To model lung nitric oxide (NO) and carbon monoxide (CO) uptake, a membrane oxygenator circuit was primed with horse blood flowing at 2.5 l/min. Its gas channel was ventilated with 5 parts/million NO, 0.02% CO, and 22% O2 at 5 l/min. NO diffusing capacity (Dno) and CO diffusing capacity (Dco) were calculated from inlet and outlet gas concentrations and flow rates: Dno = 13.45 ml·min−1·Torr−1 (SD 5.84) and Dco = 1.22 ml·min−1·Torr−1 (SD 0.3). Dno and Dco increased (P = 0.002) with blood volume/surface area. 1/Dno (P < 0.001) and 1/Dco (P < 0.001) increased with 1/Hb. Dno (P = 0.01) and Dco (P = 0.004) fell with increasing gas flow. Dno but not Dco increased with hemolysis (P = 0.001), indicating Dno dependence on red cell diffusive resistance. The posthemolysis value for membrane diffusing capacity = 41 ml·min−1·Torr−1 is the true membrane diffusing capacity of the system. No change in Dno or Dco occurred with changing blood flow rate. 1/Dco increased (P = 0.009) with increasing Po2. Dno and Dco appear to be diffusion limited, and Dco reaction limited. In this apparatus, the red cell and plasma offer a significant barrier to NO but not CO diffusion. Applying the Roughton-Forster model yields similar specific transfer conductance of blood per milliliter for NO and CO to previous estimates. This approach allows alteration of membrane area/blood volume, blood flow, gas flow, oxygen tension, red cell integrity, and hematocrit (over a larger range than encountered clinically), while keeping other variables constant. Although structurally very different, it offers a functional model of lung NO and CO transfer.
- nitric oxide
- carbon monoxide
- diffusing capacity
- membrane diffusing capacity
because of its extremely rapid and virtually irreversible reaction with oxyhemoglobin (12), nitric oxide (NO) is theoretically a better gas than oxygen (O2) or carbon monoxide (CO) for measuring lung diffusing capacity (Dl) (4, 16, 22). The diffusing capacity for NO (Dno) is generally accepted to be entirely diffusion limited and independent of capillary perfusion (18, 23). It is also believed to be independent of the rate of reaction with oxyhemoglobin (in contrast to CO). Debate continues as to whether NO transfer is solely limited to diffusion across the alveolar capillary membrane, or whether it includes diffusion within the capillary plasma or red cell (5, 23), as predicted by the finite rate of reaction of NO with the red cell in vitro (7).
In this study, we have used a flat-sheet polypropylene membrane oxygenator to model NO (and also CO) gas exchange. Altogether, we set out to answer five questions.
1) Are Dno and CO diffusing capacity (Dco) solely diffusion limited? Diffusion-limited gas transport is directly related to membrane surface area and thickness [membrane diffusing capacity (Dm)], capillary blood volume (Vc), and specific blood conductance (θ); by contrast, perfusion-limited gas transport is dependent on blood flow (βQ̇, where β is the capacitance coefficient of blood) and independent of the membrane and Vc. The relationship is described mathematically by Cotes and Meade's extension of the Roughton-Forster equation (9): (1) With a dual-chamber membrane oxygenator, it is possible to halve Dm and Vc by clamping off blood lines to one-half of the unit without altering total blood flow. It is also possible to vary blood flow 25-fold without altering Dm and Vc, merely by altering the pump settings. This experiment directly addresses whether or not Dno and Dco are diffusion or perfusion limited and also tests whether it is legitimate to apply the Roughton-Forster relationship to the oxygenator.
2) Do Dno and Dco vary with gas flow? In preliminary experiments with the oxygenator, they appeared to do so; this can be further studied by varying gas flow while keeping blood flow constant.
3) Are Dno and Dco reaction limited? Varying O2 tension alters Dco in vitro and in vivo by altering the rate of combination of CO with oxyhemoglobin and hence θCO (26). Replicating this observation in the oxygenator is a further check on the validity of Dco measurements and the Roughton-Forster relationship. It also allows estimation of Dm and, more importantly, Vc, whereby θ could be calculated for both CO and NO. Varying O2 tension should not affect Dno and does not in vivo (6).
4) Does the hematocrit and integrity of the red cell affect Dno and Dco? One approach to the debate of whether Dno = Dm or includes intracapillary diffusion has been to examine the effect of anemia. Unfortunately, the results in humans have been conflicting (5, 23), no doubt because it is difficult to find a group of anemic patients with otherwise normal lung function. By contrast, the effect of anemia on Dco is well documented (10). An even more radical approach would be to examine the effect of hemolysis, which would instantly abolish erythrocyte and plasma diffusive resistance. This would be difficult in vivo or in an isolated lung model, because the osmolarity change could permanently alter the alveolar-capillary membrane integrity, as occurs in fresh water drowning.
5) What happens to Dno under conditions of zero flow? This should give information on the volume of distribution of NO and the contribution of reaction and diffusion limitation.
- Surface area (cm2)
- Blood channel surface area (cm2)
- Inlet CO concentration (%)
- Inlet NO concentration (ppb)
- Outlet CO concentration (%)
- Outlet NO concentration (ppb)
- Diffusing capacity (ml·min−1·Torr−1)
- Diffusing capacity for carbon monoxide (ml·min−1·Torr−1)
- Diffusing capacity of oxygenator membrane (ml·min−1·Torr−1)
- DmNO react
- NO reaction conductance of polypropylene membrane (ml·min−1·Torr−1)
- Diffusing capacity for nitric oxide (ml·min−1· Torr−1)
- Diffusing capacity for nitric oxide (excluding chemical reaction with membrane) (ml·min−1·Torr−1)
- Diffusing capacity for oxygen (ml·min−1·Torr−1)
- Gas flow rate (l/min)
- Hemoglobin concentration (g/dl)
- Diffusion coefficient of CO in water at 37°C (cm2/s)
- Permeation coefficient of NO in oxygenator membrane at 37°·cm−2·min−1·Torr−1
- Diffusion coefficient of NO in water at 37°C (cm2/s)
- Path length (cm)
- Length of blood-carrying channel within oxygenator (cm)
- Third-order rate constant of reaction of CO with oxygenated red cells (s−1)
- Rate of uptake of oxygen by oxygenator (ml/min)
- Nitric oxide [parts per billion (ppb)]
- Partial pressure of NO in gas channel (Torr)
- Partial pressure of oxygen in gas channel (Torr)
- Barometric pressure (Torr)
- Pb − H2O
- Barometric pressure less saturated vapor pressure of water (Torr)
- Partial pressure of nitric oxide in blood-carrying channel within oxygenator (Torr)
- Average partial pressure of oxygen in blood-carrying channel within oxygenator (Torr)
- Partial pressure of oxygen in blood channel entering oxygenator (Torr)
- Cross-sectional surface area of blood-carrying channel within oxygenator (cm2)
- Membrane surface area per unit length (cm)
- Pulmonary capillary blood volume (ml)
- Specific diffusion resistance of blood per milliliter for CO (min−1·Torr−1)
- Specific reaction resistance of blood per milliliter per Torr Po2 for CO (min)
- Specific transfer conductance of blood per milliliter for CO (min−1·Torr−1)
- Specific transfer conductance of blood per milliliter for NO (min−1/Torr−1)
- Membrane thickness (cm)
Stock cylinders (British Oxygen Manufacturers' certificate of analysis, BOC gases, Worsley, Manchester, UK) of NO (1,000 ppm) in nitrogen and CO (0.3%), O2 (19%), and helium (11%) were connected to a therapeutic NO mixing device (Nomius 305, MTA Sahlgrewska Goteborg Sweden and Bronkhorst Hi Tech, Ruurlo, Netherlands). The helium was present because the mixture is the standard used in our laboratory for single-breath CO gas transfer. The mixing device was adjusted to give 5 ppm of NO and 0.02% of CO. The NO and CO mix was diluted with compressed air and O2 via a side arm downstream of the mixing device (Fig. 1) to give a flow rate of 5 l/min and O2 concentration ([O2]) as required (∼22% for all except experiment 3, where the [O2] was varied).
NO was analyzed using a chemiluminescent analyzer (Logan LR 2000, Logan Research, Rochester, Kent, UK) to which a custom-built CO analyzer was bolted on in series “upstream.” O2 was analyzed using a digital oxygen meter (5120, Datex Ohmeda, Louisville, KY), calibrated with 19, 21, and 100% O2.
O2 tension, CO2 tension, potassium, and pH were measured using an inline optical fluorometric analyzer (CDI 500 Terumo Cardiovascular Systems UK, Egham, Surrey, UK). Hemoglobin, methemoglobin (metHb), and carboxyhemoglobin (HbCO) concentration were measured using a blood-gas analyzer (Rapidlab 800, Bayer, Newbury, Berks, UK). Specimens (1.5 ml) were withdrawn from the arterial sampling port (whole unit) or directly from the blood line (half unit) and placed on ice before analysis at the end of the experiment.
The oxygenator consists of a microporous polypropylene membrane separating a gas stream and bloodstream moving at similar flow rates (1). Gas exchange takes place by diffusion down partial pressure gradients.
The device (Cobe Duo CML, Cobe Cardiovascular, Arvada, CO) used was of flat-sheet membrane design. It allows either half or whole unit operation. According to the manufacturer's information, the surface area is 1.3 m2 (half) and 2.6 m2 (whole), and the maximum O2 transfer rate is 400 ml/min at 8 l/min. The priming blood volume is 260 ml (half unit) and 460 ml (full unit) so that the transit time at a flow rate of 2,500 ml/min is 260/2,500 × 60 = 6.24 s for the half unit and 12.5 s the for the full unit. To optimize gas exchange, the Cobe CML series uses extruded polypropylene mesh spacers between the membrane layers on both the gas and blood sides that reduce volume, maximize surface area, and promote turbulent flow (14). Unfortunately, we have no specific information on membrane thickness, blood path width, or length. The oxygenator was maintained at 37°C using a water bath for zero-flow experiments and using the inbuilt heat exchanger for the remainder. It was primed with 0.3 liter for zero flow and 1–1.5 liter horse blood for the remaining experiments. The blood inlet and outlet lines were joined to a polyvinyl chloride reservoir (Polystan, Jostra, Bellshill, UK) using polyvinyl chloride tubing to form a closed circuit. A second deoxygenator circuit scrubbed the oxygenated blood with 8.3% CO2 in nitrogen to create normoxia and normocapnia (Fig. 1).
Commercial horse blood (TCS Biosciences, Buckingham, UK) was used within 28 days of collection. It was adjusted by the manufacturers to a hematocrit of 40–46% by adding and withdrawing serum. It was refrigerated at 4°C before use.
Experiment 1: Varying blood flow, surface area, and Vc.
To investigate the effect of varying blood flow, the oxygenator was set up in the usual manner and connected to the gas mixer and analyzers. A gas flow rate of 5 l/min was used. The blood flow rate was set at 0.1, 0.2, 0.5, 1, 1.5, 2, and 2.5 l/min using the variable flow rate on the bypass machine. The membrane surface area and blood channel volume were halved by cross clamping the arterial and venous unions. One estimate was made per blood flow rate for whole and for half units, allowing 5 min between measurements. The order of study was randomized.
Experiment 2: Variable gas flow.
The bypass machine was used in the usual manner at a blood flow rate of 2.5 l/min.
The rotameters on the compressed air cylinders were adjusted to give flow rates of 2.5, 5, 7.5, 10, 12.5, and 15 l/min in random order. After 5-min equilibration, diffusing capacity (D) was measured.
Experiment 3: Varying [O2].
The bypass machine was used in the usual manner and at a blood flow rate of 2.5 l/min and gas flow rate of 5 l/min. The effect of hyperoxia was studied by varying the [O2] of the gas inlet mixture (Fig. 1). [O2] of 19, 25, 32, 38, 44, 50, 57, 63, 71, and 84% (measured by oxygen meter on the inlet side) were created by varying the gas flow rate on the rotameters on the O2 and compressed air cylinder heads. Five-minute equilibration took place between changes in gas concentrations. The blood O2 tension was measured by the inline probe.
Experiment 4: Effects of altering hemoglobin concentration and inducing hemolysis.
To alter hemoglobin concentration from ∼1 to 10 g/dl, the circuit was preprimed with normal saline, and blood was progressively added at a rate of 60 ml/min using an additional oxygenator pump for two experimental runs. For a third run, to achieve a range of very low Hb concentration ([Hb]), 25-ml aliquots were added at 5-min intervals by hand to the saline-primed circuit using a plastic syringe. The inline hemoglobinometer gave erroneous results at <6 g/dl, so the hemoglobin was calculated from the concentration in the supplied stock blood, multiplied by the volume of blood added, divided by the system volume. To achieve hemolysis, tap water was pumped into the circuit previously primed with 1.5 liters of blood at a rate of 60 ml/min. Hemolysis was monitored by observation of increasing potassium concentration using the inline monitor.
Experiment 5: Zero blood flow.
To investigate the effect of zero blood flow, a static system was used incorporating one-half the Cobe Duo unit. The arterial and venous unions were clamped, and sampling ports were all capped to give a single gas exchange unit, which was primed with 250-ml blood and immersed in a water bath at 37°C. The standard gas mixture (but omitting CO) was passed through the oxygenator at 5 l/min for 35 min, and Dno was estimated each minute.
Each of the above experiments was carried out at least twice. No more than one of each type of experiment was performed on a given day. A fresh circuit was used each day, and, if hemolysis had been induced as part of the experiment, the oxygenator was discarded and a fresh one used for any subsequent experiments that day. Temperature was obtained over the course of the experimental day as maximum and minimum mercury thermometer and barometric pressure (Pb) by telephoning the local airforce weather station. Humidity was measured by wet and dry bulb thermometer (Met-check, Milton Keynes, UK) entrained in the gas outlet line emerging from the oxygenator.
Measurement of Back Tension
The NO and CO supplies were abruptly stopped by switching off the gas mixer at the end of a session, and the fall in concentration was observed continuously for a period of 60 s while ventilating the oxygenator with air alone.
Consider oxygenator mass balance in a small length dx of volume δV, cross-sectional area S, and gas flow rate f.
Rate of change of mass = mass in − mass out − mass consumed. where Cno(x) is gas NO concentration at distance x, Pb is barometric pressure less vapor pressure of water, and Dno′ is the diffusing capacity of an infinitesimally small length dx/L, i.e., Dno′ = Dno dx/L.
Let δV = S × dx, and L is the total length of the oxygenator, so dividing by dx S × dCno/dt = −f dCno/dx − Dno/L × Pb × Cno.
At steady state, the left-hand side = 0 Integrating over length of oxygenator, CoNO = CiNO exp(−Dno × Pb/f), where CiNO and CoNO are Cno values at the inlet and outlet ports, respectively. (2) Implicit in this calculation is that the volume of gas emerging from the oxygenator is identical to that entering. This should be the case if blood channel and gas channel O2 are in equilibrium and using the very low NO and CO gas flows we employed. Likewise, back tension was ignored. Since Dno is expressed in ml STPD·min −1·Torr−1, Eq. 1 becomes Dno = f × 273/[(273 + laboratory temperature) × (Pb in millibars)/1,000 × 750 − (saturated vapor pressure × relative humidity)/760 × loge (CiNO/CoNO). The equation for CO is identical but substituting CiCO/CoCO.
If it is presumed that all of the NO or CO that diffuses across the microporous membrane ligands with hemoglobin within the red cell, then it is legitimate to apply the Roughton-Forster relationship [which is, after all, a simple mass-transfer equation (11)] (see appendix for proof). (3) One exception to this relationship would be if there was chemical reaction with the membrane; this is considered in Eq. 4 below. Another exception would occur if there was significant uptake of gas physically dissolved in blood; this is addressed in experiment 1. Because the Krogh diffusion coefficient for NO (kNO) is twice that for CO (kCO) (16) (4) where DmNO is NO Dm. Because there has been concern that NO may react with polypropylene within membrane oxygenators (2), which could occur as it traverses the gaseous pores within the membrane, we have included this as an ohmic resistance in parallel to diffusion, hence (5) where DmNO react is reaction DmNO and Dnodiff is diffusion Dno. (Hereafter, for clarity we use Dno to mean Dnodiff, although in the calculations we have subtracted DmNO react from Dno in Eq. 1).
Equations 2 and 3 can be combined in various ways to yield different variables: (6) (7) (8) The specific blood resistance to CO transfer can be written (9, 21) as follows: (9) where α is the specific diffusion resistance for CO per milliliter of blood, and β is the specific reaction resistance per milliliter of blood for CO per Torr average partial pressure of O2 in blood-carrying channel within oxygenator (P). (10) so that, if 1/Dco is plotted against [O2]: and slope × Vc = β. Finally as previously described in reference (6) (11) (12)
Variables were recorded on a spreadsheet in Microsoft excel and were further analyzed using the linear regression option in SPSS, inserting D or 1/D as the dependent variable and gas flow rate, blood flow rate, Po2, 1/Hb, and whole or half unit as the independent variables to generate a series of univariate regression models. Where quoted, standard deviations (SD) include within- and between-experiment variation. Independent t-test was used to compare Dco and Dno pre- and posthemolysis.
The time to 90% response of the NO analyzer measured by balloon burst (9) was 5 s for NO and 30 s for CO. The signal-to-noise ratio was ∼100 for both inlet NO concentration (C) and inlet CO concentration (C), 5 for outlet NO concentration (C), and 6 for outlet CO concentration (C). The CO and NO analyzers were collinear to serial dilution in air (9) over the range of concentrations used.
Comparing Full Unit and Half Unit
Average Dno and Dco using the full unit was Dno = 13.45 ml·min−1·Torr−1 (SD 5.84) and Dco = 1.22 ml·min−1· Torr−1 (SD 0.30). There was a dramatic reduction in Dno (P = 0.002) and Dco (P = 0.002) when only one-half the unit was perfused with Dno = 7.57 ml·min−1·Torr−1 (SD 3.28) and Dco = 0.86 ml·min−1·Torr−1 (SD 0.21) (Fig. 2) (n = 18). Ratio of Dno to Dco = 10.79 (SD 6.14) (data from three experiments, n = 18).
Experiment 1: Variable blood flow.
Dno (P = 0.999) and Dco (P = 0.154) were independent of blood flow over a 25-fold variation (Fig. 2) (data from three experiments, n = 36).
Experiment 2: Variable gas flow.
Both Dno (P = 0.01) and Dco (P = 0.004) declined with increasing gas flow rates following a semilogarithmic pattern (Fig. 3) (data from three experiments, n = 18).
Experiment 3: Varying O2.
Increasing [O2] was associated with a linear rise in 1/Dco = 0.0011 [O2] + 0.6488 (P = 0.009), but no significant change in Dno (P = 0.203) (Fig. 4) (data from two experiments, n = 21).
Experiment 4: Varying hemoglobin and hemolysis.
There was a significant increase in the uptake of both gases with hemoglobin concentration and more significantly between 1/D and 1/Hb for Dno (P < 0.001) and Dco (P < 0.001) (data from three experiments, n = 30). A significant rise in Dno (P = 0.001) but not Dco (P = 0.928) occurred with hemolysis (Figs. 5, 6, and 7) (data from four experiments, n = 10).
Experiment 5: Zero blood flow.
There was a semilogarithmic decline in Dno with time of exposure to the NO mixture (Fig. 8) with a mean half-life of 26.3 min (SD 1.7) (data from two experiments). From Eq. 13 (appendix), the uptake of NO was 0.53 ml over the half-time, implying a blood volume saturated with NO of 2.7 ml for the half-unit (5.4 ml for the whole unit).
For NO, there was a rapid decline to 0 ppb (Fig. 9). For CO there was a more gradual decline to 0.04%, which we did not regard as significantly different from the noise (0.03%) (Fig. 10). No back tension adjustment was therefore made to calculations of D for either gas (Eq. 1).
The concentration of metHb was <3% and HbCO <7.5% in all experiments. In general, the metHb concentration did not vary, and HbCO increased on average by 0.2% in each experiment; no consistent association was found between metHb, HbCO, and D. The average inlet [O2] was 22.1% (SD 4.5), arterial Po2 (PaO2) 76.8 Torr (SD 37.6), Pco2 31.0 Torr (SD 9.22), and pH 7.36 (SD 0.16). The outlet relative humidity was 66%.
Dno but not Dco increased significantly following hemolysis: both altered with [Hb], with a significant linear association between 1/D and 1/Hb. These experiments support the argument that diffusion across plasma, the red cell membrane, and within the red cell is a component of Dno. These experiments show that both Dno and Dco appeared to increase with membrane surface area and/or volume and appeared to fall with increasing gas flow rate. Dco but not Dno fell with increasing O2 tension.
Relationship to the Work of Others
No previous group has measured Dno or Dco using a membrane oxygenator. One group reported values for O2 diffusing capacity (Do2) for six hollow-fiber membrane oxygenators, ranging from 2.5 to 5 ml·min−1·kpA−1 (0.33–0.66 ml·min−1·Torr−1) (28). However, because they calculated Do2 = M/(PaO2 − PvO2) rather than Do2 = M/(PaO2 − PcO2), where M is rate of O2 uptake by oxygenator, PaO2 is partial pressure of O2 in gas channel, and PvO2 is partial pressure of O2 in blood channel entering oxygenator, this is likely to be an underestimate. In support of this view, our preliminary calculations of Do2 using an oxygenator (C. Borland and H. Dunningham, unpublished observations; see appendix for methodology), estimating PcO2 by Bohr integration, give values of 0.2 to 1 ml·min−1·Torr−1, depending on blood flow.
No previous group has studied the effect of hemolysis on Dno or Dco, but Geiser and Betticher (15) found increased Do2 when isolated rabbit lungs were perfused with hemoglobin solution compared with whole blood.
One striking finding from this work is that the Dno-to-Dco ratio is significantly greater than in vivo, either in animals (22) or humans (3, 4, 6, 16) where it is 4 to 5. Three possible explanations are advanced: hemolysis, a chemical reaction with the membrane, or a different Vc-to-Dm ratio compared with in vivo. It is conceivable that free hemoglobin in stored blood occurring as a result of hemolysis or hemolysis as the blood is recycled through the oxygenator could explain the higher Dno/Dco than we have observed in vivo and the major variation and corresponding increased SD between experiments. However, if that were the case, we might expect greater variation in Dno compared with DmNO, and that is not apparent (Fig. 6). A rapid chemical reaction accounting for the higher Dno/Dco than observed in vivo is a less likely explanation. Minimal reaction was observed with the membrane oxygenator or tap water under zero-flow circumstances. Applying the Roughton-Forster model, it can be seen from Eqs. 2 and 3 that Dno/Dco would vary from 2, if θNO and θCO were infinite, to a maximal value of θNO/θCO, if Dm were infinite. The ratio of 10.8 observed must, therefore, be regarded as the lower limit for θNO/θCO under our experimental conditions. From Eq. 5, it can be seen how Dno/Dco crucially depends on the ratio Vc/DmNO for given values of θNO and θCO. In the oxygenator, in contrast to in vivo, θNO Vc might appear to limit Dno to a greater degree than Dm. We believe that a reduced Vc/DmNO in the oxygenator compared with in vivo is the explanation of the increased Dno/Dco observed, and the calculations in Values for θCO and θNO and The Physiological Significance support this.
Factors Affecting Dno and Dco
Blood flow rate.
The lack of effect of blood flow rate on Dno and Dco is not unexpected; since NO and CO are relatively water insoluble and of high D, they will be diffusion limited compared with soluble gases, such as acetylene and O2 in normoxia, which are regarded as perfusion limited (24). We have not yet studied soluble gases in this setup, but our preliminary unpublished studies of Do2 in normoxia show an increase with blood flow up to a plateau (C. Borland and H. Dunningham, unpublished observations). From this experiment, it is likely that the increases in Dno and Dco that have been observed on exercise in vivo (3, 4, 20) are due to increases in Dm and Vc rather than βQ̇.
Half and whole unit.
The approximate halving of Dno and Dco when half the unit is clamped off could be because the surface area or the volume is halved. The arguments of the second paragraph of this discussion relating to Vc/Dm strongly favor this reduction being due to change in blood volume rather than surface area. Normally, in vivo Dm and Vc will vary together (Hughes' “coupling”) (21); for example, considering a pulmonary capillary to be a cylinder if its diameter increases, the increase in surface area and hence Dm will be proportionate to the square of the diameter and the volume proportional to the cube. Using an oxygenator with greatly increased Dm/Vc has “uncoupled” Dm and Vc so that the blood phase can effectively be examined in isolation.
Varying gas flow rate.
From Fig. 3, there appears to be a decline in Dno and Dco with increasing gas flow rate. At any one point in the gas channel in the oxygenator, Dno/f will, from Eq. 1, equal 1/Pb loge (CiNO/CoNO), where CiNO is the Cno of fresh gas arriving at that point, and CoNO the Cno leaving. The magnitude of 1/Pb loge (CiNO/CoNO) will depend on the balance of bulk flow and diffusion. At high flow rates, the rate of arrival of fresh gas will be substantially greater than its removal by diffusion, and CoNO will approximate CiNO, and Dno will approach zero. At low-flow rates, diffusion will predominate, and CoNO will approach zero. This caused us some pragmatic difficulties: if we employed too rapid flow rates, we could not obtain a detectable Dco, but at too low flow rates CoNO approached the lower detectable limit (30 ppb) of the analyzer on therapeutic mode. Using higher NO or CO concentrations raised metHb and HbCO blood concentrations unacceptably. A compromise of 5 ppm NO and 0.02% CO at a rate of 5 l/min was employed, but it is plausible that the true value for Dno is the intercept of Fig. 3. A significant contribution of bulk flow of dry gas almost certainly explains why the humidity is <100%. Variation in gas flow rate and the essential need for accurately knowing the flow rate has a major impact on the measured and derived variables.
For Dco, altering O2 tension and thereby the reaction rate with oxyhemoglobin had a major effect, indeed second only to gas flow on Dco. For NO, the effect was negligible, as expected from its extremely rapid reaction with hemoglobin and from experiments in vivo (6). The reaction dependence of CO on O2 is predicted from: (13) where m′c is the third-order velocity constant, and [HbCO], [CO], [HbO2], and [O2] are the blood concentrations of HbCO, CO, oxyhemoglobin, and O2, respectively (26, 27). From the slopes and intercepts of the relationship between 1/Dco and Po2, α and β are calculated (Eq. 9) in Values for θCO and θNO.
The Red Cell
The limitation of Dno and Dco by hemoglobin concentration and the significant relationships between 1/D and 1/Hb for both gases lend support to applying the Roughton-Forster relationship to the oxygenator and to θNO being less than infinity. However, it must be acknowledged that the highly significant relationships we have demonstrated are over a unphysiological range, which is also largely outside clinical practice (0.26–9.73 g/dl) (Fig. 5).
Red cell integrity.
There is a major effect of hemolysis on Dno but not Dco. The major effect of hemolysis, like the effect of altering [Hb] on Dno, lends support to those who believe θNO is finite rather than equivalent to the effectively infinite rate with oxyhemoglobin solution. The posthemolysis figure should, given the extremely rapid reaction of NO with oxyhemoglobin, be a measure of DmNO alone. The difference between the pre- and posthemolysis figures will reflect the contribution of membrane immediately adjacent to red cell (20), plasma, and red cell interior to diffusion, and it is not possible to distinguish between them from this part of the experiment. For Dco, however, the diffusion resistance of membrane, plasma, and within the erythrocyte appears negligible in contrast to the classic observations of Roughton et al. (26) using a continuous flow rapid reaction apparatus. It is difficult to reconcile this difference; in support of our findings, Reeves and Park (25) obtained a low-diffusion resistance for the red cell-to-CO transfer using a thin-film technique, and Chakraborty et al. (8) have advanced strong theoretical arguments for rapid reaction apparatuses, creating stagnant layers, leading to underprediction of θCO. It is plausible that highly turbulent mixing conditions due to the mesh spacers within the blood channel of the oxygenator (14, 29) within an oxygenator reduce the stagnant layer effect. In support of this view, we have found no effect of hemolysis or hematocrit on Do2 (C. Borland and H. Dunningham, unpublished observations).
Limitation of Dno at Zero Flow
With zero blood flow, there is a semilogarithmic decline in Dno with time. What is limiting Dno during this time? It cannot be perfusion limitation in the classic sense, as the blood is not physically or chemically saturated with NO (free oxyhemoglobin is still available, as demonstrated by a sample aspirated close to the membrane that showed an oxyhemoglobin content of 97.5%). For the same reason, it cannot be reaction limitation, given the extremely rapid reaction of oxyhemoglobin with NO. We believe that the observed decline is due to diffusion limitation: as the surface molecules of oxyhemoglobin become irreversibly oxidized to metHb, then the path length for NO diffusion within the erythrocyte steadily increases. If this explanation is correct, then Fig. 8 is a visual depiction of Hill's “advancing front” (21).
Is There Heterogeneity?
From the above, it would be anticipated that both Dno and Dco would be altered by heterogeneity of gas flow, membrane surface area, accessible blood volume, and hematocrit within and between gas and blood channels. Both should be independent of varying blood flow between blood channels. Dco could be altered by differing Po2 between channels. It is certainly plausible that the decrease in D with gas flow is greater in some channels than others. Provided both units are completely filled with blood and because they are semitransparent, this appeared to be so, thus Dm and Vc heterogeneity are unlikely, although heterogeneity of Dco could explain the 30% fall in Dco compared with the 44% fall in Dno. From the equation, it will be noted that Dno/Dco crucially depends on Vc/Dm. A greater fall in Dm than Vc when one-half the unit is clamped off would lead to a greater fall in Dno than Dco. Heterogeneity of Dm, Vc, and hematocrit may well occur in experiment 4 due to uneven filling of the chambers, where blood is gradually added to the circuit preprimed with saline. Heterogeneity within blood channels should also be considered due to stagnant layers effect. As indicated above, such layers would instantly be abolished by hemolysis, and their existence might contribute to the increase in Dno with hemolysis. However, as already mentioned, one would anticipate that a change in Dco might also be seen with hemolysis, if there were stagnant layers.
Contribution of the Resistances to NO and CO Transfer
The reciprocal of our average Dno value 1/13.45 = 0.074 min·Torr−1·ml−1 is the overall resistance to NO transfer. 1/DmNO = 0.024 min·Torr−1·ml−1 is the membrane resistance. In theory, the difference = 0.05 min·Torr−1·ml−1 is due to the resistance of the plasma and red cell membrane and interior. However, it may include some membrane resistance, if only the membrane directly adjacent to a red cell is available for gas transfer (20). Another expression of the membrane resistance is the intercept of Fig. 5. The value for 1/Dno when 1/Hb is zero, i.e., infinite hemoglobin concentration. This value (=0.064 min·Torr−1·ml−1) is twice the posthemolysis value. The resistance of the plasma may account for some of this difference; however, some plasma resistance may be hematocrit dependent, since, as the number of red cells falls, the distance between them and hence the plasma resistance rises. For CO, the picture is more complex: the intercept of 1/Dco and 1/Hb is 0.92 min·Torr−1·ml−1, which is substantially greater than 2 × 0.024 = 0.05 min·Torr−1·ml−1 predicted from the posthemolysis value for Dno and more than twice the intercept for 1/Dno (2 × 0.064 = 0.13 min·Torr−1·ml−1). Another expression of the membrane resistance for Dco is the intercept of 1/Dco and [Po2] = 0.65 min·Torr−1·ml−1. The only explanation for these greater values for 1/Dco is that they contain terms for the reaction resistance to CO transfer. At infinite Hb, Eq. 12 does not become infinity but pseudo-second-order proportional to [CO]/[O2]. Likewise, at zero Po2, Eq. 12 becomes pseudo-second-order proportional to [CO][Hb]. If the intercept of 1/Dco and [Po2] contains a term for the reaction resistance, then CO diffusing capacity of membrane (DmCO) will always be underestimated by Roughton and Forster's method using two or more O2 tensions.
Value for Vc.
Unfortunately, it is very difficult to accurately estimate the volume of blood in contact with the membrane available for NO and CO uptake. Clearly, it will be considerably less than the priming volume of 460 ml using the oxygenator conventionally or 250 ml for the zero-flow experiments. Two approaches are outlined in the appendix. It is also possible to draw up an estimate of Vc using our data and measures of θCO and θNO (Table 1) using Eqs. 2 and 11. It is clear that methods based on Dno/Dco give the lowest values for Vc followed by Dco at more than one O2 tension, but that even these estimates are lower then the likely true Vc value of the oxygenator. Using the estimate for Vc based on the half-life of Dno under zero perfusion conditions assumes that Vc is the same, irrespective of perfusion rate. Using the estimate based on a boundary layer of 10 μm (17) assumes, almost certainly incorrectly, that NO and CO exchange with the same volume of blood as O2 and CO2. It is likely that low concentrations of these two diffusion-limited gases barely penetrate the outer layer of blood, whereas O2 will fully saturate it, particularly if intraerythrocytic gas transport is aided by facilitated diffusion. This consideration has not been emphasized when extrapolating in vitro estimates of θ, which are generally made using gas concentrations substantially in excess of in vivo experiments. Whether the same situation holds in vivo requires further study. The Roughton-Forster model assumes even distribution of gas throughout the plasma and red cells.
Values for Dm
It seems reasonable to use one-half the posthemolysis value for Dno for the whole unit = 41/2 = 20.5 ml·min−1·Torr−1 as the “gold standard” value for DmCO. From Table 1, it is clear that the negative values for Dm using Forster's estimate for θCO from 1987 and Borland and Cox's method imply overestimation of Dm. By contrast, using Dco at more than one [O2] tends to underestimate DmCO. Guenard's method of estimating DmCO as 0.5 Dno appears to give the closest measure to presumed DmCO but remains an underestimate.
Values for θCO and θNO
It is theoretically possible to calculate θCO, θNO, α, and β using Eqs. 6–9. From Table 1, we can very empirically take a median figure of ∼5 ml for the whole unit for the blood volume that actually exchanges with CO and NO using Eqs. 2 and 3: θCO Vc = 1/(1/1.22 − 2/41) = 1.3 ml·min−1·Torr−1 (where 1.22 is the overall average for Dco and 41 is the posthemolysis value for Dno = DmNO); θNO Vc = 1/(1/13.45 − 1/41) = 20 ml·min−1·Torr−1 (where 13.45 is the overall average for Dno and 41 is the posthemolysis value for Dno = DmNO). This gives values for θCO (67.5 Torr) = 0.26 ml·min−1·Torr−1, θNO = 4 ml·min−1·Torr−1, α = 3 min/Torr, and β = 0.0055 min. Despite the many assumptions, these figures are reassuringly close to those obtained by others using rapid reaction apparatus and thin-layer techniques. Although we did not specifically examine this issue, it would be anticipated that θNO and θCO would be independent of flow rate, given that Dno and Dco are completely independent of flow rate.
We believe that this model allows testing of factors that affect NO and CO exchange in a way that would be impossible in vivo or in an isolated lung preparation. It would be impossible, for example, to generate [Hb] of <1 g/dl in an intact animal without also altering blood volume, cardiac output, and hence Vc and Dm. Likewise, hemolysis or infusion of hemoglobin solutions would irreparably damage the circulation. Nonetheless, the oxygenator is a reasonable model of lung gas exchange, and it is reassuring that values for θCO and θNO obtained half a century ago under unphysiological conditions in a rapid reaction apparatus appear to apply. However, given all of the above limitations, our laboratory's previous recommendations (3) to calculate Dm and Vc from simultaneous Dno and Dco, both assuming θNO is infinity and assuming it is 4.5 min−1·Torr−1, must remain.
The Physiological Significance
Structurally, there is no doubt that the oxygenator is very different from the lung. The polypropylene membrane is thicker but is interrupted by frequent pores, giving a direct air-liquid interface. The total area is smaller (1.3–2.6 m2 compared with, say, 50–100 m2 for the lung). There is probably a greater transverse and longitudinal blood path length. The transit time is ∼10-fold greater for the half unit and 20-fold greater for the whole unit. The gas flow is not tidal but constant in the oxygenator; likewise, the blood flow is not pulsatile but constant. The journey taken by a red cell in the lung is of progressive oxygenation as it passes along the capillary; in an oxygenator, the balance between turbulent flow (29) and a growing boundary layer (17) may result in red cells moving between areas of low and high O2 tension in a random fashion. Functionally, the oxygenator is very much more like the lung. It delivers up to 400 ml/min of O2 and removes up to 450 ml/min of CO2 at physiological pH, temperature, hematocrit, and O2 and CO2 tensions by diffusion down partial pressure gradients. Importantly for NO and CO transfer, we have shown (appendix) that the classic Roughton-Forster equation is applicable to the oxygenator. The value for Dno in a healthy adult is 125 ml·min−1·Torr−1, and we calculate DmNO to be 300 ml·min−1·Torr−1. These values are, therefore, ∼9-fold and 7.5-fold greater, respectively, perhaps implying that the oxygenator “membrane”, while 20- to 40-fold smaller in area, is functionally thinner than the alveolar-capillary membrane. Our result for Dno and Dco and O2 (experiment 3) is entirely expected and identical to what is found in humans. Likewise, the major effect of surface area/volume on Dno and Dco transfer and lack of effect of blood flow is what is entirely predicted but never before directly demonstrated. The effect of gas flow is probably specific to an oxygenator, since lung gas flow is very different. The effect of hemoglobin on Dco is similar to Dco and Hb in humans. For Hb and Dno in the oxygenator, there is undoubtedly a marked effect. Since hemolysis of this degree would be fatal to humans or animals and deleterious to an isolated lung, it is not physiological. Could the effect of hematocrit and hemolysis and Dno occur in the oxygenator but not in vivo? This could occur if there were a significant stagnant plasma layer in the oxygenator that would increase the diffusion resistance of the blood (14). Another possibility would be if there were significant facilitated diffusion due to convective transport within the red cell in vivo but not the oxygenator (8): this would increase the blood resistance to NO transfer in the oxygenator. Were either of these to be the case, we might expect hemolysis to increase Dco and not just Dno. We should concede that, because of its far faster reaction with hemoglobin, a reduction in blood resistance would have greater impact on NO than CO. However, we have also found Do2 to be independent of hemolysis (C. Borland and H. Dunningham, unpublished observations), and the reaction rates of O2 and NO with hemoglobin are comparable (8).
Clearly, our results were obtained with horse blood, whereas the major interest is human blood. Our calculated values need to be interpreted with some caution, given the sensitivity of Dno and Dco to gas flow rate. Both the Dco and, in particular, Dno values are highly variable between experiments due perhaps to gas flow variation, the low signal-to-noise ratio, and, in the case of Dno, hemolysed blood in the stock solution. Other sources of variation could be between oxygenator variability and metHb and HbCO, which rise during the course of the experiment. Unfortunately, we have no information on effective membrane thickness, blood path width, or length for the Cobe Duo. We do not have details of laminar or turbulent flow for our device for differing blood and gas flows. Clearly, the relationship of Dno and Hb is not only of theoretical interest, but also of concern to clinical physiologists wishing to know whether it is necessary to adjust Dno for Hb. Given that many of our observations were made outside a clinical range and without a low-reading hemoglobinometer, we cannot advocate such an adjustment derived from our regression equation at present.
Directions for Future Work
If the value of the oxygenator volume could be accurately determined, this work suggests that, for the first time, θCO and θNO could be measured under physiological conditions using an “off-the-shelf” commercial oxygenator and gas mixtures and analyzers that are part of the equipment of many modern respiratory laboratories. We hope that others will be stimulated to test our conclusions. It would be possible to adapt the apparatus to measure Do2 and hence perhaps Dco2 also.
Oxygenator Blood Volume
The accessible volume of the oxygenator can be calculated in two ways.
1) The static boundary layer of blood in oxygenators where diffusion takes place is regarded as 10 μm (10−3 cm) thick for O2 and CO2 (17). The surface area of a single cell of the Cobe Duo is 1.3 m2 = 1.3 × 104 cm2. Therefore, the accessible volume of each cell is 13 ml.
2) There is a semilogarithmic decline in Dno with time. Let the half time for this decline be t1/2. Let total volume NO transferred between t0 and t1/2 = f t0 ∫ t1/2 (CiNO − CoNO) dt. Because NO ligands to Hb in exactly the same proportion as O2, the volume of blood saturated with (14) (The accessible volume is likely to be less than this figure.)
Proof of Application of Roughton-Forster Relationship to NO (and CO) Transfer in a Membrane Oxygenator
Ignoring any reaction with the membrane or NO dissolved in plasma, a balance exists between the mass of NO diffusing from the air channel across the membrane and that reacting with Hb/HbO2 within the red cell, i.e. (15) This equation is entirely analogous to Eq. 9 in Ref. 27, excepting that we have applied it to NO as well as CO, and the notation has been updated (the original Roughton and Forster symbols are in parentheses): S′ (S) is the surface area of a single blood channel per unit length (cm), PaNO (PaCO) is the instantaneous NO partial pressure in the gas channel (Torr), KMNO (d) is the membrane permeation coefficient for NO (cm2·min−1·Torr−1), τm (x) is membrane thickness (cm), P(Pco) is instantaneous plasma NO partial pressure (Torr), and ac (a) is cross-sectional area of a single blood channel (cm2).
Rearranging the equation in parentheses Integrating the equation in parentheses over n blood channels and total length L on the left-hand side becomes: Substituting for P gives: But n LS′ = Am (A) the membrane surface area (cm2), DmNO = Am KMNO/τm, and Vc = ac n L. The left-hand side of the part of the equation in parentheses = DmNO PaNO dt (1 + DmNO/θNO Vc) and is also = Dno PaNO dt. Dividing through by PaNO dt and rearranging: Identical arguments apply to Dco.
Calculation of Do2
Do2 was measured from gas inlet and outlet [O2] and blood inlet and outlet gas tensions. Do2 = M/(PaO2 − P), where PaO2 is the logarithmic mean of the inlet and outlet O2 gas tensions, and P is the average blood channel O2 tension calculated by Bohr integration from the inlet to outlet blood gas tensions (9). Similar values were obtained from the simpler calculation Do2 = M/(PaO2 − PvO2) × loge [(PaO2 − PvO2)/(PaO2 − PaO2)], where PaO2 is the blood outlet O2 gas tension (24).
We are grateful to Professor J. M. B. Hughes and Dr. N. M. Tsoukias for helpful comments and to Drs. Sonia Misso and Jim Chandler for help with the initial experiments.
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