Observation of Biological Cells in Rhombus Parallelepiped Flow
ChannelFumihiko SATO, Shigehiro HASHIMOTO
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/andToshitaka YASUDA
Bio-systems Engineering, Department of Electronic Engineering,Tokyo National College of Technology, Tokyo, Japan
and
Hiromichi FUJIE
Human Mechatronic Systems, Faculty of System Design,
Tokyo Metropolitan University, Tokyo, Japan

ABSTRACT
A flow channel has been designed to observe the behavior ofcells in a shear flow in vitro. A thin sheet of silicone rubber issandwiched by two transparent walls to form a parallelepiped
flow channel of 20 mm length × 0.1 mm depth. Variation ismade on the width of the channel (from 1 mm to 3 mm) with arhombus shape to vary the wall shear stress. Behavior of cellson the wall is observed under a flow with an inverted phase
contrast microscope. The shear stress on the wall is calculatedwith an estimated parabolic velocity profile between the paralleldisks. After several cells adhered to the wall, the shear stress
was applied on the cells with the flow of the medium by asyringe pump. The constant flow rate of 5 × 10-9 m3 s-1
produces the wall shear stress between 1 Pa and 3 Pa. Threekinds of cells were examined with the methodology: L929
(fibroblast-like, mouse connective tissue), HUVEC (Normal
Human Umbilical Vein Endothelial Cells) and C2C12 (Mouse
myoblast cell line originated with cross-striated muscle of C3Hmouse). The experimental results show that the response ofcells can be observed under stimulation by the fluid at thecontrolled wall shear stress in the flow channel.
Keywords: Biomedical Engineering, Flow Channel, L929,
HUVEC, C2C12, and Shear Stress.

1. INTRODUCTION
Mechanical stress is one of the interested points in theenvironment of cells, because they receive mechanical forces invivo. Several methods have been designed to apply themechanical stress to cells [1-11].
A transmission point of the stress to a specimen is important.
In many studies, the stress is applied to a scaffold [1, 2].
When the fixation between the cell and the scaffold is notenough, the stress is not transmitted to the cell.
Every cell receives the stress when it is exposed to the field,
such as gravitational field [3] or flow. A flow can be used toapply the stress to a specimen [4-11]. The specimen directly
receives the shear stress in the shear flow.
A flow chamber with a laminar flow is effective to study the
responses of cells to the shear stress quantitatively [5]. In thepresent study, responses of cells to the fluid shear stress havebeen studied with a parallelepiped channel in vitro.

2. METHODS
Rhombus Flow Channel
A one-way flow system has been designed to observe thebehavior of cells in a shear flow in vitro. The system consistsof a flow channel, a syringe pump, and tubes (Fig. 1). The
micro-syringe-pump (Fusion200, CXF1020, ISIS Co., Ltd.,
Osaka) was used for the syringe pump. A plastic tube of 3 mm
internal diameter and of 5 mm external diameter was used for aconnector to the flow channel.

A thin sheet (0.1 mm thick) of silicone rubber, which has arhombus void space of 3 mm × 20 mm (Fig. 3), is sandwiched
between the disks. The void space forms a channel of 20 mm
length × 0.1 mm depth, where the width varies from 1 mm to 3
mm.

Syringe pump

Flow
Tube

Tube

Flow chamber
Cell
Microscope

Fig. 1: Flow to syringe pump through flow channel.

The three plates stick together with their surface affinity
without adhesives. At the upper disk, two holes of 5 mmdiameter (Fig. 4) are machined by a punching tool. The
silicone tube is stuck at the holes without adhesives (Fig. 4).
The inner surface of the chamber was exposed to the oxygengas in a reactive ion etching system (RIE-10NR, Samco Inc.,
Kyoto) to be characterized as hydrophilic (oxygen plasma
ashing), before being assembled.
Immediately after the characterization, the flow path of thechamber was rinsed with a saline solution, and the suspensionof cells was introduced, successively.

Silicone sheet

PDMS disk

Observation
PDMS

disk

Fig. 2: Thin silicone rubber sheet with rhombus open space issandwiched by two transparent polydimethylsiloxane (PDMS)
disks.

Fig. 3: Dimension (mm) of flow path.

The flow channel consists of two transparent disks and a thinsheet of silicone rubber (Fig. 2). The upper disk is made ofpolydimethylsiloxane (PDMS). The lower disk is made of
PDMS or polystyrene (a culture dish).
A silicon wafer was used for a surface mold for the PDMS disk.
The diameter and the thickness of the wafer are 50 mm and 0.30mm, respectively. The surface of the wafer was cleaned with
the isopropyl alcohol, and coated with 0.001 mm thickness ofparylene in the parylene coater (PDS-2010, Speciality Coating
Systems, Indianapolis). After the wafer was enclosed with aperipheral wall of polyimide, PDMS (Sylgard 184 Silicone
Elastomer Base, Dow Corning Corporation) was poured withthe curing agent (Dow Corning Corporation) on the wafer.
After degassing, PDMS was baked at 383 K for one hour in anoven (DX401, Yamato Scientific Co., Ltd).
The diameter of two PDMS disks is 50 mm. The thicknessesof the upper and the lower disks are 10 mm and 2 mm,
respectively.

Fig. 4: Flow channel consists of two transparent
polydimethylsiloxane (PDMS) disks and thin silicone rubber
sheet, and connected to plastic tubes.

the flow test, the cells were exfoliated from the plate of theculture dish with trypsin, and suspended in the EGM-2.
C2C12 was cultured on a dish with the D-MEM (Dulbecco’s
Modified Eagle Medium) containing 10% FBS in the incubatorfor one week. Before the flow test, the cells were exfoliatedfrom the plate of the culture dish with trypsin, and suspended in
the D-MEM.
In the case of HUVEC and C2C12, the lower PDMS disk waschanged to the culture dish of polystyrene (Fig. 5).
The suspension was introduced to the channel and kept in the
incubator for 24 hours to make cells adhere to the plate of thechannel before the flow test. In some tests with C2C12, thecells were cultured in the incubator only for 3 hours before theflow test (Fig. 15).
Fig. 5: The flow chamber consists of thin silicone rubber sheet
sandwiched between transparent polydimethylsiloxane (PDMS)
disk and culture dish.

Flow Test
When the cell is observed under flow, the channel was set on
the microscope out of the incubator (Fig. 6). The constantflow of the medium was applied to the adhered cells with thesyringe pump (Fig. 1).
In the first test with L929, the flow rate increases every minutestep by step from 3 × 10-11 m3 s-1 to 6 × 10-8 m3 s-1. The wall
shear stress increases gradually, proportional to the stepwise
increase of the flow rate. The flow path was carefully
examined to avoid mixing of air bubbles, which might stir the
medium in the flow chamber and induce exfoliation of cells.
The behavior of cells on the plate of the chamber was observedwith the microscope. The photos of cells were taken during
the flow test intermittently.

Fig. 6: Observation system under flow: flow channel andmicroscope (middle), syringe pump (right).

One of the tubes is connected to the plastic syringe pump (Fig.
1). The room temperature was maintained at 25 degrees
Celsius. The chamber is placed on the inverted phase-contrast
microscope (IX71, Olympus Co., Ltd., Tokyo).
Cell Culture
Three kinds of cells were alternatively used in the experiment:
L929 (fibroblast-like, mouse connective tissue, RCB1422,
Riken Bio Resource Center, Tsukuba, passages 3–10), HUVEC(Normal Human Umbilical Vein Endothelial Cells, passages
2–5), or C2C12 (mouse myoblast cell line originated withcross-striated muscle of C3H mouse, passages 2–10). The
medium was refreshed every two days.
L929 was cultured on a dish with the E-MEM (Eagle’s minimal
essential medium) containing 10% FBS (fetal bovine serum) in
the incubator for one week. Before the flow test, the cells
were exfoliated from the plate of the culture dish with trypsin,and suspended in the E-MEM.
HUVEC was cultured on a dish with the EGM-2 (Endothelial
Cell Growth Medium) in the incubator for one week. Before

Fig. 7: Cell culture under flow: flow channel in incubator, andpump outside of incubator.

width of the flow path linearly decreases from 1.4 mm to 1.0
mm in the figures. As the decrease of the width of the flow
path, the wall shear stress increases.

Plate

Fig. 9 shows L929 on PDMS in the channel before flow
stimulation. Fig. 10 shows L929 under the flow of 6 × 10-8 m3
s-1, which generates the wall shear stress on PDMS between 12
Pa and 37 Pa estimated by Eqs. 1 & 2. Some cells elongate to
the downstream along the streamline of the flow in 41 min (A inFigs. 9 & 10). Some cells (B in Figs. 9 & 10) exfoliate from
PDMS, and flow to the downstream in 41 min.

q
D
b

G
Plate

Fig. 8: Parabolic velocity profile between parallel plates.

In the test of cell culture under flow, the channel is kept in the
incubator, and the medium is pumped with the syringe pump.
The syringe pump is located outside of the incubator, andconnected to the channel with the tube (Fig. 7).
Shear Stress on Wall
The shear rate (G, [s-1]) on the wall of the plate is calculated by
Eq. 1, in which a parabolic velocity profile between parallel
plates is hypothesized (Fig. 8).
G = 6 q / (b D2)

Fig. 11 shows L929 cultured on PDMS under the flow (1.4 ×
10-10 m3 s-1) for four days. The result shows that the numberof L929 increases to the sub-confluent state on PDMS in theflow channel under flow stimulation.
Fig. 12 shows HUVEC on the dish (Fig. 5) after flow
stimulation with the wall shear stress between 1 Pa and 3 Pa.
The results show migration and exfoliation of cells. HUVEC
moves on the wall and is exfoliated at the lower shear stressthan L929 (A, B in Fig. 12).

(1)

In Eq. 1, q is the flow rate [m3 s-1], b is the width of the channel[m] and D is the distance [m] between two parallel walls. In
the present study, D is 0.1 mm. Because the rhombus channel
has a variation on the width, b ranges from 1 mm to 3 mm (Fig.
3). The width at the inlet of the channel is 1 mm, andincreases from 1 mm to 3 mm in proportion to the distance fromthe inlet. At the middle point, the width is 3 mm, and thendecreases from 3 mm to 1 mm. The width is 1 mm at theoutlet. The variation of the width makes variation on the wall
shear stress in the channel, so that cells at variety of wall shear
stresses can be simultaneously observed in the constant flowrate.
The shear stress T [Pa] is the product of viscosity N [Pa s] of thefluid and the shear rate G [s-1] of the flow (Eq. 2).
T=NG

A

B

Fig. 9: L929 before flow stimulation. Dimension from left toright is 2.0 mm.

(2)

The viscosity of the medium was measured with the cone andplate type of viscometer (TVE-22L, Toki-Sangyo Co., Ltd.
Tokyo).

3. RESULTS
The result of measurement with the viscometer shows that theviscosity of the medium at the shear rate of 600 s-1 is 0.0010 Pa
s at 298 K, and that the viscosity is 0.0008 Pa s at 310 K. At
the flow rate of 5 × 10-9 m3 s-1, the calculated shear rate on the
PDMS wall of the flow chamber by Eq. 1 varies from 3000 s-1
to 1000 s-1, when the width of the flow path varies from 1 mm
to 3 mm. The calculated shear stress, thus, varies from 3 Pa to
1 Pa for viscosity of 0.001 Pa s, when the shear rate varies from3000 s-1 to 1000 s-1.
The distance from left to right is 2.0 mm in Figs. 9-15. The
medium flows from left to right in Figs. 9-15. The outlet ofthe chamber is located near the right end of Figs. 9-12, and theA

B

Fig. 10: L929 after flow stimulation for 41 min. A: elongate.
B: disappear.

was cultured without flow in the incubator for 24 hours foradhesion of C2C12 to the bottom of the dish. The longitudinalaxes of some cells are perpendicular to the flow direction (B in
Fig. 13). Many cells exfoliated in two days of culture (A, B in
Fig. 13).
Fig. 15 shows C2C12 after flow stimulation for 2 day with thewall shear stress between 0.1 Pa and 0.3 Pa. Before flow
stimulation, C2C12 was cultured without flow in the incubatorfor 3 hours for adhesion of C2C12 to the bottom of the dish.
Some cells exfoliate from the bottom of the dish, and flow tothe downstream.

4. DISCUSSION

Fig. 11: L929 cultured under flow for four days. Dimension
from left to right is 2.0 mm.

The cells can be cultured on the oxygenated PDMS disk,
although adhesiveness of cells is higher on the polystyrene dishthan on the PDMS disk.
The fresh medium should be supplied into the flow channel,
because the medium in the channel does not face to the oxygengas and because the volume of the medium in the cannel is verysmall. The results show that the flow rate of the medium isabove the minimum value to maintain cell culture.

A
B

Fig. 12: HUVEC after flow stimulation (wall shear stress of 1
Pa -3 Pa). To be exfoliated (A, B).

Fig. 14: C2C12 after flow stimulation for 2 day (wall shear
stress of 1 Pa -3 Pa).

A

B

Fig. 13: C2C12 after flow stimulation for 1 day (wall shear
stress of 1 Pa -3 Pa). To be exfoliated (A, B).

Figs. 13 and 14 show C2C12 on the dish after flow stimulation
with the wall shear stress between 1 Pa and 3 Pa for one day
and two days, respectively. Before flow stimulation, C2C12

Fig. 15: C2C12 after flow stimulation for 2 day (wall shear
stress of 0.1 Pa -0.3 Pa).

The area for observation is selected mainly near the outlet area,
because the flow might be more stable near the outlet than near
the inlet. The flow separation might occur near the inlet area,
where the width of the flow path increases.

Ministry of Education, Culture, Sports and Technology.

To estimate the wall shear rate in the chamber, a parabolic
velocity profile is hypothesized as a laminar flow in the present
experiment. Reynolds number (Re) is a useful index for
estimation of the laminar flow.

[1] C.A. Powell, B.L. Smiley, J. Mills and H.H. Vandenburgh,“Mechanical Stimulation Improves Tissue-engineered
Human Skeletal Muscle”, American Journal of Physiology- Cell Physiology, Vol. 283, No. 5, 2002, pp. C1557–C1565.
[2] J. Goldman, L. Zhong and S.Q. Liu, “Degradation of
α-actin Filaments in Venous Smooth Muscle Cells in
Response to Mechanical Stretch”, American Journal of
Physiology- Heart and Circulatory Physiology, Vol. 284,
2003, pp. H1839-H1847.
[3] S. Motoda, S. Hashimoto, T. Iwagawa and A. Nakajima,“Effect of Excess Gravitational Force on Cultured Myotubes
in Vitro”, Proc. 15th World Multi-Conference on
Systemics Cybernetics and Informatics, Vol. 2, 2011, pp.
118-123.
[4] H. Kang, Y. Fan and X. Deng, “Vascular Smooth Muscle
Cell Glycocalyx Modulates Shear-induced Proliferation,
Migration, and NO Production Responses”, American
Journal of Physiology - Heart and Circulatory
Physiology, Vol. 300, 2011, pp. H76–H83.
[5] F. Sato, S. Hashimoto, K. Oya and H. Fujie, “Responses ofCells to Fluid Shear Stress in Vitro”, Proc. 16th World
Multi-Conference on Systemics Cybernetics andInformatics, Vol. 2, 2012, pp. 97-102.
[6] S. Hashimoto and M. Okada, “Orientation of Cells Cultured
in Vortex Flow with Swinging Plate in Vitro”, Journal of
Systemics Cybernetics and Informatics, Vol. 9, No. 3,
2011, pp. 1-7.
[7] R.H.W. Lam, Y. Sun, W. Chen and J. Fu, “Elastomeric
Microposts Integrated into Microfluidics for Flow-mediatedEndothelial Mechanotransduction Analysis”, Lab on a Chip,
Vol. 12, 2012, pp. 1865-1873.
[8] S. Hsu, R. Thakar, D. Liepmann and S. Li, “Effects of Shear
Stress on Endothelial Cell Haptotaxis on Micropatterned
Surfaces”, Biochemical and Biophysical ResearchCommunications, Vol. 337, No. 1, 2005, pp. 401-409.
[9] M.L.C. Albuquerque, C.M. Waters, U. Savla, H.W. Schnaperand A.S. Flozak, “Shear Stress Enhances Human Endothelial
Cell Wound Closure in Vitro”, American Journal of
Physiology - Heart and Circulatory Physiology, Vol. 279,
pp. H293-H302, 2000.
[10] P. Uttayarat, M. Chen, M. Li, F.D. Allen, R.J. Composto
and P.I. Lelkes, “Microtopography and Flow Modulate the
Direction of Endothelial Cell Migration”, American
Journal of Physiology - Heart and Circulatory
Physiology, Vol. 294, 2008, pp. H1027-H1035.
[11] P.P. Hsu, S. Li, Y.S. Li, S. Usami, A. Ratcliffe, X. Wang and
S. Chien, “Effects of Flow Patterns on Endothelial Cell
Migration into a Zone of Mechanical Denudation”,
Biochemical and Biophysical Research Communications,Vol. 285, 2001, pp. 751-759.
[12] D.A. Lauffenburger and A.F. Horwitz, “Cell Migration: A
Physically Integrated Molecular Process’’, Cell, Vol. 84,
1996, pp. 359–369.
[13] A.J. Ridley, M.A. Schwartz, K. Burridge, R.A. Firtel, M.H.
Ginsberg, G. Borisy, J.T. Parsons and A.R. Horwitz, “Cell
Migration: Integrating Signals from Front to Back’’, Science,Vol. 302, 2003, pp. 1704-1709.

Re = d D v / N(3)

In Eq. 3, d is density [kg m-3] of the fluid, D is distance [m]between two parallel walls, N is viscosity [Pa s] of the fluid,
and v is the mean velocity of the flow [m s-1]. The mean
velocity is calculated by Eq. 4.
v = q / (b D)(4)

In Eq. 4, q is the flow rate [m3 s-1], and b is the width [m] of thecanal.
Re is in the range between 1.7 and 5, calculated with d (103 kgm-3), N (10-3 Pa s), D (10-4 m), q (5 × 10-9 m3 s-1), and b (ranges
from 1 mm to 3 mm) in the present experiment. The number
is small enough to estimate the laminar flow.
The parallelepiped rhombus chamber designed in the present
study realizes the wall shear stress field, where the shear stressvaries linearly along the stream line.
The chamber isconvenient to observe the response of cells simultaneously withthe variation of the wall shear stress, while the wall shear stressis constant in the parallelepiped rectangular chamber of theprevious study [5].
Both acceleration of proliferation and orientation of cells areimportant targets in the research field of regenerative medicineon the cultured biological tissue. Another study shows
mechanical stimulation improves a tissue-engineered humanskeletal muscle [1].
The previous studies show that a mechanical field, on the other
hand, governs behavior of cells [12, 13]. The shear flow
governs the orientation of endothelial cells [6-11]. Vascular
cells are subject to mechanical forces by the bood flow [2].
The shear stress affects the orientation of the smooth muscle
cells in the biological tissue [2, 4].

5. CONCLUSION
The parallelepiped flow channel has been designed to observe
the response of cells to the fluid shear stress under a microscope.
The experimental results show that both deformation andexfoliation of cells can be observed under stimulation with thefluid at the controlled wall shear stress in the rhombus flow
channel.

6. ACKNOWLEDGMENT
This work was supported by a Grant-in-Aid for Strategic
Research Foundation at Private Universities from the Japanese

REFERENCES