Artificial lung design: Tubular membrane units* Lyle F. Mockros
John D. S. Gaylor
Technological Institute, Northwestern University, Evanston, II1. 60201, USA
A b s t r a c t - - T h e overall design of tubular membrane oxygenators is considered for three blood conditions: that of a normal adult, haemodiluted adult and new-born. Variations in blood viscosity and oxygen transfer due to the Fahraeus-Lindquist effect are taken into account as well as fabrication variables, including blood header length, potted tube length and packing density of the tubes. For a laminar rectilinear flow, 50 mm Hg < pressure drop < 200 mm Hg, and practical fabrication parameters, there exists a range of tube diameters from 150/zm to 200/zm which give a minimum priming volume and small blood distribution (header) area. The analysis indicates that, with current construction techniques, low-pressure loss oxygenators are n o t feasible for adult total-bypass requirements. Such units can be practicable if transfer rates are increased with secondary mixing of the blood. For example, a threefold increase in the transfe/ rate reduces priming volume and header area by 50% of the unmixed flow values. Keywords--Artificial lung, Membrane oxygenator, Tubes, Capillaries, Design analysis
List of symbols Ah = cross-sectional area of tube sheet effective diffusivity of oxygen in whole blood D d~ = internal diameter of tube L* = dimensionless length for oxygenation, nnDL,,/2Q L a w active (gas exchange) length of tube Lh= axial length of blood-header chamber Ls length of tube in tube sheet n-~ number of tubes in parallel Q= total flow rate of blood through oxygenator internal radius of tube rl V = total priming volume of oxygenator A p = pressure drop across oxygenator 6 = spacing factor of tubes in tube sheet,
Medical and Biological Engineering
1 Introduction THE USE of an auxiliary lung, or oxygenator, for periods of days or weeks, such as in the treatment of congenital circulatory defects in newborns, hyaline membrane disease and shock lung, requires equipment that efficiently performs, in whole or in part, the function of the natural lungs and, at the same time, produces an insignificant blood trauma. Respiratory assist devices incorporating a gas permeable membrane interface between the blood and gas are known to minimise trauma and thrombogenesis, and, as a result, a multiplicity of designs have been attempted. Two main types predominate, however: one with parallel gas-permeable tubes containing
March 1975
171
blood and the other with horizontally stacked blood channels formed from parallel sheets of membrane separated by gas flow passages. A clinically acceptable unit should have a low priming volume, develop a low pressure drop and produce minimal blood trauma. To these ends the designer may vary the flow-path length and spacing and the tube bore or gap between membrane sheets; altering one of these variables to reduce, say, priming volume may produce an increase in the pressure drop and vice versa. As far as the authors are aware, no attempts have been made to relate these factors in a form that indicates the various trade-offs. This paper considers the total unit design of tubular devices and indicates practical dimensions for any set of design specifications. A later paper will consider sheet membrane devices. Units in which the blood flows parallel to the tube walls (e.g. Fig. 1), although somewhat inefficient in gas transfer, offer considerable advantages in ease of design and fabrication. Furthermore, gas transport
for which the oxyhaemoglobin saturation will rise from 65~oo to 95~oo in blood that contains 14 gm~o haemoglobin and has a 40~o haematocrit. Also implied in the criteria is that sufficient carbon dioxide is removed to maintain a normal respiratory quotient. F o r parallel-flow membrane lungs, theoretical and experimental studies have shown that in achieving the above oxygen saturation increase, with an oxygen partial pressure of approximately 720 mm Hg in the gas phase, the carbon-dioxide partial pressure in the blood will be maintained at near physiologic levels (WE[sSMAN and MOCKROS, 1969; VILLARROEL e t a l . , 1971). On the other hand, if effective transverse mixing is induced in the blood phase, the unit design can become limited by carbon-dioxide removal. The blood haemoglobin content and haematocrit chosen above are representative of common blood conditions in auxiliary lung applications. In the treatment of newborns and of patients with anaemia or haemodilution, however, the haemoglobin and haematocrit values deviate considerably from this norm. Oxygenator design requirements for these cases are also considered. For haematoc tit the haemodiluted case, the 'rated flow' criterion was arbitrarily selected as that blood flow rate through the oxygenator which increases the oxygen saturation from 6 5 ~ to 9 5 ~ in blood containing 9 g m ~ haemoglobin and 2 5 ~ haematocrit. F o r a u given flow rate, the total 02 transfer to the low ~:.~ ~ 40~176 haemoglobin blood will be less than that for the normal blood. To achieve the same total 02 transfer to the anaemic subject as that in the normal case, therefore, the blood flow rate should be augmented by the ratio of the normal to anaemic haemoglobins, S i.e. 14/9. Specifying the required arterial-venous saturation differences for neonatal infants is difficult 260 460 56o 6od since admixture of venous and arterial circulations tube internal diameter, dj, IJ occur in varying degrees through shunts in the neoFig. 2 Dependence of apparent blood viscosity at natal cardiovasculature. Extensive cardiac catheteris37~ on internal diameter of tube for haematoation of normal infants 2-34 hours old (RUDOLPH et crits of 25%, 40% and 53% al., 1961), however, yielded right ventricular and left for this geometry has been thoroughly studied, both atrial oxygen saturations of 7 6 ~ and 9 5 ~ , respecttheoretically and experimentally, and is fairly well ively. The left atrial value is in agreement with those understood. In such units, for instance, the gas ( 9 4 ~ ) found by WEISBROT et al. (1958) in infants transfer rate is limited by diffusion in the blood and 1-24 hours old. In 19 newborns, aged 1 day, the usually is independent of the wall thickness (WEISS- total haemoglobin was 18 g m ~ and haematocrit MAN and MOCKROS, 1967; BUCKLES e t a l . , 1968), 53~/o (DELIVORIA--PAPADOPOULOS et al., 1971). adding further to the ease of design and fabrication. Accordingly the 'rated flow' for neonatal oxygenators Because they are more thoroughly understood than has been chosen as that flow rate for which the inlet any other type of design and they offer construction blood at 7 5 ~ saturation will reach 9 5 ~ oxygen advantages, the parallel flow designs are considered saturation at the outlet if the haemoglobin and in detail. On the other hand, great improvements in haematocrit are 18 gm~o and 53~oo, respectively. transfer rates can be achieved by inducing transverse mixing of the blood phase (WEIsSMANand MOCKROS, 1968) and the effect of such mixing on overall design 2 Design parameters The tubular membrane oxygenator (Fig. 1) is is also investigated. A 'rated blood flow' (GALLETT[et al., 1972) is used based on the shell and tube heat-exchanger principle and is fabricated from silicone polymer tubes or in this study to standardise the requirements and facilitate comparison of units. The basic rated flow capillaries, the ends of which are potted in a matrix is defined as that flow rate through the auxiliary lung or tube sheet, commonly of silicone elastomer. Each 172
Medical and Biological Engineering
March 1975
tube sheet is enclosed by a hollow header compartment; bk~od is conveyed into the upstream header and drained from the downstream header by inlet and outlet tubes, respectively. Ventilating gas, normally 100% oxygen at 1 atm. pressure, is circulated through ports in the plastic jacket and contacts the exterior surfaces of the tubes. Deoxygenated blood enters the upstream header and passes into the lumens of the tubes, where oxygen uptake and carbon-dioxide release occurs, and the arterialised blood is collected at the outlet header chamber. The total length of each tube consists of that length which is active in gas exchange, L~ and the sections that are embedded in two tube sheets, each of thickness L~. The packing density of the tubes is denoted by the spacing factor ~, and is given by the tube-sheet cross-sectional area Ah, divided by the total internal cross sectional area of all the tubes. Thus o~ = AUmzr~ 2 . . . . . . . . (1) in which rl is the internal radius of a tube and n is the number of tubes in parallel. The thinner the tube Wall and the more tightly the tube packing, the lower the value of ~. If the tubes had zero wall thickness and were placed in the densest possible configuration, ~ would be a 1" 1; tubes with an o.d./i.d, ratio of 1 "2 [such as those used by DUTTON et al. (1971)] and packed in the densest configuration would have an ct value of 1' 58. A spacing with one tube diameter between outside walls and an o.d./i.d, ratio of 1"2 produces an ~ of 4"0. A recent report (VmLARROEL and LANHAM, 1972) indicates that insufficient carbon dioxide is removed if the tubes have a spacing with less than one tube diameter between their outside walls. Too light a spacing apparently binders the clearance of carbon dioxide outside the tube walls. 0.5 L 04 ..s
~.~.__, -~ 0-.2
normal-adult neonatal
g 0-2
haemodilution-aduR
cO
"O 0
c$o 2do 3do ,do
so6
tube internal diameter, d~, H Fig. 3 Dimensionless length required for rated-flow oxygen transfer in normal, haemodilution and neonatal applications. The f l o w is assumed to be rectilinear and laminar
On the other hand, the larger the spacing, the larger ~, and the larger the priming volume in the headers; also, the area nnr~ 2 ( ~ - 1) is dead-space area on the face of the tube sheet, a potential site for thrombogenesis and a quantity that would be minimised. The Medical and Biological Engineering
header geometry depends on a designer's ingenuity; the blood-containing space, whatever the specific geometry, however, may be considered to be an equivalent cylinder of cross-sectional area equal to that of the tube sheet Ah and an axial length Lb. Three types of quantities need to be considered in designing an oxygenator: (i) those set by clinical requirements, i.e. required oxygen transfer rate, required carbon-dioxide transfer rate, pailicular blood involved (haematocrit, viscosity, diffusivity etc.), and maximum pressure drop that is acceptable (ii) the constraints set by the fabrication technique, i.e. materials used, tube spacing factor c~, header length Lh, tube sheet thickness L~, and required exchange length L~ (iii) those open to the designer, i.e. inside diameter d~ and wall thickness of the exchange tubes. 1000 800
AP=200 mm Fig
~.~'~"
E E
~f~"
AP=5Omm Hg
._~ 200
1~. / ' / ~
1oo
8C e< >~ 4C
~-
L
20 0
/t." /,/ / / / if/ .~./ z' 7
t///
I;i Z'l
loo
. 200
normal-adult ---- . ~ U o n - o d u i t ----neonatal Ls=2Omm
Ls=2Omm .
. 3oo
. . 4oo 5o0 6 0 0
tube inLernal diameter, di, p Fig. 4 Active tube length required for rated-flow oxygenation. Pressure drop, potted length and type of clinical application are design parameters
The first type is under the purview of the physician, the second depends on existing technology and economics, and the third provides the area for optimisation. The following indicates the optimal choice of the third group, if suitable values for the first and second group are specified. The choice of values for the first group is discussed and the choices for values of the second group are values that are plausible with current technology. The selection of one oxygenator over another depends on a number of factors, some objective and some subjective. The factors involved include reliability, versatility, ease of use, ease of maintenance, cost, overall size, priming volume, pressure drop and inertness to the blood. The first four factors depend on manufacturing technology and practice, and are not considered here. In general, the cost and overall physical size are considered only by indicating the ridiculous values that would be needed to meet some sets of specifications.
March 1975
173
Specifying a single design criterion is probably impossible. All investigators would agree that certain dimensions and parameters need to be considered, but exactly what parameter should be minimised or maximised is not easy to agree upon. Some compare units on the basis of rate of gas transfer per unit membrane area, others use blood flow rate per unit membrane area, and others use priming volume. Judging the relative efficiency of oxygenators on the basis of gas transfer rate per unit membrane area or rated blood flow per unit membrane area is based on the assumption that a blood-wall interface produces blood trauma and therefore should be minimised by maximising the transfer rate through each section of membrane area. The designer, however, should use this criteria with considerable caution. To say that one unit is better than another just because it has a higher transfer rate per unit of membrane area can be quite fallacious. The trauma produced at a wall is not just proportional to the total wall area. Besides the effect that the wall material constitution might have, the local bloodflow kinematics would undoubtedly play a 1ole. That is, a unit with a better choice of materials and more favourable flow-kinematics may produce less total trauma per minute in spite of lower gas transfer rates per unit area. Also, if large surface-area contacts are to be avoided, then the criteria should be transfer rate per unit of total internal surface area, not just transfer rate per unit of membrane area. One of the least thrombogenic units, the Bramson oxygenator, not only has a large membrane area but also contains screens in the blood channels (HILL et al., 1972). Also, considering just the gas transfer area neglects the blood contact with the internal surface of the headers, the potted tube ends, etc. These latter areas are just as able to be a source of trauma; in fact, many times these areas are the likely sites of high rates of trauma. One design may have a high gas transfer rate per unit of membrane area, but because of the nature of the design the header areas may have to be large. Such a unit may produce higher rates of trauma than another unit whose membrane transfer rate may be less but whose header area can be conveniently made less. As an example, consider a coiled tube unit and a straight tube unit. Either unit, in any practical design, must consist of many small tubes in parallel. The coiled tube unit, with its induced secondary flows, has a much higher transfer rate per unit of membrane area and would require much less total length of tubing in the transfer section. The coiled tubes, however, require more space for each tube and would require the packing density to be larger or, alternately, require additional length of straight tubes in order to bring them together in a compact tube sheet. In any event, the designer is ~'equired, by the coiling, to increase the surface area not associated with gas transfer. Finally, those designers who prefer gas-transfer rates per unit of membrane area as an objective 174
criterion of performance should consider the most successful membrane lung, the natural lung. For an adult at rest the oxygen transfer rate per unit of membrane area is about 2 to 3 ( m l / m i n ) / m 2, a figure that is lower than a n y proposed artificial lung design and 100 times less than some reported artificial lungs. Table 1. Design parameters for tubular membrane oxygenators Parameter
Desirable value
Pressure drop, Ap Tube length, La Header surface area per unit rated blood flow, Ah/Q Mean residence time (priming volume per unit rated blood flow,) V/Q
50 mm Hg 50-500 mm small less than 6 seconds
Rather than use a single parameter as the criterion for relative eff• the present study considers several parameters (see Table 1) and attempts to show how tubular units should be designed if these parameters are all to be kept within reasonable bounds. The design parameters considered are pressure drop, tube length, header surface area per unit rated blood flow, and mean residence time (equivalent to priming volume per unit rated blood flow). Explicit consideration of these parameters is used to indicate feasible optimisation. In addition, the range of possible designs should be constrained to those units that do not traumatise the formed elements, denature plasma proteins, or activate the clotting, complement or inflammatory systems. Quantitative values for tolerable levels of such blood trauma are not known, nor are the crucial haemotologic parameters delineated. Consequently, the current considerations of optimisation can only implicitly include these constraints. The oxygenator priming volume, header area and pressure drop are dependent on the design variables L,, L~, ~t, n, r~ and Lb. Total priming volume V is the s u m m a t i o n of the tube bundle and header volumes: V= nzrr12(2L~+L,)+2AhLh
. . . .
(2)
A dimensionless length often used in other studies, L*, can be defined as : L* = n n D L o / 2 Q
.
.
.
.
.
.
.
(3),
in which Q is the total flow rate of blood through the oxygenator and D is the diffusivity of oxygen in blood. The value of L*, for specified changes of oxygen saturations and carbon-dioxide partial pressures, is known from previous engineering analyses (WEISSMAN and MOCKROS, 1967; BUCKLES e t aL, 1968; WEISSMAN and MOCKROS, 1969; DRINKER et al., 1969; MOC~:ROS and WEISSMAN, 1971; DORSON et aL, 1971) for various types of flow kinematics.
Medical and Biological Engineering
March 1975
Using silicone-rubber tubes and with rectilinear flow at rated flow conditions, L* i s , except for the Fahraeus-Lindquist effect (discussed below), independent of tube size. For flows with transverse mixing, however, L* will depend on the effectiveness of the mixing and the particular tube used. Substituting eqns. 1 and 3 into eqn. 2 gives V/Q = 2L* r,2(2~L, + 2Ls + L , ) / D L ,
(4)
.
The design parameter V / Q indicates the priming volume required per unit of rated blood flow rate, and can be interpreted as the mean residence time or volume turnover time. For any particular design, V / Q would be about the same for units of small or large capacity. A good design would be one in which V / Q < 0.1 min; e.g. for total bypass of an adult with Q = 5.0 1/min, the priming volume would be < 0 . 5 litres. Also, combining eqns. 1 and 3 gives a second parameter, the header area per unit of rated blood flow rate: Ah/Q = 2L* c~ri2/OL . . . . . . .
(5)
Typical dimensions would be mm2/(mm3/s) or s/mm. If A , / Q is large, the header area is large for that flow rate. A large Ah may be due to a large *r implying a potentially large area for thrombus formation, a n d / o r too large a flow area nnrl 2 in the gas exchange section, implying rapid velocity changes as the blood passes from the inlet tube to the gas exchange tubes and from the gas exchange tubes to the outlet tube. The pressure drop through the oxygenator consists of losses occurring in the headers plus entrance, exit and fully developed losses in the tubes. Since header geometries differ from design to design, it is E 0.20
John D. S. Gaylor
Technological Institute, Northwestern University, Evanston, II1. 60201, USA
A b s t r a c t - - T h e overall design of tubular membrane oxygenators is considered for three blood conditions: that of a normal adult, haemodiluted adult and new-born. Variations in blood viscosity and oxygen transfer due to the Fahraeus-Lindquist effect are taken into account as well as fabrication variables, including blood header length, potted tube length and packing density of the tubes. For a laminar rectilinear flow, 50 mm Hg < pressure drop < 200 mm Hg, and practical fabrication parameters, there exists a range of tube diameters from 150/zm to 200/zm which give a minimum priming volume and small blood distribution (header) area. The analysis indicates that, with current construction techniques, low-pressure loss oxygenators are n o t feasible for adult total-bypass requirements. Such units can be practicable if transfer rates are increased with secondary mixing of the blood. For example, a threefold increase in the transfe/ rate reduces priming volume and header area by 50% of the unmixed flow values. Keywords--Artificial lung, Membrane oxygenator, Tubes, Capillaries, Design analysis
List of symbols Ah = cross-sectional area of tube sheet effective diffusivity of oxygen in whole blood D d~ = internal diameter of tube L* = dimensionless length for oxygenation, nnDL,,/2Q L a w active (gas exchange) length of tube Lh= axial length of blood-header chamber Ls length of tube in tube sheet n-~ number of tubes in parallel Q= total flow rate of blood through oxygenator internal radius of tube rl V = total priming volume of oxygenator A p = pressure drop across oxygenator 6 = spacing factor of tubes in tube sheet,
Medical and Biological Engineering
1 Introduction THE USE of an auxiliary lung, or oxygenator, for periods of days or weeks, such as in the treatment of congenital circulatory defects in newborns, hyaline membrane disease and shock lung, requires equipment that efficiently performs, in whole or in part, the function of the natural lungs and, at the same time, produces an insignificant blood trauma. Respiratory assist devices incorporating a gas permeable membrane interface between the blood and gas are known to minimise trauma and thrombogenesis, and, as a result, a multiplicity of designs have been attempted. Two main types predominate, however: one with parallel gas-permeable tubes containing
March 1975
171
blood and the other with horizontally stacked blood channels formed from parallel sheets of membrane separated by gas flow passages. A clinically acceptable unit should have a low priming volume, develop a low pressure drop and produce minimal blood trauma. To these ends the designer may vary the flow-path length and spacing and the tube bore or gap between membrane sheets; altering one of these variables to reduce, say, priming volume may produce an increase in the pressure drop and vice versa. As far as the authors are aware, no attempts have been made to relate these factors in a form that indicates the various trade-offs. This paper considers the total unit design of tubular devices and indicates practical dimensions for any set of design specifications. A later paper will consider sheet membrane devices. Units in which the blood flows parallel to the tube walls (e.g. Fig. 1), although somewhat inefficient in gas transfer, offer considerable advantages in ease of design and fabrication. Furthermore, gas transport
for which the oxyhaemoglobin saturation will rise from 65~oo to 95~oo in blood that contains 14 gm~o haemoglobin and has a 40~o haematocrit. Also implied in the criteria is that sufficient carbon dioxide is removed to maintain a normal respiratory quotient. F o r parallel-flow membrane lungs, theoretical and experimental studies have shown that in achieving the above oxygen saturation increase, with an oxygen partial pressure of approximately 720 mm Hg in the gas phase, the carbon-dioxide partial pressure in the blood will be maintained at near physiologic levels (WE[sSMAN and MOCKROS, 1969; VILLARROEL e t a l . , 1971). On the other hand, if effective transverse mixing is induced in the blood phase, the unit design can become limited by carbon-dioxide removal. The blood haemoglobin content and haematocrit chosen above are representative of common blood conditions in auxiliary lung applications. In the treatment of newborns and of patients with anaemia or haemodilution, however, the haemoglobin and haematocrit values deviate considerably from this norm. Oxygenator design requirements for these cases are also considered. For haematoc tit the haemodiluted case, the 'rated flow' criterion was arbitrarily selected as that blood flow rate through the oxygenator which increases the oxygen saturation from 6 5 ~ to 9 5 ~ in blood containing 9 g m ~ haemoglobin and 2 5 ~ haematocrit. F o r a u given flow rate, the total 02 transfer to the low ~:.~ ~ 40~176 haemoglobin blood will be less than that for the normal blood. To achieve the same total 02 transfer to the anaemic subject as that in the normal case, therefore, the blood flow rate should be augmented by the ratio of the normal to anaemic haemoglobins, S i.e. 14/9. Specifying the required arterial-venous saturation differences for neonatal infants is difficult 260 460 56o 6od since admixture of venous and arterial circulations tube internal diameter, dj, IJ occur in varying degrees through shunts in the neoFig. 2 Dependence of apparent blood viscosity at natal cardiovasculature. Extensive cardiac catheteris37~ on internal diameter of tube for haematoation of normal infants 2-34 hours old (RUDOLPH et crits of 25%, 40% and 53% al., 1961), however, yielded right ventricular and left for this geometry has been thoroughly studied, both atrial oxygen saturations of 7 6 ~ and 9 5 ~ , respecttheoretically and experimentally, and is fairly well ively. The left atrial value is in agreement with those understood. In such units, for instance, the gas ( 9 4 ~ ) found by WEISBROT et al. (1958) in infants transfer rate is limited by diffusion in the blood and 1-24 hours old. In 19 newborns, aged 1 day, the usually is independent of the wall thickness (WEISS- total haemoglobin was 18 g m ~ and haematocrit MAN and MOCKROS, 1967; BUCKLES e t a l . , 1968), 53~/o (DELIVORIA--PAPADOPOULOS et al., 1971). adding further to the ease of design and fabrication. Accordingly the 'rated flow' for neonatal oxygenators Because they are more thoroughly understood than has been chosen as that flow rate for which the inlet any other type of design and they offer construction blood at 7 5 ~ saturation will reach 9 5 ~ oxygen advantages, the parallel flow designs are considered saturation at the outlet if the haemoglobin and in detail. On the other hand, great improvements in haematocrit are 18 gm~o and 53~oo, respectively. transfer rates can be achieved by inducing transverse mixing of the blood phase (WEIsSMANand MOCKROS, 1968) and the effect of such mixing on overall design 2 Design parameters The tubular membrane oxygenator (Fig. 1) is is also investigated. A 'rated blood flow' (GALLETT[et al., 1972) is used based on the shell and tube heat-exchanger principle and is fabricated from silicone polymer tubes or in this study to standardise the requirements and facilitate comparison of units. The basic rated flow capillaries, the ends of which are potted in a matrix is defined as that flow rate through the auxiliary lung or tube sheet, commonly of silicone elastomer. Each 172
Medical and Biological Engineering
March 1975
tube sheet is enclosed by a hollow header compartment; bk~od is conveyed into the upstream header and drained from the downstream header by inlet and outlet tubes, respectively. Ventilating gas, normally 100% oxygen at 1 atm. pressure, is circulated through ports in the plastic jacket and contacts the exterior surfaces of the tubes. Deoxygenated blood enters the upstream header and passes into the lumens of the tubes, where oxygen uptake and carbon-dioxide release occurs, and the arterialised blood is collected at the outlet header chamber. The total length of each tube consists of that length which is active in gas exchange, L~ and the sections that are embedded in two tube sheets, each of thickness L~. The packing density of the tubes is denoted by the spacing factor ~, and is given by the tube-sheet cross-sectional area Ah, divided by the total internal cross sectional area of all the tubes. Thus o~ = AUmzr~ 2 . . . . . . . . (1) in which rl is the internal radius of a tube and n is the number of tubes in parallel. The thinner the tube Wall and the more tightly the tube packing, the lower the value of ~. If the tubes had zero wall thickness and were placed in the densest possible configuration, ~ would be a 1" 1; tubes with an o.d./i.d, ratio of 1 "2 [such as those used by DUTTON et al. (1971)] and packed in the densest configuration would have an ct value of 1' 58. A spacing with one tube diameter between outside walls and an o.d./i.d, ratio of 1"2 produces an ~ of 4"0. A recent report (VmLARROEL and LANHAM, 1972) indicates that insufficient carbon dioxide is removed if the tubes have a spacing with less than one tube diameter between their outside walls. Too light a spacing apparently binders the clearance of carbon dioxide outside the tube walls. 0.5 L 04 ..s
~.~.__, -~ 0-.2
normal-adult neonatal
g 0-2
haemodilution-aduR
cO
"O 0
c$o 2do 3do ,do
so6
tube internal diameter, d~, H Fig. 3 Dimensionless length required for rated-flow oxygen transfer in normal, haemodilution and neonatal applications. The f l o w is assumed to be rectilinear and laminar
On the other hand, the larger the spacing, the larger ~, and the larger the priming volume in the headers; also, the area nnr~ 2 ( ~ - 1) is dead-space area on the face of the tube sheet, a potential site for thrombogenesis and a quantity that would be minimised. The Medical and Biological Engineering
header geometry depends on a designer's ingenuity; the blood-containing space, whatever the specific geometry, however, may be considered to be an equivalent cylinder of cross-sectional area equal to that of the tube sheet Ah and an axial length Lb. Three types of quantities need to be considered in designing an oxygenator: (i) those set by clinical requirements, i.e. required oxygen transfer rate, required carbon-dioxide transfer rate, pailicular blood involved (haematocrit, viscosity, diffusivity etc.), and maximum pressure drop that is acceptable (ii) the constraints set by the fabrication technique, i.e. materials used, tube spacing factor c~, header length Lh, tube sheet thickness L~, and required exchange length L~ (iii) those open to the designer, i.e. inside diameter d~ and wall thickness of the exchange tubes. 1000 800
AP=200 mm Fig
~.~'~"
E E
~f~"
AP=5Omm Hg
._~ 200
1~. / ' / ~
1oo
8C e< >~ 4C
~-
L
20 0
/t." /,/ / / / if/ .~./ z' 7
t///
I;i Z'l
loo
. 200
normal-adult ---- . ~ U o n - o d u i t ----neonatal Ls=2Omm
Ls=2Omm .
. 3oo
. . 4oo 5o0 6 0 0
tube inLernal diameter, di, p Fig. 4 Active tube length required for rated-flow oxygenation. Pressure drop, potted length and type of clinical application are design parameters
The first type is under the purview of the physician, the second depends on existing technology and economics, and the third provides the area for optimisation. The following indicates the optimal choice of the third group, if suitable values for the first and second group are specified. The choice of values for the first group is discussed and the choices for values of the second group are values that are plausible with current technology. The selection of one oxygenator over another depends on a number of factors, some objective and some subjective. The factors involved include reliability, versatility, ease of use, ease of maintenance, cost, overall size, priming volume, pressure drop and inertness to the blood. The first four factors depend on manufacturing technology and practice, and are not considered here. In general, the cost and overall physical size are considered only by indicating the ridiculous values that would be needed to meet some sets of specifications.
March 1975
173
Specifying a single design criterion is probably impossible. All investigators would agree that certain dimensions and parameters need to be considered, but exactly what parameter should be minimised or maximised is not easy to agree upon. Some compare units on the basis of rate of gas transfer per unit membrane area, others use blood flow rate per unit membrane area, and others use priming volume. Judging the relative efficiency of oxygenators on the basis of gas transfer rate per unit membrane area or rated blood flow per unit membrane area is based on the assumption that a blood-wall interface produces blood trauma and therefore should be minimised by maximising the transfer rate through each section of membrane area. The designer, however, should use this criteria with considerable caution. To say that one unit is better than another just because it has a higher transfer rate per unit of membrane area can be quite fallacious. The trauma produced at a wall is not just proportional to the total wall area. Besides the effect that the wall material constitution might have, the local bloodflow kinematics would undoubtedly play a 1ole. That is, a unit with a better choice of materials and more favourable flow-kinematics may produce less total trauma per minute in spite of lower gas transfer rates per unit area. Also, if large surface-area contacts are to be avoided, then the criteria should be transfer rate per unit of total internal surface area, not just transfer rate per unit of membrane area. One of the least thrombogenic units, the Bramson oxygenator, not only has a large membrane area but also contains screens in the blood channels (HILL et al., 1972). Also, considering just the gas transfer area neglects the blood contact with the internal surface of the headers, the potted tube ends, etc. These latter areas are just as able to be a source of trauma; in fact, many times these areas are the likely sites of high rates of trauma. One design may have a high gas transfer rate per unit of membrane area, but because of the nature of the design the header areas may have to be large. Such a unit may produce higher rates of trauma than another unit whose membrane transfer rate may be less but whose header area can be conveniently made less. As an example, consider a coiled tube unit and a straight tube unit. Either unit, in any practical design, must consist of many small tubes in parallel. The coiled tube unit, with its induced secondary flows, has a much higher transfer rate per unit of membrane area and would require much less total length of tubing in the transfer section. The coiled tubes, however, require more space for each tube and would require the packing density to be larger or, alternately, require additional length of straight tubes in order to bring them together in a compact tube sheet. In any event, the designer is ~'equired, by the coiling, to increase the surface area not associated with gas transfer. Finally, those designers who prefer gas-transfer rates per unit of membrane area as an objective 174
criterion of performance should consider the most successful membrane lung, the natural lung. For an adult at rest the oxygen transfer rate per unit of membrane area is about 2 to 3 ( m l / m i n ) / m 2, a figure that is lower than a n y proposed artificial lung design and 100 times less than some reported artificial lungs. Table 1. Design parameters for tubular membrane oxygenators Parameter
Desirable value
Pressure drop, Ap Tube length, La Header surface area per unit rated blood flow, Ah/Q Mean residence time (priming volume per unit rated blood flow,) V/Q
50 mm Hg 50-500 mm small less than 6 seconds
Rather than use a single parameter as the criterion for relative eff• the present study considers several parameters (see Table 1) and attempts to show how tubular units should be designed if these parameters are all to be kept within reasonable bounds. The design parameters considered are pressure drop, tube length, header surface area per unit rated blood flow, and mean residence time (equivalent to priming volume per unit rated blood flow). Explicit consideration of these parameters is used to indicate feasible optimisation. In addition, the range of possible designs should be constrained to those units that do not traumatise the formed elements, denature plasma proteins, or activate the clotting, complement or inflammatory systems. Quantitative values for tolerable levels of such blood trauma are not known, nor are the crucial haemotologic parameters delineated. Consequently, the current considerations of optimisation can only implicitly include these constraints. The oxygenator priming volume, header area and pressure drop are dependent on the design variables L,, L~, ~t, n, r~ and Lb. Total priming volume V is the s u m m a t i o n of the tube bundle and header volumes: V= nzrr12(2L~+L,)+2AhLh
. . . .
(2)
A dimensionless length often used in other studies, L*, can be defined as : L* = n n D L o / 2 Q
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(3),
in which Q is the total flow rate of blood through the oxygenator and D is the diffusivity of oxygen in blood. The value of L*, for specified changes of oxygen saturations and carbon-dioxide partial pressures, is known from previous engineering analyses (WEISSMAN and MOCKROS, 1967; BUCKLES e t aL, 1968; WEISSMAN and MOCKROS, 1969; DRINKER et al., 1969; MOC~:ROS and WEISSMAN, 1971; DORSON et aL, 1971) for various types of flow kinematics.
Medical and Biological Engineering
March 1975
Using silicone-rubber tubes and with rectilinear flow at rated flow conditions, L* i s , except for the Fahraeus-Lindquist effect (discussed below), independent of tube size. For flows with transverse mixing, however, L* will depend on the effectiveness of the mixing and the particular tube used. Substituting eqns. 1 and 3 into eqn. 2 gives V/Q = 2L* r,2(2~L, + 2Ls + L , ) / D L ,
(4)
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The design parameter V / Q indicates the priming volume required per unit of rated blood flow rate, and can be interpreted as the mean residence time or volume turnover time. For any particular design, V / Q would be about the same for units of small or large capacity. A good design would be one in which V / Q < 0.1 min; e.g. for total bypass of an adult with Q = 5.0 1/min, the priming volume would be < 0 . 5 litres. Also, combining eqns. 1 and 3 gives a second parameter, the header area per unit of rated blood flow rate: Ah/Q = 2L* c~ri2/OL . . . . . . .
(5)
Typical dimensions would be mm2/(mm3/s) or s/mm. If A , / Q is large, the header area is large for that flow rate. A large Ah may be due to a large *r implying a potentially large area for thrombus formation, a n d / o r too large a flow area nnrl 2 in the gas exchange section, implying rapid velocity changes as the blood passes from the inlet tube to the gas exchange tubes and from the gas exchange tubes to the outlet tube. The pressure drop through the oxygenator consists of losses occurring in the headers plus entrance, exit and fully developed losses in the tubes. Since header geometries differ from design to design, it is E 0.20
