Endothelial Cell Behavior After Stimulation of Shear Flow
Shigehiro HASHIMOTO, Haruka HINO, Hiromi SUGIMOTO, Yusuke TAKAHASHI, Wataru SATO
Biomedical Engineering, Department of Mechanical Engineering,
Kogakuin University, Tokyo, 163-8677, Japan
http://www.mech.kogakuin.ac.jp/labs/bio/
ABSTRACTAn experimental system of the Couette type flow with a rotating
disk has been used to apply the wall shear stress quantitatively
on the cell at the microscopic observation in vitro, and the
behavior of the cell after stimulation of shear flow has been
evaluated. The shear stress on the wall is calculated with anestimated Couette type of the velocity profile between therotating disk and the stationary culture plate. Variation wasmade on the wall shear stress of 1.0 Pa and 1.4 Pa adjusted by
the rotational speed of the disk. The rotating disk system ismounted on the stage of an inverted phase contrast microscope
to observe the behavior of HUVEC (human umbilical vein
endothelial cells) adhered on the plate after stimulation of theshear flow. Migration, deformation, and orientation of eachcell have been traced at the time-laps image for 24 hours after
the stimulation for 24 hours. The experiments show thefollowing results. HUVEC tends to make orientation parallelto the stream line, and that the tendency is maintained forseveral hours. The migration of each cell is accelerated after
stimulation of the wall shear stress of 1.4 Pa. The increase ofarea of each cell is decelerated by the higher wall shear stress.
The Couette type of rotating disk system is effective to detect
the behavior of cells after stimulation of the shear flow.
Keywords: Biomedical Engineering, Cell Culture, Shear Stress,
HUVEC and Couette Flow.

1. INTRODUCTION
A biological cell shows passive and active behaviors in anenvironment. While the shear stress deforms the cell, the cellchanges own form to adapt to the shear field. While the strong
stimulation excess the threshold damages the cell, thestimulation below the threshold remain in the cell as a memory
for the response in the next step.
The cell culture technique has been developed and several
methodologies have been clinically applied to the regenerative
medicine. The acceleration technique for differentiation andproliferation of cells has been studied to make tissue in vivo orin vitro [1-4]. The behavior of biological cells also depends onelectric and magnetic fields [5, 6]. 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 [7-19]. 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 [2, 20-30].
A transmission point of the stress to a specimen is important.
In many studies, the stress is applied to a scaffold. 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. The cells
directly receive the shear stress in the shear flow.
The high shear flow might deform a cell, peel off a cell from 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.
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 [23, 24]. When theflow has a free surface, it is difficult to estimate the shear stressin the fluid quantitatively. Between two parallel walls, on theother hand, the velocity profile is easily estimated in the laminarflow [21-23].
In the present study, an experimental system of the Couette typeflow with a rotating disk has been used to apply the wall shear
stress quantitatively on the endothelial cell at the microscopic
observation in vitro, and the behavior of the cell after
stimulation of shear flow has been evaluated.

2. METHODS
Rotating Parallel Disk System
In the present study, a rotating parallel disk system is selected tomake Couette type of flow (Fig. 1) [20]. The fluid is sheared
between a rotating disk and a stationary disk. The rotating
disk is made of polycarbonate: 44 mm diameter and 10 mmthickness. The stationary disk is the bottom of the culture dish.
In the system, the shear rate (γ) is calculated by Eq. 1.
γ=rω/d(1)

In Eq. 1, ω is the angular velocity [rad s－1], and d is the
distance [m] between the moving wall and the stationary wall(Fig. 3). In the rotating parallel disk system, the shear rate (γ[s－1]) increases in proportion to the distance (r [m]) from therotating axis.

(LCV110-SK) for 24 hours. The behavior of each cell was
analyzed at the microscopic time-laps (every five minutes)
images.

Motor

Microscopic Observation
The positions are marked by grooves on the outside surface ofthe culture dish: at 10 mm, 15 mm, 18 mm, and 20 mm.
On the microscopic image, the outline of each cell was traced,
and the contour of each cell was approximated to ellipsoid “byImage J” (Fig. 2) The irregular shape of cell is not included in
the analysis of approximation to elipsoid. As to the ellipsoid,the area, the coordinates of the centroid, the length of the major
axis (a), and the minor axis (b) were measured. The ratio ofaxes is calculated as the shape index (S.I.) by Eq. 3.

Rotating Disk

Cell

Culture Dish

S.I. = b / aFig. 1: Cell culture in Couette flow between rotating disk andstationary dish: front view (left), plan view with motor (right).

The rotational movement is transmitted by the belt, whichmakes connection between the rotating disk and the rotating
axis of the stepping motor. The rotating speed (< 400 rpm) is
controlled by the motor, which makes variation of angularvelocity ω (< 42 rad s－1). The position for the observation has
the variation on r (the distance from the rotating axis) between
12 mm and 18 mm. The distance d is estimated to 0.8 mm
from the positions of the focus of the walls at the microscope.
The shear rate (γ < 103 s－1) is calculated by these parameters.
Shear Stress on Cell
The shear rate (γ) generates the shear stress (τ [Pa]) in a viscous
fluid.
τ=ηγ
In Eq. 2, η is the viscosity of the fluid [Pa s].
medium of cell culture in the present study.

(2)
The fluid is the

The viscosity (η = 0.0014 Pa s) of the medium (Dulbecco’s
Modified Eagle Medium) is measured by the cone and plateviscometer at 310 K. The shear stress (τ < 1.4 Pa) is
calculated by Eq. 1 and Eq. 2.
The rotating disk system is mounted on the stage of an inverted
phase contrast microscope (LCV110-SK, Olympus Co., Ltd.,Tokyo). The system allows observation of cells duringexposure to the shear flow.
Cell Culture
HUVEC (human umbilical vein endothelial cells) was used in
the test. EGM+BulletKit was used for the medium. The
cells were seeded on the dish coated with collagen at the densityof 1000 cells/cm2. To make adhesion of cells to the bottom of
the dish, the cells were cultured for 24 hours in the incubator.
In the incubator, both the temperature and the partial pressure ofcarbon dioxide are maintained at 310 K and 5 percent,respectively.
After the incubation, the cells were sheared in the rotating disk
system for 24 hours in the incubator microscope (LCV110-SK).
After stopping the rotation of the disk, the cells weresuccessively cultured in the incubator microscope

At the circle, S.I. = 1.
approaches to zero.

(3)
As the ellipsoid becomes flat, S.I.

The angles (θ) between the direction of the flow and the
direction of the major axis of each cell were also measured at
the microscopic image. The direction of the flow wasconfirmed by the flowing particle at the microscopic image.
To trace the migration of each cell by the coordinates, the x axis
is corrected to the direction of the flow.

3. RESULTS
The cells were able to be continuously exposed to the Couette
type shear flow by the rotating disk for twenty-four hours in the
incubator. Fig. 3 shows the microscopic images of cells after
the shear flow stimulation for twenty-four hours at eachconstant shear stress: 0 Pa, 1.0 Pa, and 1.4 Pa. The flow
direction is from left to right in Fig. 3. Each red circle ismarked to trace the same cell in Fig. 3. The control conditionof 0 Pa shows cells cultured in static medium without shear
flow. Several cells migrate with long distance at 1.4 Pa.
Several cells tilt to the direction of flow at the end of shear
stress stimulation of 1.0 Pa and 1.4 Pa. The tendency of tilt
decreases with time.
In the following figure, proliferating cells do not included.
Ten cells were selected to be traced. The data show the
behavior of each cell every hour.

b

a

θ

Fig. 2: Tracing of contour of each cell (left), contour of eachcell approximated to ellipsoid (right).

Fig. 4 shows the trace of position of each cell on the X-Y planeof the scaffold. The flow direction is parallel to the X axis
from minus to plus. Migrations of ten cells at every hour are
exemplified in Fig. 4. Many cells migrate with the long
distance after the shear stress stimulation of 1.4 Pa. The
migration distances are short after the shear stress stimulation of
0 Pa and 1.0 Pa.
Fig. 5 shows the migration distance of the center of each cell
per every hour after stopping of the shear flow stimulation for
24 hours. In each group, the line shows the mean migration
distance of ten traced cells. Each same color of the filled
circles shows the traced same cell. In every group, themigration speed around 0.02 mm/hour at each cell is maintained
for twenty-four hours. Several cells migrates 0.05 mm/hour
after the shear stress stimulation of 1.0 Pa and of 1.4 Pa. The
most active part is in two hours after the shear stress stimulationof 1.0 Pa.

Fig. 3a: Cells at the end of shear flow stimulation for 24 hour: 0
Pa (upper left, control), 1.0 Pa (upper right), 1.4 Pa (lower left):arrow shows flow direction: bar shows 0.2 mm.

Fig. 3b: Cells at 6 hour after shear flow stimulation for 24 hour:
0 Pa (upper left, control), 1.0 Pa (upper right), 1.4 Pa (lowerleft): arrow shows flow direction: bar shows 0.2 mm.

Fig. 3c: Cells at 12 hour after shear flow stimulation for 24
hour: 0 Pa (upper left, control), 1.0 Pa (upper right), 1.4 Pa(lower left): arrow shows flow direction: bar shows 0.2 mm.

Fig. 3d: Cells at 18 hour after shear flow stimulation for 24
hour: 0 Pa (upper left, control), 1.0 Pa (upper right), 1.4 Pa(lower left): arrow shows flow direction: bar shows 0.2 mm.

Fig. 3e: Cells at 24 hour after shear flow stimulation for 24
hour: 0 Pa (upper left, control), 1.0 Pa (upper right), 1.4 Pa(lower left): arrow shows flow direction: bar shows 0.2 mm.

Fig. 7: Shape index (S.I.) of each cell every hour after stoppingof shear flow stimulation for 24 hours: 0 Pa (upper left, control),
1.0 Pa (upper right), 1.4 Pa (lower left).

Fig. 4: Migration of center of each cell for 24 hour after
stopping of shear flow stimulation for 24 hour: 0 Pa (upper left,
control), 1.0 Pa (upper right), 1.4 Pa (lower left): n = 10.

Fig. 8: Area of each cell every hour after stopping of shear flow
stimulation for 24 hours: 0 Pa (upper left, control), 1.0 Pa(upper right), 1.4 Pa (lower left).

Fig. 5: Migration distance of center of each cell per every hour
after stopping of shear flow stimulation for 24 hours: 0 Pa
(upper left, control), 1.0 Pa (upper right), 1.4 Pa (lower left).

Fig. 6 shows the angle between the longitudinal axis of the celland the direction of the X axis, which is parallel to the flow.
The zero degree shows the direction of the flow. The 90
degree shows the direction perpendicular to the flow. In eachgroup, the line shows the mean angle of ten traced cells. Eachsame color of the filled circles shows the traced same cell.
The angle distributes between zero and 90 degree in the control
group without flow stimulation. The mean value is around 45
degree. The angle distributes, on the other hand, between zeroand 60 degree in the group after flow stimulation of 1.0 Pa andof 1.4 Pa. The mean value is around 30 degree, which shows
the cell keeps tilt to the flow direction for twenty-four hours
after flow stimulation.
Fig. 7 shows the shape index (S.I.) of the cell. S.I. is unity at
the circle at the image. When the ellipse is extended to thelongitudinal direction, S.I. approaches to zero. In each group,
the line shows the mean angle of ten traced cells. Each samecolor of the filled circles shows the traced same cell. S.I. at theend of flow stimulation is smaller than S.I. without flow
stimulation. SI after the flow stimulation of 1.0 Pa gradually
approaches to the value without flow stimulation with time.

Fig. 6: Angle [degree] of each cell every hour after stopping ofshear flow stimulation for 24 hours: 0 Pa (upper left, control),
1.0 Pa (lower left), 1.4 Pa (upper right).

Fig. 8 shows the projected area of the cell. In each group, theline shows the mean angle of ten traced cells. Each same colorof the filled circles shows the traced same cell. Some cells
have the large area after flow stimulation of 1.0 Pa. The areaof each cell gradually increases without the flow stimulation.

The area of each cell tends to increase after the flow stimulationof 1.0 Pa. The area of each cell, on the other hand, keeps
small value after the flow stimulation of 1.4 Pa.

sub-lethal damage [28] by the higher shear stress. The
optimum shear stress might accelerate adaptation of the cell tothe environmental stimulation. The wall shear stress around 1
Pa in the flow might be effective to accelerate orientation of
HUVEC.

4. DISCUSSION
Many kinds of the devices of Couette type flow were designed
for quantitative experiments of biological fluid in the previous
studies.
The clot formation was quantitatively studied
between a rotating cone and a stationary plate [31], and between
a rotating concave cone and a stationary convex cone [32].
The erythrocyte destruction was studied between a rotating
concave cone and a stationary convex cone [26]. The
erythrocyte deformation was observed between counter rotating
parallel discs [27, 28].
The Couette flow system of the cone and plate type realizes theuniform shear field independent of the distance from therotational axis [31]. To keep easily the preciseness of thedimension, parallel disk system has an advantage [27, 28].
The precisely even surface can be fabricated easier at the plain
surface than at the cone surface. To keep the stable movement,
the parallel disk system has an advantage than the cone andplate system. The parallel position between disks can be
self-regulated by balance in the uniform distance between disks.
The machining of the surface is easier to make the plane thanthe cone to minimize the roughness of the surface. These
conditions make the optical observation easier.
The microscopic image at the Couette type flow system with therotating disk includes the wall shear stress distribution within
the observation frame according to the distance from therotating axis. The wall shear stress increases in proportion to
the distance from the rotating axis. This situation has
advantage to observe the migration direction of each cellaccording to the distribution of the wall shear stress [20].

In the present study, every parameter has been measured only
on sparsely populated cells to prevent interaction between cells.
The active behavior is measured every five minutes by thepresent experimental system. The proliferating cells are notincluded in the data in Figs. 4-8. In the confluent state, on theother hand, cells reveal different responses.
The angle
between the flow direction and the longitudinal axis of the cell
scatters within 60 degree in the present experiment. The
density of adhered cells might be too low to make the regularorientation of cells.

5. CONCLUSION
An experimental system of the Couette type of flow with arotating disk has been used to apply the wall shear stress (1.0 Pa,
1.4 Pa) quantitatively on the HUVEC (human umbilical vein
endothelial cell) at the microscopic observation in vitro, and the
behavior of the cell after stimulation of shear flow has been
evaluated. Migration, deformation, and orientation of eachcell have been traced at the time-laps image for 24 hours after
the stimulation for 24 hours. The experiments show that cells
tend to make orientation parallel to the stream line, and that thetendency is maintained for several hours. The migration ofeach cell is enhanced after stimulation of the wall shear stress of
1.4 Pa. The increase of area of each cell is decelerated by thehigher wall shear stress. The Couette type of rotating disk
system is effective to detect the behavior of cells after
stimulation of the shear flow.

6. ACKNOWLEDGMENT
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 0.8 m s－1 in thepresent system. The microscopic image of the flowing cells
between the rotating disk and the stationary disk does not show
turbulent flow in the present experiment.
Reynolds number is calculated by Eq. 4.
Re = ρ v d / η = ρ r ω d / η(4)In Eq. 4, ρ is density of the fluid, and v is the circumferential
velocity. Re is 400, when ρ, r, ω, d, and η are 103 kg m s－3,
0.018 m, 42 rad s s－1, 0.0008 m, and 0.0014 Pa s, respectively.
The turbulent flow may not occur in the flow of small value of
Reynolds number. The actual flow direction is confirmed by
the movement of medium adjacent to the culture plate on thevideo image in the present study.
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 [3, 14-19, 24, 29, 30].
Too high shear stress might damage cells. Extension of the
projected area of each adhered cell might decrease after theThis work was supported by a Grant-in-Aid for Strategic
Research Foundation at Private Universities from the Japanese
Ministry of Education, Culture, Sports and Technology.

REFERENCES[1] G. Yourek, S.M. McCormick, J.J Mao and G.C. Reilly,“Shear Stress Induces Osteogenic Differentiation of Human
Mesenchymal Stem Cells”, Regenerative Medicine, Vol. 5,
No. 5, 2010, pp. 713-724.
[2] H. Hino, S. Hashimoto, Y. Takahashi and H. Nakajima,“Effect of Ultrasonic Vibration on Proliferation and
Differentiation of Cells”, Journal of Systemics,
Cybernetics and Informatics, Vol. 14, No. 6, pp. 1-7, 2016.
[3] S. Obi, K. Yamamoto, N. Shimizu, S. Kumagaya, T.
Masumura, T. Sokabe, T. Asahara and J. Ando, “Fluid Shear
Stress Induces Arterial Differentiation of Endothelial
Progenitor Cells”, Journal of Applied Physiology, Vol. 106,
2009, pp. 203-211.
[4] S. Hashimoto, H. Hino and T. Iwagawa, “Effect of Excess
Gravitational Force on Cultured Myotubes in Vitro”,
Journal of Systemics, Cybernetics and Informatics, Vol.
11, No. 3, 2013, pp. 50-57.
[5] S. Hashimoto, F. Sato, R. Uemura and A. Nakajima, “Effectof Pulsatile Electric Field on Cultured Muscle Cells in Vitro”,

Journal of Systemics Cybernetics and Informatics, Vol.
10, No. 1, 2012, pp. 1-6.
[6] S. Hashimoto and K. Tachibana, “Effect of Magnetic Field
on Adhesion of Muscle Cells to Culture Plate”, Journal of
Systemics Cybernetics and Informatics, Vol. 11, No. 4,
2013, pp. 7-12.
[7] E. Cecchi, C. Giglioli, S. Valente, C. Lazzeri, G.F. Gensini, R.
Abbate, Lucia Mannini, “Role of Hemodynamic Shear
Stress in Cardiovascular Disease”, Atherosclerosis, Vol. 214,
No. 2, 2011, pp. 249–256.
[8] S.P. Downie, S.M. Raynor, D.N. Firmin, N.B. Wood, S.A.
Thom, A.D. Hughes, K.H. Parker, J.H.N. Wolfe and X.Y. Xu,“Effects of Elastic Compression Stockings on Wall Shear
Stress in Deep and Superficial Veins of the Calf”, American
Journal of Physiology. Heart and Circulatory Physiology,
Vol. 294, 2008, pp. H2112-H2120.
[9] K.A. Barbee, P.F. Davies and R. Lal, “Shear Stress-induced
Reorganization of the Surface Topography of Living
Endothelial Cells Imaged by Atomic Force Microscopy”,
Circulation Research, Vol. 74, No. 1, 1994, pp. 163-171.
[10] S. Li, S. Bhatia, Y.L. Hu, Y.T. Shiu, Y.S. Li, S. Usami and S.
Chien, “Effects of Morphological Patterning on Endothelial
Cell Migration”, Biorheology, Vol. 38, No. 2-3, 2001, pp.
101-108.
[11] I. Barkefors, S.L. Jan, L. Jakobsson, E. Hejll, G. Carlson, H.
Johansson, J. Jarvius, J.W. Park, N.L. Jeon and J. Kreuger,“Endothelial Cell Migration in Stable Gradients of VascularEndothelial Growth Factor A and Fibroblast Growth Factor
2: Effects on Chemotaxis and Chemokinesis”, The Journalof Biological Chemistry, Vol. 283, No. 20, 2008, pp.
13905-13912.
[12] J.Y. Park, S.J. Yoo, L. Patel, S.H. Lee and S.H. Lee, “CellMorphological Response to Low Shear Stress in a
Two-dimensional Culture Microsystem with Magnitudes
Comparable to Interstitial Shear Stress”, Biorheology, Vol.
47, No. 3-4, 2010, pp. 165-178.
[13] Y.X. Qi, M.J. Qu, D.K. Long, B. Liu, Q.P. Yao, S. Chien
and Z.L. Jiang, “Rho-GDP Dissociation Inhibitor Alpha
Downregulated by Low Shear Stress Promotes Vascular
Smooth Muscle Cell Migration and Apoptosis: a Proteomic
Analysis”, Cardiovascular Research, Vol. 80, No. 1, 2008,
pp. 114–122[14] X. Zhuang, D. Cross, V.L. Heath and R. Bicknell, “Shear
Stress, Tip Cells and Regulators of Endothelial Migration”,
Biochemical Society Transactions, Vol. 39, No. 6, 2011, pp.
1571-1575.
[15] G.K. Kolluru, S. Sinha, S. Majumder, A. Muley, J.H.
Siamwala, R. Gupta and S. Chatterjee, “Shear Stress
Promotes Nitric Oxide Production in Endothelial Cells by
Sub-Cellular Delocalization of eNOS: A Basis for Shear
Stress Mediated Angiogenesis”, Nitric Oxide, Vol. 22, No. 4,
2010, pp. 304-315.
[16] A.B. Fisher, S. Chien, A.I. Barakat and R.M. Nerem,“Endothelial Cellular Response to Altered Shear Stress”,
American Journal of Physiology- Lung Cellular andMolecular Physiology, Vol. 281, NO. 3, 2001, pp.
L529-L533.
[17] G. Cinamon, V. Grabovsky, E. Winter, S. Franitza, S.
Feigelson, R. Shamri, O. Dwir and R. Alon, “Novel
Chemokine Functions in Lymphocyte Migration throughVascular Endothelium under Shear Flow”, Journal of
Leukocyte Biology, Vol. 69, No. 6, 2001, pp. 860-866.
[18] 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, No. 3, 2001, pp. 751-759.
[19] S. Hsu, R. Thakar, D. Liepmann and S. Li, “Effects ofShear Stress on Endothelial Cell Haptotaxis on
Micropatterned Surfaces”, Biochemical and BiophysicalResearch Communications, Vol. 337, No. 1, 2005, pp.
401-409.
[20] H. Hino, S. Hashimoto, Y. Takahashi and M. Ochiai,“Effect of Shear Stress in Flow on Cultured Cell: Using
Rotating Disk at Microscope”, Journal of Systemics,
Cybernetics and Informatics, Vol. 14, No. 4, 2016, pp.
6-12.
[21] F. Sato, S. Hashimoto, T. Yasuda and H. Fujie,“Observation of Biological Cells in Rhombus Parallelepiped
Flow Channel”, Proc. 17th World Multi-Conference on
Systemics Cybernetics and Informatics, Vol. 1, 2013, pp.
25-30.
[22] H. Hino, S. Hashimoto, Y. Takahashi and S. Nakano,“Design of Cross Type of Flow Channel to Control
Orientation of Cell”, Proc. 20th World Multi-Conference
on Systemics Cybernetics and Informatics, Vol. 2, 2016,
pp. 117-122.
[23] S. Hashimoto, F. Sato, H. Hino, H. Fujie, H. Iwata and Y.
Sakatani, “Responses of Cells to Flow in Vitro”, Journal of
Systemics Cybernetics and Informatics, Vol. 11, No. 5,
2013, pp. 20-27.
[24] 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.
[25] M.L.C. Albuquerque, C.M. Waters, U. Savla, H.W.
Schnaper and S.A. Flozak, “Shear Stress Enhances Human
Endothelial Cell Wound Closure in Vitro”, American
Journal of Physiology - Heart and Circulatory
Physiology, Vol. 279, No. 1, 2000, pp. H293-H302.
[26] S. Hashimoto, “Erythrocyte Destruction under Periodically
Fluctuating Shear Rate; Comparative Study with Constant
Shear Rate”, Artificial Organs, Vol. 13, No. 5, 1989, pp.
458-463.
[27] S. Hashimoto, et al., “Effect of Aging on Deformability ofErythrocytes in Shear Flow”, Journal of Systemics
Cybernetics and Informatics, Vol. 3, No. 1, 2005, pp.
90-93.
[28] S. Hashimoto, “Detect of Sublethal Damage with Cyclic
Deformation of Erythrocyte in Shear Flow”, Journal of
Systemics Cybernetics and Informatics, Vol. 12, No. 3,
2014, pp. 41-46.
[29] M.J. Levesque and R.M. Nerem, “The Elongation andOrientation of Cultured Endothelial Cells in Response to
Shear Stress”, Journal of Biomechanical Engineering, Vol.
107, No. 4, 1985, pp. 341-347.
[30] M.P. Szymanski, E. Metaxa, H. Meng and J. Kolega,“Endothelial Cell Layer Subjected to Impinging Flow
Mimicking the Apex of an Arterial Bifurcation”, Annals ofBiomedical Engineering, Vol. 36, No. 10, 2008, pp.
1681-1689.
[31] S. Hashimoto, H. Maeda and T. Sasada, “Effect of Shear
Rate on Clot Growth at Foreign Surfaces”, Artificial
Organs, Vol. 9, No. 4, 1985, pp. 345-350.
[32] S. Hashimoto, “Clot Growth under Periodically Fluctuating
Shear Rate”, Biorheology, Vol.31, No. 5, 1994, pp. 521-532.