Influence of increased metabolic rate on [13C]bicarbonate washout kinetics.

Influence of increased metabolic rate on r”C]bicarbonate washout kinetics. Am. J. Phvsiol. 259 (Regulatory Integrative Comp. Physiol. 28): Rl63- Rl?l, 1990.-The effect of changes in metabolic rate on the dynamics of CO, exchange among its various compartments in the human body is not well understood. We examined COz dynamics in six healthy male subjects using an intravenous bolus of [ “‘Clbicarbonate. Subjects were studied while resting, during light exercise [50% of the lactate threshold (LT), 3-4 times resting 0, uptake (VOW)], and during moderate exercise (95% of the LT, 6 times resting VO,). The sum of three exponential terms well described the washout of 1’3C02 in ex- haled breath both at rest and during each exercise level despite substantial increases in metabolic rate accompanying the ex- ercise studies. Average recovery of “‘C label rose from 67% during rest to 80% during light and moderate exercise (P < 0.01). The estimate of CO, elimination (ho2) calculated from the washout parameters and

Influence of increased metabolic rate on r"C]bicarbonate washout kinetics. Am. J. Phvsiol. 259 (Regulatory Integrative Comp. Physiol. 28): Rl63-Rl?l, 1990.-The effect of changes in metabolic rate on the dynamics of CO, exchange among its various compartments in the human body is not well understood.
We examined COz dynamics in six healthy male subjects using an intravenous bolus of [ "'Clbicarbonate.
Subjects were studied while resting, during light exercise [50% of the lactate threshold (LT), 3-4 times resting 0, uptake (VOW)], and during moderate exercise (95% of the LT, 6 times resting VO,). The sum of three exponential terms well described the washout of 1'3C02 in exhaled breath both at rest and during each exercise level despite substantial increases in metabolic rate accompanying the exercise studies. Average recovery of "'C label rose from 67% during rest to 80% during light and moderate exercise (P < 0.01). The estimate of CO,elimination (ho2) calculated from the washout parameters and corrected for recovery was in very good agreement with the VCO~ directly measured simultaneously breath by breath (r = 0.993, SE for VCO~ = 0.079 l/min).
By use of a three-compartment mammillary model, the quantity of CO, in the central pool (Q1) doubled from rest to light exercise (233 & 60 to 479 t 76 mmol, P < 0.01) but did not change further with moderate exercise (458 & 74 mmol). Rate constants for exchange between pools and for irreversible loss from the system tended to increase with metabolic rate, but there was large variation in the responses. We conclude that the compartmental dynamics of CO, transport and storage are very sensitive to changes in metabolic rate induced by exercise. stable isotope; carbon dioxide transport; mammillary model; compartmental analysis; gas exchange THE STORES of OQ in the body are relatively small; consequently, changes in O2 uptake (VOW) observed at the mouth parallel closely the simultaneous utilization of O2 in metabolism by the various tissues of the body (2). In contrast, the body stores of COa are large, so that changes in the metabolic production of COa are not instantaneously translated to changes in CO, elimination (ko,) at the mouth (13). These stores of COz and their effect on COB transport in health and disease are not well understood.
CO? stores have been studied in the intact organism by the intravenous administration of radioactive ' C-, 14C-, or nonradioactive "C-labeled bicarbonate (6,19,31). The subsequent washout of bicarbonate as labeled CO, in the breath during resting conditions typically has been described by the sum of three exponential terms (19,20,23,32,35), implying the presence of at least three major classes of kinetically distinct processes or pools, which affect the dynamics of %oz at the mouth. These processes have been interpreted to represent washout of bicarbonate from a central pool in communication with two different tissue pools of bicarbonate with different perfusions (13,19). Because exercise produces both an increased metabolic production of CO2 and also significant changes in blood flow to several organs, we predicted that exercise would have a profound effect on the kinetics of bicarbonate washout. We also wondered how exercise affects the following two aspects of CO2 dynamics relevant to the evaluation of the oxidation of C-labeled substrates to COz: recovery of label and the average time a COz molecule would reside in the exchanging CO2 pools before being eliminated from the bicarbonate system (mean residence time; MRT). Recovery of injected bicarbonate as labeled CO, in the breath during resting conditions has been found to range between 50 and 90% (6, 11, 19-21, 34, 35) and is reported to decrease slightly with very mild exercise (31). No information is currently available regarding the effects of a wide range of metabolic rates on recovery of injected C-labeled bicarbonate or on MRT. To evaluate the influence of exercise on the dynamics of bicarbonate flux in the body and washout in the breath, we measured the washout of intravenously injected [I%] bicarbonate as breath '"CO, during the following three metabolic states: rest, light exercise (three-to fourfold increase in metabolic rate), and moderate exercise (up to sevenfold increase in metabolic rate, but below an intensity that would result in sustained metabolic acidosis from lactic acid accumulation).

METHODS
Subjects. Six male volunteers, aged 21-34 yr, gave informed consent to participate in the study. Each was free from known cardiopulmonary or metabolic disease at the time of testing. All were physically active but none were undergoing extensive endurance training. ProtocoL. Each subject performed a progressive cycle ergometer test to volitional fatigue, from which VoZmax and the lactate (or anaerobic) threshold (LT, the maximum VO, achieved before lactate begins accumulating significantly in the blood) were determined noninvasively from gas exchange and ventilatory patterns measured on a breath-to-breath basis as described below. Work rate on the cycle ergometer was increased in a ramp fashion by 30 W/min, following a 4-min period of unloaded cycling. Subject characteristics and Tjozmax are given in Table 1.
[ 'YJ]bicarbonate washout kinetics were subsequently determined on separate mornings under one of the following three conditions: seated rest or during cycle ergometry at either 50 or 95% of the LT. The washout experiments in each subject were separated by -1 wk. The experiments were performed in the morning, with the subject fasted for lo-12 h. Within 12 h before each turnover experiment, a 588 mM solution of NaH"'C03 (Merck Sharp & Dohme lot no. 1931-L, 99.0%) in saline was made and sterilized by filtration. Chemical purity of the labeled bicarbonate was determined separately by back-titration with 0.05 N HCl, while the isotopic enrichment was confirmed by independent 13C nuclear magnetic resonance. For the studies at rest, the subject sat in a chair in the lab for 0.5 h before the start of the experiment and for the subsequent 4 h during the experiment. At time 0 a bolus injection over 5 s, containing 1.176 mmol [Wlbicarbonate was made into an antecubital vein. Aliquots of exhaled gas (60 ml) for subsequent analysis for "'COz (described below) were drawn from the exhaled port of the breathing valve into plastic syringes and promptly sealed. Samples were drawn over 10 s, with the midpoint corresponding to the sample time, at the following times: -5 min before the injection and 1, 3,5,i,9,12,15,20,30,60,90,120,150,ISO.,210, and 240 min after injection. Metabolic rate (as Voz and VCO~) was measured breath by breath for a 5-min period every hour during the rest experiments. To avoid any transient hyperventilatory responses, subjects were placed on the mouthpiece at least 1 min before collection of the "COz breath samples or measurement of ho2.
In preliminary studies we observed a more rapid washout of 'COz during exercise, which reduced our ability to describe the components of the washout kinetics using the rest protocol. Therefore, a larger dose of labeled sodium bicarbonate (1.765 mmol) was administered for the exercise studies, and samples were obtained at more frequent intervals. The injection was made 20 min after Samples of exhaled gas were taken for determination of '"COJ'"CO, at time 0 (20 min into exercise) and at 1,2,3,4,5,6,8,10,12,15,20,30,45,60,75,90,105, and 120 min after injection. Vo2, VCO~, and heart rate were measured during exercise from 20 min before the injection to 20 min after injection and subsequently for 5-min intervals every 30 min after injection.
Measurement of pulmonary gas exchange. The subjects breathed through a low-impedance turbine volume transducer and breathing valve with a combined dead space of 170 ml. A three-way respiratory valve, followed by a respiratory hose with a dead space of -1 liter, was placed on the expiratory side of the breathing valve for sampling of expired gas for 'CO,. Mouth 0, and CO, tensions were determined by mass spectrometry from a sample drawn continuously from the mouthpiece at 1 ml/s. The inspired and expired volume and gas fraction signals underwent analog-to-digital conversion, from which Vo, (STPD), VCO~ (STPD), and minute expired ventilation (VE; BTPS) were calculated on line with each breath, as previously described (4). The effect of the breathing valve on these calculations was evaluat.ed by comparison with bag collection. A calibration factor was then used to obtain the final VO, and VCO~ reported here. Using this calibration factor, the SE values for ho2 and VO, were 27 and 45 ml, respectively. Heart rate during exercise was measured beat by beat using a modified V5 lead electrocardiogram.
Analysis of exhaled gas for "'CU2/"C02. The CO, was isolated from the breath samples before analysis by ion ratio mass spectrometry by passage through a trap in dry ice (to remove water vapor) and then condensed in a trap in liquid nitrogen, allowing other gases to be evacuated (7). The CO, collected from the liquid nitrogen trap was further purified by passage over Cu turnings and MnOz powder before isotopic analysis. This combined method of collection, isolation, and analysis led to greater precision (reduced variability) compared with commercial procedures. The ratio of "'CO,/'"CO, in the exhaled gas samples was det,ermined with a Nier 60" double-collecting ion-ratio mass spectrometer, as modified by . The ratio is reported in units of' S"'CO&, relative to the PDB (Belemnitella americana) standard (1.1235% ':'C) and is defined as PC( %n) = ("C/W) sample ("'C/"C) standard -1.0 1 x 1,000 (I) The value of the base line was subtracted from each value collected after injection of the ["'Cl bicarbonate, yielding a net change in 6 (delta over base line; DOB). DOB can be converted to an equivalent excess specific activity (excess 'COz/total CO,) by multiplying DOB by 1.123 x lo-?
General regression analysis of DOB data. For subsequent noncompartmental and compartmental analyses, it was necessary to find an empirical model that best fit the DOB washout data. The empirical models were se- (2) DOB = i A@ + Lo t + C (5) '= where n = 1, 2, 3, or 4'. Thus 16 candidate models were evaluated for each washo ut experiment. The Ai, Xi, L, and C are referred to as the macropara .meters of the model where Ai is the coefficien t and Xi the rate constant for the exponenti al process, L is the slope for a linear term, and C is a constant offset. Previous studies (1% included the linear trend (L) and constan t offset (0 terms in Eqs. 3-5. For a specific candidate model with fixed value-of n, the best fit to the washout data was found using the weighted least squares (WLS) programs BMDPAR and BMDP3R (10). An optimal weighting scheme was used, namely weighting each datum inversely proportional to the measurement variance at that time (24). Preliminary analysis of residuals suggested that measurement error variance was approximately proportional to the square root of the observed DOB value. Alternate weighting schemes, including unweighted least squares, gave similar results to those reported below, suggesting robustness of our l/JDOB weighting scheme. The BMDP programs provide point estimates and asymptotic standard errors for the model parameters and also for desired functions of the model parameters [e.g., area under curve (AUC) and MRT].
Because Eqs. Z-5 are from a series of nested models, the choice of-the best fitting model was made by appropriate comparisons among the WLS fits of the 16 candidate models using an F test (5, 24) and assum ing Gaussi .an errors. When co mparin .g two ne Isted models, we hypothesized that the simpler model is the true model and rejected this hypothesis in favor of the more complex model if the F statistic was sufficiently large (e.g., P < 0.05). For confirmation, we also used the Akaike Information Criterion and the Schwartz Criterion (24) to compare all 16 candidate models simultaneously. These results were very similar to the F test.
Noncompartmen tal analysis of washout kinetics. From the washout curve for 13C02 in the breath '9 the following three important quantities were estimated: AUC, recovery of injected label, and the MRT. AUC was calculated by integrating to time = 00, the best fit regression equation for each washout experiment after subtracting out any linear trend or constant offset terms. For purely exponential models (from Eq. 2) this was equal to i=l These regression-based AUC estimates compared well with results calculated directlv from the DOB data using the trapezoidal rule with a single exponential extrapola-the trapezoidal rule with a single exponential extrapolation of the tail. tion of the tail.
Recovery was calculated as Recovery was calculated as where AUC is in units of DOB. min, 1.123 X 10e5 converts DOB to the fractional enrichment of total CO2 with added 13C02, ho2 is the measured rate of CO2 elimination at the mouth in millimoles per minute, and Do is the dose in millimoles of [13C]bicarbonate injected at time 0.
where AUC is in units of DOB. min, 1.123 X 10e5 converts DOB to the fractional enrichment of total CO2 with added 13C02, ho2 is the measured rate of CO2 elimination at the mouth in millimoles per minute, and Do is the dose in millimoles of [13C]bicarbonate injected at time 0.
MRT for the whole bicarbonate system indicates the average time a labeled COn molecule, introduced into the .tral compartment as in remain in exchanging bicarbonate .g irreversibly lost either into the breath or via unaccounted loss. MRT was estimated from the washout curves as the area under the moment curve (AUMC) divided by the AUC (9), assuming that the system is linear and stationary, MRT for the whole bicarbonate system indicates the average time a labeled COn molecule, introduced into the ten central compartment as in this study, would remain in this study, would the the exchanging bicarbonate system before being irrevers-system before bein ibly lost either into the breath or via unaccounted loss. MRT was estimated from the washout curves as the area under the moment curve (AUMC) divided by the AUC (9), assuming that the system is linear and stationary, that there are no COe-bicarbonate traps within the exchanging system, and that CO2 is eliminated only from the central pool. For the purely exponential model, that there are no COe-bicarbonate traps within the exchanging system, and that CO2 is eliminated only from the central pool. For the purely exponential model, AUMC = Z(Ai/Xf). data were adequately described we analyzed the data using a Compartmental analysis. Assuming that the washout by a sum of exponentials, linear, m .ammillary compartmental system. For example, washout data with three exponentials would correspond to a three-pool 1; e.g., plasma) and two peripheral pools connecting only to compartment 1. Assuming tracer entry and CO2 loss is only via the central pool, this model is diagrammed in Fig. 1, where kG is the first order rate constant for transfer to pool i from pool j, Qi is the steady-state quantity of unlabeled CO, stores in pool i, and bl (not shown) is the fractional elimination rate for total irreversible loss of CO, from the central pool. Because recovery of label as Compartmental analysis. Assuming that the washout data were adequately described by a sum of exponentials, we analyzed the data using a linear, mammillary compartmental system. For example, washout data with three exponentials would correspond to a three-pool model with one central pool model with one central pool (compartment 1; e.g., (compartment plasma) and two peripheral pools connecting only to compartment 1. Assuming tracer entry and CO2 loss is only via the central pool, this model is diagrammed in Fig. 1, where kG is the first order rate constant for transfer to pool i from pool j, Qi is the steady-state quantity of unlabeled CO, stores in pool i, and bl (not shown) is the fractional elimination rate for total irreversible loss of CO, from the central pool. Because recovery of label as 13C02 in the breath was not lOO%, this implied loss of 13C label through nonrespiratory pathways as well as in the breath. lZBl is thus defined as the rate constant for the measured loss from the central pool in the breath, and FzLl is the rate constant for unobserved loss from the central pool via nonrespiratory mechanisms; thus kB1 + kLl = bl. We assumed that DOB data represented direct measures of 13C02 enrichment (specific activity) in the central pool (11,19,20,23). The peripheral pools were indexed such that klz > k13, so that pool 2 was considered the rapidly exchanging pool and pool 3 was a slowly exchanging site. The microparameters kG and central CO2 stores Q1 are identifiable from the DOB data and were found explicitly as functions of the macroparameters of the sums of exponentials model (25).
As we do not know the exact site(s) for entry of unlabeled endogenous COn into the system, it is not possible to explicitly estimate the peripheral quantities of COz (&z and Q3) and thus the total CO2 in the system (9). However, upper and lower bounds for Q2 and Q3 may be derived for the three-pool model. With  It can be shown that Qtl < Qt < Qt3, where Qt is the true value of Q1 + Qz + Q3 (i.e., the total COe).
Other statistical analyses. Analyses comparing SE of macroparameters and microparameters within an individual to variability across subjects tended to show that population variability was much greater than estimation variability.
Therefore, each summary measure across subjects of parameters, MRT, AUC, etc. is reported by the simple unweighted sample mean t sample SD. The effect of metabolic rate on the various parameters of the 13C02 decay curves and on the resulting mammillary model parameters was assessed by analysis of variance with repeated measures. Significant differences between the means were further evaluated using paired t tests. Significance was declared for P c 0.05 after Bonferroni correction for multiple comparisons. Linear regression was used to examine any relationship between recovery of 13COz in the exhaled breath and total VCO~.

RESULTS
Metabolic responses. The group mean for average Tjo2 over 4 h of rest was 281 t 20 ml/min and for ho2 was 216 t 15 ml/min (9.7 mmol/min: Table 2). Light exercise caused a three-to fourfold increase in both variables; mean average iTo was 929 t 133 ml/min, while VCO~ increased to 840 t 113 ml/min (37.7 mmol/min).
Moderate exercise increased Vo2 on average six times over rest (to 1,750 t 420 ml/min) and ho2 over seven times above resting values (1,639 t 454 ml/min or 73.6 mmol/ min). Light exercise represented 53% of the LT, or 30% Of ~fhrnax, while moderate exercise equated to 95% of the LT, or 57% of VOzmax.

Model identification.
The results from a typical washout experiment at each metabolic rate in one subject are shown in Fig. 2. Note that the washout dynamics at different metabolic rates were clearly distinguishable from each other and that even a mild increase in CO* production associated with light exercise caused a marked increase in the rate of loss of 13C02 into the breath. All 18 washout curves were well described by the sum of three exponential terms with no linear or constant terms (Eq. 2), as found previously by several investigators (19,20,23,(30)(31)(32)35). In 12 of these experiments, Es. 2 with n = 3 was also the statistically best description of the data DOB = Alo e"it + A2 .exzt + A3 .ehst (12) Whereas Ea. 12 resulted in excellent fits in the remaining six washout experiments, four of these curves were better fit statistically by the sum of four exponential terms (Eq. 2 with n = 4). These four more complex models were found in only two subjects, subject 3 (light and moderate exercise) and subject 6 (rest and moderate exercise). Two other experiments were best described by the sum of three exponentials plus a small constant offset term (Eq. 4 with n = 3). This occurred in subject 4 (moderate exercise) and subject 6 (light exercise).
When a three-compartment mammillary model was compared to a four-compartment model for the four data sets for which a sum of four exponentials was the better fit, it appeared that the fast peripheral pool of the threecompartment model had split into two intermediate pools, with little change associated either with the central pool or with the slowest peripheral pool. In addition, the dynamic characteristics and quantity of CO2 in the entire exchanging system were similar between the three-and four-compartment models for the same data sets. For purposes of comparison, therefore, we chose to utilize the three-exponential description of the washout (Eq. 12) for all data sets in order to estimate noncompartmental parameters (e.g., AUC and MRT) and for deriving compartmental information.
In all cases, the effect of increased metabolic rate with exercise on the washout and model parameters was much greater than any changes in the parameter estimates due to an extra constant or exponential term.
Washout characteristics and noncompartmental analysis. Table 2 gives the work rate performed by each subject, the resulting VCO~, and the parameter estimates for Eq. 12 for each of the three metabolic conditions. Asymptotic standard errors of the parameter estimates were generally much smaller than the standard deviation across subjects. Increased VCO~ associated with exercise resulted in significant reductions in Al, Aa, and all three   3. Interestingly, while there was a tendency for the rate constants to increase with light exercise over rest, these differences were not statistically significant; only moderate exercise resulted in significant speeding of the exchange dynamics. All of the rate constants except ksl were significantly greater during moderate exercise than during rest, whereas all but Fzsl and Fz13 were also greater than the corresponding values for light exercise (Table  3) 'In contrast to the changes in rate constants with exercise, the quantity of exchangeable COn in compartwlent 1 ( Q1) rose dramatically with light exercise (from 234 t 60 to 479 t 76 mmol, on average, P < 0.01) but did not change further with additional increases in metabolic rate (458 t 74 mmol) ( Table 3). As discussed in METHODS, the quantities in pools 2 and 3 can only be bounded by lower and upper limits (Qmin and Qmax for each pool). Mean estimates for COa in the "fast" pool 2 ranged from 176 to 247 mmol at rest, from 267 to 428 mmol during light exercise, and from 226 to 421 mmol for moderate exercise. Ranges for COe in the "slow" pool 3 were 496-947 mmol, 557-1,616 mmol, and 674-2,261 mmol for rest, light exercise, and moderate exercise, respectively. Table 3 also lists estimates for the total exchangeable COa in all three compartments under three possible conditions; all of the natural 'metabolic production of COa occurs either in pool 1 ( Qtl), pool 2 ( Qtz), or pool 3 (QtJ. If endogenous COa production is spread among the pools (e.g., one-third in each), then total exchangeable CO2 at steady state equals the appropriate weighted average of the Qti (e.g., ZQtJ3). If the fractional distribution of endogenous COn production among the three pools remains constant with increasing metabolic rate, then two important observations can be made from  Values are means 2 SD. ki;, rate constants for transfer to POOL i from pool j in min-l; Qi, quantity of CO2 in ~001 i in mmol; Qmaxi and Qmini, upper and lower limits of quantities of CO2 in pool i; Qti, total quantity of CO2 in pool i in mmol given endogenous CO2 production only in pool i. Estimation error is average across all 3 metabolic rates of the asymptotic SE values expressed as % of the estimate (i.e., coefficient of variation). * P < 0.05 vs. rest; t P < 0.05 vs. light exercise; $ P < 0.01 vs. rest; Q P < 0.01 vs. light exercise. in in CO2 stores with exercise. If endogenous source of CO2 production changes from compartment 3 at rest to compartment 1 during moderate exercise (dashed line), there is virtually no change in total CO2 stores (1%). Conversely, if the endogenous source of CO2 changes from compartment 1 at rest to compartment 3 with moderate exercise, total CO2 increases over 17 liters (337%; solid line). Note, however, that no negative changes (i.e., loss of C02) are predicted. endogenous COz, total exchangeable COB increases dramatically with exercise and 2) the preponderance of change is from rest to light exercise, with a slight, nonsignificant further increase in total COe from light to moderate exercise. This is shown graphically in Fig. 4A, where the mean values for Qtl, Qtz, and Qtg are plotted at the three average metabolic rates.
The rate of total VCO~ (&Q1) is analogous to clearance and can be estimated noncompartmentally from the washout data (dose divided by AUC)(S). However, clearance will be greater than the * measured SCOT because recovery is less than 100% [i.e., izol&1 estimates all loss of label, both in the breath and any nonrespiratory (unmeasured) loss]. Figure 5 shows the clearance data, corrected for the average recovery at rest (0.67) or exercise (0.80), as a function of the meas-ured VCO~ at the mouth, both in units of liters CO2 excreted per minute. The dashed line is the line of identity. Correction by the average recovery led to a very good prediction of the measured VCO~ from the washout characteristics (r = 0.993, SE for ho2 = 79 ml/min).

DISCUSSION
In the present study, washout of labeled bicarbonate was consistently and sufficiently well described by the sum of three exponential terms across a wide range of metabolic rates. In contrast, Irving et al. (19) found a small linear term suggesting a base-line drift, in addition to the three exponential terms, in their study of subjects at rest, which they attributed to changes in oxidative substrate mix, since carbohydrate and lipid differ slightly but measurably in 13C/12C (29). However, this term was only detectable between 4 and 6 h after the bolus injection of labeled bicarbonate. In the present study, respiratory quotient (RQ) (VCO~/V,Z) fell slightly on average from 0.88 to 0.72 over the first 2 h of rest experiments and from 0.91 to 0.85 during the 2 h of moderate exercise, with no consistent change during the light exercise protocols. This small change in RQ would suggest a change in background '"C02/'"C02 of only l-2%0 (3, 29). However, no significant linear drift components to the washout characteristics were found in any of the 18 individual experiments in the present study. In addition, the infrequent occurrence (2 of 18) and small size (l-2 DOB) of the constant term suggest that it is most likely not a fundamental component of the washout characteristics.
There remains uncertainty regarding the physiological correlates of the three-compartment mammillary model derived from the washout of labeled C02. The earliest observers (15,23,30,32) speculated that the capillary and cellular membranes represented a significant diffusion barrier for CO2 equilibration between extra-and intracellular spaces. Thus the central compartment represented vascular and extracellular bicarbonate, the fast peripheral compartment was intracellular bicarbonate of soft tissues, and the slower peripheral compartment, when observed, was bone carbonate.
In contrast, other investigators have suggested a perfusion-limited, organ-based model (13,19,31,35), in which the central compartment represents vascular and possibly some interstitial bicarbonate and the two peripheral compartments are composed of tissues distinguishable by different perfusions. The tissue compartment with relatively fast exchange with the central co mpartment under restin .g conditi .ons is assumed to represent metabolically active tissue with high perfusion (heart, brain, kidney, etc.), while the slower equilibrating pool is hypothesized to consist primarily of resting skeletal muscle, which has a relatively low perfusion at rest. Exchange of labeled bicarbonate with bone carbonate was envisioned to represent an essentially unidirectional loss of label over the course of a typical experiment (several hours). This interpretation is based on the electrical analog model of Farhi and Rahn (13) and is consistent with the observation that the initial ability of the body to store CO2 with rebreathing is greater when perfusion to resting skeletal muscle is increased either by vascular denervation or increased metabolic rate (16). It is interesting to note, however, that washout of solutes (28) or inert gases (27) from isolated, resting skeletal muscle demonstrates multiexponentiality, which would argue against the simple electric analog model of Farhi and Rahn (13). Thus, the precise physiological location of the three compartments remains unresolved.
The increase in Q1 seen with mild exercise may reflect an increase in total CO2 content within the bicarbonate system or a shift of bicarbonate from one of the two peripheral pools into the central pool. This large increase in Q1 is not consistent with the hypothesis that membrane transport of C02-bicarbonate is the rate-limiting process in CO2 exchange. Rather, these findings support the notion that perfusion is an important determinant of exchange, especially if the additional bicarbonate in the central pool is associated with the contracting skeletal muscles. However, if tissue perfusion, per se, was the sole limiting factor governing CO2 exchange, one would predict a linear increase in Q1 with increasing metabolic rate, which would parallel the known linear rise in blood flow which accompanies increases in metabolism (14,22). This, in fact, did not occur. An alternative interpretation is that with even small increases in metabolic rate above rest, most or all of the muscle capillaries [known to be partially closed under resting conditions (IS)] are "recruited" (i.e., opened), so that the diffusion surface approaches its maximum and the resistance to exchange for CO2 between the intracellular pool and the vascular compartment is minimized (16,18).
In contrast to the shift from rest to mild exercise, the bicarbonate model predicts that the greater rate of VCO~ elimination with moderate relative to light exercise is associated solely with an increased rate of fractional elimination from the central pool (as hl) with no further increase in the amount of CO2 in that pool (Ql). This suggests that convective processes (e.g., blood flow and pulmonary ventilation) may play a greater role in facilitating removal of CO2 from the blood to the environment at this level of exercise.
If it were known in which pool(s) the endogenous production of CO2 occurred in vivo, then the total mass of exchangeable CO2 in the three pools could be explicitly defined. However, this information can not be derived from the washout data alone (9); hence, only lower and upper bounds could be estimated for CO2 in the two peripheral pools and, thus, for total exchangeable CO2. If all of the metabolic production of CO2 occurs in the central compartment, then the total quantity of CO2 is R170 METABOLIC RATE AND BICARBONATE KINETICS explicitly defined by Qtl (Eq. 9), can be estimated noncompartmentally as the product of MRT and VCO~, and represents the minimum possible total COa content. If endogenous production of CO2 occurs in one of the peripheral compartments, with clearance remaining only from the central compartment, then the enrichment of the various COa pools will not be uniform. In this case, the total COZ in the system is greater than Qtl, with production of COz entirely in the slow pool (compartment 3) yielding the largest estimate of exchangeable COZ (Qt3). This is reflected by a 50% range in the estimates of total COa between Qtl and Qtg for the rest condition and by a range of 121% for moderate exercise (Table 3 and Fig. 4).
Similarly, the effect on the total COZ content of increased COZ production with exercise can be bounded but not calculated precisely. This is shown diagrammatically in Fig. 4B, where Qtl and Qtg have been plotted as functions of metabolic rate. For each metabolic rate, Qtl represents the minimum and Qtg the maximum estimate of total exchangeable COZ in the three pools. Depending on the hypothesized source of endogenous COZ, increases of 1% (Qt3 at rest to Qtl for moderate exercise, dashed horizontal line in Fig. 4B) up to 337% (Qtl rest to Qtg for moderate exercise, solid vertical line) can be derived for the increase in body CO2 with exercise. Independent estimates of the increase in COn stores with exercise would shed considerable light on this current uncertainty.
Recovery of injected or infused labeled bicarbonate as COa in the breath has been reported to range from 50 to 90%, whether the species is man (1,6,(19)(20)(21)31,34,35), dog (II), or cat (23). We found that recovery increased during mild exercise but did not rise further when metabolic rate was increased with moderate exercise. Similarly, Van Aerde et al. (33) found in newborn infants a variable (r = 0.64) but significant (P < 0.01) increase in recovery of 13C02 (from 70 to 84%), which was proportional to resting metabolic rate over a small range, from 5 to 7.5 ml kg-'*min? Slanger et al. (31) found that recovery fell, on average, from 83% at rest to 73% with very mild exercise (60% increase in VCO~), but this was not statistically significant (our analysis).
Unaccounted loss of labeled bicarbonate (&) was assumed by us and others (19,31,35) to occur from the central pool; this meant that all of the model rate constants (izij values) were identifiable. If loss occurred from compartments 2 and/or 3 only upper and lower bounds rather than explicit values for the rate constants associated with that pool can be found (8,25). Physiological processes that may represent effective loss of labeled bicarbonate over the course of an experiment include: 1) loss of labeled CO2 in the breath with the first pass of venous blood through the lungs (12), 2) true, irreversible loss of bicarbonate directly into the urine, sweat, or urea (23), and/or 3) transfer into alternate pools whose turnover is so slow as to represent effectively unidirectional flux over the course of the experiment, such as incorporation into bone (23) or macromolecules (17). Loss of labeled COZ with the first pass through the lungs is equivalent to a reduction in the injected dose by that amount of label. Kornberg et al. (23) found in the resting, anesthetized cat that 6% of injected [14C]bicarbonate label was found in bone after 5 h, while 3% remained as urea. Irving et al. (19) estimated that bone sequestering of bicarbonate label could be as high as 13% over 4 h of rest in humans. While incorporation of labeled bicarbonate specifically into blood glucose is low (1%; 17), accumulation of label by other moieties of intermediary metabolism could be quantitatively important. We have shown here that across subjects and a wide range of metabolic rates without metabolic acidosis, labeled COn washout dynamics generally exhibit triexponential decay. In addition, recovery of label increased with a modest increase in metabolic rate during mild exercise but did not change further during moderate exercise. We also found that metabolic rate as ho2 could be accurately predicted from the washout curve for 13C02. Finally, the three-compartment mammillary model constructed from the washout curve allowed us to evaluate the effects of increased metabolic rate with exercise on CO2 pool dynamics within the body. Characterization of the washout of labeled bicarbonate thus yields substantial information regarding the bicarbonate storage/transport system.