Rotating Disk to Apply Wall Shear Stress on Cell Culture at
Microscopic Observation
Masashi OCHIAI, Haruka HINO, Shigehiro HASHIMOTO, Yusuke TAKAHASHI
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/
ABSTRACTAn experimental system of the Couette type flow with a rotating
disk has been designed to apply wall shear stresses on the cell
culture at the microscopic observation in vitro. The shear
stress on the wall is calculated with an estimated Couette typeof the velocity profile between the rotating disk and the culture
plate. The constant rotational speed (lower than 100 rpm)
produces the wall shear stress smaller than 3 Pa. The rotating
disk system is mounted on the stage of an inverted phase
contrast microscope to observe the behavior of cells adhered on
the plate under the shear flow. The medium is refreshed at aslow speed by a syringe pump. The system is placed in an
incubator, where temperature and CO2 content are kept 310 K
and 5 percent, respectively. The experimental system allowsobservation of cells during incubation under the wall shear
stress. The designed system is useful to apply wall shear
stresses quantitatively on cell culture.
Keywords: Biomedical Engineering, Cell Culture, Shear Stressand Couette Flow.

1. INTRODUCTION
Cell culture technique has been developed and several
methodologies have been clinically applied to regenerative
medicine. The acceleration technique for orientation andproliferation of cells has been studied to make tissue in vivo orin vitro [1-4]. The behavior of biological cells depends onelectric and magnetic fields [1, 2]. Control methodology fororientation and proliferation of cells would be applied to theregenerative tissue technology.
The mechanical stress is one of the interested points in theenvironment of cells, because they receive mechanical force invivo. The mechanical stress on cells might induce various
responses: deformation, migration, proliferation, anddifferentiation. Several methods have been designed to apply
the mechanical stress to cells [3, 4].
A transmission point of the stress to a specimen is important.
In many studies, the stress is applied to a scaffold [4]. Whenfixation between the cell and the scaffold is not enough, thestress is not transmitted to the cell. A flow, on the other hand,
can be used to apply a stress field to a specimen [5, 6]. Thecells directly receive the shear stress in the shear flow (Fig. 1).

Flow

Cell
Fig. 1: Cells exposed to wall shear stress in shear flow.

The high shear flow might deform cell, peel cells off thescaffold, and inhibit proliferation as well as tissue formation.
The mild shear flow, on the other hand, might acceleratemigration, proliferation, and secretion of materials, which makethe extra cellular matrix.
The volume of the bone tissue is controlled with osteoclasts andosteoblasts: osteoblasts form bone, although osteoclasts resorbbone. The volume of the bone decreases in the microgravity
field.
In the previous study, osteoblasts were exposed to shear flow ina donut-shaped open channel, and the effect of flow stimulation
on cultured osteoblast has been studied in vitro [6]. When theflow has an open surface, it is difficult to estimate the shear
stress in the fluid.
Between two parallel walls, on the other hand, the velocityprofile is easily estimated in the laminar flow. In the presentstudy, an experimental system of the Couette type flow with arotating disk has been designed to apply the wall shear stressquantitatively on the cell culture at the microscopic observationin vitro.

2. METHODS
Rotating Parallel Disk System
A cone and plate type of instrument is often used to apply
Couette type of flow to a biological liquid. In the laminar flowin the space between a rotating cone and a stationary plate, a
uniform shear field of Couette type is generated. The cone isrotating around the co-axis of the symmetry with the plate,while the apex of the cone is touching on the plate (Fig. 2).
The shear rate (E [s-1]) is constant regardless of the distance (r[m]) from the rotating axis (Figs. 3&4).

In Eq. 2, w is the angular velocity [rad s-1].
rw

d=ryv
d(3)

In Eq. 3, y is the angle [rad] of clearance between cone andplate. Combination of Eqs. 1-3 makes Eq. 4, which shows theshear rate (E) does not depend on the distance (r) from therotating axis.
E=w/yFig. 2: Rotating cone and stationary plate.

(4)

In the present study, a rotating parallel disk system is chosen(Fig. 5). The fluid is sheared between a rotating disk and astationary disk. The stationary disk is the bottom of theculture dish. In the system, the shear rate (E) is calculated byEq. 5.

wr

E=rw/d(5)dyIn the parallel disk system, the shear rate (E) increases inproportion to the distance (r) from the rotating axis.
Shear Stress on Cell
The shear rate (E) generates the shear stress (F [Pa]) in a
viscous fluid.

Fig. 3: Cross section of rotating cone and stationary plate.

F=NEv

In Eq. 6, N is viscosity of the fluid [Pa s]. The fluid is themedium of cell culture in the present study.
The rotating disk system is mounted on the stage of an inverted
phase contrast microscope. The behavior of cells adhered on
the plate under shear stress is observed with the microscope.

dThe experimental system is placed in an incubator, where boththe temperature of 310 K and the carbon dioxide partialpressure of 5 percent are maintained. The medium is refreshedat a slow speed by a syringe pump. The system allows
observation of cells during incubation under the wall shearstress.

Fig. 4: Couette flow.

3. RESULTS AND DISCUSSIONrwv

According to the methodology of the rotating parallel disk, thesystem has been designed to coincide with the microscope andthe incubator (Fig. 6). The culture dish of 50 mm diameter has
been selected to the stationary plate. The diameter of therotating disk has been designed to be 40 mm (Fig. 7).

dThe shear stress is applied to cells on the bottom of the culturedish. The shear stress has been related to that of the bloodvessel wall. The shear stress of 3 Pa is maximum value
estimated as that is applied in the blood on the human bloodvessel wall, when the wall shear rate is calculated by Poiseuilleflow.

Fig. 5: Rotating parallel disk system.

E=v/d

(1)

In Eq. 1, v is the circumferential velocity [m s-1] of the moving
wall at the distance (r) from the rotating axis, and d is thedistance between the moving wall and the stationary wall.
v=rw

(6)

(2)

If the angular velocity (w) is selected to be 10 rad s-1, the shear
rate (E) is 3000 s-1, when the distance from the axis (r) and thedistance between the moving wall and the stationary wall (d)are 18 mm and 0.06 mm, respectively (Eq. 5).

disk from 1 rad s-1 to 10 rad s-1, which makes variation of theshear stress from 0.3 to 3 Pa. The angular velocity iscontrolled by the motor.

Syringe pump

Reynolds number is calculated by Eq. 7.
Medium in

Medium out

Finishing the surface is easier on the plane than on the circularconical surface. The roughness on the surface disturbs laminarflow between the cone and the plate. The system of parallel
plane disks has advantage for the laminar flow than the systemof cone and plate.

CellThe distance between two parallel disks is more stable than thedistance between cone and plate, because the viscous fluidsustains uniform narrow distance.

Microscope

Fig. 6: Rotating parallel disks system in the incubator. Cells
cultured in Couette type of flow are observed by microscope.

Culture dishDriver(7)

In Eq. 7, D is density of the fluid. Re is 11, when D, r, w, d,and N are 1000 kg m-3, 0.018 m, 10 rad s-1, 0.00006 m, and0.001 Pa s, respectively. The turbulent flow hardly occurs in
the flow of small value of Reynolds number.

Rotatingdisk

CO2 Incubator

Re = D v d / N = D r w d / N

The donut-shaped open channel is convenient to study the effectof flow direction on the cell culture [5, 6], but it is not easy toestimate quantitatively the shear stress in the fluid because of
the free surface.
Many kinds of the channels of Couette type flow were designedfor quantitative experiments of biological fluid in the previousstudies.
The clot formation was quantitatively studied
between a rotating cone and a stationary plate [7], and between
a rotating concave cone and a stationary convex cone [8]. The
erythrocyte destruction was studied between a rotating concave
cone and a stationary convex cone [9]. The erythrocyte
deformation was observed between counter rotating parallel
discs [10, 11].

Motor
MediumsupplyMediumdrainage

Rotating disk
Culture dishCells
Fig. 7: Cells are cultured in shear flow generated by rotatingdisk. The lower figure shows the cross section of the culturedish.

The rotating flow induces the secondary flow by the centrifugal
effect. The effect is smaller in the system with the rotation ofouter concave cone than with that of inner convex cone. The
effect decreases with decrease of the rotational speed. The
rotational speed of the disk is smaller than 0.2 m s-1 in thepresent system.
Poiseuille type of flow is also convenient to estimate the shear
stress in the fluid. The behavior of cells was observed in thetwo dimensional Poiseuille type of flow between parallel wallsin the previous study [12].
Several experimental systems were designed to observe theeffect of shear flow on cells in the previous studies [13-16].

At the constant angular velocity of 10 rad s-1, the shear rate (E)increases from 2700 s-1 to 3000 s-1, when the distance from theaxis (r) increases from 16 mm to 18 mm in the observation area.
The gradient of shear stress enables the simultaneous
observation of the behavior of cells related to variation of theshear stress in the same view.

An experimental system with a rotating disk has been designed
to apply wall shear stresses on the cell culture at themicroscopic observation in vitro. The designed system isuseful to apply wall shear stresses quantitatively on cell culture.

When the viscosity (N) of the culture medium at 310 K is 0.001
Pa s, shear stress (F) is 3 Pa at 3000 s-1 (Eq. 6)

5. ACKNOWLEDGMENT

Variation has been made on the angular velocity of the rotatingThis work was supported by a Grant-in-Aid for Strategic

4. CONCLUSION

Research Foundation at Private Universities from the Japanese
Ministry of Education, Culture, Sports and Technology.

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