Abstract
Adequate assessment of circulatory and gasexchange interactions may involve the quantification of the Haldane effect (HE) and of the changes in blood
PCO2
mediated by changes in HbO_{2} saturation and O_{2}linked CO_{2} binding. This is commonly prevented by the complexity of the involved calculations. To simplify the task, a large series of patient measurements has been processed by regression analysis, thus developing an accurate fit for this quantification(va)PCO2HE= 0.460 [(av)HbO2)]0.999e0.015(PvCO2)−0.852(Hct)
(n= 247, r
^{2} = 0.99,P ≪ 0.001), where (va)Pco
_{2 HE}is the reduction in venous
PCO2
(
PvCO2
, Torr) allowed by the chemical binding of CO_{2} in blood due to the HE (Torr), (av)HbO_{2} is the arteriovenous difference in Hbbound O_{2} (ml/dl), and Hct is hematocrit fraction. Values of (va)Pco
_{2 HE}estimated by this expression compared well with the results of previously published experiments. This formula is useful in assessing the impact of HE on
PvCO2
and venoarterial
PCO2
gradient and the survival advantage offered by HE in extreme conditions. Use may be extended to all investigative and clinical settings in which changes in blood O_{2} saturation and O_{2}linked CO_{2} binding must be converted into the corresponding changes in dissolved CO_{2} and
PCO2
.
 carbon dioxide exchange
 circulatory failure
 respiratory failure
 shock
 venous hypercapnia
 sepsis
the Haldane effect (HE) is a physicochemical phenomenon involving an increase in blood CO_{2}combining capacity, with opposite changes in dissolved CO_{2}and
PCO2
, as a consequence of oxyhemoglobin (HbO_{2}) desaturation (3). Although HE is an important component of circulatory and gasexchange 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 O_{2} saturation and O_{2}linked CO_{2} binding into the corresponding changes in dissolved CO_{2} 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
(
PvCO2
, Torr) and venoarterial
PCO2
difference [(va)
PCO2
, Torr].
METHODS
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 m^{2}. There were 73 patients with intraabdominal 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).
Table 1.
Patient variables
The measurements, all performed for clinical purposes and in accordance with institutional guidelines, were based on the simultaneous analysis of arterial and mixedvenous blood gases. From these, arteriovenous difference in Hbbound O_{2}[(av)HbO_{2}, ml/dl blood] was calculated from O_{2} saturation difference and Hb concentration, with Hufner’s coefficient of 1.36 ml O_{2}/g Hb. The venoarterial CO_{2} concentration difference [(va)CO_{2}, ml CO_{2}/dl blood] was determined by a model combining the PetersVan Slyke equation for the buffer line of plasma from arterial blood with the HendersonHasselbalch equation for venous plasma (9), thus calculating the following quantities on the CO_{2} equilibration curve for arterial blood: 1) the increment in CO_{2} concentration (Cco
_{2}) related to the (va)
PCO2
increment at constant O_{2} saturation by an iteration related to the NewtonRaphson procedure;2) the further increase in Cco
_{2} at constant
PCO2
mediated by HbO_{2} desaturation and O_{2}linked CO_{2} binding [(va)CO_{2} due to HE, (va)CO_{2 HE}, ml CO_{2}/dl blood] by a complex fit to the experimental data obtained at 37°C by Klocke (15);3) the increase in
PvCO2
avoided by the O_{2}linked CO_{2} binding [reduction in (va)
PCO2
due to HE, (va)Pco
_{2 HE}, Torr] by continuation of the iteration stepwise to find the increase in
PCO2
above
PvCO2
necessary to obtain an increase in Cco
_{2} equal to (va)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 (va)Pco
_{2 HE}was verified by a comparison with experimental values of (va)Pco
_{2 HE}[(va)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 HEmediated change in arterial
PCO2
(
PaCO2
) from increased O_{2} breathing. The latter effect is equivalent, in terms of HEinduced changes in
PCO2
, to that observed by changing O_{2} saturation in venous blood (if linearity of HE at different HbO_{2}saturations is assumed) (16). Because in tonometric experiments the Cco
_{2} values in reduced and oxygenated blood (
CrCO2
and
CoCO2
, respectively, ml/dl) were not the same, an unbiased and verifiable comparison was carried out as follows. Thirddegree polynomials [y =f (x
^{3},x
^{2},x)] were fitted pragmatically to the data for oxygenated blood (r
^{2} > 0.99 for each fit). Then, for any point measurement reported for reduced blood, (va)Pco
_{2 exp}was determined as the difference between the
PCO2
yielded by the polynomial at a Cco
_{2} equal to
CrCO2
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
CrCO2
. The obtained (va)Pco
_{2 exp}values were then compared with the values of (va)Pco
_{2 HE} estimated by our nonlinear regression on the basis of the (av)HbO_{2},
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 O_{2}linked
PCO2
changes. A total of 34 (va)Pco
_{2 exp}values, available for comparison from these sources, was pooled together and processed.
RESULTS
The (va)
PCO2
gradient was 5.70 ± 2.70 (SD) Torr, (va)CO_{2} was 3.71 ± 1.45 ml/dl, (av)HbO_{2} was 3.93 ± 1.46 ml/dl, (va)CO_{2 HE} was 1.06 ± 0.41 ml/dl, and (va)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 (va)Pco
_{2 HE}and to select the best simultaneous correlation by Mallows’ Cp criteria (22). This was provided by the (Pv_{CO2}) following fit(va)PCO2HE
=0.460 [(av)HbO2]0.999e0.015(PvCO2)−0.852(Hct)
Equation 1wherer
^{2} = 0.99,P ≪ 0.001 for whole regression and each independent variable; partialr
^{2} for (av)HbO_{2} = 0.77 and for (av)HbO_{2} +
PvCO2
= 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 (av)HbO_{2} reflected the relevance of HbO_{2} desaturation as a determinant of HE, and that the simultaneous nonlinear correlation with
PvCO2
and Hct was mediated by the impact of these variables on the slope of the CO_{2} equilibration curve. Unexpectedly, there was a lack of simultaneous correlation with pH. This was because part of the variability of (va)Pco
_{2 HE}related to pH was already accounted for by
PvCO2
. Besides, the impact of pH on the CO_{2}combining capacity of blood related to HE was balanced by a simultaneous impact on that unrelated to HE [because (va)Pco
_{2 HE}is the horizontal distance between the equilibration curves for arterial and venous blood, changes in this distance expected from pHmediated changes in magnitude of HE were balanced by pHmediated 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 (va)Pco
_{2 HE}is likely to decrease. Reliability of the developed fit was supported by a high r
^{2} = 0.99 and a SE of estimate = 0.07 Torr, thus implicating comprehension of estimated (va)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 (va)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 (av)HbO_{2}, as this involved only a slight overestimation of (va)Pco
_{2 HE}, which never exceeded 0.25%. Comparison with the results of published experiments showed that the estimated (va)Pco
_{2 HE}was in good agreement with (va)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 (va)Pco
_{2 exp}and (va)Pco
_{2 HE}: (va)Pco
_{2 exp}= 1.04[(va)Pco
_{2 HE}] + 0.16, r
^{2}= 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 (va)Pco
_{2 exp}values (7.50 ± 4.65 Torr) by a method developed from measurements with smaller (va)Pco
_{2 HE}(2.46 ± 0.99 Torr).
Fig. 2.
Correlation between actual values of (va)Pco
_{2 HE}and values estimated by Eq. 1
, with identity line.
DISCUSSION
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 (va)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 gasexchange interactions. For instance, increases in (va)
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 CO_{2} loading per unit blood flow) and metabolic acidosis (with reduced blood CO_{2} binding and larger increases in
PCO2
for any given CO_{2} loading) (1). An additional and unrecognized cause of increases in (va)
PCO2
, and thus in
PvCO2
for any given
PaCO2
, is the reduction of (va)Pco
_{2 HE}. Indeed, (va)Pco
_{2 HE} is the buffering that is exerted constantly by HE on (va)
PCO2
for any given (va)CO_{2}. In sepsis with impaired O_{2} extraction and reduction of (av)HbO_{2}, 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 (va)
PCO2
and
PvCO2
were observed in our septic patients with circulatory failure when they developed overimposed metabolic failure with impaired O_{2}extraction and thus a reduction of (va)Pco
_{2 HE}. With the exception of extreme cases, however, the buffering of pH from O_{2}linked H^{+} binding has a greater general relevance than the buffering of
PCO2
(for instance, small changes in ventilation may affect
PaCO2
and
PvCO2
to a much greater extent than the HE). Quantifiable evidence of the O_{2}linked H^{+} binding was provided by us in a previous study (8). This is obviously related to the O_{2}linked CO_{2} 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 O_{2} saturation and O_{2}linked CO_{2} binding must be converted into the corresponding changes of dissolved CO_{2} and
PCO2
. As mentioned already, (va)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
PaCO2
caused by the HE when inspired O_{2} 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 HbO_{2} due to O_{2} breathing into (av)HbO_{2 HE} and the basal
PaCO2
into
PvCO2
, Eq.1
will calculate this quantity instead of (va)Pco
_{2 HE}. Similarly, Eq. 1
may be applied to assess changes in
PaCO2
during apneic oxygenation, rebreathing, and breath holding and in the simulation of blood CO_{2} exchange under a variety of conditions. In effect, the reliability of Eq.1
was also supported by using published results on Haldanemediated changes in
PaCO2
when the inspired O_{2} 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 byEq. 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
CoCO2
and
CrCO2
from the measured pH,
PCO2
, and Hct by using any general expression, including ours in Ref. 9, of the form Cco
_{2} =a ⋅
PCO2
⋅ 10^{pH − p}
^{K}
^{′}[1 − Hct(1 −r)]. Then the data of Peters and Van Slyke (21) for dCco
_{2}/dpH may allow estimation of the pH value at which
CoCO2
equals
CrCO2
and of the corresponding
PCO2
in oxygenated blood. The difference with the original
PCO2
in reduced blood may finally be compared with the (va)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 Cco
_{2} and (va)CO_{2} by the procedure used previously. Then, the data of Peters et al. (20) may allow conversion of (va)CO_{2} into the (va)
PCO2
and
PvCO2
, which should be expected in the absence of HE. The difference with the actual
PvCO2
may finally be compared with the (va)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 Haldanemediated changes in
PCO2
estimated by Eq. 1
(Fig. 3).
Fig. 3.
Comparison between (va)Pco
_{2 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 (
∼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 CO_{2} exchange, for (av)HbO_{2} = 4.0 ml/dl and
= 65 Torr. Small □, mean (va)Pco
_{2 HE}for measurements by Brandt et al. (2) in apneic oxygenation. ○, Mean (va)Pco
_{2 HE}for similar measurements by Merkelbach et al. (19). •, Extreme data points (
= 20 and 70 Torr, respectively) from Lenfant nomogram (17) for Hb = 16.0 g/dl and change in HbO_{2} 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 (av)HbO_{2}or decreasing
, due likely to the peculiar setting (extracorporeal support in respiratory insufficiency) and to report of a simplified linear relationship for (va)Pco
_{2 HE}in the study.
Finally, as an additional implication, it should be mentioned that our formula for (va)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 (va)
PCO2
and thus in
PvCO2
and tissue
PCO2
. This is an important phenomenon in organs with high O_{2} uptake and CO_{2} release per unit blood flow, such as the heart and the brain (10). Maximum (va)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
PvCO2
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
PvCO2
(allowing increasingly larger reductions in
PCO2
) (3, 13, 24) and is also consistent with the values of (va)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.
Footnotes

Address for reprint requests and other correspondence: I. Giovannini, Via Alessandro VII, 45, I00167 Rome, Italy.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.
 Copyright © 1999 the American Physiological Society