University of Groningen Strategies for optimisation of paediatric cardiopulmonary bypass Somer, Filip Maria Jan Jozef De IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2003 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Somer, F. M. J. J. D. (2003). Strategies for optimisation of paediatric cardiopulmonary bypass s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 13-07-2018
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
Table 1: Priming volumes for different tubing diameters Tubing diameter 1 Inch mm Priming volume per 10 cm of length (ml) 1/8 3.17 0.792 4.76 1.781 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
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]. UD Re = 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: µplasma 1800 exp 5.64 + ( 273) T + = 100 µ = µ plasma exp( 2.31Hct) ρ = [ 1.09Hct + 1.035(1 Hct) ] 23
µ plasma = 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 Blood viscosity [x 10-6 N/m².s] 4.0 3.5 3.0 2.5 Hct 36% Hct 34% Hct 32% Hct 30% Hct 28% Hct 26% Hct 24% Hct 22% Hct 20% 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
P = f 2 L U D 2g where f = friction factor, g = gravitational acceleration [m/s²] and 64 f = when flow is laminar. Re However when the flow regimen is turbulent f is calculated using the Colebrook equation: 1 ε 2.51 = 2log + f 3.7D Re f 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
From Figure 2 we learn that both and 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 inch diameter is chosen. This difference is acceptable so a inch line gives the best compromise between priming volume and pressure-flow characteristics. Figure 2. Flow regimen in paediatric arterial lines Characteristics of " and " arterial lines. 150 Length: 150 cm Temperature: 37 Celsius Haematocrit: 30% Pressure drop [mmhg] 100 50 0 Reynolds < 2000 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 Blood flow [L/min] Suppose it is decided to use a inch venous line in the above described case and the height difference between the operating table and the oxygenator is 35 cm H 2 0. 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
This is approximately 10% higher than the maximum flow we anticipate. Thus, a inch venous line is a correct choice for this particular case. Figure 3. Flow characteristics of a inch venous line Characteristics of a " venous line 1.0 0.9 Blood flow at 37 C Blood flow at 20 C Reynolds number at 37 C Reynolds number at 20 C 2500 2000 Blood flow [L/min] 0.8 0.7 1500 Reynolds number 0.6 1000 0.5 Tubing length: 150 cm Height difference between oxygenator and patient: 35 cm H 2 O 20 22 24 26 28 30 Hematocrit [%] 500 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
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 cosθ 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
Figure 4 Equilibrium position Pore size [D] wetting angle P 2 Hydrophylic material of filter screen Θ P 1 Direction of fluid flow circumference of pore π D Θ γ surface tension 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
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
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
32