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Cell Biology International (2006) 30, 439–444 (Printed in Great Britain)
Design of compliance chamber and after-load in apparatus for cultured endothelial cells subjected to stresses
Hao Dingab, Aike Qiaoa, Lixing Shenb, Mingyang Lib, Zhenglong Chenb, Xiaojun Yuc and Yanjun Zengac*
aBiomechanics & Medical Information Institute, Beijing University of Technology, No. 100 PingLeYuan, Beijing 100022, China
bThe Medical Instrumentation College, University of Shanghai for Science and Technology, Shanghai 200093, China
cMedical College of Shantou University, Shantou 515031, China


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.

Keywords: Biomechanics, Hemodynamic environment, Experiment, Simulation, Blood flow, Artery.

*Corresponding author. Biomechanics & Medical Information Institute, Beijing University of Technology, No. 100 PingLeYuan, Beijing 100022, China. Tel.: +86 10 67391685.

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 conditions, normal stress, with magnitudes of 15,996/10,664Pa (120/80mmHg) in the systolic and diastolic cardiac phases, respectively, is 5300–8000 times greater than shear stress (2Pa) (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 systolic and diastolic pressure (systolic pressure: 15,996–23,994Pa, i.e. 120–180mmHg; diastolic pressure: 7998–15,996Pa, i.e. 60–120mmHg); second, the above-mentioned parameters should be adjustable within a stated range.

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):

(1) where ΔV 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=P2, V0 is infinite.

2.2 Principle of the after-load

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 τ as follows (Diao, 1991; Liu and Li, 1997):

(2) where Q is the volume flow rate, μ the viscosity and d the diameter of blood vessel.

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

(3) where b is the width of the rectangular chamber, and δ 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):

(4) where ΔP=P1P2 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 ΔP. 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.

3 Implementation

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.

Fig. 1

Semantic of the testing circulation system.

3.1 Compliance chamber

The compliance chamber (54mm long, 72mm wide, 82mm 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 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.

Fig. 2

The structure (a) and photograph (b) of compliance chamber.

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 (43mm long, 19mm wide, 50mm 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.

Fig. 3

The structure (a) and photograph (b) of the after-load.

3.3 Specifications of the design

The rectangular chamber in our test apparatus has an orifice of ∅24mm×0.5mm on which the cover-slip of ∅24mm×0.5mm is located. The ECs are planted on the cover-slip (Fig. 4). The following specifications were applied in our design.


Systolic pressure is 15,996–23,994Pa.

Fig. 4

The structure of rectangular chamber.


Diastolic pressure is 7998–15,996Pa.


The pump's flow rate must be in the range of 20–600ml/min.

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 2–300dyn/cm3, then the flow rate of the pump should be 20–600ml/min according to the dimension of our designed apparatus. According to Eq. (3), the shear stress is 2dyn/cm3 when μ=11.68×10−4PaS, δ=0.56mm, b=30mm and Q=20ml/min; the shear stress is 300dyn/cm3 when μ=11.68×10−4PaS, δ=0.56mm, b=30mm and Q=600ml/min.


Pulsatile frequency should be 40–200r/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 40–200r/min.


In order to make the pulsatile amplitude adjustable within a stated range, the total compliance chamber volume should be between 200 and 300ml. Here, .

The cavity of the compliance chamber is 250ml, and the maximum flow rate of the designed apparatus is 600ml/min. Suppose that the heart rate is 70 beats per minute and the heart output per pulse is be , we can obtain the following data (Table 1) according to Eq. (1).

Table 1.

Relationship between the value of gas/liquid and P2/P1

Value of gas/liquidGas volume V0Liquid volumeP2/P1

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 (1–0) 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. 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 after-load 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 15,996/10,664Pa (120/80mmHg) (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.

Fig. 5

Simulating the normal systolic pressure and diastolic pressure (15,996/10,664Pa or 120/80mmHg).

Fig. 6

Regulating the amplitude of pulsatile flow.

Fig. 7

Regulating the absolute value of blood pressure.

5 Discussion

Although the apparatus is able to accomplish our intention, it still has some drawbacks as follows:


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.


The ECs are planted on an inflexible cover-slip, which is different to the elastic foundation base of arteries.


The shear stress is obtained indirectly from the calculation of pressure difference, and there is no direct and simple measurement at the present time.


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.

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.


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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Received 28 November 2005/10 January 2006; accepted 14 February 2006


ISSN Print: 1065-6995
ISSN Electronic: 1095-8355
Published by Portland Press Limited on behalf of the International Federation for Cell Biology (IFCB)