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

Effect of Shear Stress on Myoblasts Cultured under Couette
Type of Shear Flow between Parallel Disks
Yuji ENDO, Shigehiro HASHIMOTO, Hiroki ERI
Biomedical Engineering, Department of Mechanical Engineering,
Kogakuin University, Tokyo, 163-8677, Japan
http://www.mech.kogakuin.ac.jp/labs/bio/
ABSTRACTof the distance from the wall [17–23].

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 differentiate to myotubes under shear
stress < 2 Pa. Both the cell cycle and the cell length tend to
scatter in the wider range, and the longitudinal axis of the cell
tends to align to the flow direction by the shear stress of 1 Pa.
The experimental system is useful to study the quantitative
relationships between the shear stress and the cell behaviors:
deformation, orientation, and differentiation.

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 (< 2 Pa) on the myoblast has beenstudied about deformation, orientation, and differentiation.

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

γ=rω/d

2. METHODS
Couette Type of Shear Flow Device
A Couette type of shear flow device has been designed in thepresent study: 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 (diameter 60 mm).
In the devise, the shear rate (γ) in the medium is calculated by
Eq. (1).
(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.

1. INTRODUCTION

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 made orientation perpendicular to the direction of theflow, although HUVEC made orientation along the streamlineof the flow [12]. The orientation of each cell in the tissue
depends on that of neighbor’s cell. To analyze the mechanismof making orientation of cells, the behavior of each cell in theshear flow field should be quantitatively observed in vitro.

The angular velocity ω (< 22 rad s－1) 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 0.56 mm. Variations
on the shear rates (γ) between 0.7×103 s－1 and 1.4×103 s－1 aremade in the present experiment by adjustment of theseparameters.
The shear stress (τ [Pa]) is calculated by the viscosity (η [Pa s])of the medium.

At the wall shear stress, a cell might show the following
responses: elongation [1–3], tilting to the stream line [4, 5],migration [6, 7], deformation to be rounded, proliferation [7, 8,13], and exfoliation from the wall of the scaffold [14–16].

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 1.0 Pa
and 2.0 Pa.

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 regardless1

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

ω
rω
r
v

Flow direction

d

θ
τ

Cell

Cell

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

Fig. 2: Angle (θ) between longitudinal axis of myotube(yellow) and flow (arrow) direction.

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.

In the extra test, the flow adjacent to the scaffold surface of theculture dish was traced by the movement of microspheres(borosilicate glass particles: diameter of 10 ± 1.0 μm, anddensity of 2.4 g / cm3) recorded by a high speed camera.

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.

The acute angle (−90 degree < θ < 90 degree) between thelongitudinal axis of the cell and the flow direction wasmeasured at the microscopic image of each cell (Fig. 2).

3. RESULTS
Fig. 3 shows tracings of the microspheres rolling on the surfaceof stationary plate in the shear flow field. The tracings show
the steady parallel linear movements.

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. 4 shows the area ratio occupied by cells after seven days
culture under the shear flow in relation to the wall shear stress.
Cells proliferate to make the confluent mono layer on thesurface of the stationary plate in seven days of culture undershear stress lower than 1 Pa. Under the shear stress higher
than 1 Pa, the area ratio occupied by cells is lower than 20 %.
Several cells were exfoliated at proliferation, because of thedecrease of the contact area to the scaffold at the cell division.

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.

Fig. 5 exemplifies tracings of the angle of the cell without
proliferation under the shear stress of 1.5 Pa. In Fig. 5, both
＋90 degree and －90 degree are the same direction, which isperpendicular to the flow direction. Within 20 hours, each cellchanges direction every thirty minutes. One of the cells
rotates its longitudinal axis to make perpendicular direction to
the flow direction after 20 hours of culture. In eighty hours ofculture, the angles of two cells approach to zero degree, whichis flow direction. In each case of Fig. 5, the area ratio
occupied by cells is lower than 20 %. In densely populated
cells, each cell tends to follow the direction of the neighbor cell.

The contour of each cell adhered on the stationary plate of thescaffold was traced, and the projected two-dimensional area (S)at the image of each cell was calculated. The area ratio
occupied by cells was calculated by Eq. (3).
Rs = 100 × (Σ Si) / A(3)

In Eq. (3), Σ Si is accumulated total area of cells, and A is thecorresponding scaffold area.
In the confluent case, Rs
becomes 100 %.

Fig 6 shows the cell cycle of each cell related to the shear stress.
The mean value of the cell cycle is 15 hours regardless of theshear stress. At the shear stress of 1 Pa, the cell cycle scatters:
the cell cycle extends to a period of 20 hours or longer in somecells.

After fusion of cells were observed, the length of each myotube(L) was measured.
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.

Fig. 7 exemplifies the tracings of the area of the cell before
exfoliation. The area of each cell decreases within six hours.
The cell exfoliates regardless of the initial size.

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

Angle [degree]

Fig. 8 shows the relationship between the term of differentiationand the shear stress. The term of differentiation tends toincrease with the shear stress. Even under the shear stress of 2
Pa, myoblasts differentiate into myotubes within six days ofculture without the medium exchange.
Fig. 9 shows the relationship between the length of myotube
and the shear stress after seven days of culture. The mean
length is 40 μm regardless of the shear stress. At the shear
stress of 1 Pa, the length scatters: the length extends longer than
50 μm at one cell.

Time [hour]

Figs. 10-12 show the angle of each cell. In Figs. 10-12, every
data is plotted in ascending order, to avoid the dependency on
the way of segmentation of the parameter in the histogram.
Figs 10a, 11a, and 12a show the angle before exposure to theshear flow. Figs 10b, 11b, and 12b show the angle after
exposure to the shear flow for three days. Figs 10c, 11c, and12c show the angle after exposure to the shear flow for sevendays. Before exposure to the shear flow, the direction of thecell is random (Figs 10a & 12a), in which data align on thestraight line. In Fig. 11a, it is coincidences that many cells tilt
from the flow direction with the angle of 60 degree before
exposure to the shear flow. Many cells tilt to the flow
direction (zero degree) after exposure to the flow (1 Pa and 1.5
Pa) for seven days (Figs. 10c & 11c). At 2 Pa, many cells tilt
to the oblique (30 degree) direction from the flow direction after
exposure to the flow for seven days (Fig. 12c).

Fig. 5: Tracings of angle of cell [degree]: shear stress 1.5 Pa.

Fig. 6: Cell cycle [hour] vs. shear stress [Pa].

0.2 mmFig. 3: Tracings of microspheres on surface of stationary platein shear flow field: flow direction (arrow).

Fig. 7: Area tracings of each cell.

Rs [%]

Differentiation term [day]Shear stress τ [Pa]Fig. 8: Differentiation term [day] vs. shear stress [Pa].

Shear stress τ [Pa]Fig. 4: Area ratio occupied by cells (Rs [%]) vs. shear stress (τ[Pa]) after 7 days of cultivation.

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

Fig. 9: Length of myotube (L [μm]) vs. shear stress [Pa]: 7days.

Fig. 11a: Before flow stimulation, angle (θ [degree]) of C2C12:
1.5 Pa.

Fig. 11b: After three days of continuous flow stimulation, angle(θ [degree]) of C2C12: 1.5 Pa.

Fig. 10a: Before flow stimulation, angle (θ [degree]) of C2C12:
1 Pa.

Fig. 11c: After seven days of continuous flow stimulation,
angle (θ [degree]) of C2C12: 1.5 Pa.

Fig. 10b: After three days of continuous flow stimulation, angle(θ [degree]) of C2C12: 1 Pa.

Fig. 12a: Before flow stimulation, angle (θ [degree]) of C2C12:
2 Pa.

Fig. 10c: After seven days of continuous flow stimulation,
angle (θ [degree]) of C2C12: 1 Pa.

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

biological fluid in the previous studies [17−23]. The cone-and-plate type device has the uniform shear field in the entire space
between the rotating cone and the stationary plate [18−21].
The shear stress is constant independent of the distance from therotating axis. The clot formation was quantitatively studied
between the rotating cone and the stationary plate [19], andbetween the rotating concave cone and the stationary convex
cone [20]. The erythrocyte destruction was studied between
the rotating concave cone and the stationary convex cone [21].
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. The floating erythrocyte deformation wasobserved between counter rotating parallel discs [22, 23].

Fig. 12b: After three days of continuous flow stimulation, angle(θ [degree]) of C2C12: 2 Pa.

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 of 22 rad s－1 (d =0.0003 m), 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 (Eq. (1)). 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 [17]. 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 thesteady flow in the present experiment. Reynolds number (Re)is calculated by Eq. (4).

Fig. 12c: After seven days of continuous flow stimulation,
angle (θ [degree]) of C2C12: 2 Pa.

4. DISCUSSION
Re = ρ v d / η = ρ r ω d / ηEndothelial 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]. 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 [5, 9].
The hysteresis effect governs the active response of the cell.

(4)

In Eq. (4), 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 1.5×102, when ρ, r, ω, d,and η are 1×103 kg m－3, 0.018 m, 22 rad s－1, 0.00056 m, and
0.0015 Pa s, respectively. The turbulent flow may not occur inthe flow of small value of Reynolds number. The steady
actual flow direction adjacent to the scaffold surface of cell
culture has been confirmed by the streamline traced by the
direction of exfoliation of the cell and of the moving particle
adjacent to the surface. The flow velocity, which increases inproportional to the distance from the rotating axis, has also been
confirmed by tracings of the moving particle adjacent to thesurface.

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 [17].

The interaction between cells also governs the behavior of eachcell. The orientation of each cell depends also on theorientation of the neighbor cell. The most of myoblasts tend
to migrate to the oblique direction of the lower shear stress field
at 1 Pa. The effect of shear flow on cells depends on the cell
types. The dependency might be applied to the cell sorting
technology. The quantitative relationships between the shear
stress and the cell orientation might be applied to tissue
technology to control of cells in vitro.

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 ofIn the present experiment in vitro, the myoblast tends to be5Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)“Temporal Gradients in Shear, but Not Spatial Gradients,
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exfoliated, when the area of the attachment to the scaffold
decreases during proliferation. The myoblast proliferates
regardless of the shear flow stimulation. The cell cycle does
not vary under the shear flow. When myoblasts are cultured in
the continuous steady shear flow without change of the medium
between the plates, myoblasts differentiate to myotubes.
Myotubes do not proliferate, so that the contact area did notdecrease. The movement of each cell is able to be traced by
the time-lapse image with the interval of thirty minutes in thepresent experiment.

5. CONCLUSION
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 behavior of each cell (C2C12)
was traced at the time-lapse image observed by an inverted
phase contrast microscope placed in an incubator for 7 days.
The experimental results show that cells differentiate tomyotubes under shear stress < 2 Pa. Both the cell cycle andthe cell length tend to scatter in the wider range, and thelongitudinal axis of the cell tends to align to the flow direction
by the shear stress of 1 Pa. The experimental system is usefulto study the quantitative relationships between the shear stressand the cell behaviors: deformation, orientation, anddifferentiation.

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