Computer-Assisted Analysis of the Impact of Respiratory Quotient on Blood CO2Tension and pH Changes

COMPUTERS AND BIOMEDICAL RESEARCH ARTICLE NO.

31, 90–99 (1998)

CO981468

Computer-Assisted Analysis of the Impact of Respiratory Quotient on Blood CO2 Tension and pH Changes1 Ivo Giovannini, Carlo Chiarla, Giuseppe Boldrini, and Gennaro Nuzzo Department of Surgery (Geriatric Surgery) and CNR Center for the Study of Pathophysiology of Shock, School of Medicine, Catholic University of the Sacred Heart, Rome, Italy

Received August 20, 1996

A computer model for the accurate quantification of blood gas exchange components was used to assess the impact of respiratory quotient (RQ) on venoarterial CO2 tension and pH differences over a large group of patient measurements. The combined use of measured and computer-generated data has shown that, for any given increase in blood CO2 concentration (i.e., when the arterial blood becomes venous), the associated increase in CO2 tension and decrease in pH are inversely related to the RQ, and that this relationship is mediated by the Haldane effect. These results are useful for a thorough understanding of blood gas and metabolic interactions in normal and abnormal states, and for improving the interpretation of changes in venoarterial CO2 tension gradient in clinical monitoring.  1998 Academic Press

INTRODUCTION The increase in blood CO2 concentration (DC, ml CO2 /dl blood) which takes place when arterial blood flows through the tissues and becomes venous is paralleled by a simultaneous increase in CO2 tension (DP, mmHg) and decrease in pH (2DpH). The relative magnitude of the changes in CO2 tension and pH for a given change in CO2 concentration (i.e., DP/DC and 2DpH/DC) depends on the acid–base status of the blood and on the shape of the CO2 equilibration curve (1–6). However, it has also been noted that the magnitude of these changes is related to the respiratory quotient (RQ), and it has been postulated that this relationship might be mediated by the Haldane effect (7, 8). This could not be proved in the past, due to the complexity of CO2 exchange calculations, to the difficulty of dealing with very small and often unmeasurable pH quantities, and to the need to quantify virtual changes in CO2 tension and pH which do not occur as such in reality, but represent intermediary steps of the real processes. In addition, there were no methods for a precise quantification of Haldane effect 1

Presented in part at the Congress of the European Shock Society, Manchester, U.K., April 18–20, 1996. 90 0010-4809/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.

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(the CO2 and H1 binding in blood which are due to hemoglobin desaturation) under different acid–base conditions. The relevance of the issue extends beyond the mere assessment of physicochemical phenomena. There is specific clinical relevance for improved patient monitoring (especially in intensive care settings), which is related to improved understanding of metabolic RQ, O2 –CO2 exchange and acid–base interactions in critical illnesses. Besides, exact recognition of the role of Haldane effect in these interactions is important to assess the mechanisms of metabolic control and protection against venous and tissue hypercapnia and acidosis in extreme illness and shock (circulatory failure, respiratory failure) or in therapeutically induced states (permissive hypercapnia). In our investigation the computational problems have been overcome by the availability of a computer model, suitable for accurate calculation of blood CO2 exchange and pH quantities. This has been used to assess in detail the impact of RQ on venoarterial CO2 tension and pH differences and the role exerted by the Haldane effect in these interactions in a large group of patient measurements. MATERIALS AND METHOD Data from 247 measurements performed in 91 patients with sepsis were processed, and the necessary data were generated by the model. Age of patients was 53 6 18 yr (mean 6 SD), body weight 64.3 6 12.8 Kg, ratio of actual to ideal body weight 1.03 6 0.17 (9), body surface area 1.72 6 0.19 m2 (10). Sepsis was caused by spontaneous perforation or traumatic rupture of hollow viscus, or postoperative complications of abdominal surgery (73 patients), retroperitoneal abscesses originating from pancreas, kidney, or posterior perforation of sigmoid colon (11 patients), biliary obstruction complicated by severe cholangitis (6 patients), gangrenous fasciitis (1 patient). The diagnosis of sepsis was based on previously described criteria (11); 39 patients survived and 52 died as a result of respiratory or multiple organ failure, myocardial depression, or infarction and pulmonary embolism. At the time of the measurements the sepsis severity score (12) ranged from less than 10 to more than 20, with a normal Gaussian distribution and a mean 6 SD of 15.8 6 4.0. There was a continuous distribution of conditions, from compensated to severely diseased states, which was suitable for a detailed assessment of the RQ relationships over a wide range of cardiorespiratory and metabolic abnormalities (Table 1). Each measurement was motivated by the clinical need for a cardiorespiratory and metabolic assessment which was based on the simultaneous analysis of arterial and mixed venous blood gas data. The measured variables included arterial and mixed venous O2 tensions and saturations, CO2 tensions, plasma pH, hemoglobin concentration, and hematocrit. From these, the model yielded the venoarterial CO2 concentration increment (DC, ml/dl) with the relative contribution of Haldane effect (HALD, fraction of the total increment), and the virtual values of DP and 2DpH which should have been expected in the absence of Haldane effect (DPEXP , 2DpHEXP). It was considered that the measured 2DpH is the sum of two different components: 2DpH1 , the decrease in pH

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GIOVANNINI ET AL. TABLE 1 Mean 6 SD and Ranges of Blood Gas Variables Arterial O2 tension, mmHg Arterial O2 saturation, fraction Arterial CO2 tension, mmHg Arterial pH Mixed venous O2 tension, mmHg Mixed venous O2 saturation, fraction Mixed venous CO2 tension, mmHg Mixed venous pH Hematocrit, % Hemoglobin, g/100 ml

73.1 0.93 33.1 7.45 35.6 0.65 38.7 7.41 32.2 10.4

6 6 6 6 6 6 6 6 6 6

17.6 (32.3–154.0) 0.04 (0.59–0.99) 8.2 (14.0–64.0) 0.08 (6.95–7.68) 6.7 (18.3–62.1) 0.10 (0.32–0.86) 9.0 (18.0–72.0) 0.09 (6.86–7.62) 6.5 (14.0–53.3) 2.1 (4.5–17.2)

related to the increase in CO2 tension from the arterial to the venous value, and DpH2 , the small increase in pH from Haldane-mediated H1 binding (13, 14): these components cannot be separated in vivo, but were quantified separately by the model. Respiratory quotient (RQ), the ratio between CO2 production and O2 consumption, was determined by dividing DC by the arterio-venous O2 concentration difference (the two ratios are equivalent, as the latter is obtained from the former by dividing both the numerator and the denominator by cardiac output) (2). The model generated all the necessary data by simulating the progressive enrichment in CO2 which takes place in arterial blood when it flows through the tissues and becomes venous. The Peters–Van Slyke equation for the buffer line of plasma of oxygenated blood (15), combined with the exponential Henderson–Hasselbalch equation for venous blood, was solved iteratively with a procedure related to the Newton–Raphson method for the ‘‘root finding of a nonlinear equation’’ (16, 17). This made it possible to calculate the increase in plasma CO2 concentration and the corresponding decrease in pH (2DpH1) which were due to the increase in CO2 tension from the arterial to the venous value. Subtraction of 2DpH1 from the measured 2DpH quantified the Haldane-mediated DpH2 . Conversion of the increase in plasma CO2 concentration into whole blood CO2 concentration was allowed by the Gibbs–Donnan equilibrium relationships for combined CO2 in blood (18). The contribution of the Haldane effect was then calculated by a complex polynomial developed from experimental data by Klocke (13, 16) together with the total increase in blood CO2 concentration. By continuing the iteration stepwise (19) it was possible to calculate the virtual values of DP and 2DpH (DPEXP , 2DpHEXP) which should have been expected in the absence of the Haldane effect. All considered CO2 tension and pH quantities are reported in graphical display in Fig. 1. It should be emphasized that, although the patients had various degrees of severity of illness, all measurements used in this study were performed in a stable hemodynamic and respiratory condition; measurements performed in ‘‘unsteady

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FIG. 1. Arterial (A) and venous (V) points on the CO2 equilibration curves for arterial and venous blood, with indication of arterial and venous pH (pHa , pHv) and of the pH values expected theoretically by increasing CO2 tension from the arterial to the venous value at constant O2 saturation (pHt) or in the absence of Haldane effect (pHEXP). H is the O2-linked CO2 exchange.

state’’ were excluded to avoid the possibility that transient changes in body and blood CO2 stores might artifactually influence the results. The actually measured and the computer-generated data were processed further by regression analysis, with analysis of residuals, skewness and kurtosis control, and a ‘‘simplest best fit’’ procedure allowing selection of the simplest possible regressions yielding the best control of variability, based on Mallows’ Cp criteria (20). RESULTS The DP gradient was 5.70 6 2.70 mmHg (mean 6 SD), DC was 3.71 6 1.45 ml/dl, and RQ was 0.88 6 0.13. HALD was 0.31 6 0.08, DPEXP was 8.2 6 3.5 mmHg, 2DpHEXP was 20.067 6 0.030, 2DpH1 was 20.048 6 0.024, and DpH2 was 0.016 6 0.012. A series of regressions was generated (Table 2) which quantified in detail the relationship between DP, 2DpH, and RQ and the role of the Haldane effect. These showed that RQ was an important determinant of the relative increment in CO2 tension per unit increase in CO2 concentration, explaining more than 50% of its variability (regression [1], Table 1; inclusion of venous pH and CO2 tension as simultaneous independent variables in regression [1] brought the total explained variability to above 90%, as shown in regression

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GIOVANNINI ET AL. TABLE 2 (Regressions—Symbols and Units as in the Text)

DP/DC 5 2.197–0.596/RQ DP/DC 5 15.407 2 0.547/RQ 2 1.871(pHv) 1 0.015(PvCO2) DP/DPEXP 5 0.976 2 0.260/RQ HALD 5 0.001 1 0.265/RQ DP/DPEXP 5 0.981 2 0.983(HALD) 2DpH/DC 5 20.018 1 0.009/RQ 2DpH1 /DC 5 20.018 1 0.005/RQ DpH2 /DC 5 0.000 1 0.004/RQ 2DpH1 /2DpH12EXP 5 0.999 2 0.266/RQ 2DpH1 /2DpH12EXP 5 1.002 2 1.005(HALD)

r2 r2 r2 r2 r2 r2 r2 r2 r2 r2

5 5 5 5 5 5 5 5 5 5

0.52, 0.91, 0.97, 0.98, 0.99, 0.86, 0.67, 0.80, 0.98, 0.99,

p p p p p p p p p p

, , , , , , , , , ,

0.001 [1] 0.001* [1a] 0.001 [2] 0.001 [3] 0.001 [4] 0.001 [5] 0.001 [6] 0.001 [7] 0.001 [8] 0.001 [9]

* Note. p , 0.001 for each independent variable; partial r 2 for RQ plus pHv 5 0.72.

[1a]). In contrast, the virtual DPEXP was unrelated to RQ (r 2 5 0.00, p . 0.05). This was explained by the fact that the relative magnitude of DP, for any given DPEXP , was very tightly regulated by RQ (regression [2]). Analysis of the relationships between RQ, HALD, DP, and DPEXP was consistent with a role of Haldane effect in mediating these interactions: the results showed that RQ was the main determinant of the relative contribution of Haldane effect to total CO2 exchange (regression [3]), which, in turn, determined the value of DP for any given DPEXP (regression [4]). The analysis showed further that RQ was also a main determinant of the value of 2DpH for any given DC (regression [5]), while 2DpHEXP was unrelated to RQ (r 2 5 0.00, p . 0.05). To assess in greater detail the involved relationships, 2DpH1 and DpH2 , the two virtual components of 2DpH, were considered separately. It was found that the relative magnitudes of both 2DpH1 and DpH2 , for any given DC, was strongly related to RQ (regressions [6] and [7]). In analogy to the results observed for DP (regressions [2] and [3]), it was found that the relative magnitude of 2DpH1 , for any given 2DpH12EXP (corresponding to the total 2DpHEXP), was tightly regulated by RQ (regression [8]). This relationship was explained by a strong dependency of the magnitude of 2DpH1 , for any given 2DpH12EXP , on the contribution of the Haldane effect (regression [9]), which in turn, as shown previously (regression [3]), depended on the value of RQ. Concerning DpH2 , the value expected in the absence of the Haldane effect was zero, and there was no need to carry on any further analysis. Reproduction of the results in graphical display is available in Fig. 2. DISCUSSION This study provides a detailed quantitative description of the relationship existing between DP, 2DpH, and RQ. It demonstrates that RQ is the main determinant of the increase in CO2 tension and of the decrease in pH, per unit increase in CO2 concentration, which take place when arterial blood becomes

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FIG. 2. Effect of respiratory quotient, for any given venoarterial CO2 concentration difference, as a determinant of changes in O2-linked CO2 exchange and Haldane fraction (HALD) paralleling those of arterio-venous O2 concentration difference, with opposite changes in venoarterial CO2 tension (DP) and pH (2DpH) differences and in the ratios with the differences expected in the absence of Haldane effect (DP/DPEXP , 2DpH1 /2DpHEXP). O2-linked CO2 exchange (labeled with different symbols in different ranges to enhance clarity of the display) and arterio-venous O2 concentration difference were quantified as described in Materials and Method. Additional isolines and scales were generated from the regressions in Table 2 and from the regression O2-linked CO2 exchange 5 20.047 1 0.279 (venoarterial CO2 conc. diff.)/RQ, r 2 5 0.98, p , 0.001. Approximations in these estimates were related to the r 2 values in the regressions, and were larger for the DP isolines, because these did not account for the simultaneous effect of venous pH and CO2 tension (see regressions [1] and [1a] in Table 2). The spread in RQ values was related to large differences in nutritional support regimens and in the clinical status of the patients.

venous. In addition, the results are consistent with a unique role of the Haldane effect in mediating these interactions. This may be explained by the fact that changes in RQ modify the relative prevalence of O2 over CO2 exchange, and thus the relative contribution of the Haldane effect (O2-linked CO2 binding) to total CO2 exchange. The Haldane effect moderates the increment in CO2 tension which is associated with any

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increase in CO2 concentration by increasing the CO2-combining capacity of blood (for any given CO2 concentration, the desaturation of hemoglobin increases the amount of CO2 which is chemically combined and decreases the amount which is physically dissolved) (21). The simultaneous effect in moderating the decrease in pH is in part coupled with the moderation of DP (and thus of dissolved CO2 and carbonic acid concentration differences) and in part due to H1 binding associated with hemoglobin desaturation. The O2-linked CO2 and H1 binding are related but not equivalent processes (13, 14), and need to be quantified separately. As mentioned already, these relationships could not be assessed in detail in the past. In spite of important advances in the calculation of blood CO2 concentration (22), a reliable quantification of blood CO2 exchange components has remained unachieved. The availability of the model used in this study has made it possible, by generating also a series of regressions which exactly quantify all the involved interactions. Regression analysis by the least-squares technique was used for these quantifications. With this technique, the regression coefficient (the value by which the independent variable is multiplied) quantifies the mean change of the dependent variable per unit change of the independent one, the r 2 quantifies the percentage of variability (expressed as a fraction of 1.0) of the dependent variable which is controlled by the independent one, and the p value quantifies the probability (expressed also as a fraction of 1.0) that the relationship under examination is not significant. In multiple regressions, such as regression [1a] in Table 2, the relationship with more than one independent variable is evaluated simultaneously, thus obtaining a partial r 2 and p value for each independent variable and a total r 2 and p for the whole regression. For instance, regression [1a] in Table 2 indicates that DP/DC decreases as a mean by 0.547 units per unit increase in the 1/RQ ratio, decreases simultaneously by 1.871 units per unit increase in pHv and increases by 0.015 units per unit increase in PvCO2 ; as indicated already in regression [1], 1/RQ controls 52% of the variability of DP/ DC (r 2 5 0.52) with a highly significant p (p , 0.001); inclusion of pHv and PvCO2 as independent variables increased the total controlled variability of DP/ DC to 91% (r 2 5 0.91) and there was a highly significant p for each additional independent variable and for the whole regression (p , 0.001). In evaluating Table 2, it may be observed that the simultaneous obtainment of many regressions may increase the chances of obtaining falsely significant ones, due to the random effect of multiple testing. However, this is likely to happen when dealing with borderline r 2 and p values, and not with the extremely high r 2 and low p values constantly obtained in our case. Although the very high r 2’s in Table 2 might suggest the possibility of some mathematical coupling (from using the same method to obtain different variables), these were more likely due to a very accurate mathematical description of physiological couplings (that is, of physiological phenomena which were tightly interrelated). It is worth mentioning that the data generated by the computer were in close agreement with partial results of previous studies and experiments. For instance, this is true for the mean contribution of the Haldane effect to CO2 exchange, which in our study was 31% of the total (13, 14, 23). Also, the mean O2-linked

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CO2 binding per unit O2 exchange, quantified as 0.265 ml CO2 /ml O2 by the regression coefficient in regression [3], was in agreement with previous findings (23). The relative magnitude of DPEXP , compared to the real DP, was in agreement with previous estimates of the impact of Haldane-mediated CO2 exchange on blood CO2 tensions (24). Finally, the virtual value of DpH2 calculated by the model, 0.016 6 0.012, was also consistent with the value of 0.015 6 0.006, obtainable in our case by interpolating the relationships developed experimentally by Kelman (25). In this study, to emphasize the unique role of RQ, other variables influencing the absolute DP and DpH changes were not considered (except in regression [1a], Table 2). These included, for instance, the absolute value of pH and hemoglobin concentration, which explained part of the residual variability of some regressions in Table 2. The influence of these variables on DP and DpH was not unexpected, because both are determinant of the buffering capacity and of the CO2 and H1 binding capacity of blood. The DP/DPEXP and 2DpH1 /2DpH12EXP ratios, however, tended to be independent of the absolute pH and Hb values, because these had similar effects on both the numerator and the denominator of the ratios. Finally it was interesting to note that, contrary to intuitive expectancies, HALD was independent of Hb and pH. This was explained by the circumstance that changes in hemoglobin concentration were associated with parallel changes in both the blood CO2 binding related to the Haldane effect and the slope of the blood CO2 equilibration curve (and thus the blood CO2 binding unrelated to the Haldane effect). So that the HALD ratio remained relatively independent of Hb. Similar considerations could be made for the changes in pH, which involved in a parallel fashion both the blood CO2 binding related to the Haldane effect and that unrelated to it (which is a reasonable finding in the range of values considered in our paper), so that the HALD ratio remained relatively independent also of pH. The results in our study, in addition to improving understanding of physiology, have a specific clinical relevance, since the DP increment is used in the monitoring of critically ill patients. In the past, evidence of a relationship between DP and RQ has been confined mostly to extreme cases of circulatory failure, where acute loading of CO2 into venous blood and acute discharge of CO2 from the body (from decreases in body CO2 stores) cause DP and RQ to rise simultaneously while 2DpH widens (1–6, 26, 27). In these instances the RQ is more properly defined as the ‘‘respiratory exchange ratio’’ because CO2 excretion does not equal true metabolic CO2 production, but reflects a transient loss of body CO2 stores (2). Our results provide a quantitative basis for assessing in greater detail the influence that the real RQ exerts constantly on DP for any given DC, the parallel impact on venoarterial pH difference, and the role of the Haldane effect. This may be useful to understand and interpret the effect of changes in RQ on blood gases, when these are caused either by common events (i.e., changes in nutritional support regimen) or by abnormal metabolism (i.e., metabolic dysregulation in decompensating sepsis) (28, 29). A further implication relates to our quantification of the ‘‘buffering’’ exerted by

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Haldane effect on the magnitude of DP and 2DpH, compared to the theoretical DPEXP and 2DpHEXP . This is not appreciated commonly in its full extent. Regression [4] indicates that normally (HALD P 0.3) the observed DP is about two-thirds of the value which should be expected in the absence of the Haldane effect; and the buffering of 2DpH is even larger, due to additional H1 binding. Magnitude of this buffering increases further with increasing HALD at low RQ (regression [3]). It may be estimated from the regressions that in a hypodynamic patient with a high DP (for instance 15 mmHg) and a low RQ (P0.7) the DPEXP expected in the absence of the Haldane effect is P25 mmHg, with a relatively greater impact on 2DpH. Values on this order of magnitude were actually calculated by the model in individual patient cases. However, even larger effects may be predicted by the regressions when simulating more severe hypodynamism, the presence of very low pulmonary ventilation : perfusion ratios, or acute transients in body CO2 stores, when the contribution of the Haldane effect to CO2 exchange becomes prominent (13, 14). In these extreme cases, evidence of very large buffering of DP and 2DpH is relevant for assessing the Haldane-mediated protection against toxic increases in CO2 tension and decreases in pH in venous blood and in the tissues. APPENDIX List of Symbols RQ DC DP DPEXP 2DpH 2DpHEXP 2DpH1 2DpH12EXP DpH2 pHv PvCO2

respiratory quotient (fraction). venoarterial CO2 concentration difference (ml/dl) venoarterial CO2 tension difference (mmHg). virtual value of DP expected in the absence of Haldane effect. venoarterial plasma pH difference (pH units). virtual value of 2DpH expected in the absence of Haldane effect. virtual decrease in plasma pH due only to the increase in CO2 tension from the arterial to the venous value at constant O2 saturation (5 pHt 2 pHa in Fig. 1). value of 2DpH1 expected in the absence of Haldane effect, corresponding also to the total 2DpHEXP (5 pHEXP 2 pHa in Fig. 1). virtual increase in plasma pH due to O2-linked H1 binding. mixed venous pH. mixed venous CO2 tension. ACKNOWLEDGMENTS

The authors acknowledge the kind contribution of Dr. Paolo Coppa, from the Department of Mechanical Engineering of the University of Rome ‘‘Tor Vergata,’’ for helpful discussion in the development of this work.

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