INTRODUCTION

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THE HALDANE EFFECT (HE) is a physicochemical phenomenon involving an increase in blood CO₂-combining capacity, with opposite changes in dissolved CO₂ and PCO₂, as a consequence of oxyhemoglobin (HbO₂) desaturation (3). Although HE is an important component of circulatory and gas-exchange interactions, especially in circulatory and respiratory failure, its relevance is not commonly emphasized. This is due to a lack of easily available methods for its quantification, which involves complex mathematical procedures and models. In particular, an unsolved problem in physiological studies and in clinical monitoring is the inability to convert easily changes in blood O₂ saturation and O₂-linked CO₂ binding into the corresponding changes in dissolved CO₂ and PCO₂. This paper describes the results of a study performed on a large series of patient measurements to develop a new computational method for this purpose and to quantify the impact of HE on venous PCO₂ (Pv_CO2, Torr) and venoarterial PCO₂ difference [(v-a)PCO₂, Torr].

	METHODS

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Measurements (247) performed in 91 patients were processed. Patients were 53 ± 18 (SD) yr of age, with a body weight of 64.3 ± 12.8 kg, and a body surface area of 1.72 ± 0.19 m². There were 73 patients with intra-abdominal sepsis, 11 had retroperitoneal abscesses, 6 had cholangitis, and 1 had gangrenous fasciitis; 39 patients survived and 52 died of respiratory or multiple organ failure, myocardial depression or infarction, or pulmonary embolism. Sepsis severity score (5) ranged from <10 to >20, with a normal Gaussian distribution and a mean ± SD of 15.8 ± 4.0. This patient population provided a continuous distribution of observations, from relatively compensated to extremely diseased states with shock, which allowed for a detailed quantification of the magnitude of HE over a wide spectrum of cardiorespiratory and metabolic abnormalities (Table 1).

The measurements, all performed for clinical purposes and in accordance with institutional guidelines, were based on the simultaneous analysis of arterial and mixed-venous blood gases. From these, arteriovenous difference in Hb-bound O₂ [(a-v)HbO₂, ml/dl blood] was calculated from O₂ saturation difference and Hb concentration, with Hufner's coefficient of 1.36 ml O₂/g Hb. The venoarterial CO₂ concentration difference [(v-a)CO₂, ml CO₂/dl blood] was determined by a model combining the Peters-Van Slyke equation for the buffer line of plasma from arterial blood with the Henderson-Hasselbalch equation for venous plasma (9), thus calculating the following quantities on the CO₂ equilibration curve for arterial blood: 1) the increment in CO₂ concentration (CCO₂) related to the (v-a)PCO₂ increment at constant O₂ saturation by an iteration related to the Newton-Raphson procedure; 2) the further increase in CCO₂ at constant PCO₂ mediated by HbO₂ desaturation and O₂-linked CO₂ binding [(v-a)CO₂ due to HE, (v-a)CO_{2 HE}, ml CO₂/dl blood] by a complex fit to the experimental data obtained at 37°C by Klocke (15); 3) the increase in Pv_CO2 avoided by the O₂-linked CO₂ binding [reduction in (v-a)PCO₂ due to HE, (v-a)PCO_{2 HE}, Torr] by continuation of the iteration stepwise to find the increase in PCO₂ above Pv_CO2 necessary to obtain an increase in CCO₂ equal to (v-a)CO_{2 HE}.

Data processing was based on regression analysis, with analysis of residuals, skewness and kurtosis control, and a "simplest best fit" procedure that allowed selection of the simplest possible regression yielding the best control of variability of the dependent variable, based on Mallows' Cp criteria (22). Reliability of a nonlinear regression developed to estimate (v-a)PCO_{2 HE} was verified by a comparison with experimental values of (v-a)PCO_{2 HE} [(v-a)PCO_{2 exp}, Torr] obtainable from previously published studies. These included the tonometric data reported by Henderson (11) for the experiments of Christiansen et al. (3), the data of Joffe and Poulton (13) for the blood of J. J. and W. R., and also the data of Luft et al. (18) for the HE-mediated change in arterial PCO₂ (Pa_CO2) from increased O₂ breathing. The latter effect is equivalent, in terms of HE-induced changes in PCO₂, to that observed by changing O₂ saturation in venous blood (if linearity of HE at different HbO₂ saturations is assumed) (16). Because in tonometric experiments the CCO₂ values in reduced and oxygenated blood (Cr_CO2 and Co_CO2, respectively, ml/dl) were not the same, an unbiased and verifiable comparison was carried out as follows. Third-degree polynomials [y = f (x³, x², x)] were fitted pragmatically to the data for oxygenated blood (r² > 0.99 for each fit). Then, for any point measurement reported for reduced blood, (v-a)PCO_{2 exp} was determined as the difference between the PCO₂ yielded by the polynomial at a CCO₂ equal to Cr_CO2 and the PCO₂ measured in reduced blood (without extrapolations outside the range of published experiments and of PCO₂ values reported in Table 1). This corresponded to the determination of the horizontal distance between the equilibration curves for oxygenated and reduced blood for any given measured Cr_CO2. The obtained (v-a)PCO_{2 exp} values were then compared with the values of (v-a)PCO_2 HE estimated by our nonlinear regression on the basis of the (a-v)HbO₂, PCO₂, and Hct values reported in the experiments. For the data in Ref. 18, a mean Hct of 0.47 was used for all cases, and case 8 was dropped because of inexplicably large O₂-linked PCO₂ changes. A total of 34 (v-a)PCO_{2 exp} values, available for comparison from these sources, was pooled together and processed.

	RESULTS

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The (v-a)PCO₂ gradient was 5.70 ± 2.70 (SD) Torr, (v-a)CO₂ was 3.71 ± 1.45 ml/dl, (a-v)HbO₂ was 3.93 ± 1.46 ml/dl, (v-a)CO_{2 HE} was 1.06 ± 0.41 ml/dl, and (v-a)PCO_{2 HE} was 2.46 ± 0.99 Torr. Linear and nonlinear regression analyses were performed extensively on blood gas and derived variables to assess the correlates of (v-a)PCO_{2 HE} and to select the best simultaneous correlation by Mallows' Cp criteria (22). This was provided by the (Pv_CO2) following fit

(1)

where r² = 0.99, P 0.001 for whole regression and each independent variable; partial r² for (a-v)HbO₂ = 0.77 and for (a-v)HbO₂ + Pv_CO2 = 0.97.

A graphical display of the fit, with source measurements, is reported in Fig. 1. The analysis showed further that the very good correlation with (a-v)HbO₂ reflected the relevance of HbO₂ desaturation as a determinant of HE, and that the simultaneous nonlinear correlation with Pv_CO2 and Hct was mediated by the impact of these variables on the slope of the CO₂ equilibration curve. Unexpectedly, there was a lack of simultaneous correlation with pH. This was because part of the variability of (v-a)PCO_{2 HE} related to pH was already accounted for by Pv_CO2. Besides, the impact of pH on the CO₂-combining capacity of blood related to HE was balanced by a simultaneous impact on that unrelated to HE [because (v-a)PCO_{2 HE} is the horizontal distance between the equilibration curves for arterial and venous blood, changes in this distance expected from pH-mediated changes in magnitude of HE were balanced by pH-mediated changes in the slope of the curves]. This explanation was validated by use of our model within the range of distribution of our measurements; outside this range, in particular at very low pH, accuracy of the estimated (v-a)PCO_{2 HE} is likely to decrease. Reliability of the developed fit was supported by a high r² = 0.99 and a SE of estimate = 0.07 Torr, thus implicating comprehension of estimated (v-a)PCO_{2 HE} within ±0.14 Torr of the real value in 95% of cases. This was validated further by showing that actual and estimated values of (v-a)PCO_{2 HE} correlated linearly, with slope and intercept not significantly different from 1.0 and 0.0, respectively (P > 0.05 for both) and with a perfectly balanced distribution of residuals over the whole range of distribution (Fig. 2). It was verified also that Eq. 1 could be simplified further by eliminating the exponent of (a-v)HbO₂, as this involved only a slight overestimation of (v-a)PCO_{2 HE}, which never exceeded 0.25%. Comparison with the results of published experiments showed that the estimated (v-a)PCO_{2 HE} was in good agreement with (v-a)PCO_{2 exp} (7.12 ± 4.16 vs. 7.50 ± 4.65 Torr, n = 34, P > 0.05). Regression analysis also showed a good correlation between (v-a)PCO_{2 exp} and (v-a)PCO_{2 HE}: (v-a)PCO_{2 exp} = 1.04[(v-a)PCO_{2 HE}] + 0.16, r² = 0.87, P < 0.01, with slope and intercept not significantly different from 1.0 and 0.0, respectively. This was a satisfactory achievement, given the nature of the comparison (already involving by itself some uncontrolled variability) and the magnification of this variability expected from estimating large (v-a)PCO_{2 exp} values (7.50 ± 4.65 Torr) by a method developed from measurements with smaller (v-a)PCO_{2 HE} (2.46 ± 0.99 Torr).

View larger version (47K): [in this window] [in a new window]   Fig. 1.   Display of relationship among reduction in venoarterial PCO2 difference due to Haldane effect [(v-a)PCO2 HE], venous PCO2 (PvCO2), arteriovenous difference in Hb-bound O2 [(a-v)HbO2], and hematocrit fraction (Hct). Isolines for (a-v)HbO2 were obtained by Eq. 1 at different Hct values. Because (a-v)HbO2 corresponds to O2 consumption/blood flow, isolines also quantify impact of any combination of changes in O2 consumption and cardiac output on (v-a)PCO2 HE.

View larger version (33K): [in this window] [in a new window]   Fig. 2.   Correlation between actual values of (v-a)PCO2 HE and values estimated by Eq. 1, with identity line.

	DISCUSSION

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There are several implications of the assessment of HE performed in our study. The availability of Eq. 1 is important in estimating rapidly and accurately the magnitude of (v-a)PCO_{2 HE} in physiological and clinical studies without resorting to complex mathematical procedures or models. This is also useful in assessing and monitoring cardiocirculatory and gas-exchange interactions. For instance, increases in (v-a)PCO₂ in critical illness are associated with increasing severity of illness and poor prognosis, because these reflect decreases in cardiac output and circulatory failure (with larger CO₂ loading per unit blood flow) and metabolic acidosis (with reduced blood CO₂ binding and larger increases in PCO₂ for any given CO₂ loading) (1). An additional and unrecognized cause of increases in (v-a)PCO₂, and thus in Pv_CO2 for any given Pa_CO2, is the reduction of (v-a)PCO_{2 HE}. Indeed, (v-a)PCO_{2 HE} is the buffering that is exerted constantly by HE on (v-a)PCO₂ for any given (v-a)CO₂. In sepsis with impaired O₂ extraction and reduction of (a-v)HbO₂, loss of this buffering may become an important determinant of the venous hypercapnia and acidosis that characterize this stage of the disease (7, 8, 23). In fact, maximum increases in (v-a)PCO₂ and Pv_CO2 were observed in our septic patients with circulatory failure when they developed overimposed metabolic failure with impaired O₂ extraction and thus a reduction of (v-a)PCO_{2 HE}. With the exception of extreme cases, however, the buffering of pH from O₂-linked H⁺ binding has a greater general relevance than the buffering of PCO₂ (for instance, small changes in ventilation may affect Pa_CO2 and Pv_CO2 to a much greater extent than the HE). Quantifiable evidence of the O₂-linked H⁺ binding was provided by us in a previous study (8). This is obviously related to the O₂-linked CO₂ binding that has been addressed in this study; however, the two effects are not quantitatively equivalent, and their relationship has not yet been adequately assessed (16).

Use of Eq. 1 may be extended advantageously to many investigative and clinical settings in which changes in blood O₂ saturation and O₂-linked CO₂ binding must be converted into the corresponding changes of dissolved CO₂ and PCO₂. As mentioned already, (v-a)PCO_{2 HE} is the horizontal distance between the equilibration curves for arterial and venous blood. Determination of this quantity may be needed for several purposes, including, for instance, assessment of the increase in Pa_CO2 caused by the HE when inspired O₂ concentration is increased. Complex procedures are usually required for this purpose, whereas Eq. 1 may provide this quantity more simply. In fact, by substituting the increase in arterial HbO₂ due to O₂ breathing into (a-v)HbO_{2 HE} and the basal Pa_CO2 into Pv_CO2, Eq. 1 will calculate this quantity instead of (v-a)PCO_{2 HE}. Similarly, Eq. 1 may be applied to assess changes in Pa_CO2 during apneic oxygenation, rebreathing, and breath holding and in the simulation of blood CO₂ exchange under a variety of conditions. In effect, the reliability of Eq. 1 was also supported by using published results on Haldane-mediated changes in Pa_CO2 when the inspired O₂ concentration is increased (18). Although many other published experiments do not contain sufficient data for strict and direct comparisons, it may be easily verified that the impact of HE on blood PCO₂ values, as quantified in those experiments, is in good agreement with that estimated by Eq. 1. An example is provided by the tonometric results in Ref. 14, although some elaboration is needed for the comparison. This may involve calculation of Co_CO2 and Cr_CO2 from the measured pH, PCO₂, and Hct by using any general expression, including ours in Ref. 9, of the form CCO₂ = a · PCO₂ · 10^pH  pK'[1  Hct(1  r)]. Then the data of Peters and Van Slyke (21) for dCCO₂/dpH may allow estimation of the pH value at which Co_CO2 equals Cr_CO2 and of the corresponding PCO₂ in oxygenated blood. The difference with the original PCO₂ in reduced blood may finally be compared with the (v-a)PCO_{2 HE} obtained by Eq. 1, thus showing good agreement (Fig. 3). Another example is provided by the experimental results on dilutional anemia in Ref. 4. The comparison is possible, for instance, by calculating values of arterial CCO₂ and (v-a)CO₂ by the procedure used previously. Then, the data of Peters et al. (20) may allow conversion of (v-a)CO₂ into the (v-a)PCO₂ and Pv_CO2, which should be expected in the absence of HE. The difference with the actual Pv_CO2 may finally be compared with the (v-a)PCO_{2 HE} obtained by Eq. 1, thus showing again satisfactory agreement. Easier comparisons may be made with the data in Refs. 2, 12, 17, and 19, all showing agreement with the Haldane-mediated changes in PCO₂ estimated by Eq. 1 (Fig. 3).

View larger version (24K): [in this window] [in a new window]   Fig. 3.   Comparison between (v-a)PCO2 HE obtained from studies with incomplete data (see text for elaborations and assumptions) and values estimated by Eq. 1 from basic data in same studies, with identity line. Large , extreme data points (PCO2 ~28.5 and 57.0 Torr, respectively) for determinations by Kalhoff et al. (14) in fully oxygenated and reduced adult human blood. , Data points from mean values of Deem et al. (4) for 8 sets of measurements on dilutional anemia in rabbits (Hb from 11.6 to 3.9 g/dl). , Data point from relationship of Hoffmann et al. (12) in extracorporeal CO2 exchange, for (a-v)HbO2 = 4.0 ml/dl and PCO2 = 65 Torr. Small , mean (v-a)PCO2 HE for measurements by Brandt et al. (2) in apneic oxygenation. , Mean (v-a)PCO2 HE for similar measurements by Merkelbach et al. (19). , Extreme data points (PCO2 = 20 and 70 Torr, respectively) from Lenfant nomogram (17) for Hb = 16.0 g/dl and change in HbO2 saturation = 100%. Adequacy of fit may vary slightly by varying assumptions and approximations in the elaborations. It varies more for the point from Ref. 12 with increasing (a-v)HbO2 or decreasing PCO2, due likely to the peculiar setting (extracorporeal support in respiratory insufficiency) and to report of a simplified linear relationship for (v-a)PCO2 HE in the study.

Finally, as an additional implication, it should be mentioned that our formula for (v-a)PCO_{2 HE} is useful in quantifying exactly the survival advantage offered by the HE in extreme conditions (i.e., circulatory shock, severe hypercapnia, anemia) by protecting against excessive rises in (v-a)PCO₂ and thus in Pv_CO2 and tissue PCO₂. This is an important phenomenon in organs with high O₂ uptake and CO₂ release per unit blood flow, such as the heart and the brain (10). Maximum (v-a)PCO_{2 HE} in our results was close to 7.0 Torr and was 12.0 Torr in an additional case not included in the study. Although our study does not permit reliable extrapolations much above a Pv_CO2 of 70 Torr, a more relevant protection against tissue hypercapnia should be expected above such level. This is supported by the evidence that HE remains operative at high Pv_CO2 (allowing increasingly larger reductions in PCO₂) (3, 13, 24) and is also consistent with the values of (v-a)PCO_{2 HE} predictable by Eq. 1. More work is needed to verify this specific aspect in additional studies to improve understanding of the mechanisms of survival in extreme conditions.