ANNALS OF BIOMEDICAL ENGINEERING 6, 48--59
(1978)
Carbon Dioxide Transfer in a Membrane Blood Oxygenator SHIGEO KATOH AND FUMITAKE YOSHIDA*
Chemical Engineering Department, Kyoto University, Kyoto 606, Japan Received March 25, 1977 Rates of desorption of CO2 from bovine blood, as well as bovine serum, aqueous hemoglobin solutions, and water in a fiat-plate-type experimental membrane blood oxygenator using silicone rubber and microporous polypropylene membranes were measured. The experimental data showed good agreement with the rigorous theoretical predictions based on an assumption that the CO2 transfer in the liquid phase is facilitated by simultaneous diffusion of bicarbonate ions produced by the instantaneous hydration of CO.o catalyzed by carbonic anhydrase existing in the red cells. Effects of screen turbulence promoters in the liquid channel were also studied. The overall resistance for CO2 transfer in membrane oxygenators including the blood phase resistance is usually smaller than that for oxygen transfer, unless the liquid phase mass transfer resistance is small relative to the membrane resistance. Thus, a membrane oxygenator designed on the basis of oxygen transfer rates will almost always have a sufficient capacity for CO2 transfer. INTRODUCTION Removal of C02 from the venous blood as well as oxygenation of hemoglobin are performed in the blood oxygenator. With the direct gas-blood contact-type oxygenators, such as the bubble-type, it is often necessary to mix some CO2 in the incoming oxygen to suppress excessive removal of C02. This can be understood from the fact that, if pure oxygen is used, the driving potential for C02 in the liquid phase is greater for C02 than for oxygen, since the ratio of the physical solubilities of C02 and oxygen in blood is 20: 1, while the ratio of the partial pressure difference for CO2 transfer to that for oxygen transfer is 1:14. On the other hand, it is often stated that the rate of C02 transfer in the membrane oxygenator is lower than t h a t of oxygen transfer. However, the problem is not so simple, since the resistances for CO2 transfer consist of the membrane and the blood phase resistances. The present work was intended to obtain experimental and theoretical bases for the design of the flat-plate-type membrane oxygenators, in which blood flows parallel with the permeable membranes, with and without screen turbu* To whom correspondence should be addressed. 48
0090-6964/78/0061-0048502.00/0 Copyright ~ 1978 by Academic Press, Inc. All rights of reproduction in any form reserved.
CO2 TRANSFER IN MEMBRANE OXYGENATOR 300 .......
-
49
p
IUU
FIG. 1. Experimental membrane oxygenator. lence promoters in the blood channel. Our studies on the oxygen transfer rates in the same type of apparatus were reported elsewhere (Katoh and Yoshida, 1973). APPARATUS AND PROCEDURE Figure 1 shows the details of the experimental membrane oxygenator. A pair of silicone rubber membranes (Fuji Systems Co., Japan, 100 ~m thick) or microporous polypropylene membranes (Celanese Corp. U.S.A., 20 ~m thick) were sandwiched between two acrylic resin supporting plates, each of which had a rectangular recessed portion, 5 cm wide, 10 cm long, and 0.5 mm deep, holding a 14 mesh Saran screen flush with the surface of the plate. The merebranes were as large as the supporting plates. The total effective surface area of the membrane was 0.01 m 2. To keep the clearance between the two merebranes (thickness of the blood channel) constant, a hard acrylic resin gasket, 1 mm thick, was placed between the two membranes along the periphery of the supporting plates as shown in Fig. 1. The liquid inlet and outlet nozzles were attached to the liquid-distributing grooves cut near both ends of each supporting plate perpendicular to the liquid flow direction. The blood channels between the supporting plates upstream and downstream of the effective portion of the membranes, each 7 cm long, served as the calming sections to develop parabolic velocity distribution in the liquid flow which was always laminar. The gas inlet and outlet nozzles were attached to the respective ends of the recessed portion of each supporting plate. Figure 2 shows a schematic diagram of the experimental setup. A batch of blood (or other liquids) was stored in a 2-liter acrylic resin liquid reservoir with a temperature-controlled water jacket. An a i r - C Q mixture of a known composition was sparged into the blood to adjust the CO2 concentration in the sample. The gas mixture was prepared b y continuously mixing the air from a blower with the C02 from a cylinder, both gases being metered b y rotameters separately. During an experiment the blood sample in the reservoir
50
KATOH AND YOSHIDA
water [
reservoir
(36 5 C ) r - - u - ~ , F ~ J : ~
rotameter
I water J~l | / ( 36.5~c)~q~]
r---~
i
oxygenator l
~
> ~
air
to CO, analyzer rap
water ~" ~ : ~ (O~
FIG. 2. Schematic diagram of experimental setup. was kept at 36.5~ and continuously stirred to prevent sedimentation of red cells. After an equilibrium was reached between the CO2 contents of the blood and the sparging gas, the blood was supplied to the horizontally placed oxygenator by gravity. The pH of blood at the inlet of the oxygenator was ca. 7.3. No gas bubbles remained in the blood channel. The blood flow rate was regulated by a needle valve and was measured with a graduated cylinder and a stopwatch. Then, the air from the blower, humidified, temperature-controlled at 36.5~ and metered using the same system with the one used for preparing the sparging gas for blood, was passed through the gas channels of the oxygenator. The CQ-eontaining air coming out of the oxygenator was passed through the vapor trap, which was kept at 0~ by passing ice water through the jacket. The gas was led to the infrared CO2 analyzer (Shimadzu, Type URA-2S) after temperature measurement. The rate of CO2 desorption was obtained from the COs content and the flow rate of the gas from the oxygenator. For comparison some experiments were performed on the desorption of COs from blood to which benzenesulfonamide was added to inactivate carbonic anhydrase in the red cells. Bovine blood, defibrinated by the procedure previously described (Yoshida and Ohshima, 1966), bovine serum, aqueous solutions of hemoglobin, as well as pure water, were used in the desorption experiments. The hematoerit of blood was adjusted to a desired value by blending appropriate amounts of centrifuged serum and red cells. It was determined by the usual method using a centrifuge and capillary. The COs permeability of the silicone rubber membrane and the mieroporous
CO2 TRANSFER IN MEMBRANE OXYGENATOR
51
polypropylene membrane were determined by measuring the rates of CO2 desorption from water through the membrane in an agitated vessel operM.ed at various agitator speeds by the method previously reported (Katoh and Yoshida, 1972). The values obtained were 3.4 X 10-5 cm a (STP)/cm2/sec/cm Hg for the silicone rubber, and 4.1 X 10-4 cm a (STP)/cm2/see/em Hg for the polypropylene membrane. THEORETICAL Carbon dioxide exists in blood as three species, i.e., dissolved CO2, bicarbonate ions HC03-, and carbaminohemoglobin. The C02-bicarbonate ion interchange is a rapid reaction catalyzed by an enzyme carbonic anhydrase contained in the red cells. Dissociation of carbaminohemoglobin is also a very rapid reaction. Thus, it can be considered that the total amount of C Q existing as various forms in blood reaches equilibrium with the Pco~ almost instantaneously. The C02 dissociation curve such as shown in Fig. 3 (Bell et al., 1965) gives the relationship between the total amount of C02 in blood and pco~. In Fig. 3 the upper two curves are for the total amounts of CO2 for the hematocrits of 42 and 8.5%, and the lower straight line is for the amount of CO2 physically dissolved in blood. The line for the hematocrit of 8.5% does not pass through the origin. Only part of bicarbonate ions can be converted to CO2 gas because the buffering action of hemoglobin is insufficient at this hematocrit. It is assumed that the COs transfer in blood is facilitated by simultaneous diffusion of bicarbonate ions, which will be dehydrated to give COs and H:O at the gas-liquid interface with the presence of carbonic anhydrase. Dorson and Voorhees (1974) presented an approximate analysis using averaged values of the slopes of the total COs content and the HCO~- content versus the COs partial pressure. In the analysis of COs desorption through a high-permeable membrane such as the microporous polypropylene membrane, however, the C02 partial pressure in the region near the membrane surface becomes low. At lower COs partial pressures the curvature of the COs dissociation curve is significant, so the linear approximation to the coneentrations of COs and HCO3- of Dorson and Voorhees would be inaccurate. In this work the values of the slopes of the COs dissociation curve at respective values 50
>
c ou
Ht=42% 25
physicat[y 0
10
20
dissotved 3'0
CO 2 410
50
Pcoz, mmHg
Fro. 3. Carbon dioxide dissociation curve.
KATOH AND YOSHIDA
52
of the CO2 partial pressure were used and the corresponding facilitated diffusivities of C02 were calculated. B y use of these facilitated diffusivities numericM solutions of the CO2 desorption r~te were obtained. With assumptions of reaction equilibrium and Newtonian behavior of blood, the CO2 balance for a volume element of liquid in laminar flow in the x-direction gives
(OCco~ v~ \ ~x
OB) + ~-x
02Cco~ = Dco~----
Oy2
02CHco3+ DHco~----
(1)
Oy2
If H e n r y ' s law, i.e., OCco~/Op = H is assumed,
__ vxH
= Doo,H
0~P ~- DHCO3
( 0 0CHc03-~ Op
Oy~
O-y
Op
/ Oy OCHco3- Op~
+ Dnco~-
Op
Oy2
.
(2)
The term O/Oy(OCuco3-/Op) is negligible, because the term OCHeo3-/Op is nearly constant in a narrow range of CO2 partial pressure in the membrane blood oxygenator. Thus,
vxH 1 ~- H O p
Oxx = Dco~.H oy 2 + D ~ c o ~
Op
Oy2"
(3)
Dividing Eq. (3) b y H,
The term [-OC~co~-/Op(1/H)]D~co3- represents the effect of simultaneous fusion of bicarbonate ions on the rate of CO2 transfer. The gradient of bicarbonate ion concentration was obtained from the dissociation curve the carbaminohemoglobin concentration given in the literature (Bell et 1965). Thus, the facilitated diffusivity of CO2 can be expressed b y Eq. (5) : Dco~,] = Dco2 -k OCHcoa-/Op(1/H)D~co~-.
difthe and
al., (5)
With an assumption of parabolic velocity distribution Eq. (4) can be written in the dimensionless form:
Oy.2
-
2
(2y* -- y,2)
1 Jr- - -
---
Op*/\Ox*/
Dco.ffDco2.f,
(6)
where
x* = xDco2/ (ua2),
(7)
y* = (a -- y)/a,
(8)
P* = P/Pe.
(9)
In Eq. (6), B* is the dimensionless total concentration of chemically combined
CO~ TRANSFER IN MEMBRANE OXYGENATOR
53
COs in blood, i.e., existing as bicarbonate and carbaminohemoglobin. Equation (6) was solved by the finite-difference procedures of Crank and Nieolson (1947) with the following boundary conditions : Op*/Oy* = 0
p* = ( D e o ~ . f / P a ) ( O p * / O y * ) p* = 1
(10)
a t y* = 1,
at y* = 0,
a t x* = O.
(11) (12)
The total C02 content in each layer of the outgoing liquid parallel to x-axis was calculated as a function of transverse position, and was multiplied by the velocity at each position. The mixing cup concentration of COs in the whole outgoing liquid was obtained by numerical integration. Subtraction of this mixing cup concentration from the initial COs concentration gave the total COs desorption. To study the effect of the simultaneous diffusion of bicarbonate ions, rates of COs desorption from blood were calculated on the assumptions of the following two cases: (A) Physically dissolved COs alone diffuses in blood: Dco~,/
=
Dco~.
(B) Both physically dissolved CO2 and dicarbonate ions diffuse in blood: Dco~.~ = Dco2 ~1- OCHco~-/Op(1/H)DHco~-. The effective diffusivity of COs in blood of a given hematocrit was estimated by multiplying the effective diffusivity of oxygen in blood of the corresponding hematocrit (Katoh and Yoshida, 1972) by the ratio of the diffusivity of COs in water to that of oxygen. The effective diffusivity of bicarbonate ions was estimated in a like manner from the value in water given in the literature (Kigoshi and Hashitani, 1963). RESULTS AND DISCUSSIONS Figure 4 shows the experimental data on the physical desorption of CO2 from water through two kinds of membranes. The ordinate is the dimensionless concentration of COs and the abscissa is the dimensionless ratio involving the channel length x, the half channel height a, the diffusivity D, and the average liquid velocity u. The curves in Fig. 4 represent the theoretical rates (Katoh and Yoshida, 1973) of COs desorption with the two membranes, respectively. The experimental data points show general agreement with the theoretical curves, which seems to indicate the soundness of the values of the physical properties used in the calculations. Figure 5 compares theoretical predictions with the experimental data on CO2 desorption from blood at peo~ of 49 mm Hg through the microporous polypropylene membranes. In this case the membrane resistance to C02 transfer is much smaller than the liquid phase resistance. The broken lines are for the theoretical values for case A without simultaneous diffusion of bicarbonate
54
KATOH AND
1.~ I ~'~..~. ,.
'
'
~
0'91
YOSHIDA
b b e r
memb . . . . ; ~)sili. . . . . .
mrnHg Pco=32 ! ,~9
32 49
=
~m (.9
0.8 I
0"750 "
I
002
0 0 8
I
0.04 xD/ua z
0.06
FIG. 4. Physical desorption of COs from water. ions, and the solid curves show the theoretical values for case B, in which simultaneous diffusion of bicarbonate ions is assumed. The measured rates of desorption of C02 from blood are higher t h a n the theoretical values for case A, but show general agreement with the theoretical curves for case B. This seems to i m p l y t h a t the rate of CO2 desorption is facilitated b y the simultaneous diffusion of bicarbonate ions. The broken curve for zero h e m a t o c r i t shows the theoretical values of the rates of physical desorption of C02 from serum. The fact t h a t experimental values for this case are slightly higher t h a n theoretical predictions, although the rate of dehydration of bicarbonate ions should be slow in the absence of carbonic anhydrase, might be due to the buffering action of serum proteins. Figure 6 shows the data for the runs with the silicone rubber m e m b r a n e s compared with theoretical predictions. The rates of CO2 desorption for these runs are lower and affected to a lesser extent b y the difference in hematocrit c o m p a r e d with the runs with the microporous polypropylene m e m b r a n e s because 1.5
I
I
l
I
Ht
9 4 2 - 46 ~ :( --e- 2 7 % 7.5% o 0% (serum)
.E E
J
42%
~
to 42% 85"/* 0
0
o 0.s
-
__
- - - -
- -
0
%
-u e~
C
(9
0
I
I
I
I
50
100
150
200
Blood
f{ow
rate,
250
cc/min
F I G . 5. Carbon dioxide desorption from blood through microporous polypropylene membranes (pco2 = 49 mm Hg).
COs TRANSFER IN MEMBRANE OXYGENATOR 1.5
55
I
E E
9
Ht 42 ~ 5 %
u
/",
0 ~176
1.0
9
~
9 o
0.5
42"/* 42% 8.5%
L)
0
I
I
[
I
50
100
150
200
Blood
fiow
rate,
250
cc/rnin
FIG. 6. Carbon dioxide desorption from blood through silicone rubber membranes (pc% = 49 mm Hg). of the relatively higher mass transfer resistance of the silicone r u b b e r m e m branes. In this figure the broken and solid lines show the theoretical values for eases A and B, respectively. For the h e m a t o e r i t of 8.5% the theoretical values for the two eases are almost identical. Table I compares the smoothed values of present data for C02 desorption from blood (hematoerit 42-430-/0) with the values calculated for the conditions of the present experiments b y the procedure proposed b y Dorson and Voorhees (1974). Prediction b y the Dorson procedure using linear a p p r o x i m a t i o n shows sufficiently good agreement with the experimental d a t a with the silicone rubber m e m b r a n e . With the mieroporous polypropylene m e m b r a n e , however, it gives the higher desorption rates t h a n the present data. Figure 7 shows a comparison of the experimental data and theoretical predictions for COs desorption from aqueous solutions of hemoglobin with hemoglobin concentrations corresponding to the hematocrit values of 42-43%. In calculating the theoretical values of the desorption rates, the diffusivities of COs and bicarbonate ions in hemoglobin solutions were estimated f r o m the values of the oxygen diffusivity in the corresponding hemoglobin solutions TABLE I Comparison of Present Data with Prediction by the Procedure of Dorson and Voorhees (1974) Blood flow rate (em3/min)
60 120 180
COs desorption rate (cm3/min) Microporous potypropylene
Silicone rubber
This work
Dorson
This work
Dorson
0.83 1.02 1.16
1.04 1.22 1.37
0.47 0.56 0.62
0.54 0.60 0.65
KATOH AND YOSHIDA
56
1.5
I
I
I
l
.E E
g 1.0
r
1
"o
I
f
f~ 0.5
Ht
I 100
5
rate
Flow
of
42- 4 3 "lo
f 150
Hb s o l u t i o n ,
r 200
250
cc/min
FIG. 7. Carbon dioxide desorption from hemoglobin solutions through ruler9 propylene membranes (peo~ = 49 m m H g ) .
poly-
(Katoh and Yoshida, 1972). Again in Figs. 6 and 7 the solid lines for case B show better agreement with the experimental data points than the broken lines for case A. This seems to imply that the rate of CO2 desorption from blood and hemoglobin solutions is facilitated by diffusion of bicarbonate ions in blood. Figure 8 shows the experimental data for CO2 desorption from blood and serum which contains benzenesulfonamide, an inhibitor for carbonic anhydrase. Addition of the inhibitor should reduce the rate of dehydration of bicarbonate ions. Consequently, the rates of CO2 desorption from blood containing the inhibitor would be lower and closer to the CO2 desorption rates from serum. The rates of CO2 desorption from serum showed no appreciable change by addition of the inhibitor, indicating that carbonic anhydrase did not exist outside the red cells. 1.5 c
E *1.0 r~
e - Ht 2 8 % ( b e n z e n e - s u l f o n a m i d e 9 Ht 2 7 % -o-serum (benzene-sulfonamide o serum
220rag/bblood 200mg/.s
)
serum)
9
- O - ~
71 -
o 05
o -o
t§
-
-~
~
/
O
~:--------'------
O--
o 6"
g c.)
I
0
50 Blood
I
I
I
100
150
200
flow
rate,
250
cc/min
FIG. 8. Carbon dioxide desorption from blood to which benzenesulfonamide was added (Pc 9 = 49 m m Hg).
57
COs T R A N S F E R IN M E M B R A N E O X Y G E N A T O R
In actual blood oxygenators the respiration quotient requires that the rate of C02 desorption should be 0.8 to 1.0 times that of oxygen absorption. Mockros and Weissman (1971) stated that gas transfer in membrane oxygenators was usually limited by transfer in the liquid phase. In such cases the rates of C02 desorption would be high in comparison with those of O2 absorption. The rates of C Q desorption observed in this work were sufficiently high in view of the previously observed values of oxygen absorption rates (Katoh and Yoshida, 1973) even for the runs with the silicone rubber membranes. Reduction of the liquid phase mass transfer resistance by insertion of a screen between the two silicone rubber membranes should increase the overall rate of oxygen absorption considerably (Katoh and Yoshida, 1973). It also increases the overall rate of CO2 desorption to some extent as shown in Fig. 9, in which the data on C02 desorption from blood and water are plotted. This means that the liquid phase mass transfer resistance is still significant in oxygenators with turbulence promotors. Since the resistance of silicone rubber membrane relative to the overall mass transfer resistance is larger for C02 desorption than for oxygen absorption, the increase in the overall transfer rate due to the decrease in the liquid phase mass transfer resistance would be less remarkable in the former case. Even in this case, however, the rate of COs desorption is sufficiently high relative to that of oxygen absorption. For example, as shown in Fig. 9, the rate of CO2 desorption from blood per unit membrane area was 72 cm3/m2/min at a blood flow rate of 3 liter/m2/min. At the same flow rate the rate of oxygen absorption into blood of 80% hemoglobin saturation was 74 cm3/m2/min in the previously reported experiment (Katoh and Yoshida, 1974), in which the channel height of the apparatus was ca. 0.5 mm and a Dacron screen was used between silicone rubber membranes. Thus it may be concluded that membrane oxygenators with turbulence promotors in the blood channel, such as the one used to obtain the data of Fig. 9, have a sufficient capacity for COs desorption 1.5 c E
"
1.0
with lO-mesh screen (blood)
~
esh screen(water)
o~
o
0.5
no screen(water)
I
,
50 Liquid
f
f
I
100
150
200
flow
rate,
250
cc/min
F~G. 9. Carbon dioxide desorption from blood in oxygenator with turbulence promotor (silicone rubber membranes, pco 2 = 49 mm Hg).
58
KATOH AND u
compared with that for 02 absorption, unless the liquid phase mass transfer resistance is small relative to the membrane resistance. Several factors which could have affected the a c c u r a c y of the experimental data are conceivable. The same membrane was used for two or three runs. However, no appreciable increase in the mass transfer resistance due to fouling of the membrane surface was observed. Absorption rates were reproducible within + 1 0 % with blood of hematocrit values of 42 to 43%. The bulk flow of liquid through the membrane due to the pressure difference was considered negligible, because hydrophobie membranes were used. The whole blood is known to be a non-Newtonian fluid to a slight extent. In this work Newtonian behavior of the blood was assumed in the ealeulation, sinee assuming nonNewtonian behavior would make only few percent differenee in the calculated values of the C02 desorption rate. The effect of sedimentation of red cells was considered negligible in view of the short residence time of blood in the oxygenator. The infrared CO~. analyzer was calibrated with pure nitrogen and a standard gas mixture (nitrogen containing 1740 ppm CO2). The sample gas was dehumidified by the vapor trap so that the effect of humidity on the meter reading was negligible. CONCLUSIONS
Desorption of CO2 from blood is facilitated by simultaneous diffusion of bicarbonate ions. The desorption rate can be estimated by a calculation procedure proposed in the present work, which is based on a numerical solution of a differential equation with use of the facilitated diffusivity of CO2. The rates of C02 desorption in membrane oxygenators are sufficiently high compared with those of oxygen absorption, unless the liquid phase mass transfer resistance is small relative to the membrane resistance, which is not the case in practice. NOMENCLATUIgE a
B Cco 2 CHCO3-
Dco Dco2, f
Dnco3H P P U vx
Half channel height (em) Total concentration of chemically combined CO2 (g mole/era 3) Concentration of CO,, (g mole/em a) Concentration of bicarbonate ions (g mole/era 3) Diffusivity of C02 in liquid (em2/sec) Facilitated diffusivity of CO~ in liquid (cm2/see) Diffusivity of bicarbonate ions (em2/sec) Constant (g mole/(em 3 ram Hg)) Membrane permeability (era/see) Partial pressure of CO2 (mm Hg) Average velocity (era/see) Velocity in x direction (cm/see) Coordinate along the channel Coordinate perpendicular to the membrane
CO~ TRANSFER IN MEMBRANE OXYGENATOR
59
Subscript e equilibrium value Superscript * dimensionless value REFERENCES Bell, G. H., l)avidson, J. N., and Scarborough, H. Textbook of physiology and biochemistry, 6th ed. London: Livingstone, 1965. Crank, J., and Nicolson, J. Proc. Cambridge Philos. Soc. 1947, 43, p. 50, referred to in J. D. Smith, Numerical solution of partial differential equations. London : Oxford Univ. Press, 1965. Dorson, Jr. W. J., and Voorhees, M. Limiting Models for the Transfer of CO2 and 02 in Membrane Oxygenator. Transactions of the American Society for Artificial Internal Organs 1974, 20, 219 228. Katoh, S., a!~d Yoshida, F. Rates of Absorption of Oxygen into Blood under Turbulent Conditions. Chemical E~gineering Journal 1972, 3, 276-285. Katoh, S., and Yoshida, F. Rate of Blood Oxygenation in a Flat Plate Membrane Oxygenator. Chemical Engineering Journal 1973, 6, 51 58. Katoh, S., and Yoshida, F. A new membrane-type blood oxygenator. Jinko Zoki (Artificial Internal Organs, in Japanese) 1974, 3, 324 329. Kigoshi, K., and Hashitani, T. The self-diffusion coefficients of carbon dioxide, hydrogen carbonate ions and carbonate ions in aqueous solutions. Bulletin of Chemical Society, Japan 1963, 36, 1372. Moekros, L. F., and Weissman, M. H. The artificial hmg. In Biomedical Engineering. Philadelphia: F. A. Davis Co., 1971. P. 325. Yoshida, F., and Ohshima, N. 1)iffusivity of oxygen in blood serum. Journal of Applied Physiology 1966, 21, 915-919.