INTRODUCTION

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MOLECULAR CO₂ has a high solubility-diffusivity product (~20 times that for O₂), and on that basis it has been tacitly assumed that equilibration of CO₂ between alveolar gas and capillary blood occurs almost instantaneously. CO₂ is only moderately soluble in aqueous media, and the transport of CO₂ in physical solution alone is inadequate to keep pace with metabolic CO₂ production (6, 21-23). CO₂, produced in metabolically active cells as a by-product of fuel utilization or lipogenesis, diffuses freely through tissues on the basis of its small molecular size and relatively high lipid solubility and behaves as a weak acid that hydrates to yield and H⁺ via the following reaction: CO₂ + H₂O  H₂CO₃   + H⁺ (pK ~ 6.1). Under physiological conditions (pH 7.4), the majority of CO₂ is in the form of . CO₂ excretion (CO₂) in the lungs requires transformation of intravascular stores to molecular CO₂ via the Jacobs-Stewart cycle (18). The ratelimiting step in the reaction is the hydration/dehydration of CO₂/, which when catalyzed by carbonic anhydrase (CA) is reduced from a half time (t_1/2) of 5-8 s to 5-10 ms (6, 22, 23). In addition, /Cl exchange is important in facilitating transfer of from the extracellular to intraerythrocyte space for conversion to molecular CO₂ and subsequent excretion (t_1/2 = 125 ms) (11, 17, 19, 20). Therefore, CO₂ in vivo requires efficient catalysis of dehydration by red cell CA during pulmonary capillary transit (6, 22, 26). Under normal physiological conditions, there is sufficient red cell CA activity to accelerate the dehydration reaction by 6,500-fold, and CO₂ reaches completion during the early phase of pulmonary capillary transit time (750 ms) (6, 23). Inhibition of CA activity should affect the kinetics of intracapillary gas exchange and the kinetics of intravascular pH equilibration (5, 6) but not the steady-state CO₂. In an earlier study, Bidani and Crandall (3) measured postcapillary pH disequilibria during differential grades of CA inhibition. The study indicated complex postcapillary pH disequilibria depending on the activities of red cell and intravascular CA (3, 6). Subsequently, Bidani (2) used a detailed mathematical analysis to quantify the contributions of red cell anion exchange and vascular and red cell CA activities in maintaining CO₂ during rest and exercise. On the basis of a calculated transfer capacity for CO₂ (T_CO2), estimates were obtained for the alterations in alveolar ventilation and cardiac output necessary to maintain CO₂ when red cell anion exchange and/or CA activities are inhibited (2). Swenson et al. (25) reported the quantitative effects of red cell anion exchange and CA inhibitors on CO₂ in anesthetized, paralyzed, and mechanically ventilated dogs. Although the experimental results were in general agreement with the previous predictions (2), Swenson et al. estimated the effects of anion exchange and CA inhibitors on single-pass CO₂ but not on steady-state excretion.

Taki et al. (29) evaluated the effects of progressive CA inhibition on CO₂ in anesthetized and paralyzed dogs. Their experimental protocol consisted of measurements of end-tidal (ET_CO2), arterial (Pa_CO2), and mixed venous blood PCO₂ () after the administration of 5 mg/kg acetazolamide (Actz) at 10-min intervals up to a cumulative dose of 20 mg/kg. No significant decrements in CO₂ were reported. The authors did note a gradual increment in Pa_CO2 from ~33 to 52 Torr, whereas increased from ~43 to 58 Torr at the end of the experimental protocol. The "estimated" alveolar PCO₂ (PA_CO2) fell from 32 to 27 Torr after the first dose of 5 mg/kg Actz, but no change was noted with three successive doses of 5 mg/kg Actz. The authors used the electrometric method of Wilbur and Anderson (30) to estimate the extent of red cell CA inhibition after each successive dose of 5 mg/kg Actz. The maximum degree of red cell CA inhibition was estimated to be ~73% at the end of the experimental protocol (cumulative dose of 20 mg/kg Actz). A significant problem with the study of Taki et al. is the lack of an adequate time to reach steady state. The lack of any significant transient decrement in CO₂ after Actz administration does not agree with the previous study of Berthelsen and Dich-Nielson (1). It also is difficult to reconcile the estimates of Taki et al. on the extent of red cell CA inhibition with earlier estimates of Swenson and Maren (26) and Wistrand (31), who reported that no significant differences in alveolar-blood PCO₂ gradient would be expected for CA inhibition <95%. Maren noted that a dose of 5 mg/kg Actz, as was utilized by Taki et al., should inhibit >98% of red cell CA activity. It is interesting that a recent study by Taki et al. (28) found significant widening of the alveolar-arterial blood PCO₂ gradient [(A-a)PCO₂] at 5 mg/kg Actz in anesthetized dogs. This PCO₂ gradient increased progressively with the dose of Actz up to a total of 30 mg/kg.

Reestablishment of a steady state for CO₂ after CA inhibition can be mediated by alterations in cardiac output, alveolar ventilation, and/or increments in tissue PCO₂ (2, 9, 10). Our present study was designed to quantify the transient and quasi-steady-state effects of progressive CA inhibition in vivo using intravenous Actz administration on CO₂ in anesthetized mechanically ventilated dogs. A few experiments also were performed with the weakly permeant CA inhibitor benzolamide. The goal was to evaluate the veracity of previous predictions of the extent of mixed venous blood-alveolar PCO₂ gradient [(-A)PCO₂] necessary to maintain CO₂ for different levels of CA inhibition. Additionally, we have utilized our previous mathematical model (2, 7) to predict the kinetics of intravascular PCO₂ and pH equilibration as blood travels around the circulation during different levels of CA inhibition, after reestablishment of a steady state. The model computations indicate hysteresis loops of the instantaneous CO₂--H⁺ relationship and in vivo blood PCO₂-pH relationship due to the finite reaction times for the CO₂--H⁺ reactions. The shape of the hysteresis loops is affected by the extent of Actz inhibition of CA in red blood cells and plasma.

	METHODS

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Animal preparation. Five unconditioned mixed-breed dogs of either sex (20-24 kg body mass) underwent anesthetic induction with an intravenous bolus injection of 30 mg/kg pentobarbital sodium (Nembutal, Abbott Laboratories, N. Chicago, IL). A midline tracheostomy was performed, and the animal was placed on a volume-cycled ventilator (Harvard Apparatus, Millis, MA). Pancuronium bromide, a nondepolarizing paralytic agent (Pavulon, Organon), was administered via intravenous bolus of 2 mg every 1-2 h to eliminate spontaneous respirations. Tidal volume was set at 15 ml/kg, and rate was adjusted to obtain a baseline PA_CO2 of 36 ± 2 Torr. Depth of anesthesia was determined utilizing pupillary light reflex, lacrimation, and salivation as markers and was maintained using intermittent intravenous pentobarbital at 5-10 mg/kg every 1-2 h. Cannulas were placed in a femoral artery (via arteriotomy) and the contralateral femoral vein (percutaneous). An 8-F introducer was inserted into the external jugular vein (venotomy), and an oximetric pulmonary arterial catheter (Abbott Laboratories) was floated into position under waveform guidance. Core temperature was monitored utilizing the pulmonary arterial catheter thermistor and maintained at 37.5 ± 1.5°C by the use of an external heating/cooling blanket. After completion of surgery, the animal was given an intravenous bolus of 2,000 U of heparin sodium and placed on a constant infusion of 1,000 U/h to minimize intravascular hemolysis.

Calculations. CO₂ was calculated by the expression where I is the inspired minute volume and the gas fractions are the values as determined by mass spectroscopy of mixed expired CO_{2 CO2}) and inspired and expired N₂ (FI_N2 and FE_N2, respectively). Expired minute ventilation (E) was estimated from ET_CO2 was obtained from the continuous airway CO₂ tracings as recorded with the chart recorder. Dead space ratios (VD/VT) were calculated using the equation where ET_CO2 was used as an approximation of PA_CO2 and PB is barometric pressure.

Statistical analyses. Values are means ± SE. Significance was determined using the method of sum of least squares with P < 0.05.

Mathematical model computations. The experimental data were analyzed using a previously described model of capillary gas exchange (2, 7). Several simplifying assumptions are incorporated into the mathematical model. Alveolar gas is assumed to be well mixed and uniform throughout the lung. Alveolar and tissue-gas tensions are assumed to be time invariant. Blood is considered to consist of two well-mixed compartments (plasma and erythrocyte). The residence time of blood in the pulmonary capillaries is taken as 1 s and that in the tissue capillaries as 2 s. Blood flow in the capillaries is assumed to be constant and uniform, and axial and radial diffusion are considered negligible.

Parameter values for the mathematical model. Input parameters for the model included kinetic parameters, estimated alveolar gas tensions (assumed equal to the measured end-tidal values), metabolic rates (based on measurements during the control period), hematocrit, cardiac output, and appropriate catalytic factors (A_o and A_i). The kinetic parameters have been provided previously (2, 7, 12). The adjustable parameters for steady-state simulation of each experimental condition were the tissue PO₂ and tissue PCO₂ needed to match the measured O₂ consumption (O₂) and CO₂ as well as the measured Pa_CO2, arterial PO₂ (Pa_O2), arterial pH (pH_a), , central mixed venous PO₂ (), and central mixed venous pH (pH).

	RESULTS

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A summary of the experimental data on the quasi-steady-state mixed venous and arterial blood gas parameters for all experimental groups is provided in Table 1. Measurements of hematocrit, I, ET_CO2, and cardiac output as well as the measured values for O₂ and CO₂ are provided in Table 2. Pulmonary arterial pressures were not monitored continuously. Intermittent measurements of pulmonary arterial systolic pressure were 18-24 mmHg, and pulmonary arterial diastolic pressure ranged from 12 to 16 mmHg. The pulmonary capillary wedge pressure, also sampled intermittently, was 9-13 mmHg.

The effect of progressive CA inhibition on CO₂ is shown in Fig. 1A, with CO₂ expressed as percentage of baseline value (i.e., time 0) and the line fitted by eye. After 5 mg/kg Actz, there was a slow monotonic decrement in CO₂ to 90% of control, with no significant recovery over 1 h. After an additional 15 mg/kg Actz, CO₂ fell rapidly to 80% of baseline and recovered to 85% over 1 h. Subsequent administration of 80 mg/kg Actz caused a fall in CO₂ to 75% of baseline, with a gradual return to 80% of control over 1 h. Thus, for all levels of CA inhibition, there was significant decrement in CO₂ followed by incomplete recovery over 1 h. This also is reflected by the significant reduction in the respiratory exchange ratio (R; Table 2). The time course of changes in ET_CO2 (Fig. 1B) roughly paralleled the changes in CO₂. Complete inhibition of extracellular CA (5 mg/kg Actz) resulted in a fall of ET_CO2 to 82% of baseline (t_1/2 = 5 min), with minimal recovery to 85% over 1 h. Moderate inhibition of red cell CA (20 mg/kg Actz) resulted in a further decline of ET_CO2 to 63% of control, with a t_1/2 of <1 min, followed by recovery to 78% of control with t_1/2 of 10 min. "Complete" inhibition of all CA activity (100 mg/kg Actz) resulted in a fall in ET_CO2 to 64% of control, with a t_1/2 of 1 min, followed by recovery to 73% of baseline. A few experiments were performed with the slowly permeant CA inhibitor benzolamide. CO₂ fell an average of 10% from control values at 10 min after 2 mg/kg benzolamide (n = 3).

View larger version (15K): [in this window] [in a new window]   Fig. 1.   Effects of acetazolamide (Actz) on pulmonary CO2 excretion (CO2). A: measured CO2 as a function of time for all experimental animals. B: measured end-tidal CO2 (ETCO2, expressed as percentage of control) as a function of time for all experimental animals. Values are means ± SE.

Figure 2A shows the measured time course of changes in (-A)PCO₂, where ET_CO2 was used to approximate PA_CO2. A stepwise increment in (-A)PCO₂, the effective driving force for CO₂, was noted for each level of CA inhibition. The average (-A)PCO₂ increased from ~4 Torr at time 0 to 9 Torr (5 mg/kg Actz), 22 Torr (20 mg/kg Actz), and 27 Torr (100 mg/kg Actz). The corresponding time course of changes in the arterial-alveolar PCO₂ gradient [(A-a)PCO₂] is shown in Fig. 2B. Because of the CO₂--H⁺ disequilibrium associated with progressive CA inhibition, there is a progressive widening of (A-a)PCO₂ from 2 Torr at baseline to 20 Torr at 60 min after a cumulative dose of 100 mg/kg Actz.

View larger version (13K): [in this window] [in a new window]   Fig. 2.   Effects of Actz on blood-alveolar gas PCO2 gradients. A: estimated central mixed venous blood-alveolar gas PCO2 gradient [(-A)PCO2] as a function of time for all experimental animals. B: estimated arterial blood-alveolar gas PCO2 gradient [(a-A)PCO2] as a function of time for all experimental animals. Values are means ± SE.

I was maintained constant throughout the duration of each experiment (Table 2). Measured blood hematocrit declined somewhat because of blood sampling over the duration of the experiments, more in certain animals than in others. No red cell transfusions were given. Cardiac output remained stable at 4 l/min, except in the last 60-min experimental period, when it declined ~15-20%. Indirect evidence for a slight worsening of ventilation-perfusion mismatch with progressive CA inhibition can be deduced from the estimated alveolar-arterial pressure gradient for O₂ [(A-a)PO₂] using the simplified alveolar gas equation and the measured R values (Table 2), with ET_CO2 used in place of PA_CO2. (A-a)PO₂ increased from a control value of 6.3 Torr to 8.9 Torr for 5 mg/kg Actz and to 10.5 Torr at 100 mg/kg Actz.

Figures 3-5 show the steady-state computed time courses of blood PCO₂, CO₂ content ([CO₂]), and plasma pH as blood travels around the entire ("closed-loop") circulation for a representative animal under control conditions, 60 min after 5 mg/kg Actz, and 60 min after 100 mg/kg Actz. Computed results for the case of 20 mg/kg Actz were intermediate between those for 5 and 100 mg/kg and are not shown. For the control condition (Fig. 3) before the administration of any Actz, as blood arrives in the pulmonary capillaries, blood PCO₂ falls almost instantaneously from that in the central mixed venous blood (37 Torr) to that in the alveolar gas (33 Torr) and remains at that level during pulmonary capillary transit. Associated with this very rapid fall in blood PCO₂ is a rapid fall in [CO₂] as blood enters the pulmonary capillaries. For the remainder of pulmonary capillary transit, there is a small fall in [CO₂] due to the continued dehydration of plasma and red cell to molecular CO₂. Because sufficient CA activity is available on the pulmonary capillary endothelium (A_o = 100) and because of the low non- buffer capacity (~6 mM/pH unit), plasma pH rises from 7.39 in central mixed venous blood to 7.43 early during pulmonary capillary transit. By the time blood leaves the pulmonary capillaries, there is net depletion of plasma H⁺ concentration ([H⁺]) relative to that in the red blood cell. This disequilibrium of H⁺ across the red cell membrane is dissipated in postcapillary blood via the Jacobs-Stewart cycle (5, 18), wherein the "excess" red cell H⁺ combine with intraerythrocytic to generate molecular CO₂, which diffuses into plasma and is dehydrated there to generate H⁺ and . Simultaneously, the newly generated plasma is transported into the red blood cell in exchange for Cl by band 3-mediated anion exchange. As a result, plasma pH falls by 0.01 unit (in postcapillary blood) and blood PCO₂ rises very slightly. The time course of these internal changes in blood is determined by the CA activity available to postcapillary blood (via that due to red cell hemolysis, A_o = 2) and the rate of the red cell /Cl exchange. For the control condition, the t_1/2 is ~1 s. Analogous changes, but opposite in direction, occur in the tissue capillaries. Blood PCO₂ falls and plasma pH rises in the posttissue capillaries (Fig. 3).

View larger version (9K): [in this window] [in a new window]   Fig. 3.   Computed steady-state time course of blood PCO2 (A), CO2 content ([CO2]; B), and plasma pH (pHo; C) as blood travels around entire circulation for a typical control animal (0 mg/kg Actz). Input parameters for model calculations are as follows: hematocrit = 38%, cardiac output = 3.0 l/min, alveolar PCO2 (PACO2 ) = 32.5 Torr, alveolar PO2 (PAO2 ) = 100.0 Torr, tissue PCO2 = 39.5 Torr, tissue PO2 = 39.5 Torr, catalytic factor for red cell reactions (Ai) = 6,500, catalytic factor for plasma reactions (Ao) = 100 for blood in capillary bed and Ao = 2 for postcapillary blood. Measured values for this simulation are as follows: CO2 = 99.0 ml/min, O2 consumption (O2) = 124.0 ml/min, arterial PO2 (PaO2 ) = 96.6 Torr, arterial PCO2 (PaCO2 ) = 31.7 Torr, arterial pH (pHa) = 7.41, mixed venous PO2 () = 39.5 Torr, mixed venous PCO2 ( = 37.6 Torr, mixed venous pH (pH) = 7.39. Model-computed values are as follows: CO2 = 97.9 ml/min, O2 = 118.5 ml/min, PaO2 = 99.9 Torr, PaCO2 = 32.9 Torr, pHa = 7.42,  = 39.8 Torr,  = 37.7 Torr, pH = 7.39.

View larger version (10K): [in this window] [in a new window]   Fig. 4.   Computed steady-state time course of blood PCO2 (A), [CO2] (B), and pHo (C) as blood travels around entire circulation for a typical animal given 5 mg/kg Actz. Input parameters for model calculations are as follows: hematocrit = 38%, cardiac output = 3.0 l/min, PACO2 = 26.6 Torr, PAO2 = 100.0 Torr, tissue PCO2 = 39.8 Torr, tissue PO2 = 42.0 Torr, Ai = 110, Ao = 1 for blood in capillary bed and for postcapillary blood. Measured values for this simulation are as follows: CO2 = 92.0 ml/min, O2 = 119.0 ml/min, PaO2 = 94.0 Torr, PaCO2 = 33.3 Torr, pHa = 7.37,  = 45.0 Torr,  = 38.4 Torr, pH = 7.34. Model-computed values are as follows: CO2 = 92.7 ml/min, O2 = 116.0 ml/min, PaO2 = 100.7 Torr, PaCO2 = 32.2 Torr, pHa = 7.39,  = 42.3 Torr, = 37.2 Torr, pH = 7.36.

View larger version (10K): [in this window] [in a new window]   Fig. 5.   Computed steady-state time course of blood PCO2 (A), [CO2] (B), and pHo (C) as blood travels around entire circulation for a typical animal given 100 mg/kg (cumulative) Actz. Input parameters for model calculations are as follows: hematocrit = 31%, cardiac output = 3.0 l/min, PACO2 = 22.8 Torr, PAO2 = 110.0 Torr, tissue PCO2 = 60.0 Torr, tissue PO2 = 46.3 Torr, Ai = 2.3, Ao = 1 for blood in capillary bed and for postcapillary blood. Measured values for this simulation are as follows: CO2 = 72.0 ml/min, O2 = 104.0 ml/min, PaO2 = 112.8 Torr, PaCO2 = 38.9 Torr, pHa = 7.29,  = 45.2 Torr,  = 46.3 Torr, pH = 7.27. Model-computed values are as follows: CO2 = 67.0 ml/min, O2 = 94.0 ml/min, PaO2 = 113.6 Torr, PaCO2 = 42.0 Torr, pHa = 7.29,  = 46.2 Torr, = 45.6 Torr, pH = 7.27.

For the steady-state condition after 5 mg/kg Actz (Fig. 4), central mixed venous blood (not internally at equilibrium) arrives at the lung with a PCO₂ of 37 Torr and, soon after entering the pulmonary capillaries, falls to the alveolar level of 27 Torr and remains at that level during pulmonary capillary transit. An initial rapid decrement in [CO₂] is associated with the fall in blood PCO₂. For the remainder of the pulmonary capillary transit, there is a small fall in [CO₂] due to the continued slow dehydration of plasma and red cell to molecular CO₂. Plasma pH rises from 7.365 in central mixed venous blood to 7.370 during pulmonary capillary transit. Because no CA activity is available to capillary blood plasma under these conditions (complete inhibition of endothelium-associated and free CA activity in plasma, A_o = 1), as blood leaves the pulmonary capillaries, plasma concentration ([]) × [H⁺] > [CO₂], and consequently blood PCO₂ rises in postcapillary blood from the end-capillary ( alveolar) level of 27 to 32 Torr (Fig. 4). Additionally, by the time blood leaves the pulmonary capillaries, there is net depletion of red cell [H⁺] relative to that in the plasma. This disequilibrium of H⁺ across the red cell membrane is dissipated in postcapillary blood via the Jacobs-Stewart cycle (5, 18), as described above. As a result, plasma pH rises by 0.01 unit (in postcapillary blood). However, before a new electrochemical equilibrium can be established between plasma and red blood cells, blood arrives at the tissue and is in a state of electrochemical disequilibrium (Fig. 4). For open-loop conditions where arterial blood is followed to equilibrium, there is good agreement between the predicted and measured arterial blood-gas/pH parameters (measured Pa_O2 = 94.0 Torr, Pa_CO2 = 33.3 Torr, pH_a = 7.37; calculated Pa_O2 = 100.7 Torr, Pa_CO2 = 32.2 Torr, pH_a = 7.39). Analogous changes, but opposite in direction, occur in the tissue capillaries and are shown in Fig. 4. Blood PCO₂ and plasma pH fall in the posttissue capillaries, but because of the limited tissue-to-lung transit time, electrochemical equilibrium is not established as central mixed venous blood arrives at the lung under closed-loop conditions. For open-loop conditions where central mixed venous blood is followed to equilibrium, there is good agreement between the predicted and measured mixed venous blood gas/pH parameters (measured = 45.0 Torr,  = 38.4 Torr, pH = 7.34; calculated  = 42.3 Torr,  = 37.2 Torr, pH = 7.36).

For the steady-state condition after 100 mg/kg Actz (Fig. 5), central mixed venous blood (not internally at equilibrium) arrives at the lung with a PCO₂ of 47 Torr and, soon after entering the pulmonary capillaries, falls to the alveolar level of 22 Torr and remains at that level during pulmonary capillary transit. After the initial rapid decrement in blood [CO₂] associated with the fall in blood PCO₂, there is minimal change for the remainder of the pulmonary capillary transit due to the very slow dehydration of plasma and red cell to molecular CO₂. Plasma pH rises minimally from 7.25 in central mixed venous blood to 7.26 during pulmonary capillary transit. Because no CA activity is available to capillary blood plasma and very minimal residual activity is present in the red blood cells (A_i = 2.3), as blood leaves the pulmonary capillaries, plasma [] × [H⁺]  [CO₂], and consequently blood PCO₂ rises slowly in postcapillary blood from the end-capillary ( alveolar) level of 23 to 39 Torr during lung-to-tissue transit. Associated with this rise in blood PCO₂, there is a slow rise in plasma pH from 7.27 to 7.35 in postcapillary blood. Additionally, by the time blood leaves the pulmonary capillaries, there is net depletion of plasma [H⁺] relative to that in the red blood cell. This disequilibrium of H⁺ across the red cell membrane would be dissipated in postcapillary blood via the Jacobs-Stewart cycle and ensuing plasma CO₂--H⁺ reactions (5, 18), as described above. However, because of the longer time required for this H⁺ equilibration (t_1/2 = 15 s) and the limited lung-to-tissue transit time (14 s), these changes do not take place and blood arriving at the tissue capillaries is in a state of significant electrochemical disequilibrium. Analogous changes, but opposite in direction, occur in the tissue capillaries (Fig. 5). Blood PCO₂ rises rapidly to the tissue level (60 Torr) and falls in posttissue capillaries. Because of the longer tissue-to-lung transit time, the predicted biphasic changes in plasma pH are manifested. A fall in plasma pH due to the CO₂ hydration-dehydration equilibration in plasma and red blood cells occurs first, and subsequently the initial phase of H⁺ equilibration across the red cell membrane via the Jacobs-Stewart cycle (18) results in a slow rise in plasma pH. Despite the somewhat longer tissue-to-lung transit time, electrochemical equilibrium is not established as central mixed venous blood arrives at the lung. For open-loop conditions where arterial and central mixed venous blood are followed to equilibrium, there is good agreement between the predicted and measured arterial and mixed venous blood-gas/pH parameters (measured Pa_O2 = 112.8 Torr, Pa_CO2 = 38.9 Torr, pH_a = 7.29,  = 45.2 Torr, = 46.3 Torr, pH = 7.27; calculated Pa_O2 = 113.6 Torr, Pa_CO2 = 42.0 Torr, pH_a = 7.29,  = 46.2 Torr,  = 45.6 Torr, pH = 7.27).

No significant changes in CO₂, O₂, or arterial and mixed venous blood-gas parameters were noted in the one animal that was given a sham infusion of alkalinized saline with pH similar to the Actz solution (pH 9.5) under conditions of no CA inhibition and complete (100 mg/kg Actz) inhibition (data not shown).

	DISCUSSION

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On the basis of our computations and the experimental results, the following conclusions can be made. 1) In the face of fixed I, compensatory recovery of CO₂ after CA inhibition occurs primarily by an increase in the (-A)PCO₂ with minimal changes in cardiac output. 2) During significant CA inhibition, in vivo Pa_CO2 is overestimated and in vivo is underestimated by use of in vitro equilibrated blood measurements. 3) Even in the presence of plasma CA activity, the instantaneous relationship between blood [CO₂] and PCO₂ is different for CO₂ uptake in tissues vs. that for CO₂ in the lung. This results in a hysteresis loop. 4) The shape of the in vivo blood PCO₂-pH relationship is complex and depends on the CA activity available to plasma and in red blood cells. Under control conditions, CA activity is available to plasma during capillary transit (via that associated with capillary endothelium) and to plasma in postcapillary blood (via that released in plasma from hemolysis of red blood cells), and a great excess of endogenous CA activity exists in the red blood cells. After administration of 5 mg/kg Actz, CA activity on the capillary endothelium, as well as that in plasma due to red cell hemolysis, is inhibited (A_o = 1). Despite substantial inhibition of red cell CA with this dose of Actz (3), there is significant residual CA activity (A_i = 110). Sixty minutes after the administration of 100 mg/kg Actz, there is essentially complete (99.98%) inhibition of red cell CA (A_i = 2.3).

Quantitative comparison of previous model predictions and present results. Previous calculations (2) utilized the concept of a transfer capacity for CO₂, i.e., T_CO2 = CO₂/(-A)PCO₂, to estimate the efficiency of CO₂. At rest, it was estimated that T_CO2 in normal humans is 25.2 ml CO₂ · min¹ · Torr¹ when capillary endothelium-associated CA activity is intact but no CA is available in postcapillary plasma. In the absence of CA inhibition, we estimate a T_CO2 of 27.2 ml CO₂ · min¹ · Torr¹ on the basis of our present results. However, the transfer coefficient K_CO2 (= T_CO2/, where is blood flow rate) in the present study of 6.8 ml CO₂ · Torr¹ · l¹ is significantly higher than that predicted previously (K_CO2 = 4.6 ml CO₂ · Torr¹ · l¹) (2). We ascribe this difference to the extra CA activity available in plasma due to red cell hemolysis, which was not considered in the previous calculations (2). When red cell CA activity is intact but endothelial CA activity is inhibited, it was predicted that K_CO2 = 4.1 ml CO₂ · Torr¹ · l¹ (2), which is considerably higher than the value obtained by us in this study of 2.5 ml CO₂ · Torr¹ · l¹ after 5 mg/kg Actz (Tables 1 and 2). We ascribe this difference to the significant red cell CA inhibition associated with 5 mg/kg Actz (98.5%). For the case where all CA activity is inhibited, our estimate of K_CO2 (0.94 ml CO₂ · Torr¹ · l¹) is comparable to that predicted earlier (0.8 ml CO₂ · Torr¹ · l¹) (2). The slightly higher value in our present study is likely due to the lower hematocrit (<45%; Table 2) than in previous calculations (45%) (2).

In vitro CO₂ dissociation curves vs. in vivo relationships. The instantaneous (dynamic) in vivo blood [CO₂]-PCO₂ relationship differs significantly from the "equilibrium" or "static" CO₂ dissociation curve and forms hysteresis loops around the in vitro linearized CO₂ dissociation curve. The width of these hysteresis loops is dependent on the available CA activity (Fig. 6). During control conditions, as blood passes through the pulmonary capillaries, blood PCO₂ falls very rapidly relative to the total change in blood [CO₂]. Later in the capillary, blood PCO₂ changes very little while blood [CO₂] continues to change slowly because of ongoing mobilization of plasma via anion exchange across the red cell membrane and subsequent dehydration within the red blood cell. In postpulmonary capillaries, total blood [CO₂] remains constant while internal electrochemical equilibrium between PCO₂, [], and [H⁺] is established. Even when CA activity is available in plasma and via capillary endothelium, a hysteresis loop is present (Fig. 6A), rather than a symmetrical change in blood [CO₂] and PCO₂ along the in vitro line, equilibrated central venous blood (VBG)  equilibrated arterial blood (ABG) (dashed line in Fig. 6). These differences become significantly larger as CA activity is progressively inhibited. For 5 mg/kg Actz, the in vitro line, VBG  ABG, has a much higher slope ("capacitance coefficient") than the in vivo relationship across the lung (mv  a, where mv is mixed venous blood entering the pulmonary capillaries and a is blood leaving the pulmonary capillaries) or that across the tissues (at  vt, where at is arterial blood entering the tissue capillaries and vt is venous blood leaving the tissue capillaries). The largest differences occur when CA activity is completely inhibited. The hysteresis loop is much wider and the in vitro capacitance coefficient is much higher than the instantaneous dynamic in vivo capacitance coefficient.

View larger version (14K): [in this window] [in a new window]   Fig. 6.   Computed hysteresis loops of instantaneous CO2 dissociation curves corresponding to control conditions (A), 60 min after 5 mg/kg Actz (B), and 60 min after 100 mg/kg Actz (C). L, lung; T, tissue; a, blood leaving pulmonary capillaries; at, arterial blood entering tissue capillaries; vt, venous blood leaving tissue capillaries; mv, mixed venous blood entering pulmonary capillaries; ABG, equilibrated arterial blood; VBG, equilibrated central venous blood. See legends of Figs. 3-5 for values of input parameters, measured and calculated CO2 and O2, and measured and calculated equilibrated arterial and mixed venous blood-gas/pH parameters.

In vitro vs. in vivo acid-base relationships. As a consequence of CO₂--H⁺ disequilibrium, the in vivo plasma pH-blood PCO₂ relationship is nonlinear and is manifested as a hysteresis loop around the in vitro pH-PCO₂ relationship across the lung (mv  a) and that across the tissues (at  vt; Fig. 7). The two in vitro lines are parallel but slightly displaced.

View larger version (11K): [in this window] [in a new window]   Fig. 7.   Computed hysteresis loops of instantaneous blood PCO2 vs. plasma pH as blood recirculates between lungs and tissues corresponding to control conditions (A), 60 min after 5 mg/kg Actz (B), and 60 min after 100 mg/kg Actz (C). Note different ordinate scales in A-C. See Fig. 6 legend for definition of abbreviations.

at  vt

mv  a

ABG  VBG

mv  a

vt  at

ABG  VBG

mv  a

vt  at

Sensitivity of model predictions to input parameters. In our mathematical simulation we assumed that 5 mg/kg Actz resulted in 98.3% inhibition of red cell CA activity. Thus an A_i of 110 was chosen for these conditions on the basis of an acceleration factor of 6,500 for "normal" red cell CA activity (2, 7). Computations using A_i of 33, which corresponds to 99.5% inhibition of red cell CA, are shown in Fig. 8 and compared with those using the nominal value of A_i of 110. Although the qualitative trends are preserved, a higher tissue PCO₂ of 53.2 Torr (compared with a tissue PCO₂ of 39.8 Torr used when A_i = 110) is required to ensure adequate CO₂ uptake during tissue capillary transit. Additionally, there is a significant discrepancy between the measured and calculated Pa_CO2 (measured = 33.3 Torr, calculated = 40.0 Torr) and (measured = 38.4 Torr, calculated = 42.3 Torr).

View larger version (14K): [in this window] [in a new window]   Fig. 8.   Computed hysteresis loops of instantaneous blood PCO2 vs. pHo as blood recirculates between lungs and tissues corresponding to 5 mg/kg Actz and with Ai = 110 ("nominal value" corresponding to 98.5% inhibition of red cell CA activity) or Ai = 33 (corresponding to 99.95% inhibition of red cell CA activity). L, T, a, at, vt, mv, ABG, and VBG have same meaning as in Fig. 6 and correspond to results with Ai = 110 (same as Fig. 7B). L, T, (a), (at), (vt), (mv), (ABG), and (VBG) represent analogous values for results obtained using Ai = 33. See Fig. 4 legend for values of input parameters, measured and calculated CO2 and O2, and measured and calculated equilibrated arterial and mixed venous blood gas/pH parameters for Ai = 110. For Ai = 33, values are as follows: PACO2 = 26.6 Torr, PAO2 = 100.0 Torr, tissue PCO2 = 53.2 Torr, tissue PO2 = 42.0 Torr. Measured values for this simulation are as follows: CO2 = 92.0 ml/min, O2 = 119.0 ml/min, PaO2 = 94.0 Torr, PaCO2 = 33.3 Torr, pHa = 7.37,  = 45.0 Torr,  = 38.4 Torr, pH = 7.34. Model-computed values for Ai = 33 are as follows: CO2 = 95.3 ml/min, O2 = 110.0 ml/min, PaO2 = 100.5 Torr, PaCO2 = 40.0 Torr, pHa = 7.39,  = 42.3 Torr,  = 45.2 Torr, pH = 7.36.

View larger version (14K): [in this window] [in a new window]   Fig. 9.   Computed hysteresis loops of instantaneous blood PCO2 vs. pHo as blood recirculates between lungs and tissues corresponding to 100 mg/kg Actz and with Ai = 2.3 ("nominal value" corresponding to 99.95% inhibition of red cell CA activity) or Ai = 1.0 (corresponding to 100% inhibition of red cell CA activity). See legends to Figs. 6 and 8 for definition of abbreviations; see Fig. 5 legend for values of input parameters, measured and calculated CO2 and O2, and measured and calculated equilibrated arterial and mixed venous blood gas/pH parameters for Ai = 2.3. For Ai = 1, values are as follows: PACO2 = 22.8 Torr, PAO2 = 110.0 Torr, tissue PCO2 = 62.3 Torr, tissue PO2 = 45.3 Torr. Measured values for this simulation are as follows: CO2 = 72.0 ml/min, O2 = 104.0 ml/min, PaO2 = 112.8 Torr, PaCO2 = 38.9 Torr, pHa = 7.29,  = 45.2 Torr,  = 46.3 Torr, pH = 7.27. Model-computed values for Ai = 1 are as follows: CO2 = 67.5 ml/min, O2 = 95.0 ml/min, PaO2 = 110.8 Torr, PaCO2 = 44.6 Torr, pHa = 7.26,  = 45.1 Torr,  = 48.5 Torr, pH = 7.24.

Limitations of experimental methods and mathematical analyses. Quasi-steady-state CO₂ at the end of the experimental period (generally 4 h), 60 min after a cumulative dose of 100 mg/kg Actz, was ~10-15% lower than at the initiation of the experiments (Table 2). This could be due to inadequate time to reach a true steady state or a global reduction in metabolic CO₂ production. The latter could be due to pentobarbital anesthesia (3), a slight lowering of animal core temperature, or a depressive effect of systemic acidosis on glycolysis. Cardiac output generally remained constant throughout the experimental period, except during the last 60 min, when there tended to be a decrement of 10-15%.

Summary. Progressive inhibition of vascular plus red cell CA activity was associated with stepwise increments in the equilibrated (-A)PCO₂. The maximum decrements in CO₂ were 10% at 5 mg/kg Actz, 24% at 20 mg/kg Actz, and 26% at 100 mg/kg Actz, without full recovery of CO₂ at 1 h postinfusion. Equilibrated Pa_CO2 overestimated PA_CO2, and tissue PCO₂ was underestimated by the measured . Model computations, used to predict the kinetics of steady-state intravascular PCO₂ and pH equilibration as blood travels around the circulation during different levels of CA inhibition, indicate hysteresis loops of the instantaneous CO₂--H⁺ relationship and in vivo blood PCO₂-pH relationship due to the finite reaction times for the CO₂--H⁺ reactions. The shape of the hysteresis loops is affected by the extent of Actz inhibition of CA in red blood cells and plasma.