Chapter 3
Chapter 3 Circuit design
The cardiopulmonary bypass circuit consists basically of venous and arterial
(often including an arterial filter) tubing lines and an oxygenator with
integrated heat exchanger. This chapter deals with the hydrodynamic design
of the tubing and arterial filter. The artificial lung or oxygenator is discussed in
chapter 4.
3.1. Tubing
3.1.1. Priming volume
Once cardiopulmonary bypass is started, the volume in the arterial and
venous line as well as the priming volume of the oxygenator enlarges the total
circulating blood volume of the baby. Additionally, suction and vent lines that
are empty before starting cardiopulmonary bypass, remove an important
amount of blood out of the circulation once in use. Subsequently this blood is
returned into the circulation just before weaning cardiopulmonary bypass. As
a result important and rapid changes in circulating blood volume occur during
cardiopulmonary bypass. Because of this it is important to keep volumes in
the complete extracorporeal circulation as small as possible without
jeopardising flow requirements of the given lines. Its length and diameter
(Table 1) determine the volume of a line
21
Chapter 3
Table 1: Priming volumes for different tubing diameters
Tubing diameter 1
Priming volume per 10 cm of
Inch
mm
length (mL)
1/8
3.17
0.792
3/16
4.76
1.781
1/4
6.35
3.167
3/8
9.53
7.126
1/2
12.70
12.668
3.1.2. Dimensions of the tubing
3.1.2.1. Introduction
The dimensions of the venous and arterial lines depend on the desired blood
flow rate and the height difference between table and oxygenator. When
gravity drainage is used a height difference between 30 and 40 cm is
generally accepted [1]. In many institutions sizing of tubing is established in
an empirical way. A more objective way is to decide based on fluid dynamic
parameters [2], thus limiting the dead volume in the aspiration lines to an
absolute minimum. The resulting reduction in priming volume results in less
homologous blood product utilisation [3,4].
3.1.2.2. Laminar or turbulent flow
Two types of steady flow of real fluids exist: laminar flow and turbulent flow
with a transition zone in between. Different fluid dynamic laws govern the two
types of flow.
1
1 inch = 25.4 mm
22
Chapter 3
In laminar flow, fluid particles move along straight, parallel paths in layers.
Magnitudes of velocities of adjacent layers are not the same. The viscosity of
the fluid is dominant and thus suppresses any tendency for turbulent
conditions due to the inertia of the fluid.
In turbulent flow, fluid particles move in a haphazard fashion in all directions.
The critical velocity is the velocity below which all turbulence is damped out by
the viscosity of the fluid. It is found that a Reynolds number of about 2000
represents the upper limit of laminar steady flow of practical interest. The
Reynolds number is a dimensionless number, representing the ratio of inertia
forces to viscous forces, in circular pipes [2].
Re =
UD
ν
U = mean velocity [m/s], D = diameter [m], ν =kinematic viscosity [m²/s]
with
ν=
µ
ρ
where ρ = density [kg/m³], µ = absolute blood viscosity [N/m² .s]
3.1.2.3. Blood viscosity
Dynamic viscosity of a fluid (µ) is either determined from literature data or
measured in a viscosity meter. Blood viscosity can be described by
exponential formula with:

1800 
exp− 5.64 +
(T + 273) 

µplasma =
100
µ = µplasma exp(2.31Hct )
ρ = [1.09 Hct + 1.035(1 − Hct )]
23
Chapter 3
µplasma = plasma viscosity [N/m².s], T = absolute temperature [°C], Hct =
haematocrit [expressed as fraction]
Figure 1: Relationship between haematocrit, temperature and kinematic
blood viscosity
Blood viscosity calculation
4.0
Hct 36%
Hct 34%
Hct 32%
Hct 30%
Hct 28%
Hct 26%
Hct 24%
Hct 22%
Hct 20%
Blood viscosity [x 10-6 N/m².s]
3.5
3.0
2.5
2.0
1.5
20
22
24
26
28
30
32
34
36
38
Blood temperature [°C]
Based on these calculations a nomogram can be constructed for a quick
estimate of blood viscosity when haematocrit and temperature are known
(Figure 1).
3.1.2.4. Pressure-flow relationship
In general the pressure drop can be calculated in function of diameter, length,
blood viscosity and height difference between patient and heart-lung machine,
using the equation:
24
Chapter 3
∆P = f
L U2
D 2g
where f = friction factor, g = gravitational acceleration [m/s²] and
f =
64
when flow is laminar.
Re
However when the flow regimen is turbulent f is calculated using the
Colebrook equation:
 ε
2.51
= −2 log
+
 3.7 D Re f
f

1




with ε the roughness parameter.
Besides the Colebrook equation the Blasius formula is valid for smooth pipes
and low Reynold numbers. The friction factor becomes independent of the
roughness of the tube
f = 0.316 Re
−
1
4
By using these equations flow diagrams can be calculated for venous and
arterial lines in function of length, diameter, required blood flow, viscosity and
desired pressure drop.
3.1.2.5. Case study
If a baby needs cardiopulmonary bypass support one can calculate what
should be the appropriate diameter for both arterial and venous line. In our
example, the cardiopulmonary bypass circuit has an arterial and venous line
of 150 cm. The surgeon wants for this specific case a haematocrit of 30% and
no hypothermia during cardiopulmonary bypass. The maximum blood flow to
ensure adequate tissue perfusion is 700 mL/min.
25
Chapter 3
From Figure 2 we learn that both 3/16 and 1/4 inch arterial lines generate
laminar flow (shaded zone) for the given conditions. However, the pressure
loss over the arterial line will be approximately 20 mmHg higher if a 3/16 inch
diameter is chosen. This difference is acceptable so a 3/16 inch line gives the
best compromise between priming volume and pressure-flow characteristics.
Figure 2. Flow regimen in paediatric arterial lines
Characteristics of 3/16" and 1/4" arterial lines.
3/16
Length: 150 cm
3/16
Tem perature: 37° Celsius
150
Haem atocrit: 30%
3/16
Pressure drop [mmHg]
3/16
3/16
3/16
100
3/16
3/16
3/16
3/16
3/16
50
3/16
3/16
3/16
3/16
3/16
0
3/16
3/16 1/4
1/4 1/4
3/16
1/4 3/16
3/16
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
Reynolds < 2000
0.1
0.3
0.5
0.7
0.9
1.1
Blood flow [L/min]
1.3
1.5
1.7
1.9
Suppose it is decided to use a 3/16 inch venous line in the above described
case and the height difference between the operating table and the
oxygenator is 35 cm H20. We can determine the limitations of this choice by
using Figure 3. On the right Y-axis we notice that the Reynolds number
(squares), when using a haematocrit of 30% (X-axis) and a blood temperature
of 37°C, is below 2000 for a blood flow of 700 mL/min. The maximum blood
flow we can drain for these conditions (circles) is 770 mL/min (left Y-axis).
26
Chapter 3
This is approximately 10% higher than the maximum flow we anticipate. Thus,
a 3/16 inch venous line is a correct choice for this particular case.
Figure 3. Flow characteristics of a 3/16 inch venous line
Characteristics of a 3/16" venous line
Blood flow at 37°C
Blood flow at 20°C
Reynolds number at 37°C
Reynolds number at 20°C
1.0
2500
0.9
0.8
1500
0.7
Reynolds number
Blood flow [L/min]
2000
1000
0.6
Tubing length: 150 cm
Height difference between oxygenator and patient: 35 cm H2O
0.5
500
20
22
24
26
28
30
Hematocrit [%]
It is important to notice that in Figure 2 and 3 paediatric cardiopulmonary
bypass blood flow is laminar up to 1 L/min, this in contrast to adult
cardiopulmonary bypass where blood flow is mostly turbulent. As a
consequence pressure losses will be smaller in paediatric cases and less
energy will be needed for generating a given blood flow.
3.3. Arterial filter
Arterial filters were introduced during the era of bubble oxygenators. Those
elderly generation oxygenators were well known sources of gaseous
27
Chapter 3
microemboli. At the end of the eighties membrane oxygenators became the
standard resulting in almost no gaseous microemboli. The removal of
gaseous microemboli by arterial filters is based on the concept of the bubble
trap and the bubble barrier. The bubble trap concept exploits the tendency of
bubbles to rise in a liquid if given the opportunity. This can be accomplished
by reducing the velocity of the incoming blood so that the natural buoyancy of
the bubbles becomes the dominant force. If an escape path is provided these
bubbles can be eliminated. This technique can remove bubbles of 300 µm or
more in diameter. Gas separation based on the surface tension phenomena
at a wetted screen is employed for the removal of bubbles less than 300 µm.
The mechanism takes advantage of the surface tension of the liquid. In simple
terms the pressure applied across a pore of the filter screen, must be
sufficient to disrupt the surface tension and only then air can be driven
through the pore (Figure 4).
The critical pressure or bubble point pressure, below which no air can pass
the pore, is calculated by the equation:
P=
4γ cos Θ
D
where P is bubble point pressure [mmHg], γ is the surface tension [dynes/cm],
D is the diameter of the pore [cm], Θ is the wetting angle.
For most filters, Θ approaches 0 and thus cos Θ = 1.
28
Chapter 3
Figure 4 Equilibrium position
Pore size [D]
wetting angle
P2
Hydrophylic material of
filter screen
Θ
P1
Direction of fluid flow
circumference
of pore π D
γ surface
tension
Θ
γ cos Θ
surface tension
acts at contact with
pore)
surface of
gas bubble
For a typical system γ = 50 dynes/cm and D = 40 µm, resulting in a bubble
point pressure of 37 mmHg. The pressure drop over a clean 40 µm screen is
about 3 mmHg at a blood flow of 5 L/min, the wetted screen can act as a
barrier to gas micro-emboli until the bubble point is reached. Any increase in
pressure drop above the bubble point pressure will result in passage of the
bubble, any decrease in pressure drop over the filter screen will the bubble
retract from the pore.
Unfortunately in paediatric cardiopulmonary bypass the gas escape path of
the arterial filter, the vent at the top of the filter, cannot be opened
continuously since this will create an important arterio-venous shunt. As a
consequence the arterial filter in combination with its bypass line will enlarge
the circuit volume and thus the circulating blood volume of the child with
29
Chapter 3
approximately 50 mL. This volume increase represents approximately 25% of
the total circuit volume.
However, the microporous fibres of the membrane can actively remove
gaseous microemboli. When blood enters the oxygenator its velocity will be
reduced, in the same manner as in an arterial filter, due to the larger open
area for blood flow. When gas comes into contact with the microporous fibres
it will be transported through the micropores due to the pressure difference
between the blood and gas side. This process is in function of pressure drop,
contact area and the availability of gas exchange fibres at the entrance of the
oxygenator.
3.4. Conclusions
The use of hydrodynamic formulas for the calculation of tubing length and
diameter allows the surgical team to define the best possible solution for a
given clinical situation based on desired pressure drop and flow pattern.
The use of an arterial line filter is debatable since it is a passive device that
cannot operate with open vent line during paediatric cardiopulmonary bypass.
The exclusion of the arterial filter in combination with an adequate choice of
tubing will result in an important reduction of dead volume and less
haemodilution, leading to a reduced use of homologous blood products.
30
Chapter 3
References
1. JE Brodie, RB Johnson. In The manual of clinical perfusion. Augusta,
Glendale Medical Corporation, 1994, 9-14.
2. P Dierickx, D De Wachter, P Verdonck. Fluid mechanical approach of
extracorporeal circulation. Course notes Institute Biomedical Technology,
Hydraulics laboratory Ghent University, 1998.
3. Elliot M. Minimizing the bypass circuit: a rational step in the development
of pediatric perfusion. Perfusion 1993; 8: 81-86
4. Tyndal M, Berryessa RG, Campbell DN, Clarke DR. Micro-Prime Circuit
Facilitating Minimal Blood use during Infant Perfusion. J. Extra-Corpor.
Technol. 1987, 19: 352-357
31
Chapter 3
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