Journal of Applied Physiology
Vol. 83, No. 1, pp. 240-246, July 1997
GAS EXCHANGE, MECHANICS, AND AIRWAYS

CO₂ transport in normovolemic anemia: complete compensation and stability of blood CO₂ tensions

Steven Deem, Michael K. Alberts, Michael J. Bishop, Akhil Bidani, and Erik R. Swenson

Departments of Anesthesiology and Medicine, University of Washington, Seattle, 98195; Anesthesiology and Medical Services, Veterans Affairs Medical Center, Seattle, Washington 98108; and Department of Medicine, University of Texas Medical Branch, Galveston, Texas 77550

ABSTRACT

INTRODUCTION

METHODS

RESULTS

DISCUSSION

ACKNOWLEDGEMENTS

FOOTNOTES

REFERENCES

ABSTRACT

Deem, Steven A., Michael K. Alberts, Michael J. Bishop, Akhil Bidani, and Erik R. Swenson. CO₂ transport in normovolemic anemia: complete compensation and stability of blood CO₂ tensions. J. Appl. Physiol. 83(1): 240-246, 1997.Isovolemic hemodilution does not appear to impair CO₂ elimination nor cause CO₂ retention despite the important role of red blood cells in blood CO₂ transport. We studied this phenomenon and its physiological basis in eight New Zealand White rabbits that were anesthetized, paralyzed, and mechanically ventilated at a fixed minute ventilation. Isovolemic anemia was induced by simultaneous blood withdrawal and infusion of 6% hetastarch in sequential stages; exchange transfusions ranged from 15-30 ml in volume. Variables measured after each hemodilution included hematocrit (Hct), arterial and venous blood gases, mixed expired PCO₂ and PO₂, and blood pressure; also, O₂ consumption, CO₂ production, cardiac output (), and physiological dead space were calculated. Data were analyzed by comparison of changes in variables with changes in Hct and by using the model of capillary gas exchange described by Bidani (J. Appl. Physiol. 70: 1686-1699, 1991). There was complete compensation for anemia with stability of venous and arterial PCO₂ between Hct values of 36 ± 3 and 12 ± 1%, which was predicted by the mathematical model. Over this range of hemodilution, rose 50%, and the O₂ extraction ratio increased 61% without a decline in CO₂ production or a rise in alveolar ventilation. The dominant compensations maintaining CO₂ transport in normovolemic anemia include an increased and an augmented Haldane effect arising from the accompanying greater O₂ extraction.

anemia; carbon dioxide; hemodilution; pulmonary gas exchange

INTRODUCTION

THE QUANTITATIVE IMPORTANCE of red blood cells in blood O₂ transport is a function of the direct binding of O₂ to hemoglobin. The nearly equivalent role of red blood cells in blood CO₂ transport is not generally appreciated, since CO₂ is roughly twenty times more soluble than O₂ in plasma and only 5% of total blood CO₂ is bound to hemoglobin. However, physically dissolved CO₂ accounts for only another 5% of CO₂ content; the remainder of CO₂ carriage in blood occurs because of the contributions of hemoglobin and two other red cell proteins, carbonic anhydrase and band 3 protein (a membrane-bound Cl/HCO₃ exchanger). Although direct CO₂ binding to hemoglobin as carbamate accounts for only 5% of blood CO₂ content, it contributes roughly 15% to CO₂ exchange because of the oxylabile characteristics of hemoglobin (Haldane effect). More importantly, 80% of CO₂ is carried in blood in the form of HCO₃, the formation of which is catalyzed within the red blood cell by carbonic anhydrase (7, 24, 43). A high rate of HCO₃ formation within the red blood cell is promoted by the large oxylabile buffering capacity of hemoglobin and rapid extrusion of HCO₃ into plasma across the red cell membrane in exchange for Cl (Cl shift). These processes forestall a rate-limiting accumulation of H⁺ and HCO₃, thereby facilitating greater HCO₃ formation from CO₂. The net result is the transport of large amounts of CO₂ at the expense of only small tissue-to-blood and blood-to-alveolar PCO₂ differences (7, 24, 43).

The effect of a diminished red blood cell concentration on CO₂ homeostasis can be predicted by mathematical modeling. With a sophisticated model of human blood-gas transport, Bidani and Crandall (6) predicted that moderate anemia [hematocrit (Hct) ~30%] will result in a 25% reduction in CO₂ elimination (CO₂), whereas severe anemia (Hct ~15%) will result in a 50% reduction in the absence of any compensatory changes in metabolism, ventilation-perfusion ratio (A/) relationships, ventilation, and cardiac output (). Similar results were obtained in an earlier model simulation by Hill et al. (21). In vivo, a reduction in CO₂ would necessarily lead to CO₂ retention and ultimately bring CO₂ elimination back into a steady state with its production, albeit at the expense of higher venoarterial PCO₂ gradients. Other evidence that anemia may affect CO₂ homeostasis comes from a model of brain gas exchange (40). This model predicts that without changes in metabolism or blood flow, and assuming a constant arterial PCO₂ (Pa_CO2), brain tissue PCO₂ would rise ~6 Torr with a fall in Hct from 42 to 15%. In the absence of compensations, therefore, anemia should result in either hypercarbia or a reduction in CO₂ output.

Only a few studies have directly addressed the impact of anemia on CO₂ transport and, in general, although documenting remarkable stability of PCO₂ in the presence of anemia, these studies have been incomplete in that they have not measured or controlled for all the variables involved in CO₂ transport and elimination (4, 12, 31). Our study was designed to measure and quantitate the relevant physiological parameters influencing CO₂ homeostasis in the rabbit during isovolemic hemodilution. A second aim was to model the gas-exchange and hemodynamic data to determine whether the measured compensations to anemia in vivo are sufficient to predict our measured venous CO₂ gas tension (Pv_CO2) and Pa_CO2 or whether additional mechanisms of compensation need to be invoked.

METHODS

The protocol was approved by the Animal Care Committee of the Seattle Veterans Affairs Medical Center. Eight New Zealand White rabbits weighing 3-4 kg were anesthetized with 15 mg/kg iv ketamine and 0.33 mg/kg iv xylazine, and their tracheas were intubated. Mechanical ventilation with a Harvard dual-phase ventilator was initiated at a tidal volume of ~15 ml/kg and a respiratory rate of 25-30 breaths/min to achieve a baseline Pa_CO2 of 35-40 Torr. The inspired O₂ fraction was set at 0.209. Bilateral femoral arterial catheters were placed surgically for blood pressure monitoring and blood withdrawal. An internal jugular venous catheter was surgically placed and advanced into the right ventricle for withdrawal of mixed venous blood gases and pressure measurements. Anesthesia was maintained with pentobarbital sodium, ~10 mg · kg¹ · h¹ by intravenous infusion, and animals were monitored closely for sudden increases in blood pressure and/or heart rate that might indicate insufficient anesthesia. Muscle relaxation was provided by intravenous pancuronium, 0.3-0.4 mg · kg¹ · h¹ after tracheal intubation.

After stabilization, baseline measurements including mean arterial pressure, right ventricular pressure, , airway pressure, temperature, and Hct were recorded. Mixed venous and arterial samples were drawn for blood-gas analysis, and expired gas was sampled from a 250-ml mixing chamber attached to the expiratory limb of the ventilator circuit.

Isovolemic anemia was then induced by simultaneous blood withdrawal (via an arterial catheter) and infusion (via the jugular vein) of an equal volume 6% hetastarch in sequential stages; exchange transfusions ranged from 15 to 30 ml in volume. Repeat measurements were made 30 min after each hemodilution or when mixed expired PCO₂ had stabilized. Minute ventilation (E) and inspired O₂ fraction were maintained constant throughout each experiment, and E was measured by a timed collection of expired gas at the conclusion of the experiment. At the conclusion of the experiment (achievement of a Hct of ~15% or severe hemodynamic derangement), the rabbits were euthanized with an overdose of pentobarbital sodium.

Venous and arterial blood gases and mixed expired CO₂ and O₂ were measured by an IL 1306 blood-gas machine (Instrumentation Laboratory, Lexington, MA). Mixed expired CO₂ was also continuously measured by using a 1100 medical gas analyzer mass spectrometer (Perkin-Elmer, Norwalk, CT). Venous and arterial O₂ content were measured using an IL 482 CO-oximeter (Instrumentation Laboratory).

Calculations

Data Analysis and Statistics

Method 1. The slopes of the lines generated by plotting Hct vs. individual measured variables at baseline and after each hemodilution were calculated for individual rabbits by using ordinary least squares. Student's t-test (2-tailed) was then used to determine whether the mean of individual slopes was significantly different from zero. A P value of <0.05 was accepted as statistically significant.

Method 2. The experimental data were analyzed by using a previously described model of capillary gas exchange (5). Several simplifying assumptions are incorporated in the mathematical model: alveolar gas is assumed to be well mixed and uniform throughout the lung, and alveolar gas tensions are assumed to be time invariant. Blood is considered to consist of two well-mixed compartments (plasma and red blood cell) that have the same residence time in the pulmonary capillaries. Blood flow in the capillaries is assumed to be constant and uniform, and axial and radial diffusions are considered negligible. A kinetic mathematical description of pulmonary capillary O₂ and CO₂ exchange is obtained by deriving mass balance equations for each of the chemical species included. These include CO₂, O₂, water (or volume), hemoglobin-carbamate (oxygenated and reduced), HCO₃, Cl, and H⁺. Because the latter three exist at different concentrations in the plasma and red cell compartments, the behavior of eleven variables must be described as a function of time (from the time blood enters the pulmonary capillaries). The mass balances describing the time rates of change of the eleven variables involve: 1) rate of consumption or production of that species by chemical reaction within its compartment, and/or 2) net transport of the species into or out of its compartment.

Processes included in the quantitative analysis are 1) CO₂-H₂CO₃ hydration-dehydration reactions in plasma and red blood cells; 2) CO₂ reactions with hemoglobin; 3) O₂ binding to hemoglobin and the release of Bohr protons from hemoglobin on oxygenation; 4) buffering of H⁺ intra- and extracellularly by hemoglobin and plasma proteins, respectively; 5) HCO₃/Cl exchange across the red cell membrane mediated by band 3 protein; 6) transcellular movement of water in responses to changes in osmolality; and 7) diffusion of O₂ and CO₂ between alveolar gas and pulmonary capillary blood. Bohr and Haldane effects are included. Ion and water fluxes are described assuming passive diffusion down their respective electrochemical potential and osmotic gradients. Red cell anion exchange is described in terms of a "phenomenological permeability coefficient (PHCO₃)" (5). To account for the availability of pulmonary vascular carbonic anhydrase activity to plasma during capillary transit, an acceleration factor of 200 was used (8).

The mathematical model consists of a set of eleven simultaneous nonlinear ordinary differential equations. The only difference between capillary and postcapillary equations is that net O₂ and CO₂ movement can take place into or out of the blood only while blood is in the pulmonary capillaries; however, after blood enters the postcapillary vessels, it becomes a closed system, and total O₂ and CO₂ contents remain constant.

Numerical integration of the model differential equations was implemented by using the Gear algorithm (15), ideally suited for stiff differential systems. Input parameters for solution included kinetic parameters (Table 1; Ref. 5), estimated alveolar gas tensions, central venous blood-gas parameters, and corresponding to each experimental condition. To provide uniform groups and to include all rabbits in this analysis, plots were constructed for each variable vs. Hct and values interpolated at percentages of baseline Hct of 100, 84, 76, 52, and 44% (some rabbits did not survive <44% of baseline Hct). Interpolated values of Hct, Pv_CO2, venous PO₂ (Pv_O2), , and venous pH were entered into the model, which subsequently generated predicted values for Pa_CO2, CO₂, and O₂.

Table  1.   Values for kinetic parameters used in model computations Parameter Value Acid dissociation constant for H2CO3, K 0.35 mM CO2-HCO3 equilibrium constant, K   7.91 × 104 mM CO2 hydration velocity constant, ku 0.13 s1 H2CO3 dehydration velocity constant, kv 57.5 s1 Intracellular buffer capacity, i 2.9 (mM acid/mM Hb) (pH1) Solubility of CO2, CO2 3.0 × 102 mM/Torr Solubility of O2, CO2 1.35 × 103 mM/Torr CO2-Hb reaction forward rate constant, ka 5.0 mM1 · s1 Hb amino group ionization constant, KZR 3.98 × 105 mM O2Hb amino group ionization constant, KZO 1.79 × 105 mM CO2-Hb reaction ionization constant, KCR 2.15 × 102 mM CO2-O2Hb reaction ionization constant, KCO 1.13 × 102 mM Alveolar membrane O2 diffusing capacity per unit capillary blood volume, DmO2/(Vc) 0.425 (mmol O2/liter blood) (s · Torr)1 (rest) CO2 diffusing capacity per unit capillary blood volume, DLCO2/(Vc) 8.55 (mmol CO2/liter blood) (s · Torr)1 (rest) Hydraulic coefficient for water movements across red cell membrane, Lp 0.0425 cm1 O2 capacity of blood 1.34 ml O2/g Hb H+ released via Hb oxygenation, o 0.7 (mmol H+ released)/(mmol O2Hb formed) H+ released via carbamate formation, c 1.8 (mmol H+ released)/(mmol carbamate formed) Intracellular carbonic anhydrase catalyzing factor, Ai 6,500 Hb, hemoglobin.

RESULTS

Six to seven hemodilutions were performed per rabbit, with only five rabbits surviving seven hemodilutions. Data from measurements taken at baseline and with each hemodilution are reported in Table 2. Starting Hct was 36 ± 3% and fell to 12 ± 1%, or 32% of baseline, at its lowest point. There were no significant changes in Pa_CO2, Pv_CO2, venoarterial PCO₂ difference, CO₂, and arterial PO₂ (Pa_O2) with hemodilution, whereas VDS/VT increased minimally (Fig. 1 and Table 2). and ER_O2 both increased significantly with hemodilution (Fig. 2). Despite the rise in , both systemic and right ventricular pressures remained unchanged. Pv_O2, O₂, and arterial pH all fell with hemodilution.

Table  2.   Changes in measured variables with hemodilution Measurement Baseline HD 1  HD 2  HD 3  HD 4  HD 5  HD 6  HD 7  Slope P Value Hct, %  36 ± 3  32 ± 3  28 ± 3  24 ± 3  21 ± 2  17 ± 2  14 ± 2  12 ± 1  PaCO2, Torr 28.1 ± 5.7  27.3 ± 6.1  28.3 ± 6.6  27.7 ± 6.6  28.5 ± 7.2  28.6 ± 8.2  29.1 ± 8.9  28.8 ± 7.2   0.056 ± 0.193  0.4356 PvCO2, Torr 33.8 ± 6.7  33.3 ± 6.9  32.9 ± 6.1  34.0 ± 7.9  34.4 ± 7.8  35.5 ± 8.8  35.5 ± 8.9  34.7 ± 7.7   0.099 ± 0.234  0.269 (v-a)DCO2, Torr 5.7 ± 2.2  6.0 ± 1.7  4.6 ± 1.0  6.4 ± 2.3  5.9 ± 1.3  6.9 ± 1.3  6.5 ± 1.9  6.3 ± 1.0   0.043 ± 0.067  0.194 PaO2, Torr 99 ± 13  102 ± 15  97 ± 15  99 ± 5  99 ± 18  101 ± 19  97 ± 20  94 ± 13  0.075 ± 0.491  0.6794 PvO2, Torr 37 ± 2  35 ± 3  35 ± 4  33 ± 3  31 ± 4  30 ± 3  30 ± 4  28 ± 5  0.362 ± 0.205  0.0016* pH 7.47 ± 0.06  7.48± 0.06  7.46 ± 0.06  7.45 ± 0.05  7.42 ± 0.06  7.39 ± 0.06  7.34 ± 0.07  7.26 ± 0.12  0.007 ± 0.004  0.0015*  CO2, ml · kg1 ·   min1 5.91 ± 1.22  6.01 ± 1.42  5.86 ± 1.50  5.77 ± 1.58  5.85 ± 1.72  5.85 ± 1.78  5.76 ± 1.65  5.79 ± 1.69  0.007 ± 0.037  0.591  O2, ml · kg1 ·   min1 6.25 ± 1.46  5.95 ± 1.47  5.88 ± 1.08  5.90 ± 1.15  5.47 ± 1.57  5.45 ± 1.70  5.11 ± 1.63  4.79 ± 1.64  0.043 ± 0.042  0.023*  , ml/min 296 ± 67  294 ± 75  317 ± 79  335 ± 77  332 ± 109  387 ± 126  396 ± 118  447 ± 150   6.135 ± 5.093  0.011* VDS/VT, %  40 ± 8  38 ± 7  42 ± 5  41 ± 5  42 ± 5  42 ± 6  43 ± 6  48 ± 6   0.002 ± 0.002  0.036* ERO2 0.42 ± 0.06  0.46 ± 0.07  0.48 ± 0.07  0.52 ± 0.08  0.57 ± 0.08  0.61 ± 0.08  0.63 ± 0.08  0.68 ± 0.07   0.01 ± 0.003  0.0001* Values are means ± SD. Slopes were calculated from plots of individual measured values vs. hematocrit (Hct) for each rabbit and then averaged, as described in text. HD, sequential hemodilation; PaCO2, arterial PCO2; PvCO2, venous PCO2; (v-a)DCO2, venoarterial PCO2 difference; PaO2, arterial PO2; PvO2, venous PO2; CO2, CO2 production; O2, O2 consumption; , cardiac output; VDS/VT, fraction of physiological dead space; ERO2, O2 extraction ratio. * Statistically significant difference between slope and zero, indicating a change in measured variable with a change in Hct.

Data from the mathematical model are presented in Table 3. Because of the previously described derivation by interpolation of data used in the model, the numbers of data points after baseline differ slightly from those reported in Table 2. Using our input data, the model predicts that Pa_CO2 should remain virtually unchanged with each subsequent hemodilution, whereas CO₂ and O₂ are predicted to fall only slightly. There is close agreement (<5% difference) between measured (interpolated) values and predicted values using modeling for all variables except O₂. Measured O₂ falls more than predicted O₂, particularly at the last analysis point (44% of baseline Hct) where there is a 20% difference between measured and predicted values. For this last data set, if it is assumed that hemodilution and acute anemia result in a small fall in 2,3-diphosphoglycerate, with a corresponding left shift of the oxyhemoglobin dissociation curve (change in PO₂ at 50% saturation of hemoglobin, ~5 Torr), there is closer agreement between measured and predicted O₂ (3% difference in values). The difference between measured and predicted Pa_CO2, however, becomes slightly greater when using this correction, although the difference is still only 7%.

Table  3.   Measured vs. predicted values derived from mathematical modeling Hct % and (%baseline)  CO2, ml · kg1 · min1  O2, ml · kg1 · min1 PaCO2, Torr Measured Predicted Measured Predicted Measured Predicted 36.0 (100) 5.91 5.91 6.25 6.47 28.1 27.2 30.3 (84) 5.91 5.76 5.91 6.16 27.7 27.3 24.8 (76) 5.73 5.73 5.91 6.16 27.8 27.5 18.9 (52) 5.79 5.67 5.39 5.85 28.3 27.4 16.0 (44) 5.73 5.88 4.77 5.97 28.8 27.4 16.0 (44) 5.73 5.67* 4.77 4.93* 28.8 26.7* * Values calculated with the assumption that acute hemodilution results in a fall in 2,3-diphosphoglycerate, with resulting left shift of oxyhemoglobin curve.

DISCUSSION

Our main findings are that acute normovolemic hemodilution to Hct values <40% of normal in anesthetized and mechanically ventilated rabbits does not alter Pa_CO2 and mixed venous PCO₂ or the venoarterial PCO₂ difference. Stability of PCO₂ values occurs despite an unchanged total and slightly lower alveolar ventilation and no decline in CO₂. Although rises with anemia, it is not fully compensatory for O₂ transport, since we found the classic progressive widening of the arteriovenous PO₂ difference (i.e., greater ER_O2) with decreasing Hct. Modeling of our hemodynamic and respiratory data predicts the observed stability in PCO₂ values.

Critique of Methods

Comparison with Previous Studies

1

1

Analysis of Factors Preventing CO₂ Retention with Anemia

. Although several compensations exist to ensure maintenance of normal O₂ and CO₂ during acute isovolemic anemia, the most important is an increase in . increases in anemia predominantly because of a fall in blood viscosity, which results in a reduction in peripheral vascular resistance (9). An increased will permit greater CO₂ transfer for the same CO₂ driving gradients as long as capillary recruitment prevents a fall in capillary transit time, since CO₂ equilibration between blood and tissue or alveolar gas requires almost the entire normal transit time of 0.5-1.0 s for completion (6, 24, 43). increased in our animals by ~50% with a reduction in Hct of 66%, similar to the findings of other studies in this area referenced above (average increase over the same Hct range was 40-70%). As expected, this increase was not sufficient to prevent a progressive increase in O₂ extraction with greater anemia and would not be sufficient to prevent CO₂ retention in the absence of other compensations. When using the human gas-exchange model of Bidani (5), it would be necessary to increase 170% for the same Hct reduction if no other compensations, including an increase in O₂ extraction, are permitted (Fig. 3).

ACKNOWLEDGEMENTS

This project was supported by grants from the American Heart Association-Washington Affiliate (95-WA-503 to S. Deem) and the National Heart, Lung, and Blood Institute (2R01-HL-45571 to E.R. Swenson).

FOOTNOTES

Address for reprint requests: S. Deem, Univ. of Washington, Dept. of Anesthesiology, Box 356540, Seattle, WA 98195-6540.

Received 20 September 1996; accepted in final form 7 March 1997.

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