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

Cultured Myoblasts Orientation under Couette Type of Shear
Flow between Parallel Disks: Fusion and Division
Yuji ENDO, Shigehiro HASHIMOTO, Sora TOMA, Akira ASAHINO
Biomedical Engineering, Department of Mechanical Engineering, Kogakuin University
Tokyo, 163-8677, Japan
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

ABSTRACTconstant regardless of the distance from the wall [17, 19, 20].

The effect of shear stress on myoblast has been investigatedunder the uniform shear flow 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 thelower culture disk was controlled by the rotating speed of theupper disk. C2C12 (mouse myoblast cell line) was used in thetest. After cultivation without flow for 24 hours for adhesionof cells on the lower plate, τ was continuously applied on cells
for 7 days in the incubator. The behavior of each cell 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 both division and fusion undershear stress < 2 Pa. Interaction between divided cells
decreases with the distance between cells. The smaller cell
tends to follow the bigger cell related to the alignment.

It takes several hours for adhesion of cells to the scaffold. The
effect of the shear flow depends on the alignment of the cell.
At division [21] as well as at fusion, the alignment of the cellchanges. Variations can be made on the alignment of cells at
the timing.
In the present study, an experimental system of the Couette typeflow in the constant gap with a rotating disk has been used toapply the shear stress (2 Pa) quantitatively on the myoblast
during incubation at the microscopic observation in vitro. The
behavior of each cell has been traced at division and at fusion.

2. METHODS
Couette Type of Shear Flow Device
A Couette type of shear flow device has been used in thepresent study: between a rotating disk and a stationary dish (Fig.
1) [19]. The medium is sheared between a rotating wall and astationary wall. The stationary wall is the bottom of theculture dish (diameter 60 mm).

Keywords: Biomedical Engineering, Shear Stress, C2C12,
Orientation, Division and Fusion.

1. INTRODUCTION
In the device, the shear rate (γ) in the medium is calculated by
Eq. (1).

The effect of the shear flow on the endothelial cells, which areexposed to the blood flow on the inner surface of the vessel wall,
were investigated in many studies [1–10]. In the previous
study with the vortex flow [11] by the swinging plate in vitro,
C2C12 (mouse myoblast cell line) made orientation
perpendicular to the direction of the flow, although HUVEC(human umbilical vein endothelial cell) made orientation along
the streamline of the flow [12]. The orientation of each cell inthe tissue depends on that of neighbor’s cell. To analyze themechanism of making orientation of cells, the behavior of eachcell in the shear flow field should be quantitatively observed
during tissue making.

γ=rω/d

(1)
ω

rω
r
v

At the wall shear stress, a cell shows the following responses:
deformation [1–3], rotation [4, 5], migration [6, 7], division [7,8, 13], exfoliation [14–16], and fusion [17].

d

τ
Cell

Cell

Fig. 1: Couette flow velocity (v) distribution between rotating(angular velocity ω) wall and stationary wall at r (radius) with d(distance; left): shear stress (τ) on stationary wall (right) [17].

In the Poiseuille type of flow, the shear rate depends on the
distance from the wall: highest at the wall [14–16, 18]. In the
Couette type of flow, on the other hand, the shear rate is1

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

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 in
the whole space. The shear rate (γ [s㸫1]) in the gap between
walls increases in proportion to the distance (r [m]) from therotating axis.

S2
θ2

θ
x

The angular velocity ω (< 22 rad s ) was controlled by the
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 between 0.28 mm and 0.38 mm. Variations
on the shear rates (γ) between 1×103 s㸫1 and 1.4×103 s㸫1 aremade in the present experiment by adjustment of theseparameters.

Flow
θ1

Division

㸫1

S1

S2
Fusion

Δθ

S’2

θ2

θ’2

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

θ’1
θ1

(2)

S’1

Flow
’

S1

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 variations of theshear stress τ have been calculated as the value between 1.5 Pa
and 2.0 Pa.

Fig. 2a: Angle (θ) between longitudinal axis of each cell andflow direction; area (S): division, and fusion.

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.

Cell
Flow
θ

Cell Culture
C2C12 (mouse myoblast cell line originated with cross-striatedmuscle of C3H mouse, passage between eight and ten) was usedin the test. Cells were cultured in D-MEM (Dulbecco’s
Modified Eagle’s Medium): containing 10% decomplemented
FBS (fetal bovine serum), sodium hydrogen carbonate(NaHCO3), and 1% penicillin/ streptomycin.

−θ
Δθ

Cell
20 µm

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).

Fig. 2b: Angle (θ) between longitudinal axis of each cell andflow direction before fusion of cells.

After the incubation for 24 hours, the cells were continuously
sheared with the rotating disk for 7 days in the incubator at theconstant rotating speed without the medium exchange. The
constant speed was preset for each test to keep the designed
shear stress.
Measurement of Cell
The time-lapse microscopic image was taken every thirty
minutes during the cultivation. The contour of each cell
adhered on the stationary plate of the scaffold was traced, andthe projected two-dimensional area (S) at the image of each cell
was calculated. The contour of each cell was approximated toellipsoid, and the centroid of each cell was used to measure thedistance (x) between cells (Fig. 2). The area ratio (0 < R < 1)
between two cells (the couple before fusion, or after division)
was calculated by Eq. (3).
Rs = S1 / S2

0.1 mmFig. 3a: Cells (marked with each circle) traced under shear
stress field of 2 Pa: flow from left to right.

(3)2

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

0.1 mmTime [hour]Fig. 3b: Cells (marked with each circle) traced under shear
stress field of 1.5 Pa: flow from left to right.

Fig. 6: Angle (θ) before and after division under shear stressfield of 1.5 Pa: couple is shown by same marker.

θ [degree]

In Eq. (3), both S1 and S2 are areas of “cell 1” and “cell 2”,
respectively (S1 < S2). The acute angle (−90 degree < θ < 90degree) between the longitudinal axis of the cell and the flow
direction was measured at the microscopic image of each cell(Fig. 2). The difference of angles between two cells (0 degree<Δθ < 90 degree) was also measured.

3. RESULTS
Fig. 3 exemplifies images picked up from time-lapse images ofcells under the shear stress field: 2 Pa in Fig. 3a, and 1.5 Pa in
Fig. 3b, respectively. The behavior of each cell was traced
easily by the time-lapse images every thirty minutes under shear
stress field. The flow direction is from left to right in Fig. 3.
Time [hour]Fig. 4 shows the angle (θ) before and after division under the
shear stress field of 2 Pa. The time zero corresponds to thetiming of division of each cell. The negative time corresponds
to the time before cell division. The direction of each cellchanges at the division. The same marker corresponds totracings of each cell. Same color of line shows tracings ofrelated cells after division. In many cases, cells alignseparately after division each other. In the case of cells of theparallel direction to the flow before division, some cells tilt tothe direction perpendicular to the flow after division. In Fig. 4,
every cell distributes in the direction range parallel to the flow(−30 degree < θ < 30 degree) before division. The angle of 90
degree corresponds to the same alignment as that of −90 degree.

Fig. 4: Angle (θ) before and after division under shear stressfield of 2 Pa: couple is shown by same marker.
θ [degree]

Fig. 5 shows the angle (θ) before and after fusion under the
shear stress field of 2 Pa. Several cells tilt to the flow
direction after fusion. The alignment distribution of cells isconcentrated to the parallel direction (−30 degree < θ < 30
degree) after fusion. Each cell keeps its own alignment forseveral hours even after fusion.
Fig. 6 shows angle (θ) before and after division under shear
stress field of 1.5 Pa. Under the shear stress field of 1.5 Pa,alignments of cell distribute widely.

Time [hour]Fig. 5: Angle (θ) before and after fusion under shear stress fieldof 2 Pa: couple is shown by same marker.

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

Fig. 7 exemplifies the tracings of the angle (Δθ) between two
cells related to the distance (x) between two cells, after division
for 5 hours under the shear stress field of 1.5 Pa. After
division, cells have different alignments each other with theinteraction between cells.

Δθ [degree]

In Fig. 8, angles (Δθ) between two cells are collected in relation
to the distance (x) between two cells after division for 5 hours
under the shear stress field of 2 Pa. The same marker
corresponds to traced data of the same couple of cells after
division. The dotted line shows the regression line, where thecorrelation coefficient is small (r2 = 0.05). The cell tends tokeep position parallel to the adjacent cell. The angle between
cells tends to increase with the distance between cells.
In Fig. 9, angles (Δθ) between two cells collected at the sametiming as data in Fig.8 are illustrated in relation to the area ratio(R) between two cells under the shear stress field of 2 Pa. The
dotted line shows the regression line, where the correlation
coefficient (r2) is 0.31. The angle (Δθ) tends to increase withthe area ratio. Several cells keep perpendicular position after
division at the comparable areas.

Area ratio (R)Fig. 9: Angle (Δθ) between two cells vs. area ratio (R) between
two cells after division for 5 hours under shear stress field of 2
Pa: Δθ = 89 R – 26, r2 = 0.31.

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 [1−10]. Cells are
exfoliated under the shear flow at the wall shear stress higher
than 2 Pa [14−16]. A biological cell shows passive and active
responses in an environment [6, 22]. While the flow enhances
the cell migration to the downstream, a cell migrates to adapt tothe shear field. While the strong stimulation above thethreshold damages the cell, the stimulation below the thresholdremains in the cell as a memory for the response in the next step[5, 9]. The hysteresis effect governs the active response of thecell.

Fig. 7: Tracings of angle (Δθ) between two cells vs. distance (x)between two cells after division for 5 hours: 1.5 Pa.

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 [11, 12]. 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 disk channel [14],the rhombus channel [15], the cross flow channel [16], and therotating disk type [19].

Δθ [degree]

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 [19, 20]. The cone-and-plate type device has the uniform shear field in the entire space
between the rotating cone and the stationary plate [20]. The
shear stress is constant independent of the distance from therotating axis.

x [µm]
Fig. 8: Angle (Δθ) between two cells vs. distance (x) between
two cells after division for 5 hours under shear stress field of 2
Pa: Δθ = 0.21 x – 21, r2 = 0.05.

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

study, mechanical stress was studied on differentiation of stem
cells [24]. Mechanical stimulation was studied on tissue
formation [25]. Property of the scaffold affects differentiationof stem cells [26, 27]. Orientation of cells can be controlled
by design of the scaffold [28]. Mechanism to make orientationin the tissue might be analyzed by the study on the tracings ofthe alignment of each cell during division and fusion [29, 30].

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.
In the present study, the rotating parallel disk system is selected
to make Couette type of flow instead of the cone and platesystem. At the constant angular velocity, the shear rate (γ)
increases with the distance from the axis (r) in the observation
area (Eq. (1)). The variation of the shear rate enables thesimultaneous observation of the behavior of cells related tovariation of the shear stress [19]. 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. (4).
Re = ρ v d / η = ρ r ω d / η

5. CONCLUSION
The effect of shear stress on myoblast has been investigatedunder the uniform shear flow in vitro. Couette type of shear
flow field was made between a lower stationary culture plate
and an upper rotating parallel plate. The wall shear stress (τ)
was continuously applied on C2C12 (mouse myoblast cell line)
for 7 days, and the behavior of each cell 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 both division and fusion under shear stress< 2 Pa. Interaction between divided cells decreases with the
distance between cells. The smaller cell tends to follow thebigger cell related to the alignment.

(4)

In Eq. (4), 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 1×102, when ρ,r, ω, d, and η are 1×103 kg m㸫3, 0.018 m, 22 rad s㸫1, 0.00038
m, and 0.0015 Pa s, respectively. The turbulent flow may notoccur in the flow of small value of Reynolds number.

ACKNOWLEDGMENT
The authors thank to Mr. Hiroki Eri for his assistance of theexperiment.

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