting disk channel [11], therhombus channel [15], the cross flow channel [16], and therotating disk type [12].
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. Several kinds of the devices of Couette
type flow were designed for quantitative experiments ofbiological fluid in the previous studies [12, 13, 17−19]. The
cone-and-plate type device has the uniform shear field in theentire space between the rotating cone and the stationary plate[13]. The shear stress is constant independent of the distancefrom the rotating axis. The erythrocyte destruction wasstudied between the rotating concave cone and the stationary
convex cone [20].

Fig. 7a: Velocity of the migration before division of 3T3-L1
under shear stress field of 1 Pa.

A parallel disks system between rotating disk and the stationary
disk, on the other hand, has several advantages: stability of therotating motion of the disk, stability of the optical path for the
microscopic observation, morphologic preciseness of the planeof the disks, and simultaneous observation over the range ofvariation of the shear rate proportional to the radius from therotational axis [1]. The floating erythrocyte deformation wasobserved between counter rotating parallel discs [21].
In the present study, the rotating parallel disk system is selected
to make Couette type of flow instead of the cone and platesystem. The shear rate (γ) increases from 0.88×103 s㸫1 to
1.3×103 s㸫1 (Eq. (1)), when the distance from the axis (r)increases from 12 mm to 18 mm in the observation area at theconstant angular velocity of 22 rad s㸫1 (d = 0.3 mm). The
range of the shear rate enables the simultaneous observation of
the behavior of cells related to variation of the shear stressbetween 1.3 Pa and 2.0 Pa [12]. The rotating flow might
induce the secondary flow by the centrifugal effect. The
rotational speed of the disk is smaller than 0.4 m s㸫1 in thepresent system. The microscopic video image of the flowing
cells between the rotating disk and the stationary disk shows thesteady flow in the present experiment. Reynolds number (Re)is calculated by Eq. (3).

Fig. 7b: Velocity of the migration after division of 3T3-L1
under shear stress field of 1 Pa.

Fig. 7 shows the velocity of the migration (Fig. 3) before (Fig.
7a) and after (Fig. 7b) division of 3T3-L1 under shear stressfield of 1 Pa. 3T3-L1 migrates to the parallel direction to theflow frequently than to the perpendicular direction to the flow.
Cells tend to migrate downstream. Several cells migrate
downstream at higher velocity (data in 3rd quadrant) after
division.

4.

Re = ρ v d / η = ρ r ω d / η

DISCUSSION(3)

In Eq. (3), ρ is density of the fluid [kg m 㸫 3], v is thecircumferential velocity [m s㸫1], ω is the angular velocity [rads㸫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 is the viscosity of the fluid [Pa s]. Re is 1.5×102, when ρ,r, ω, d, and η are 1×103 kg m㸫3, 18 mm, 22 rad s㸫1, 0.56 mm,
and 0.0015 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 streamline traced by the
direction of exfoliation of the cell and of the moving particle

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 [4−8]. Cells are
exfoliated under the shear flow at the wall shear stress higher
than 2 Pa [11]. A biological cell shows passive and active
responses in an environment [1]. While the flow enhances thecell migration to the 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.

40

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in proportional to the distance from the rotating axis, has also
been confirmed by tracings of the moving particle adjacent tothe surface.
The most of myoblasts tend to migrate to the oblique directionof the lower shear stress field at 1 Pa [10]. The effect of shear
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The cells proliferate regardless of the shear flow stimulation.
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movement of each cell can be traced by the time lapse images
with the interval of ten minutes in the present experiment.
The effect of shear flow on cells was investigated in many
previous studies. The shear flow affects adhesion of each cell[22]. Adhesion of cells can be controlled with design of thescaffold [23]. The behavior of cells in the shear flow wassimulated in the previous study [24]. The effect of fluid
induced shear stresses on osteoblasts was studied in theprevious study [25].

5.

CONCLUSION

The effect of shear flow field on the migration of each cell has
been investigated under the Couette type of the shear flow fieldin vitro. The area of each cell adhere to the scaffold decreases
before division. The decrease of the area of 3T3-L1 before
division is slower than that of L929. After division, the areaof each cell returns to that of before division. Some cells of
L929 migrate to the direction of the rotating axis, where thewall shear stress is lower.
3T3-L1 tends to migrate
downstream.

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

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41Proceedings of The 24th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2020)

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