Cell Biology International 30 (2006) 439e444
www.elsevier.com/locate/cellbi
Design of compliance chamber and after-load in apparatus
for cultured endothelial cells subjected to stresses
Hao Ding a,b, Aike Qiao a, Lixing Shen b, Mingyang Li b, Zhenglong Chen b,
Xiaojun Yu c, Yanjun Zeng a,c,*
a
Biomechanics & Medical Information Institute, Beijing University of Technology, No. 100 PingLeYuan, Beijing 100022, China
b
The Medical Instrumentation College, University of Shanghai for Science and Technology, Shanghai 200093, China
c
Medical College of Shantou University, Shantou 515031, China
Received 28 November 2005; revised 10 January 2006; accepted 14 February 2006
Abstract
In order to create a hemodynamic environment that can simulate the physiological condition of arteries, an in vitro experiment apparatus was
designed whose key modules were compliance chamber and after-load. These two modules were developed based on the theories of hemodynamics. Both the normal and shear stress to which endothelial cells are exposed can be controlled with these modules, thus facilitating the
research of endothelial cells subjected to stresses.
Ó 2006 International Federation for Cell Biology. Published by Elsevier Ltd. All rights reserved.
Keywords: Biomechanics; Hemodynamic environment; Experiment; Simulation; Blood flow; Artery
1. Introduction
Endothelial cells (ECs), which form a layer of membrane
covering heart valves and blood vessels, play a very important
role in the physiological and pathological activities of the
cardiovascular system. Changes in their structure and function
are key events in the occurrence and development of some
vascular diseases, such as hypertension and atherosclerosis
(Dewey et al., 1981; Franke et al., 1984; Eskin et al., 1984;
Helmlinger et al., 1991). ECs in vivo are always exposed to
a hemodynamic environment. Many previous research studies
have considered that shear stress of blood flow is the main factor
influencing ECs (Frame et al., 1998; Passerini et al., 2003; Chen
et al., 2003; Greisler et al., 1990; Brooks et al., 2002; Mu and Du,
2004). In fact, besides shear stress, normal stress (i.e. blood
pressure) also acts on ECs. Under normal physiological
* Corresponding author. Biomechanics & Medical Information Institute,
Beijing University of Technology, No. 100 PingLeYuan, Beijing 100022,
China. Tel.: þ86 10 67391685.
E-mail address: yjzeng@bjut.edu.cn (Y. Zeng).
conditions, normal stress, with magnitudes of 15,996/10,664 Pa
(120/80 mm Hg) in the systolic and diastolic cardiac phases,
respectively, is 5300e8000 times greater than shear stress
(2 Pa) (Liu et al., 1997, 2001). Obviously normal stress is an
important factor affecting ECs that cannot be ignored.
In view of the fact that it is impossible to measure the shear
stress of blood flow in arteries both in vivo and in vitro, many
in vitro experiments have been conducted to calculate shear
stress indirectly (Liu et al., 2001). In order to create a realistic
hemodynamic environment (including both shear stress and
normal stress) to which the ECs are exposed, we developed an
apparatus that can simulate steady and pulsatile blood flow phenomena in arteries. In this apparatus, the compliance chamber
and after-load modules are two key modules for the simulation
of in vitro experiments. The purpose of this paper is to show the
design of these two important modules in the apparatus.
2. Methodology
Technically, the compliance chamber and after-load should satisfy the following requirements: first, they are able to simulate normal human aorta
1065-6995/$ - see front matter Ó 2006 International Federation for Cell Biology. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.cellbi.2006.02.003
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H. Ding et al. / Cell Biology International 30 (2006) 439e444
systolic and diastolic pressure (systolic pressure: 15,996e23,994 Pa, i.e. 120e
180 mm Hg; diastolic pressure: 7998e15,996 Pa, i.e. 60e120 mm Hg);
second, the above-mentioned parameters should be adjustable within a stated
range.
In our design, the test apparatus has a rectangular flow chamber whose
height is much less than its width and where the ECs are planted. For Poiseuille flow in a rectangular chamber, the wall shear stress can be denoted as
t¼
2.1. Principle of the compliance chamber
The function of the compliance chamber is to simulate elastic function of
the aorta, and change the intermittent blood ejection of the pulsatile pump into
a continuous pulsatile flow. The compliance chamber, which is composed of
a gas chamber and a liquid chamber to simulate the elastic artery, stores and
discharges energy for the test system. Its gas chamber volume can be calculated with (Zhang and Huang, 1991):
V0 ¼
P2
DV
1
1
P2 P1
ð1Þ
where DV is pump’s output per pulse; P1 and P2 are the systolic pressure and
the diastolic pressure, respectively.
The total gas volume V0 correspondingly varies with different P1 and P2 .
But the following law is always satisfied: the smaller the difference between
P1 and P2 , the bigger the V0 . When P1 ¼ P2 , V0 is infinite.
6m
Q
bd2
ð3Þ
where b is the width of the rectangular chamber, and d the height of the
rectangular chamber.
Obviously, the shear stress is proportional to the flow rate. The flow rate in
the pipe can be obtained from the following equation (Diao, 1991; Liu and Li,
1997):
Q¼
DP
R
ð4Þ
where DP ¼ P1 P2 is the pressure drop along the pipeline, and R the total
peripheral resistance.
The flow rate of the heart pump keeps constant if the output per pulse and
the heart rate do not vary. Thus, the pressure drop is proportional to the resistance. Increasing R can induce the increase of DP. Blood flow downstream
from the after-load is open to the atmosphere directly in the apparatus; therefore, the pressure drop is just the blood pressure in the artery. Thus, the blood
pressure in the artery increases with the increase of peripheral resistance and
vice versa.
2.2. Principle of the after-load
3. Implementation
The function of the after-load is to simulate the peripheral resistance of the
micro-vessels and capillary vessels (‘‘lump resistance model’’).
Blood pressure is the only normal stress acting on the ECs. The blood pressure level can be changed by adjusting the opening of the after-load. We have
found that the throttle, as an effective load, plays a key role in adjusting
peripheral resistance of the vascular system. The throttle is a ‘‘lump resistance
model’’ whose role is not different from that of capillary vessels when studying
large arteries in hemodynamics. Physiologically, the total length of capillary
vessels is very long and the resistance distributes along the total length without
converging at one point. The distribution of resistance is different depending
on the difference in diameter, length and branch of capillary vessels. In this
case, the ‘‘lump resistance model’’ has no effect when studying the behavior
of capillary vessels. However, when studying the blood flow in large arteries
far upstream from capillary vessels, it is not only feasible but also technically
convenient to consider the influence of capillary vessels as ‘‘lump resistance’’.
As a preliminary study, we assume that the blood flow is a laminar flow in
a rigid circular pipe. The shear stress acting on the ECs is just the shear wall
stress of arteries. According to Poiseuille’s law, parabolic velocity profile leads
to wall shear stress t as follows (Diao, 1991; Liu and Li, 1997):
This apparatus consists of a pulsatile pump, a compliance
chamber, a rectangular chamber, a reservoir, a thermostatic device, an after-load system and joint pipelines. A diagram of the
testing circulation system is shown in Fig. 1.
t¼
32mQ
pd3
ð2Þ
where Q is the volume flow rate, m the viscosity and d the diameter of blood
vessel.
3.1. Compliance chamber
The compliance chamber (54 mm long, 72 mm wide,
82 mm high) includes a gas chamber, gas loading valve
and purge valve (Fig. 2). The compressed liquid medium
from the pulsatile pump is divided into two ways: one
enters the pipeline system; the other enters the compliance
chamber, which can compress air in the gas chamber and
store pressure energy. The pressure level of the pipeline
decreases when the pump sucks liquid in. The compressed
air in the compliance chamber extrudes pressure liquid
into the pipeline. So the compliance chamber functions
like a buffer that not only decreases higher pressure by absorbing pressure energy but also increases lower pressure by
discharging pressure energy. Thus, the compliance chamber
Fig. 1. Semantic of the testing circulation system.
H. Ding et al. / Cell Biology International 30 (2006) 439e444
441
Fig. 2. The structure (a) and photograph (b) of compliance chamber.
transforms intermittent blood ejection of the heart pump
into a continuous pulsatile flow. In practical apparatus,
when the compliance chamber is not working, the minimum
output pressure of the pump is zero or even negative. But
when it is working, the pressure wave presents arterial
flow with both the maximum and minimum pressure positive, thereby simulating systolic and diastolic pressure in
the blood vessels.
Adjusting the ratio of gas to liquid (gas/liquid) changes the
amplitude of pulsatile flow. Compressing the gas loading
valve and boosting air into the gas chamber, the gas/liquid increases and the amplitude of pulsatile flow decreases. Turning
on the purge valve, the gas/liquid reduces and the amplitude of
pulsatile flow augments.
3.2. After-load
The after-load (43 mm long, 19 mm wide, 50 mm high) is
composed of a valve body, a valve needle and an adjustment
knob (Fig. 3). The cross-sectional size of the opening is
changeable by adjusting the knob and moving the valve needle
up and down, which consequently regulates the magnitude of
the after-load. Regulating after-load can precisely control
normal stress.
3.3. Specifications of the design
The rectangular chamber in our test apparatus has an
orifice of B24 mm 0.5 mm on which the cover-slip of
Fig. 3. The structure (a) and photograph (b) of the after-load.
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H. Ding et al. / Cell Biology International 30 (2006) 439e444
B24 mm 0.5 mm is located. The ECs are planted on the
cover-slip (Fig. 4). The following specifications were applied
in our design.
Table 1
Relationship between the value of gas/liquid and P2/P1
Value of gas/
liquid
Gas
volume V0
Liquid
volume
P2/P1
(1) Systolic pressure is 15,996e23,994 Pa.
(2) Diastolic pressure is 7998e15,996 Pa.
(3) The pump’s flow rate must be in the range of 20e600 ml/
min.
28:1
4:1
2:1
1:1
1:2
1:4
1:28
241.4
200
167
125
83
50
8.6
8.6
50
83
125
167
200
241.4
0.964
0.957
0.948
0.931
0.896
0.828
0
As mentioned above, the shear stress is proportional to the
flow rate and varies within a certain range in the human body.
If we want to obtain physiological shear stresses of
2e300 dyn/cm3, then the flow rate of the pump should be 20e
600 ml/min according to the dimension of our designed apparatus. According to Eq. (3), the shear stress is 2 dyn/cm3 when
m ¼ 11.68 104 Pa S, d ¼ 0.56 mm, b ¼ 30 mm and Q ¼ 20
ml/min; the shear stress is 300 dyn/cm3 when m ¼ 11.68 104
Pa S, d ¼ 0.56 mm, b ¼ 30 mm and Q ¼ 600 ml/min.
(4) Pulsatile frequency should be 40e200 r/min.
Pulsatile frequency reflects heart rate, and the normal heart
rate of man is 75 beats per min. But in order to simulate the
normal heart rate and the abnormal one we have to choose
a larger measuring range in this apparatus, therefore the value
of pulsatile frequency is 40e200 r/min.
(5) In order to make the pulsatile amplitude adjustable within
a stated range, the total compliance chamber volume V0
should be between 200 and 300 ml. Here, V0 ¼
gas volume þ liquid volume.
The cavity of the compliance chamber is 250 ml, and the
maximum flow rate of the designed apparatus is 600 ml/min.
Suppose that the heart rate is 70 beats per minute and the heart
output per pulse is be DV ¼ 8:6 ml, we can obtain the following data (Table 1) according to Eq. (1).
Analyzing the data in Table 1, we can obtain the following
conclusion: first, when the value of gas/liquid changed, P1/P2
changed correspondingly in the range of (1e0) that can be regulated according to the experiment requirements. Second, the
greater the value of gas/liquid, the smaller the rigidity of compliance chamber, and the smaller the difference of P1 and P2.
Fig. 4. The structure of rectangular chamber.
Third, the smaller the value of gas/liquid, and thus the greater
the rigidity of compliance chamber, the greater the difference
of P1 and P2.
4. Results
The working procedure of compliance chamber and afterload in the apparatus for cultured endothelial cells subjected
to stresses designed in this paper is shown as follows.
Not blood but nourishing fluids were employed in the apparatus to feed the ECs on the rectangular chamber. The liquid
pumped by pulsatile pump is divided into two branches after
the compliance chamber: one is connected to a throttle and
then flows back to the reservoir, the other enters the rectangular chamber, and then flows back to the reservoir through the
after-load (Fig. 1).
This device can simulate the normal systolic and diastolic
pressure of 15,996/10,664 Pa (120/80 mm Hg) (Fig. 5). It
can adjust the amplitude of pulsatile flow by changing the
value of gas/liquid in the compliance chamber (Fig. 6). It
can also regulate the absolute value of blood pressure by adjusting the after-load (Fig. 7). Shunt volume can be regulated
by changing the opening of the throttle to regulate the shear
stress in the rectangular chamber.
5. Discussion
Although the apparatus is able to accomplish our intention,
it still has some drawbacks as follows:
(1) The purpose of this apparatus is to create a hemodynamic
environment that is similar to the physiological condition
of arteries. In order to observe ECs’ changing states more
conveniently, three-dimensional flow field in the arteries is
simplified into one-dimensional flow field in the rectangular
chamber (Fig. 4), but the simplification creates a difference
between the realistic condition and the experimental one.
(2) The ECs are planted on an inflexible cover-slip, which is
different to the elastic foundation base of arteries.
(3) The shear stress is obtained indirectly from the calculation
of pressure difference, and there is no direct and simple
measurement at the present time.
(4) The after-load mentioned by this paper is a ‘‘lump resistance
model’’, which simulates the resistance of capillary vessels
to blood flow. However, the ‘‘lump resistance model’’ has no
effect when studying the behavior of capillary vessels.
H. Ding et al. / Cell Biology International 30 (2006) 439e444
443
Fig. 5. Simulating the normal systolic pressure and diastolic pressure (15,996/10,664 Pa or 120/80 mm Hg).
6. Conclusion
Since the shear stress acting on vascular endothelium is
inaccessible in vivo, we designed an in vitro experiment apparatus in which the compliance chamber and the after-load are
two key modules in order to simulate the hemodynamic environment for cultured ECs subjected to both normal stress and
shear stress. By adjusting these two modules, we can change
the normal stress and the shear stress to which ECs are
exposed. This apparatus is supplied as a trial production to
Shanghai Cerebrovascular Disease Prevention Research Institute and Life Sciences College of Tongji University. Their experimental findings were inspiring and confirmed the
practicability of the designed apparatus. Therefore, with this
apparatus, more realistic hemodynamic conditions can be obtained for in vitro experiments using ECs under physiological
conditions, thus facilitating the research of ECs subjected to
stresses.
Fig. 6. Regulating the amplitude of pulsatile flow.
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H. Ding et al. / Cell Biology International 30 (2006) 439e444
Fig. 7. Regulating the absolute value of blood pressure.
Acknowledgments
For significant contribution to this work, the authors wish to
thank Prof. Shixiong Xu from Fudan University for his support
and assistance.
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