Migration Velocity of Cell under Shear Flow Field:
After and Before Division
Shigehiro Hashimoto, Member IEEE
dept. Mechanical Engineering
Kogakuin University
Tokyo, Japan
shashimoto@cc.kogakuin.ac.jp
Abstract— The migration velocity of each single cell under
the Couette type of the shear flow field has been studied inrelation to the area adhere to the scaffold before and after
division in vitro. The shear field was made in a constant gap
between a lower stationary culture plate and an upper rotating
parallel plate. Two types of cells were used in the test: L929
(mouse fibroblast connective tissue), and 3T3-L1 (mouse fat
precursor cells). After adhesion of cells on the lower plate, thewall shear stress of 1 Pa was continuously applied on cells for
24 hours in an incubator. The migration velocity of each cell
was traced at the time lapse images observed by an inverted
phase contrast microscope placed in an incubator.
Experimental results show that the migration of each cell is
accelerated with the smaller contact area between the cell andthe scaffold around the term of division of the cell. Several cellsof L929 migrate to the direction perpendicular to the flow justbefore division. Although many cells migrate upstream, 3T3L1 tends to migrate downstream.
Keywords— biomedical engineering, shear stress, division,
migration, L929, 3T3-L1, Couette flow

I. INTRODUCTION
Biological cells perform various activities on thescaffold: migration, deformation, proliferation, orientation,and differentiation. These activities of each cell lead to thetissue formation through interaction between cells. Eachtissue has its own cell arrangement. The control
methodology can be applied to the innovative technology forthe engineered tissue formation.
Cells receive various forces, sense the forces, andrespond to the forces in vivo. The uniform mechanical force
field around the whole cell can be realized easier with thefluid than with the solid. The shear flow field of the medium
has been used to apply the force field to cells [1]. Endothelial
cells, for example, are exposed to a shear fluid field of theblood flow, and align to the flow direction on the innersurface of the vessel wall. The effects of the shear flow on
the endothelial cells were investigated in many studies [2–6].
Myoblasts, on the other hand, align perpendicular to the flow.
In the previous study with the vortex flow by the swinging
plate in vitro, C2C12 made orientation perpendicular to thedirection of the flow, although HUVEC made orientation
along the streamline of the flow [7].
The interaction between cells governs the activity of eachcell. The alignment of each cell depends on that of adjacentcells [8]. In the basic present study, cells have been sparsely
cultured, and the activity of each single cell has been traced.
The orientation of each cell affects the orientation of cells in
subsequently formed tissues. Cell movement is not only
passive, but also active. The direction of active migration canbe associated with subsequent cell activity.

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

Kiyoshi Yoshinaka
Health and Medical Research InstituteNational Institute of Advanced Industrial Science & Technology
Tsukuba, Japank.yoshinaka@aist.go.jp

In several cases, cells are exposed to the shear stress bothin vivo and in vitro. The direction of the shear stress fieldmight affect the direction of the migration of the cell [1]. The
effect might be maintained as the memory in the cell. The
hysteresis also can affect the direction of the migration [9].
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 the flow stimulation. Eachcell, on the other hand, can make division under the wall
shear stress field [8]. Is the effect maintained in each cell
after division? The adhesion status of the cell is controlled byitself after division. In the present study, the timing ofdivision has been used for the natural initial state for the test
exposure to the force field. The migration of each cell has
been traced after the division in the shear stress field of themedium in the present study.
At the wall shear stress, a cell might show the following
responses: elongation [4], tilting to the streamline [7],migration [5, 10], deformation to be rounded [10],proliferation [6], and exfoliation from the wall of the scaffold[11]. The mild wall shear stress of 1 Pa has been applied in
the present study to observe migration of cells during the cell
culture in vitro.
In the Hagen-Poiseuille type of flow, the shear ratedepends on the distance from the wall: highest at the wall. In
the Couette type of flow, on the other hand, the shear rate isconstant regardless of the distance from the wall [2, 12]. In
the present study, A parallel disk type of device for Couette
flow in the constant gap between a rotating disk and astationary dish has been designed to apply the shear stressquantitatively on the cell during incubation at the
microscopic observation in vitro. The migration velocity ofeach single cell under the Couette type of the shear flow fieldhas been studied in relation to the area adhere to the scaffold
before and after division in vitro.
II. METHODS
A. Parallel Disk Type of Device for Couette Flow
A parallel disk type of device for Couette flow has been
used: between a rotating disk and a stationary dish (Fig. 1).
The medium is sheared between a rotating wall and astationary wall. The stationary wall is the bottom of theculture dish of 60 mm diameter.
In the device, the shear rate (γ) in the medium is
calculated by (1).
γ=rω/d()In (1), ω is the angular velocity, and d is the distance
between a rotating wall and a stationary wall. Between twoparallel walls, d is constant. The shear rate (γ) in the gap
between two walls increases in proportion to the distance (r)from the rotating axis (1).
The angular velocity ω smaller than 22 rad s−1 wascontrolled by the stepping motor. The value of r varies
between 17 mm and 18 mm in the observation area of the
microscope. The distance d was around 0.6 mm, which wasmeasured by the positions of the walls at the focus of theobjective lens of the microscope. Each wall surface positionof the gap can be detected by focusing at the microscope.
The focusing point can be reproduced by the memory of theposition of the focus adjusting ring of the microscope. The
shear rates (γ) of 6.7×102 s−1 are made in the present
experiment by adjustment of these parameters.
The shear stress (τ) is calculated by the viscosity (η) of
the medium.

τ
Flow

v
vy
y
vx

Cell

x

Fig. 3. Migration velocity (vx, vy) of cell: wall shear stress (τ) distribution;x, parallel to flow; y, perpendicular to flow.

The density of cells was adjusted 3000 cells/cm2 forseeding. Before each flow test, cells were cultured for 24
τ=ηγ(2) hours in the incubator without flow stimulation (without
rotation of the disk) to make adhesion of cells to the bottom
The viscosity of the medium of 1.5×10−3 Pa s wasof the culture dish stable.
measured by a cone and plate viscometer at 310 K. The shear
After the pre-incubation for 24 hours without shear, thestress τ has been calculated as the value of 1 Pa.
cells were continuously sheared with the rotating disk for 24
The parallel disk type of device was mounted on thehours in the incubator at the constant rotating speed. The
stage of the inverted phase contrast microscope. The
value for the constant speed of the disk was preset for eachmicroscope with the device was placed in the incubator. The
test to adjust the shear stress field as the designed value.
experimental system allows the microscopic observation ofcells cultured on the stationary wall during exposure to the
C. Migration Velocity and Area of Cell
shear flow.
During the cultivation of cell under the shear flow, thetime-lapse microscopic images were taken every ten minutes.
B. Cell Types
At each two-dimensional image, the contour of each cellTwo types of cells were used in the test: L929 (fibroblast
adhered on the stationary plate of the scaffold was traced.
connective tissue of C3H mouse), and 3T3-L1 (mouse fat
The projected area (S) at the image of each cell was
precursor cells, a cell line derived from cells of mouse 3T3).
calculated (Fig. 2). The area of each cell was traced before
Cells were cultured in D-MEM (Dulbecco’s Modified
and after division: from S1 to S2 before division; from S’1 toEagle’s Medium): containing 10% decomplemented FBS
S’2, and from S’’1 to S’’2 after division, respectively. The(fetal bovine serum), and 1% penicillin/ streptomycin.
contour of each cell was approximated to ellipsoid, and thecentroid of each cell was used to track the migration of theωcell (Fig. 3). The flow direction was defined as x axis. The
direction to the rotating axis was defined as y axis, which isperpendicular to x axis. The components of the migration
velocity were calculated as vx and vy. As y increases, rr
decreases. The shear stress (τ) decreases with y (1).
V
dIII. RESULTS
vy

S

vx
Cell

Fig. 1. Couette flow (velocity (V) distribution) between rotating (angularvelocity ω) wall and stationary wall at r (radius) with distance d: migration
velocity (vx, vy) of cell on stationary wall.
S’1

S1

S2
Rounding

S’2

S’’1
DivisionFig. 2. Area (S) change of cell before and after division.

S’’2

Tracings of the area (S) before and after division of eachcell under the shear stress field of 1 Pa are displayed in Fig. 4(L929) and Fig. 5 (3T3-L1). The time “zero” corresponds tothe timing of division of the cell. The decrease of the area (S)before division corresponds to the rounding of the cell before
division. The markers of the same color show the same cell.
After division, the markers of the same color correspond tocells divided from the same mother cell. After division, thearea of each cell tends to return gradually to that of before
division. The order of the size of cells after division tends tosame as that before division.
The area of each cell before division is larger at L929
(Fig. 4) than at 3T3-L1 (Fig. 5). The area of each cell at
division is around 1000 µm2 regardless of the cell types. The
decrease of the area of 3T3-L1 before division is slower thanthat of L929. The increase of the area of L929 after division
is faster than that of 3T3-L1 in some cells.

The velocity of the migration of each cell under the shear
stress field of 1 Pa is displayed at the x-y plane in Figs. 6-9:
L929 (Figs. 6 and 7), and 3T3-L1 (Figs. 8 and 9). The
markers of data with the same color are correspond toclassification by the term from the time of division of eachcell: from −120 min to −100 min, from −100 min to −80 min,from −80 min to −60 min, from −60 min to −40 min, from
−40 min to −20 min, and from −20 min to 0 min before
division; from 0 min to 10 min, from 10 min to 20 min, from20 min to 40 min, from 40 min to 60 min, from 60 min to 80
min, from 80 min to 100 min, and 100 min to 120 min after
division, respectively. In each x-y plane, the distance fromthe origin of each datum point corresponds to the absolutevalue of the velocity of the cell. The datum point in thepositive area of x corresponds to the migration to thedownstream direction. The datum point in the negative areaof x corresponds to the migration to the upstream direction.
The datum point in the positive area of y corresponds to themigration to the rotating axis direction, where the shear
stress is lower. The datum point in the negative area of ycorresponds to the migration leaving from the rotating axis.
The shear stress increases as the cell leaves from the rotating
axis.
Concentrated distribution of data around the origin
corresponds to the low velocities of cells. Several cells of
L929 migrate to the direction perpendicular to the flow justbefore division (Fig. 6). Symmetric distribution of datashows the migration to random directions of L929 after
division in Fig. 7. Some cells migrate with higher velocity to
the direction of the rotating axis, where the wall shear stressis lower (Fig. 6). In some cells, the migration velocity ishigher before division than after division. Quite a large
number of cells migrate upstream (Fig. 7). The horizontal
distribution of data shows that 3T3-L1 migrates parallel tothe flow direction than the perpendicular direction (Figs. 8
and 9). Extended distribution to the positive x axis shows thatcells tend to migrate downstream with the higher velocity(Figs. 8 and 9). Some cells migrate downstream with thehigher velocity just after division (Fig. 9). Most of migration
with the higher velocity occurred around the term of divisionof each cell.
The velocity components of vx and vy are plotted inrelation to the area (S) of each cell in Figs. 10-17. The
markers of data with the same color are correspond toclassification by the term from the time of division of eachcell: from −120 min to −100 min, from −100 min to −80 min,from −80 min to −60 min, from −60 min to −40 min, from
−40 min to −20 min, and from −20 min to 0 min before
division; from 0 min to 10 min, from 10 min to 20 min, from20 min to 40 min, from 40 min to 60 min, from 60 min to 80
min, from 80 min to 100 min, and 100 min to 120 min after
division. Data of L929 are displayed in Figs. 10-13. Data of
3T3-L1 are displayed in Figs. 14-17. Data before division aredisplayed in Figs. 10, 12, 14, and 16. Data after division aredisplayed in Figs. 11, 13, 15, and 17. Data of vx are collected
in Fig. 12, 13, 16, and 17. Data of vy are collected in Fig. 10,
11, 14, and 15. The absolute value of the velocity of the cell
migration tends to decrease with the increase of the area (S)(Figs. 10, 11, 12, 13, 15, 16, and 17). The migration of eachcell accelerates at the smaller contact area around the term ofdivision of the cell. Some cells of L929 make migration withthe higher velocity at the direction perpendicular to the flow
(Figs. 10 and 11).

Fig. 4. Tracings of area (S) at division of L929 under shear stress field of 1
Pa: before (left, minus), and after (right, plus). Same color shows tracingsof each cell.

Fig. 5. Tracings of area (S) at division of 3T3-L1 under shear stress fieldof 1 Pa: before (left, minus), and after (right, plus). Same color shows
tracings of each cell.

(min)Fig. 6. Velocity of the migration (vx, vy) before division of L929 undershear stress field of 1 Pa.

(min)
Fig. 7. Velocity of the migration (vx, vy) after division of L929 under shear
stress field of 1 Pa.

(min)
Fig. 8. Velocity of the migration (vx, vy) before division of 3T3-L1 undershear stress field of 1 Pa.

(min)
Fig. 10. Velocity of the migration vy before division of L929 under shear
stress field of 1 Pa in relation to area S.

(min)Fig. 11. Velocity of the migration vy after division of L929 under shear
stress field of 1 Pa in relation to area S.

1

(min)
Fig. 9. Velocity of the migration (vx, vy) after division of 3T3-L1 undershear stress field of 1 Pa.

(min)

Fig. 12. Velocity of the migration vx before division of L929 under shear
stress field of 1 Pa in relation to area S.

(min)
Fig. 13. Velocity of the migration vx after division of L929 under shear
stress field of 1 Pa in relation to area S.

(min)Fig. 14. Velocity of the migration vy before division of 3T3-L1 under shear
stress field of 1 Pa in relation to area S.

(min)Fig. 16. Velocity of the migration vx before division of 3T3-L1 under shear
stress field of 1 Pa in relation to area S.

(min)Fig. 17. Velocity of the migration vx after division of 3T3-L1 under shear
stress field of 1 Pa in relation to area S.

IV. DISCUSSION
Endothelial cells are exposed to the shear flow in the
blood vessels in vivo. The effect of shear flow on endothelial
cells was investigated in the previous studies [2−6]. 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
the cell migration to the downstream, a cell migrates to adapt
to the shear field. While the strong stimulation above thethreshold damages the cell, the stimulation below thethreshold remains in the cell as a memory for the response in
the next step [13]. The hysteresis effect governs the active
response of the cell.

(min)Fig. 15. Velocity of the migration vy after division of 3T3-L1 under shear
stress field of 1 Pa in relation to area S.

In the previous study, cells were exposed to the shear
flow in a donut-shaped open channel, and the effect of flow
stimulation on cultured cells has been studied in vitro [7].
When the flow has an open surface, it is difficult to estimate
the shear stress value in the fluid. Between two parallel walls,
on the other hand, the parabolic velocity profile can be
estimated in the laminar flow. In the previous studies, several

preparations were designed to study the effect of mechanicalflow stimulations on biological cells: the tilting disk flow
channel [11], the rhombus flow channel [14], the cross flow
channel [15], and the rotating disk type [12].
The Couette type of flow is convenient to estimate theshear stress in the flow with the constant shear rate between
the moving wall and the stationary wall, which is alsoavailable to non-Newtonian fluid. Several kinds of thedevices of Couette type flow were designed for quantitative
experiments of biological fluid in the previous studies [16,17]. The cone-and-plate type device has the uniform shear
field in the entire space between the rotating cone and thestationary plate [2, 3]. The shear stress is constant
independent of the distance from the rotating axis. The
erythrocyte destruction was studied between the rotating
concave cone and the stationary convex cone [18].
A parallel disks system between rotating disk and thestationary disk, on the other hand, has several advantages:
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 [1]. In theradial direction, the field has the wall shear stress gradient.
The shear stress gradients were also studied as the parameter
which affects cells behavior [4, 6]. The floating erythrocyte
deformation was observed between counter rotating parallel
discs [19].
In the present study, the rotating parallel disk system isselected to make Couette type of flow instead of the cone andplate system. At the constant angular velocity of 22 rad s−1 (d= 0.3 mm), the shear rate (γ) increases from 0.88×103 s−1 to
1.3×103 s−1, when the distance from the axis (r) increases
from 0.012 m to 0.018 m in the observation area (1). The
range of the shear rate enables the simultaneous observationof 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−1 in thepresent system. The microscopic video image of the flowing
cells between the rotating disk and the stationary disk shows
the steady flow in the present experiment. Reynolds number(Re) is calculated by (3).

The most of myoblasts tend to migrate to the oblique
direction of the lower shear stress field at 1 Pa [10]. The
effect of shear flow on cells depends on the cell types. The
dependency might be applied to the cell sorting technology[16]. After division, cells tend to migrate counter direction
each other. The tendency makes symmetrical distribution of
the migration velocity of cells in Fig. 7. Tracing of the cell
after division is convenient to study on the initial behavior of
the cell.
The cells proliferate regardless of the shear flow
stimulation. The cell cycle does not vary under the shear
flow [8]. The movement of each cell can be tracked by thetime lapse image with the interval of ten minutes in thepresent experiment.
To evaluate the response depending on the cell type,comparison with the experimental results of more cell types
is necessary [10]. A lot of supplementary works in molecularbiology are necessary to analyze the mechanism of build-up
tissue of oriented cells. More long term experiments are also
necessary to trace the relation between the migration
direction of the single cell and the orientation of cells in thetissue.
V. CONCLUSION
The migration velocity of each single cell under the
Couette type of the shear flow field has been studied inrelation to the area adhere to the scaffold before and after
division in vitro. The migration of each cell accelerates at thesmaller contact area around the term of division of the cell.
Several cells of L929 migrate to the direction perpendicular
to the flow just before division. Although many cells migrate
upstream, 3T3-L1 tends to migrate downstream.
ACKNOWLEDGMENT
The authors thank to Mr. Hiromi Sugimoto and Mr.
Kosuke Shimada for their assistance of the experiment.
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Re = ρ v d / η = ρ r ω d / η(3)

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