Combining the Physical–Chemical Approach with Standard Base Excess to Understand the Compensation of Respiratory Acid–Base Derangements: An Individual Participant Meta-analysis Approach to Data from Multiple Canine and Human Experiments

This study followed an individual participant data meta-analysis approach to data extracted from multiple canine and human experiments.¹⁰  A structured, systematic search of the literature was performed according to the methods of Preferred Reporting Items for Systematic Reviews and Meta-Analyses checklist (https://links.lww.com/ALN/D286) to retrieve studies describing respiratory acid–base alterations.¹¹  Moreover, the Strengthening the Reporting of Observational Studies in Epidemiology checklist (https://links.lww.com/ALN/D287) was used to guide reporting of the results of the study.¹² 

We searched into MEDLINE database for any type of publication published up to April 29, 2021. The research was performed using the following Medical Subject Headings research string: “respiratory acid-base imbalance/analysis” OR “respiratory acid-base imbalance/blood” OR “acute respiratory acidosis,” “acute hypercapnic acidosis” OR “acute hypercapnia” OR “carbon dioxide titration” OR “acidosis, respiratory” OR “chronic respiratory acidosis” OR “chronic hypercapnic acidosis” OR “chronic hypercapnia” OR “acute respiratory alkalosis” OR “acute hypocapnic alkalosis” OR “acute hypocapnia” OR “chronic respiratory alkalosis” OR “chronic hypocapnic alkalosis” OR “chronic hypocapnia.”

We selected publications written in English describing experimental in vivo studies conducted on humans or dogs, testing the effect of the induction of an acute or chronic respiratory acidosis or alkalosis. In order to be included in the analyses, values of Paco₂, pH, HCO₃⁻, sodium, chloride, and potassium before and after the induction of the respiratory alteration had to be reported.

We excluded studies reporting data about subjects or animals with pre-existing chronic respiratory, renal, metabolic, or cardiac impairment, and studies in which the subject received per protocol intravenous fluids and/or drugs (e.g., normal saline, sodium bicarbonate, diuretics) that could alter the acid–base balance significantly.

Two authors (F.Z. and A.D.) independently selected eligible articles using Rayyan software.¹³  As a first step, duplicated studies were identified and removed. The relevance of each article was evaluated by examining the title, abstract, and full text. Data from the included studies were manually extracted. Each manuscript could include more groups (e.g., different inspiratory carbon dioxide concentrations). Reported average values of each group were used as this. If the study reported only disaggregated data, the average of the variables of interest was calculated for each group and used for analysis. Based on the time interval between the respiratory alteration onset and the following measurement, the acid–base derangements were classified as “acute” if the measurement were obtained within 2 h, or “chronic” when more than 72 h were intercurred. For further details, refer to Supplemental Table S2 (https://links.lww.com/ALN/D285).

A simplified strong ion difference was calculated from the electrolytes retrieved in the selected manuscripts as follows:

where [Na⁺], [K⁺], and [Cl⁻] are sodium, potassium, and chloride concentrations expressed as millimoles/liter.

The difference between sodium and chloride concentration (Na-Cl) was also calculated as a proxy of the strong ion difference.

For every set of experimental data, the relative contribution of sodium (∆Na%) and chloride (∆Cl%) to total strong ion difference variation was computed using the difference in sodium and chloride (∆Na⁺ and ∆ Cl⁻, respectively) between the points with the highest and lowest Paco₂ as follows:

To address the in vivo alteration of the metabolic component of acid–base equilibrium, independently from the coexisting respiratory derangements, standard base excess was calculated for every pH and bicarbonate couple as follows:

considering a noncarbonic buffer power (⁠$β$⁠) of the extracellular fluid of 16.2 mM.^7,14 

Results are presented as mean ± SD. The normality of each distribution was tested via the Shapiro–Wilk test. Data from respiratory acidosis and alkalosis of the same timeframe (i.e., acute or chronic) were pooled and analyzed together. Within each time group, the different contributions of sodium and chloride to strong ion difference variation were evaluated via Student’s paired t test, or Wilcoxon signed-rank test. A P value < 0.05 was considered statistically significant.

For every couple of continuous variables, changes of the dependent variable over the explanatory one were modeled according to a polynomial multilevel linear regression model (generalized linear mixed models) with random intercept and random slope both at group level, as previously described.⁴  Random intercept and random slope were included in the model according to model-based likelihood ratio tests, with a cutoff P value of 0.050. The exponential power of the polynomial function was assessed by comparing models of increasing degree by model-based likelihood ratio tests (cutoff P value 0.05). Interaction between the explanatory variables and the time group (i.e., acute coded as “0” and chronic coded as “1”) was also included in the model according to model-based likelihood ratio tests (cutoff P value 0.001). The models were weighted for the sample size, i.e., the number of subjects forming the group. To compare the potential differences, the model generated by pooling together the different studies was plotted against the Boston rules (simplified linear equations) and the original equations from which they were derived. Statistical analyses were performed using the SAS 9.4 statistical package (Statistical Analysis Software Institute Inc., USA).

A total of 3378 citations were identified. Eleven articles published between 1961 and 1994 matched the inclusion criteria (Supplemental Figure S1, https://links.lww.com/ALN/D285), three performed on humans and eight on dogs. A total of 31 dogs and 19 humans from four different studies were included in the acute respiratory derangement group, while 60 dogs and 4 humans from seven studies were included in the chronic respiratory derangement group. Six articles focused on respiratory acidosis induced by increases in inspiratory fraction of carbon dioxide.^3,15–19  Five articles explored respiratory alkalosis, which was induced either through an increase in mechanical ventilation (acute) or by decreasing the inspiratory fraction of oxygen,^20,21  thus exploiting the hypoxic respiratory drive,²²  in spontaneously breathing dogs (chronic).^23–25  A summary of the analyzed studies is reported in table 1.

A range of Paco₂ between 21 and 142 mmHg was explored. The resulting pH and bicarbonate values ranged from 6.93 to 7.55 and from 12.3 to 43.8 mM, respectively. The relationship between pH versus Paco₂ (Supplemental Figure S2, https://links.lww.com/ALN/D285) and bicarbonate versus Paco₂ (fig. 1A, and Supplemental Figure S3, https://links.lww.com/ALN/D285) differed according to the duration of the respiratory disorder (P < 0.001 for both). For a similar perturbation of Paco₂, smaller changes in pH and greater bicarbonate variations were observed in chronic compared to acute disorders.

Both in acute and chronic respiratory disorders, a rise in strong ion difference was observed after the increase in Paco₂ (observed range, 32.6 to 60.0 mEq/l; fig. 1B, and Supplemental Figure S4, https://links.lww.com/ALN/D285). Similar to the bicarbonate versus Paco₂ curve_, the Paco₂-induced strong ion difference variation was more pronounced in the chronic group. A similar slope (β-coefficient, 1.2; 95% CI, 1.2 to 1.3; P < 0.001 for both) between bicarbonate and strong ion difference was observed in the acute and chronic settings (fig. 1C, and Supplemental Figure S5, https://links.lww.com/ALN/D285).

A statistically significant but clinically negligible relationship was found between standard base excess and Paco₂ in the acute response to Paco₂ variations (β-coefficient, –0.01; 95% CI, –0.02 to –0.01; P < 0.001). On the contrary, a positive, clinically relevant linear association was present in the chronic time group (β-coefficient, 0.29; 95% CI, 0.29 to 0.32; P < 0.001; fig. 2A, and Supplemental Figure S6, https://links.lww.com/ALN/D285). In the acute setting, no relationship was found between standard base excess and HCO₃⁻ (β-coefficient, 0.02; 95% CI, –0.01 to 0.06; P = 0.238; fig. 2B, and Supplemental Figure S7, https://links.lww.com/ALN/D285), or between standard base excess and strong ion difference (β-coefficient, –0.02, 95% CI, –0.11 to 0.07; P = 0.719; fig. 2C, and Supplemental Figure S8, https://links.lww.com/ALN/D285). Differently, in the chronic time frame, both the associations of parameters were positively correlated (β-coefficient, 0.88; 95% CI, 0.80 to 0.95; P < 0.001; and β-coefficient, 1.04; 95% CI, 0.84 to 1.24; P < 0.001, respectively).

In both time groups, a positive linear association was found between sodium and Paco₂ (fig. 3A, and Supplemental Figure S9, https://links.lww.com/ALN/D285), while chloride variations were negatively associated with Paco₂ only in chronic experiments (fig. 3B, and Supplemental Figure S10, https://links.lww.com/ALN/D285). A significant association (P < 0.001) was found between potassium and Paco₂ in both timeframes (Supplemental Figure S11, https://links.lww.com/ALN/D285). However, potassium variations were quantitatively negligible, and thus, the Na-Cl difference strictly paralleled strong ion difference changes in response to Paco₂ modifications within a clinically relevant range of Paco₂ (Supplemental Figure S12, https://links.lww.com/ALN/D285).

Finally, the behavior of sodium (fig. 4A, and Supplemental Figure S13, https://links.lww.com/ALN/D285) and chloride (fig. 4B, and Supplemental Figure S14, https://links.lww.com/ALN/D285) variations and their impact on strong ion difference was different between time groups. In particular, sodium was the main determinant of strong ion difference variations during acute respiratory alterations (ΔNa% = 80 ± 27% vs. ΔCl% = 16 ± 30% of strong ion difference variation, P = 0.040), while chloride played the major role in chronic alterations (ΔNa% = 18 ± 23% vs. ΔCl% = 80 ± 22% of strong ion difference variation, P = 0.002).

The model developed in the current work resembles the equations derived from the four original studies (fig. 5, and Supplemental Table S1, https://links.lww.com/ALN/D285). Conversely, as compared to our model, the simplified, linear Boston rules overestimate the bicarbonate compensations during hypercapnia.

In this study, we used an individual participant data meta-analysis method to describe the metabolic compensation to primary acute or chronic respiratory acid–base derangements according to the physical–chemical approach. Our results confirmed the key role of time in determining the degree of Paco₂-associated bicarbonate changes, which resulted associated with strong ion difference variations. In particular, in the acute setting, sodium variations were the major determinant of strong ion difference changes, while chloride was the key electrolyte in chronic experiments. Last, no association was found between strong ion difference variations and standard base excess in acute respiratory acid–base disorders, while this relationship was present in the chronic phase.

Several electrolytes contribute to the change in strong ion difference, which is paralleled by bicarbonate variations, regardless of the length of the respiratory alterations. According to the electrical neutrality concept, the sum of all cations (e.g., sodium, potassium) is equal to the sum of negative charges, deriving from strong anions (e.g., chloride), dissociated weak noncarbonic acids, and bicarbonate. In the current study, the contribution of unmeasured anions (e.g., lactate) is likely negligible, as only healthy subjects were studied.^26,27  Indeed, the observed stability of the anion gap (Supplemental Table S3, https://links.lww.com/ALN/D285) confirmed that unmeasured anions were likely constant during the experiments. According to these premises, changes in bicarbonate were paralleled by strong ion difference variations regardless of the timing of the respiratory derangement.

Both in the acute and chronic settings, we observed an increase in sodium and a decrease in plasma chloride concentration, moving from hypocapnia to hypercapnia. The entity of sodium variations was modest and similar in acute and chronic conditions. The small magnitude of sodium variations is not surprising, as sodium is the primary determinant of osmolarity, and its concentration is strictly regulated by several hormones.²⁸  On the contrary, moving from acute to chronic hypercapnia, the chloride decrease became more remarkable, reaching variations up to 20 mM (fig. 3B). Consequently, sodium played a major role in acute respiratory derangements, while chloride was the key electrolyte in chronic adaptation (fig. 4). These different behaviors can be explained by two physiologic mechanisms.

During acute hypercapnia, carbon dioxide is hydrated to bicarbonate prevalently within red blood cells. This process transiently increases intracellular osmolarity fostering the shift of water from the extra to the intracellular space, ultimately increasing plasma sodium concentration. In contrast, chloride decreases during acute hypercapnia due to the Hamburger effect.^29,30  Last, a quantitatively less important cause of both sodium and chloride acute shifts is their direct pH-dependent release from plasma proteins.^4,31 

During chronic hypercapnia, the kidneys are responsible for the observed chloride variation, mainly due to the excretion of ammonium chloride.³²  While the renal response to an acid–base disorder is extremely powerful and rapidly established,³³  it requires up to 1 week to fully compensate for respiratory acid–base alterations.^17,19,32 

To summarize, the compensation for a respiratory derangement can be divided into two distinct phases. Acutely, the degree of carbon dioxide variation and the noncarbonic buffer power are the determinants of pH. In this context, the strong ion difference variation is a consequence of water and electrolyte shifts between intra- and extracellular fluids, as the amount of electrolytes removed from or added to the system by the kidneys is limited per definition.³⁴  Accordingly, these variations in strong ion difference are not paralleled by changes in standard base excess (fig. 2C, and Supplemental Figure S8, https://links.lww.com/ALN/D285).

On the contrary, during chronic carbon dioxide exposure, pH is determined by Paco₂, noncarbonic buffer power, and strong ion difference variations induced by active renal electrolyte manipulation. In this context, the strong ion difference change represents the metabolic adaptation and is mirrored by standard base excess. Of note, a similar relationship between standard base excess and acute or chronic Paco₂ variations was described in humans by Schlichtig et al.³⁵ 

Last, in line with previous studies,^4,36  our data from acute experiments underline the dependency of “plasma” strong ion difference on Paco₂. While one might argue that this observation discredits the physical–chemical approach, we think that a reallocation of independent variable status from “plasma” to “extracellular” strong ion difference (i.e., strong ion difference of whole blood and interstitial fluid) reconciles the model. Of note, standard base excess describes the metabolic status of the same compartment, which remains stable during electrolyte shifts between red blood cells and plasma, as no electrolytes are added and/or removed.

The Boston school described the secondary adaptation of bicarbonate to primary respiratory derangements and developed four different equations, which were simplified to linear equations: the Boston rules (Supplemental Table S1, https://links.lww.com/ALN/D285).^3,17,20,23  Not surprisingly, our model, which includes the results of these studies, is in line with the original equations (fig. 5). Conversely, a different behavior was observed when the simplified Boston equations were compared to the model. For instance, the simplified, linear rules have lower performances than the original equations. The chronic respiratory Boston equation describes a complete metabolic compensation to chronic respiratory acidosis, requiring several days.^17,19,32  As compared to the original equation, the simplified Boston rule for chronic acidosis overestimates the bicarbonate adaptation, becoming less precise at higher Paco₂. For example, considering a pure, chronic respiratory acidosis at 75 mmHg Paco₂, the difference in bicarbonate between the simplified and the original equation is about 5 mM. If a complete evaluation, including the measurement of electrolytes and the application of the electrical neutrality concept, is not performed, the lower-than-expected value of bicarbonate could misleadingly suggest a concomitant metabolic acidosis. Despite similar limits, the simplified rule for acute acidosis seems more reliable.

Understanding compensatory mechanisms of respiratory derangements could be extremely useful during clinical practice. For instance, since chloride variations are only of a few millimoles during the acute adaptation to carbon dioxide, finding a decreased plasma chloride concentration in a patient without other causes of hypochloremia (e.g., vomiting) could reveal the presence of renal adaptation to chronic hypercapnia. A second important consideration concerns the intraoperative management of patients with chronic obstructive pulmonary disease. In this context, the intraoperative use of high chloride content fluids (e.g., NaCl 0.9%) could rapidly disrupt the compensatory hypochloremia.³⁷  Similar attention should be paid when dealing with pregnant women undergoing surgery. These patients are characterized by chronic respiratory alkalosis compensated by a reduced strong ion difference.³⁸  In this context, misinterpreting the low standard base excess and administering alkalinizing agents or fluids to correct metabolic acidosis could interfere with the mother’s and developing fetus’s physiologic homeostasis.

In critically ill patients, multiple confounders altering the acid–base equilibrium might be present. The physical–chemical approach considers all measured variables, applying the key concept of electrical neutrality. However, it does not provide any tool to estimate the time that has elapsed since the onset of the disorder. In the absence of hypoalbuminemia and unmeasured anions, hints about the onset time of the respiratory disorder can be derived by calculating the difference between the actual strong ion difference and a reference value of 40 mM and comparing this value with standard base excess. Being independent of acute Paco₂ variations, standard base excess can differentiate between “plasma” strong ion difference variation, i.e., due to electrolyte redistribution (acute) and “extracellular” strong ion difference variation, i.e., true metabolic adaptation (chronic). For example, a poor quantitative agreement (e.g., above 2 mM) between the absolute value of standard base excess and the strong ion difference variation defines the presence of an acute respiratory disorder whose onset is likely within 2 h from the sample collection. On the contrary, a good agreement between strong ion difference variation and standard base excess would suggest the presence of a chronic respiratory disorder.

Several limitations need to be addressed. First, the nature of the study is a limitation per se as it relies on data retrieved from experimental studies performed up to 60 yr ago. Second, the chronic respiratory acidosis branch of our model relies only on canine data. However, canine and human acid–base physiologies are similar,^39,40  and data derived exclusively from human studies are in line with ours.³⁵  Third, we computed strong ion difference based only on sodium, potassium, and chloride. However, this simplification had minimal effect on the analyses since data were derived from healthy subjects where lactate and unmeasured anions likely have a minor role. Finally, using hypoxia to induce chronic hypocapnia could have limited the chloride increase in response to chronic alkalosis since the taut form of hemoglobin has a higher chloride binding affinity than the relaxed form.^30,41  However, this hemoglobin “chloride retention” is conceivably of minor entity (i.e., less than1.5 mmol) in our population.^23,24,40,41 

The secondary bicarbonate adaptation after primary respiratory alterations is associated with strong ion difference variations. The variation of plasma sodium induced by Paco₂ is similar in acute and chronic settings. In contrast, chloride concentration is mainly altered in chronic respiratory derangements, where it becomes the major determinant of strong ion difference variations. Standard base excess does not change during acute respiratory derangements, while it accurately describes variations in strong ion difference in chronic respiratory disorders.

Support was provided solely from institutional and/or departmental sources.

The authors declare no competing interests.

The authors are indebted to Dr. Davide Bernasconi, a statistician from the Department of Medicine and Surgery of the University of Milan-Bicocca, Milan, Italy, for his statistical revision and advice.

Online Supplemental Content, https://links.lww.com/ALN/D285

Preferred Reporting Items for Systematic Reviews and Meta-Analyses checklist, https://links.lww.com/ALN/D286

Strengthening the Reporting of Observational Studies in Epidemiology checklist, https://links.lww.com/ALN/D287