<figure><img src="image_1.png" /></figure>

HAL
open science

# Ratio of venous-to-arterial PCO2 to arteriovenous oxygen content difference during regional ischemic or hypoxic hypoxia

Jihad Mallat, Benoit Vallet

► To cite this version:

Jihad Mallat, Benoit Vallet. Ratio of venous-to-arterial PCO2 to arteriovenous oxygen content difference during regional ischemic or hypoxic hypoxia. Scientific Reports, 2021, Scientific Reports, 11, pp.10172. 10.1038/s41598-021-89703-5. hal-04456533

HAL Id: hal-04456533

https://hal.univ-lille.fr/hal-04456533

Submitted on 14 Feb 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_1.png" /></figure>

HAL
open science

# Ratio of venous-to-arterial PCO2 to arteriovenous oxygen content difference during regional ischemic or hypoxic hypoxia

Jihad Mallat, Benoit Vallet

► To cite this version:

Jihad Mallat, Benoit Vallet. Ratio of venous-to-arterial PCO2 to arteriovenous oxygen content difference during regional ischemic or hypoxic hypoxia. Scientific Reports, 2021, Scientific Reports, 11, pp.10172. 10.1038/s41598-021-89703-5. hal-04456533

HAL Id: hal-04456533

https://lilloa.hal.science/hal-04456533v1

Submitted on 14 Feb 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_3.png" /></figure>

OPEN

# Ratio of venous-to-arterial PCO₂ to arteriovenous oxygen content difference during regional ischemic or hypoxic hypoxia

Jihad Mallat<fnref n="1" />,²,³✉ & Benoit Vallet⁴

The purpose of the study was to evaluate the behavior of the venous-to-arterial CO₂ tension difference (ΔPCO₂) over the arterial-to-venous oxygen content difference (ΔO₂) ratio (ΔPCO₂/ΔO₂) and the difference between venous-to-arterial CO₂ content calculated with the Douglas' equation (ΔCCO₂D) over ΔO₂ ratio (ΔCCO₂D/ΔO₂) and their abilities to reflect the occurrence of anaerobic metabolism in two experimental models of tissue hypoxia: ischemic hypoxia (IH) and hypoxic hypoxia (HH). We also aimed to assess the influence of metabolic acidosis and Haldane effects on the PCO₂/CO₂ content relationship. In a vascularly isolated, innervated dog hindlimb perfused with a pump-membrane oxygenator system, the oxygen delivery (DO₂) was lowered in a stepwise manner to decrease it beyond critical DO₂ (DO₂crit) by lowering either arterial PO₂ (HH-model) or flow (IH-model). Twelve anesthetized and mechanically ventilated dogs were studied, 6 in each model. Limb DO₂, oxygen consumption (VO₂), ΔPCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ were obtained every 15 min. Beyond DO₂crit, VO₂ decreased, indicating dysoxia. ΔPCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ increased significantly only after reaching DO₂crit in both models. At DO₂crit, ΔPCO₂/ΔO₂ was significantly higher in the HH-model than in the IH-model (1.82 ± 0.09 vs. 1.39 ± 0.06, *p* = 0.002). At DO₂crit, ΔCCO₂D/ΔO₂ was not significantly different between the two groups (0.87 ± 0.05 for IH vs. 1.01 ± 0.06 for HH, *p* = 0.09). Below DO₂crit, we observed a discrepancy between the behavior of the two indices. In both models, ΔPCO₂/ΔO₂ continued to increase significantly (higher in the HH-model), whereas ΔCCO₂D/ΔO₂ tended to decrease to become not significantly different from its baseline in the IH-model. Metabolic acidosis significantly influenced the PCO₂/CO₂ content relationship, but not the Haldane effect. ΔPCO₂/ΔO₂ was able to depict the occurrence of anaerobic metabolism in both tissue hypoxia models. However, at very low DO₂ values, ΔPCO₂/ΔO₂ did not only reflect the ongoing anaerobic metabolism; it was confounded by the effects of metabolic acidosis on the CO₂–hemoglobin dissociation curve, and then it should be interpreted with caution.

## Abbreviations

CO₂ Carbon dioxide

VO₂ Oxygen consumption

VCO₂ Carbon dioxide production

DO₂ Oxygen delivery

RQ Respiratory quotient

ΔPCO₂ Venous-to-arterial carbon dioxide tension difference

CCO₂ CO₂ content

ΔCCO₂ Venous-to-arterial carbon dioxide content difference

CCvCO₂ Venous CO₂ content

CCaCO₂ Arterial CO₂ content

ΔO₂ Arterial-to-venous oxygen content difference

PaCO₂ Partial arterial carbon dioxide tension

<footnote n="1">¹Department of Critical Care Medicine, Critical Care Institute, Cleveland Clinic Abu Dhabi, Al Maryah Island, Abu Dhabi, UAE. ²Cleveland Clinic Lerner College of Medicine of Case Western Reserve University, Cleveland, OH, USA. ³Normandy University, UNICAEN, ED 497, Caen, France. ⁴EA2694, University of Lille, Lille, France. ✉email: mallatjihad@gmail.com</footnote>
<figure><img src="image_3.png" /></figure>

OPEN

# Ratio of venous-to-arterial PCO₂ to arteriovenous oxygen content difference during regional ischemic or hypoxic hypoxia

Jihad Mallat<fnref n="1" />,²,³✉ & Benoit Vallet⁴

The purpose of the study was to evaluate the behavior of the venous-to-arterial CO₂ tension difference (ΔPCO₂) over the arterial-to-venous oxygen content difference (ΔO₂) ratio (ΔPCO₂/ΔO₂) and the difference between venous-to-arterial CO₂ content calculated with the Douglas' equation (ΔCCO₂D) over ΔO₂ ratio (ΔCCO₂D/ΔO₂) and their abilities to reflect the occurrence of anaerobic metabolism in two experimental models of tissue hypoxia: ischemic hypoxia (IH) and hypoxic hypoxia (HH). We also aimed to assess the influence of metabolic acidosis and Haldane effects on the PCO₂/CO₂ content relationship. In a vascularly isolated, innervated dog hindlimb perfused with a pump-membrane oxygenator system, the oxygen delivery (DO₂) was lowered in a stepwise manner to decrease it beyond critical DO₂ (DO₂crit) by lowering either arterial PO₂ (HH-model) or flow (IH-model). Twelve anesthetized and mechanically ventilated dogs were studied, 6 in each model. Limb DO₂, oxygen consumption (VO₂), ΔPCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ were obtained every 15 min. Beyond DO₂crit, VO₂ decreased, indicating dysoxia. ΔPCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ increased significantly only after reaching DO₂crit in both models. At DO₂crit, ΔPCO₂/ΔO₂ was significantly higher in the HH-model than in the IH-model (1.82 ± 0.09 vs. 1.39 ± 0.06, *p* = 0.002). At DO₂crit, ΔCCO₂D/ΔO₂ was not significantly different between the two groups (0.87 ± 0.05 for IH vs. 1.01 ± 0.06 for HH, *p* = 0.09). Below DO₂crit, we observed a discrepancy between the behavior of the two indices. In both models, ΔPCO₂/ΔO₂ continued to increase significantly (higher in the HH-model), whereas ΔCCO₂D/ΔO₂ tended to decrease to become not significantly different from its baseline in the IH-model. Metabolic acidosis significantly influenced the PCO₂/CO₂ content relationship, but not the Haldane effect. ΔPCO₂/ΔO₂ was able to depict the occurrence of anaerobic metabolism in both tissue hypoxia models. However, at very low DO₂ values, ΔPCO₂/ΔO₂ did not only reflect the ongoing anaerobic metabolism; it was confounded by the effects of metabolic acidosis on the CO₂–hemoglobin dissociation curve, and then it should be interpreted with caution.

**Abbreviations**

CO₂ Carbon dioxide

VO₂ Oxygen consumption

VCO₂ Carbon dioxide production

DO₂ Oxygen delivery

RQ Respiratory quotient

ΔPCO₂ Venous-to-arterial carbon dioxide tension difference

CCO₂ CO₂ content

ΔCCO₂ Venous-to-arterial carbon dioxide content difference

CCvCO₂ Venous CO₂ content

CCaCO₂ Arterial CO₂ content

ΔO₂ Arterial-to-venous oxygen content difference

PaCO₂ Partial arterial carbon dioxide tension

<footnote n="1">¹Department of Critical Care Medicine, Critical Care Institute, Cleveland Clinic Abu Dhabi, Al Maryah Island, Abu Dhabi, UAE. ²Cleveland Clinic Lerner College of Medicine of Case Western Reserve University, Cleveland, OH, USA. ³Normandy University, UNICAEN, ED 497, Caen, France. ⁴EA2694, University of Lille, Lille, France. ✉email: mallatjihad@gmail.com</footnote>
PvCO₂ Partial venous carbon dioxide tension

SvO₂ Venous oxygen saturation

SaO₂ Arterial oxygen saturation

PaO₂ Partial arterial oxygen tension

PvO₂ Partial venous oxygen tension

Hb Hemoglobin

In a landmark study, Vallet et al. demonstrated the determinant role of blood flow in the tissue hypoxia-induced increased venous-to-arterial CO₂ tension difference (ΔPCO₂)¹. Their data supported the hypothesis that increases in the venous PCO₂ are primarily a function of changes in regional blood flow, independently of the degree of hypoxia. Gutierrez G has confirmed this conclusion in a mathematical model of tissue-to-blood CO₂ exchange during hypoxia². In these previous publications, the behavior of ΔPCO₂ over the arterial-to-venous oxygen content difference (ΔO₂) ratio (ΔPCO₂/ΔO₂), and the difference between venous-to-arterial CO₂ content (ΔCCO₂) over ΔO₂ ratio (ΔCCO₂/ΔO₂) in a model of progressive tissue hypoxia generated by reducing either flow [ischemic hypoxia (IH)] or arterial oxygen tension [hypoxic hypoxia (HH)], were not investigated³,².

Several clinical studies³⁻⁷ have shown that ΔPCO₂/ΔO₂ ratio, taken as a surrogate of respiratory quotient (RQ), was associated with elevated lactate levels and oxygen supply dependency considered, in those studies, as indices of global anaerobic metabolism in critically ill patients with tissue hypoperfusion. However, in an experimental study, Dubin et al. found that ΔPCO₂/ΔO₂ ratio was a poor indicator of anaerobic metabolism in the hemodilution model of tissue hypoxia, where anemia was associated with preserved blood flow⁸. Similarly, other authors suggested that ΔPCO₂/ΔO₂ ratio might not rise during tissue hypoxia conditions when associated with normal/high blood flow because venous blood flow seemed to guarantee a sufficient clearance of CO₂ generated by the anaerobic metabolism⁹. Thus, it is unclear if the ΔPCO₂/ΔO₂ ratio would be able to depict the presence of anaerobic metabolism in patients with maintained blood flow (cardiac output).

Furthermore, one estimates that the ΔPCO₂/ΔO₂ ratio might be affected by other factors than anaerobic metabolism by influencing the relationship between CO₂ content (CCO₂) and PCO₂. Indeed, metabolic acidosis can change the PCO₂/CCO₂ relationship so that PCO₂ is higher for a given CCO₂. Low oxygen saturation, by promoting more CO₂ binding to hemoglobin (Haldane effect), increases the CCO₂ for a given PCO₂¹⁰. It is not completely clear to what extent these factors would impact the PCO₂/CCO₂ relationship and influence the ΔPCO₂/ΔO₂ ratio. Answering this question would help to define the applicability of this ratio in different clinical situations.

Therefore, we used, in secondary analysis, the original study published by Vallet et al.¹ with the aim to assess the behavior of ΔPCO₂/ΔO₂ ratio, ΔCCO₂/ΔO₂ ratio, and their components in the regional model of progressive tissue hypoxia generated by IH or HH¹. We also investigated the metabolic acidosis (pH) and Haldane effects on the PCO₂/CCO₂ relationship. Since the flow was maintained unchanged in the HH model, we hypothesized that ΔPCO₂/ΔO₂ and ΔCCO₂/ΔO₂ ratios might not be able to detect the occurrence of anaerobic metabolism as the sustained blood flow would be sufficient to wash out the CO₂ generated by hypoxic cells in that model.

## Methods

**Animal preparation.** The original study was approved by the University of Alabama at Birmingham Institutional Animal Care and Use Committee. The study is reported in accordance with the ARRIVE guidelines. All experiments were performed in accordance with relevant guidelines and regulations. Twelve dogs of either sex and mixed breed were used¹. All animals were anesthetized with intravenous 30 mg/kg of sodium phenobarbital and mechanically ventilated with a Harvard animal respirator at 10 breaths/min. Lamps suspended above the operating table were used to maintain core temperature near 37 °C. Tidal volume was varied to maintain systemic arterial PCO₂ between 30 and 35 mmHg. The ventilator setting was kept unchanged during the rest of the experiment. A 20 mg of succinylcholine chloride was given intramuscularly and a continuous infusion (0.1 mg/mL/min) was begun. Anesthesia depth was checked regularly by vigorous toe pinching, and additional anesthetic was given if systemic blood pressure and heart rate responded.

Catheters were inserted into the pulmonary artery (through the internal jugular vein) and common carotid artery for continuous measurements of vascular pressures and blood sampling. Arterial inflow (Q) and venous outflow from the left hindlimb were isolated, as previously described¹,¹¹ (Supplemental Digital Content 1, Appendix). A roller occlusive pump directed blood flow from the right hindlimb femoral artery to the femoral artery of the vascularly isolated left hindlimb. A sampling port and pressure transducer were placed in this circuit proximal to the limb. A membrane oxygenator (model 0800-2A, Sci Med) was interposed in the perfusion circuit. A gas flow mixer (model GF-3, Cameron Instruments) supplied O₂, N₂, and CO₂ to the oxygenator, as needed, to produce normoxia or hypoxia with normocapnia in the blood supply to the hindlimb. A water bath warmed the oxygenator so that perfusion to the isolated hindlimb was at 37 °C after heat loss through the tubing.

**Measurements.** Blood samples from the carotid, femoral, and pulmonary arteries and femoral vein were obtained simultaneously. Blood gas tensions and pH were measured in an acid-base analyzer (ABL-30, Radiometer, Westlake, OH) at 37 °C and later corrected to esophageal temperature at the time of sampling. Oxygen saturation was measured with a co-oximeter calibrated for dog blood (IL-282, Instrumentation Lab, Lexington, MA). Arterial oxygen content was calculated as CaO₂ (mL) = 1.34 × Hb (g/dL) × SaO₂ + 0.0031 × PaO₂ (mmHg), where SaO₂ is the oxygen saturation of arterial blood, Hb the hemoglobin concentration, and PaO₂ the arterial oxygen tension. Hindlimb venous oxygen content was calculated as CvO₂ (mL) = 1.34 × Hb (g/dL) × SvO₂ + 0.0031 × PvO₂ (mmHg), where PvO₂ is the hindlimb venous oxygen tension, and SvO₂ is the hindlimb venous oxygen saturation. ΔO₂ was calculated as CaO₂ - CvO₂. Hindlimb VO₂ (VO₂) was calculated
PvCO₂ Partial venous carbon dioxide tension

SvO₂ Venous oxygen saturation

SaO₂ Arterial oxygen saturation

PaO₂ Partial arterial oxygen tension

PvO₂ Partial venous oxygen tension

Hb Hemoglobin

In a landmark study, Vallet et al. demonstrated the determinant role of blood flow in the tissue hypoxia-induced increased venous-to-arterial CO₂ tension difference (ΔPCO₂)¹. Their data supported the hypothesis that increases in the venous PCO₂ are primarily a function of changes in regional blood flow, independently of the degree of hypoxia. Gutierrez G has confirmed this conclusion in a mathematical model of tissue-to-blood CO₂ exchange during hypoxia². In these previous publications, the behavior of ΔPCO₂ over the arterial-to-venous oxygen content difference (ΔO₂) ratio (ΔPCO₂/ΔO₂), and the difference between venous-to-arterial CO₂ content (ΔCCO₂) over ΔO₂ ratio (ΔCCO₂/ΔO₂) in a model of progressive tissue hypoxia generated by reducing either flow [ischemic hypoxia (IH)] or arterial oxygen tension [hypoxic hypoxia (HH)], were not investigated³,².

Several clinical studies³⁻⁷ have shown that ΔPCO₂/ΔO₂ ratio, taken as a surrogate of respiratory quotient (RQ), was associated with elevated lactate levels and oxygen supply dependency considered, in those studies, as indices of global anaerobic metabolism in critically ill patients with tissue hypoperfusion. However, in an experimental study, Dubin et al. found that ΔPCO₂/ΔO₂ ratio was a poor indicator of anaerobic metabolism in the hemodilution model of tissue hypoxia, where anemia was associated with preserved blood flow⁸. Similarly, other authors suggested that ΔPCO₂/ΔO₂ ratio might not rise during tissue hypoxia conditions when associated with normal/high blood flow because venous blood flow seemed to guarantee a sufficient clearance of CO₂ generated by the anaerobic metabolism⁹. Thus, it is unclear if the ΔPCO₂/ΔO₂ ratio would be able to depict the presence of anaerobic metabolism in patients with maintained blood flow (cardiac output).

Furthermore, one estimates that the ΔPCO₂/ΔO₂ ratio might be affected by other factors than anaerobic metabolism by influencing the relationship between CO₂ content (CCO₂) and PCO₂. Indeed, metabolic acidosis can change the PCO₂/CCO₂ relationship so that PCO₂ is higher for a given CCO₂. Low oxygen saturation, by promoting more CO₂ binding to hemoglobin (Haldane effect), increases the CCO₂ for a given PCO₂¹⁰. It is not completely clear to what extent these factors would impact the PCO₂/CCO₂ relationship and influence the ΔPCO₂/ΔO₂ ratio. Answering this question would help to define the applicability of this ratio in different clinical situations.

Therefore, we used, in secondary analysis, the original study published by Vallet et al.¹ with the aim to assess the behavior of ΔPCO₂/ΔO₂ ratio, ΔCCO₂/ΔO₂ ratio, and their components in the regional model of progressive tissue hypoxia generated by IH or HH¹. We also investigated the metabolic acidosis (pH) and Haldane effects on the PCO₂/CCO₂ relationship. Since the flow was maintained unchanged in the HH model, we hypothesized that ΔPCO₂/ΔO₂ and ΔCCO₂/ΔO₂ ratios might not be able to detect the occurrence of anaerobic metabolism as the sustained blood flow would be sufficient to wash out the CO₂ generated by hypoxic cells in that model.

## Methods

**Animal preparation.** The original study was approved by the University of Alabama at Birmingham Institutional Animal Care and Use Committee. The study is reported in accordance with the ARRIVE guidelines. All experiments were performed in accordance with relevant guidelines and regulations. Twelve dogs of either sex and mixed breed were used¹. All animals were anesthetized with intravenous 30 mg/kg of sodium phenobarbital and mechanically ventilated with a Harvard animal respirator at 10 breaths/min. Lamps suspended above the operating table were used to maintain core temperature near 37 °C. Tidal volume was varied to maintain systemic arterial PCO₂ between 30 and 35 mmHg. The ventilator setting was kept unchanged during the rest of the experiment. A 20 mg of succinylcholine chloride was given intramuscularly and a continuous infusion (0.1 mg/mL/min) was begun. Anesthesia depth was checked regularly by vigorous toe pinching, and additional anesthetic was given if systemic blood pressure and heart rate responded.

Catheters were inserted into the pulmonary artery (through the internal jugular vein) and common carotid artery for continuous measurements of vascular pressures and blood sampling. Arterial inflow (Q) and venous outflow from the left hindlimb were isolated, as previously described¹,¹¹ (Supplemental Digital Content 1, Appendix). A roller occlusive pump directed blood flow from the right hindlimb femoral artery to the femoral artery of the vascularity isolated left hindlimb. A sampling port and pressure transducer were placed in this circuit proximal to the limb. A membrane oxygenator (model 0800-2A, Sci Med) was interposed in the perfusion circuit. A gas flow mixer (model GF-3, Cameron Instruments) supplied O₂, N₂, and CO₂ to the oxygenator, as needed, to produce normoxia or hypoxia with normocapnia in the blood supply to the hindlimb. A water bath warmed the oxygenator so that perfusion to the isolated hindlimb was at 37 °C after heat loss through the tubing.

**Measurements.** Blood samples from the carotid, femoral, and pulmonary arteries and femoral vein were obtained simultaneously. Blood gas tensions and pH were measured in an acid-base analyzer (ABL-30, Radiometer, Westlake, OH) at 37 °C and later corrected to esophageal temperature at the time of sampling. Oxygen saturation was measured with a co-oximeter calibrated for dog blood (IL-282, Instrumentation Lab, Lexington, MA). Arterial oxygen content was calculated as CaO₂ (mL) = 1.34 × Hb (g/dL) × SaO₂ + 0.0031 × PaO₂ (mmHg), where SaO₂ is the oxygen saturation of arterial blood, Hb the hemoglobin concentration, and PaO₂ the arterial oxygen tension. Hindlimb venous oxygen content was calculated as CvO₂ (mL) = 1.34 × Hb (g/dL) × SvO₂ + 0.0031 × PvO₂ (mmHg), where PvO₂ is the hindlimb venous oxygen tension, and SvO₂ is the hindlimb venous oxygen saturation. ΔO₂ was calculated as CaO₂ - CvO₂. Hindlimb VO₂ (VO₂) was calculated
as the product of Q (leg blood flow) and ΔO₂. Hindlimb oxygen delivery (DO₂) was calculated by using the formula: DO₂ (mL/min) = CaO₂ × Q × 10. Hindlimb oxygen extraction (OE) was defined as: OE = V̇O₂/DO₂.

ΔPCO₂ was calculated as the difference between the hindlimb venous carbon dioxide tension (PvCO₂) and hindlimb arterial PCO₂ (PaCO₂). In the original study, the hindlimb difference between venous-to-arterial CO₂ content (CvCO₂ - CaCO₂) was calculated with the McHardy equation (as proposed by Neviere et al.¹²): ΔCCO₂ = 11.02 × [(PvCO₂)⁰.³⁹⁶ - (PaCO₂)⁰.³⁹⁶] - (15 - Hb) × 0.015 × (PvCO₂ - PaCO₂) - (95 - SaO₂) × 0.064. However, the most used equation to calculate the blood CO₂ content is the Douglas equation¹³, which includes pH:

$$ \text{Blood CO}_{2\text{D}} \text{ content [blood Douglas CCO}_{2} \text{ (mL)]} \\ = \text{Plasma CCO}_{2} \times [1-0.0289 \times (\text{Hb})/(3.352-0.456 \times \text{SO}_{2}) \times (8.142-\text{pH})] $$

where plasma CCO₂ = 2.226 × S × plasma PCO₂ × (1 + 10pH-pK'), CCO₂ is CO₂ content, SO₂ is oxygen saturation, S is the plasma CO₂ solubility coefficient, and pK' is the apparent pK.

S and pK' were calculated as follow:

$$ S = 0.0307 + [0.00057 \times (37-T)] + [0.00002 \times (37-T)^2] $$

and

$$ pK' = 6.086 + [0.042 \times (7.4-pH)] + ((38-T) \times \{0.00472 + [0.00139 \times (7.4-pH)]\}) $$

where T is the temperature expressed as °C.

The difference between venous-to-arterial CCO₂ calculated with the Douglas equation was: ΔCCO₂D = CvCO₂D - CaCO₂D.

To investigate the metabolic acidosis and Haldane effects on the PCO₂/CCO₂ relationship, default (Def) values of blood CCO₂ were calculated with the Douglas's equation by using only the resting values of pH and SvO₂ for each dog as following: DefpH-ΔCCO₂D = DefpH-CvCO₂D - DefpH-CaCO₂D, and DefSvO₂-ΔCCO₂D = DefSvO₂-CvCO₂D - DefSvO₂-CaCO₂D.

Leg blood flow, DO₂, and V̇O₂ were reported per kilogram of muscle mass.

We also calculated the hindlimb ΔPCO₂/ΔO₂, ΔCCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ ratios.

**Experimental protocol.** The experimental model was already described previously¹. After all pressures and flows were stable for at least 30 min, the experiment began with a 30-min control period, during which measurements were obtained every 15 min. In the progressive ischemic hypoxia (IH) group, Q was then decreased every 15 min to produce Q values of ~ 60, 45, 40, 30, 20, 15, and 10 mL/kg/min. In the hypoxic hypoxia (HH) group, Q was set at 60 mL/kg/min and limb DO₂ was reduced by decreasing arterial PO₂ from 100 to ~ 15 mmHg (i.e., CaO₂ of 17 to 2 mL O₂/100 mL) in eight steps at 15-min intervals. A flow rate of 60 mL/kg/min was chosen for progressive hypoxia because it is within the range of resting blood flow to normal skeletal muscle and for the practical reason that a moderate flow was necessary to achieve the desired low PO₂ values using the membrane oxygenator. Oxygen and CO₂-derived variables were determined every 15 min, 13 min after the change in hindlimb arterial flow or PO₂.

For each experiment, regression lines were fitted to the delivery independent and dependent portions of the delivery-uptake curve using a dual-line, least squares method¹⁴. The intercept of these two lines defined the critical DO₂ (DO₂crit), that is, the delivery at which V̇O₂ began to fall with any further decline in DO₂.

**Statistical analysis.** All data are expressed as mean ± SEM after assessed for normality using the Kolmogorov-Smirnov test.

Comparisons of data within and between groups were performed using a mixed ANOVA. Post-hoc paired and unpaired t tests were used, as appropriate, for one-time comparisons. The Bonferroni method was used to adjust for multiple comparisons.

Statistical analysis was performed using GraphPad Prism 6.0 software for windows (San Diego, California, USA). p < 0.006 and p < 0.007 were considered statistically significant for the between-group and within-group (with the baseline) comparisons, respectively. All reported p values are two-sided.

## Results

Systemic hemodynamics and oxygen-derived variables remain unchanged throughout the protocol with no differences between the IH and HH models (Supplemental Digital Content 2, Table S1).

In both groups, the V̇O₂/DO₂ graph depicts the typical biphasic relationship (Supplemental Digital Content 3, Figure S1). There was no statistically significant difference between the mean DO₂crit in the HH and IH models (6.9 ± 0.6 vs. 6.0 ± 0.5 mL/kg/min, p = 0.28, respectively). SvO₂ at DO₂crit was not statistically different between the two groups (25 ± 1.7% in HH vs. 26 ± 1.5% in IH, p = 0.66). However, for the lower DO₂ values, SvO₂ was significantly higher in the IH model than in the HH group (Supplemental Digital Content 4, Figure S2). EO₂ at DO₂crit was significantly higher in the IH group than in the HH model (74 ± 2% vs. 60 ± 4%, p = 0.01) and increased continuously and similarly in both groups (Supplemental Digital Content 5, Figure S3). ΔPCO₂ risen significantly in the IH model and did not change in the HH model (Supplemental Digital Content 6, Figure S4).

**Time course of venous-to-arterial CCO₂ difference.** ΔCCO₂ calculated with the McHardy equation increased progressively along with the decrease in DO₂ in the IH group but remained unchanged and even significantly decreased at the lowest DO₂ value on the HH group (Fig. 1A). At DO₂crit, ΔCCO₂ was significantly
as the product of Q (leg blood flow) and ΔO₂. Hindlimb oxygen delivery (DO₂) was calculated by using the formula: DO₂ (mL/min) = CaO₂ × Q × 10. Hindlimb oxygen extraction (OE) was defined as: OE = V̇O₂/DO₂.

ΔPCO₂ was calculated as the difference between the hindlimb venous carbon dioxide tension (PvCO₂) and hindlimb arterial PCO₂ (PaCO₂). In the original study, the hindlimb difference between venous-to-arterial CO₂ content (CvCO₂ - CaCO₂) was calculated with the McHardy equation (as proposed by Neviere et al.¹²): ΔCCO₂ = 11.02 × [(PvCO₂)⁰.³⁹⁶ - (PaCO₂)⁰.³⁹⁶] - (15 - Hb) × 0.015 × (PvCO₂ - PaCO₂) - (95 - SaO₂) × 0.064. However, the most used equation to calculate the blood CO₂ content is the Douglas equation¹³, which includes pH:

$$ \text{Blood CO}_{2\text{D}} \text{ content [blood Douglas CCO}_2 \text{ (mL)]} \\ = \text{Plasma CCO}_2 \times [1 - 0.0289 \times (\text{Hb})/(3.352 - 0.456 \times \text{SO}_2) \times (8.142 - \text{pH})] $$

where plasma CCO₂ = 2.226 × S × plasma PCO₂ × (1 + 10pH-pK'), CCO₂ is CO₂ content, SO₂ is oxygen saturation, S is the plasma CO₂ solubility coefficient, and pK' is the apparent pK.

S and pK' were calculated as follows:

$$ S = 0.0307 + [0.00057 \times (37-T)] + [0.00002 \times (37-T)^2] $$

and

$$ pK' = 6.086 + [0.042 \times (7.4-pH)] + ((38-T) \times \{0.00472 + [0.00139 \times (7.4-pH)]\}) $$

where T is the temperature expressed as °C.

The difference between venous-to-arterial CCO₂ calculated with the Douglas equation was: ΔCCO₂D = CvCO₂D - CaCO₂D.

To investigate the metabolic acidosis and Haldane effects on the PCO₂/CCO₂ relationship, default (Def) values of blood CCO₂ were calculated with the Douglas's equation by using only the resting values of pH and SvO₂ for each dog as following: DefpH-ΔCCO₂D = DefpH-CvCO₂D - DefpH-CaCO₂D, and DefSvO₂-ΔCCO₂D = DefSvO₂-CvCO₂D - DefSvO₂-CaCO₂D.

Leg blood flow, DO₂, and V̇O₂ were reported per kilogram of muscle mass.

We also calculated the hindlimb ΔPCO₂/ΔO₂, ΔCCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ ratios.

**Experimental protocol.** The experimental model was already described previously¹. After all pressures and flows were stable for at least 30 min, the experiment began with a 30-min control period, during which measurements were obtained every 15 min. In the progressive ischemic hypoxia (IH) group, Q was then decreased every 15 min to produce Q values of ~ 60, 45, 40, 30, 20, 15, and 10 mL/kg/min. In the hypoxic hypoxia (HH) group, Q was set at 60 mL/kg/min and limb DO₂ was reduced by decreasing arterial PO₂ from 100 to ~ 15 mmHg (i.e., CaO₂ of 17 to 2 mL O₂/100 mL) in eight steps at 15-min intervals. A flow rate of 60 mL/kg/min was chosen for progressive hypoxia because it is within the range of resting blood flow to normal skeletal muscle and for the practical reason that a moderate flow was necessary to achieve the desired low PO₂ values using the membrane oxygenator. Oxygen and CO₂-derived variables were determined every 15 min, 13 min after the change in hindlimb arterial flow or PO₂.

For each experiment, regression lines were fitted to the delivery independent and dependent portions of the delivery-uptake curve using a dual-line, least squares method¹⁴. The intercept of these two lines defined the critical DO₂ (DO₂crit), that is, the delivery at which V̇O₂ began to fall with any further decline in DO₂.

**Statistical analysis.** All data are expressed as mean ± SEM after assessed for normality using the Kolmogorov-Smirnov test.

Comparisons of data within and between groups were performed using a mixed ANOVA. Post-hoc paired and unpaired t tests were used, as appropriate, for one-time comparisons. The Bonferroni method was used to adjust for multiple comparisons.

Statistical analysis was performed using GraphPad Prism 6.0 software for windows (San Diego, California, USA). p < 0.006 and p < 0.007 were considered statistically significant for the between-group and within-group (with the baseline) comparisons, respectively. All reported p values are two-sided.

## Results

Systemic hemodynamics and oxygen-derived variables remain unchanged throughout the protocol with no differences between the IH and HH models (Supplemental Digital Content 2, Table S1).

In both groups, the V̇O₂/DO₂ graph depicts the typical biphasic relationship (Supplemental Digital Content 3, Figure S1). There was no statistically significant difference between the mean DO₂crit in the HH and IH models (6.9 ± 0.6 vs. 6.0 ± 0.5 mL/kg/min, p = 0.28, respectively). SvO₂ at DO₂crit was not statistically different between the two groups (25 ± 1.7% in HH vs. 26 ± 1.5% in IH, p = 0.66). However, for the lower DO₂ values, SvO₂ was significantly higher in the IH model than in the HH group (Supplemental Digital Content 4, Figure S2). EO₂ at DO₂crit was significantly higher in the IH group than in the HH model (74 ± 2% vs. 60 ± 4%, p = 0.01) and increased continuously and similarly in both groups (Supplemental Digital Content 5, Figure S3). ΔPCO₂ risen significantly in the IH model and did not change in the HH model (Supplemental Digital Content 6, Figure S4).

**Time course of venous-to-arterial CCO₂ difference.** ΔCCO₂ calculated with the McHardy equation increased progressively along with the decrease in DO₂ in the IH group but remained unchanged and even significantly decreased at the lowest DO₂ value on the HH group (Fig. 1A). At DO₂crit, ΔCCO₂ was significantly
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Hindlimb venous-to-arterial CO₂ content difference (ΔCCO₂) calculated with McHardy equation (A) and with Douglas equation (ΔCCO₂D) (B) as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). \*p*<0.006 vs. HH, \*\*p*<0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Hindlimb venous pH as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). \*p*<0.006 vs. HH, \*\*p*<0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

higher in the IH group than in the HH group (7.5±0.66 vs. 4.6±0.5 mL, *p*=0.006, respectively), and it was significantly different from the baseline only in the IH group (*p*=0.0023).

ΔCCO₂D calculated with the Douglas equation, in the IH group, increased with the decrease in DO₂ down to DO₂crit. However, beyond DO₂crit, ΔCCO₂D started to decrease with the further decline in DO₂ to become not significantly different from its baseline value at the lowest value of DO₂ (Fig. 1B). In the HH group, ΔCCO₂D had the same pattern as ΔCCO₂ calculated with the McHardy equation (Fig. 1A,B), which remained unchanged in parallel with the decreases in DO₂ to become significantly lower than its baseline (*p*<0.001) only at the end of the experiment. At DO₂crit, ΔCCO₂D was greater in the IH group compared to the HH group (11.0±0.88 vs. 7.0±0.56 mL, *p*=0.003, respectively), and it was significantly higher than its baseline value (*p*<0.001) only in the IH group (Fig. 1B).

**pH and Haldane effects on the PCO₂/CCO₂ relationship.** Hindlimb venous pH (pHv) remained unchanged with the decline in DO₂ down to DO₂crit in both groups (Fig. 2). However, beyond DO₂crit, pHv decreased significantly only in the IH group and remained stable in the HH group (Fig. 2).

The venous CCO₂ calculated, with the Douglas equation, by acknowledging the changes in pHv (CvCO₂D) increased first with the rise in PvCO₂, but then after, it stabilized despite further increases in PvCO₂, due to the fall in pHv. Eventually, despite the continuously increasing PvCO₂, CvCO₂D decreased due to the marked decline in pHv (Fig. 3). On the contrary, there was almost a linear increase in DefpH-CvCO₂D (without accounting for the changes in pHv) with the increase in PvCO₂ (Fig. 4). Also, DefpH-ΔCCO₂D increased linearly with the decreases in DO₂ in the IH group, while it remained unchanged in the HH group (Supplemental Digital Content 7, Figure S5).

The relationship between PvCO₂ and CCO₂ calculated without accounting for the changes in SvO₂ was the same as that if we acknowledged the variations in SvO₂ (Supplemental Digital Content 8, Figure S6).
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Hindlimb venous-to-arterial CO₂ content difference (ΔCCO₂) calculated with McHardy equation (A) and with Douglas equation (ΔCCO₂D) (B) as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). \*p*<0.006 vs. HH, \*\*p*<0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Hindlimb venous pH as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). \*p*<0.006 vs. HH, \*\*p*<0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

higher in the IH group than in the HH group (7.5±0.66 vs. 4.6±0.5 mL, *p*=0.006, respectively), and it was significantly different from the baseline only in the IH group (*p*=0.0023).

ΔCCO₂D calculated with the Douglas equation, in the IH group, increased with the decrease in DO₂ down to DO₂crit. However, beyond DO₂crit, ΔCCO₂D started to decrease with the further decline in DO₂ to become not significantly different from its baseline value at the lowest value of DO₂ (Fig. 1B). In the HH group, ΔCCO₂D had the same pattern as ΔCCO₂ calculated with the McHardy equation (Fig. 1A,B), which remained unchanged in parallel with the decreases in DO₂ to become significantly lower than its baseline (*p*<0.001) only at the end of the experiment. At DO₂crit, ΔCCO₂D was greater in the IH group compared to the HH group (11.0±0.88 vs. 7.0±0.56 mL, *p*=0.003, respectively), and it was significantly higher than its baseline value (*p*<0.001) only in the IH group (Fig. 1B).

**pH and Haldane effects on the PCO₂/CCO₂ relationship.** Hindlimb venous pH (pHv) remained unchanged with the decline in DO₂ down to DO₂crit in both groups (Fig. 2). However, beyond DO₂crit, pHv decreased significantly only in the IH group and remained stable in the HH group (Fig. 2).

The venous CCO₂ calculated, with the Douglas equation, by acknowledging the changes in pHv (CvCO₂D) increased first with the rise in PvCO₂, but then after, it stabilized despite further increases in PvCO₂, due to the fall in pHv. Eventually, despite the continuously increasing PvCO₂, CvCO₂D decreased due to the marked decline in pHv (Fig. 3). On the contrary, there was almost a linear increase in DefpH-CvCO₂D (without accounting for the changes in pHv) with the increase in PvCO₂ (Fig. 4). Also, DefpH-ΔCCO₂D increased linearly with the decreases in DO₂ in the IH group, while it remained unchanged in the HH group (Supplemental Digital Content 7, Figure S5).

The relationship between PvCO₂ and CCO₂ calculated without accounting for the changes in SvO₂ was the same as that if we acknowledged the variations in SvO₂ (Supplemental Digital Content 8, Figure S6).
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Hindlimb venous CO₂ content (CCO₂) as a function of hindlimb venous PCO₂ for CCO₂ calculated with accounting for pH changes (with_pH) and without accounting for pH changes (without_pH) using Douglas equation (CCO₂D). \*p < 0.006 vs. HH, \*\*p < 0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Hindlimb venous-to-arterial PCO₂ difference (ΔPCO₂) over the arterial-to-venous O₂ difference (ΔO₂) ratio (ΔPCO₂/ΔO₂) as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). At DO₂crit, ΔPCO₂/ΔO₂ was significantly higher in HH model (1.82 ± 0.09) than IH model (1.39 ± 0.06). \*p < 0.006 vs. HH, \*\*p < 0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

**Time course of ΔPCO₂/ΔO₂, ΔCCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ ratios.** ΔO₂ increased significantly in the IH and decreased in the HH in parallel with the decreases in DO₂ (Supplemental Digital Content 9, Figure S7).

At DO₂crit, ΔPCO₂/ΔO₂ ratio was significantly higher in the HH group than in the IH group (1.82 ± 0.09 mmHg/mL vs. 1.39 ± 0.06 mmHg/mL, *p* = 0.002, respectively). In both groups, ΔPCO₂/ΔO₂ ratio increased significantly only after reaching DO₂crit (Fig. 4). Also, the increase in ΔPCO₂/ΔO₂ ratio was significantly higher in the HH than in the IH group.

ΔCCO₂/ΔO₂ ratio increased after DO₂crit was reached in both groups, with a trend to decrease by the end of the experiment in the HH group (Supplemental Digital Content 10, Figure S8). At DO₂crit, there was no significant difference between the two groups (IH: 0.59 ± 0.02 vs. HH: 0.67 ± 0.03, *p* = 0.05).

In both groups, ΔCCO₂D/ΔO₂ ratio increased significantly after reaching DO₂crit. However, in the HH group, at lower values of DO₂, ΔCCO₂D/ΔO₂ ratio started to decline but remained significantly higher than its baseline value. In the IH group, beyond DO₂crit, ΔCCO₂D/ΔO₂ ratio begun to decrease at a higher value of DO₂ than in the HH group, to become not significantly different from its baseline value at the end of the experiment (Fig. 5). At DO₂crit, ΔCCO₂D/ΔO₂ was not significantly different between the two groups (0.87 ± 0.05 for IH vs. 1.01 ± 0.06 for HH, *p* = 0.09).

In both groups, DefpH-ΔCCO₂D/ΔO₂ (without accounting for pH changes) increased similarly and linearly in parallel with the decrease in DO₂ (Supplemental Digital Content 11, Figure S9). The increase in DefpH-ΔCCO₂D/ΔO₂ in IH occurred before reaching DO₂crit.

**Discussion**

The main findings of our study were that: (1) in both groups, ΔPCO₂/ΔO₂ as well as ΔCCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ increases significantly in parallel with the decreases in DO₂ only after reaching DO₂crit; (2) beyond DO₂crit, the time course of ΔPCO₂/ΔO₂ ratio was different from that of ΔCCO₂D/ΔO₂ or ΔCCO₂/ΔO₂ ratio, in both
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Hindlimb venous CO₂ content (CCO₂) as a function of hindlimb venous PCO₂ for CCO₂ calculated with accounting for pH changes (with_pH) and without accounting for pH changes (without_pH) using Douglas equation (CCO₂D). \*p < 0.006 vs. HH, \*\*p < 0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Hindlimb venous-to-arterial PCO₂ difference (ΔPCO₂) over the arterial-to-venous O₂ difference (ΔO₂) ratio (ΔPCO₂/ΔO₂) as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). At DO₂crit, ΔPCO₂/ΔO₂ was significantly higher in HH model (1.82 ± 0.09) than IH model (1.39 ± 0.06). \*p < 0.006 vs. HH, \*\*p < 0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

**Time course of ΔPCO₂/ΔO₂, ΔCCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ ratios.** ΔO₂ increased significantly in the IH and decreased in the HH in parallel with the decreases in DO₂ (Supplemental Digital Content 9, Figure S7).

At DO₂crit, ΔPCO₂/ΔO₂ ratio was significantly higher in the HH group than in the IH group (1.82 ± 0.09 mmHg/mL vs. 1.39 ± 0.06 mmHg/mL, *p* = 0.002, respectively). In both groups, ΔPCO₂/ΔO₂ ratio increased significantly only after reaching DO₂crit (Fig. 4). Also, the increase in ΔPCO₂/ΔO₂ ratio was significantly higher in the HH than in the IH group.

ΔCCO₂/ΔO₂ ratio increased after DO₂crit was reached in both groups, with a trend to decrease by the end of the experiment in the HH group (Supplemental Digital Content 10, Figure S8). At DO₂crit, there was no significant difference between the two groups (IH: 0.59 ± 0.02 vs. HH: 0.67 ± 0.03, *p* = 0.05).

In both groups, ΔCCO₂D/ΔO₂ ratio increased significantly after reaching DO₂crit. However, in the HH group, at lower values of DO₂, ΔCCO₂D/ΔO₂ ratio started to decline but remained significantly higher than its baseline value. In the IH group, beyond DO₂crit, ΔCCO₂D/ΔO₂ ratio begun to decrease at a higher value of DO₂ than in the HH group, to become not significantly different from its baseline value at the end of the experiment (Fig. 5). At DO₂crit, ΔCCO₂D/ΔO₂ was not significantly different between the two groups (0.87 ± 0.05 for IH vs. 1.01 ± 0.06 for HH, *p* = 0.09).

In both groups, DefpH-ΔCCO₂D/ΔO₂ (without accounting for pH changes) increased similarly and linearly in parallel with the decrease in DO₂ (Supplemental Digital Content 11, Figure S9). The increase in DefpH-ΔCCO₂D/ΔO₂ in IH occurred before reaching DO₂crit.

**Discussion**

The main findings of our study were that: (1) in both groups, ΔPCO₂/ΔO₂ as well as ΔCCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ increases significantly in parallel with the decreases in DO₂ only after reaching DO₂crit; (2) beyond DO₂crit, the time course of ΔPCO₂/ΔO₂ ratio was different from that of ΔCCO₂D/ΔO₂ or ΔCCO₂/ΔO₂ ratio, in both
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Hindlimb venous-to-arterial CO₂ content difference calculated with Douglas equation (ΔCCO₂D) over the arterial-to-venous O₂ difference (ΔO₂) ratio (ΔCCO₂D/ΔO₂) as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). At DO₂crit, there was no significantly difference between HH model (1.01 ± 0.06) and IH model (0.87 ± 0.05). \*p < 0.006 vs. HH, \*\*p < 0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

groups; (3) metabolic acidosis, but not Haldane effect influenced significantly the PCO₂/CCO₂ relationship explaining the discrepancy between ΔPCO₂ and ΔCCO₂D; (4) the method of CCO₂ calculation had a considerable impact on the results and yielded different conclusions.

Anaerobic metabolism occurrence is usually due to cellular hypoxia¹⁵. Whenever oxygen delivery decreases relative to demand, and the compensatory mechanism is exhausted, extra-mitochondrial anaerobic glycolysis occurs, and lactic acidosis develops¹⁶. We aimed to investigate if ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂ could reflect the development of anaerobic metabolism in two regional models of tissue hypoxia: IH, where the oxygen delivery progressively decreased by decreasing the blood flow, and HH, where the blood flow was maintained unchanged, and the oxygen delivery was reduced by decreasing the arterial oxygen content.

In experimental conditions of tissue hypoxia, the drop in VO₂ leads to decreased total VCO₂ generation, mainly related to the decrease in aerobic CO₂ production. However, under situations of hypoxia, tissue CO₂ increases as hydrogen ions generated by anaerobic sources of energy (hydrolysis of high-energy phosphates) are buffering by bicarbonate existing in the cells (anaerobic CO₂ production)¹⁷. Therefore, VCO₂ being reduced less than VO₂, the RQ (VCO₂/VO₂) should increase. Accordingly, the increase in RQ has been shown to be a useful marker of global tissue hypoxia¹⁸,¹⁹. Indeed, Groeneveld et al.¹⁸ observed, in an experimental model of a graded increase in positive end-expiratory pressure-induced a decrease in cardiac output and oxygen delivery in pigs, that the decline in VCO₂ (by 21 ± 2%) was less than in VO₂ (by 27 ± 2%).

However, airway RQ measurement necessitates a specific monitoring device (indirect calorimetry) that many hospitals might not have. Recently, there has been a growing interest in the ΔPCO₂/ΔO₂ ratio as a surrogate of the RQ to detect the development of global anaerobic metabolism in critically ill patients³⁻⁷. Indeed, several studies found an association between increased ΔPCO₂/ΔO₂ ratio and hyperlactatemia⁵ and decreased lactate clearance⁶,⁷, which were taken as markers of anaerobic metabolism activation. We⁴ and other authors³ have also shown that ΔPCO₂/ΔO₂ ratio had an excellent ability to detect the presence of VO₂/DO₂ dependency phenomenon, better than central venous oxygen saturation and blood lactate levels, in septic shock patients. Recently, Mesquida et al.²⁰ reported an association between ΔPCO₂/ΔO₂ ratio and ICU mortality in septic shock patients. In contrast, in other studies, ΔPCO₂/ΔO₂ was unable to predict hyperlactatemia, poor lactate clearance, or VO₂/DO₂ dependency and was not associated with outcome in septic shock or cardiac surgery patients⁹,²¹⁻²³. Thus, the relationship between ΔPCO₂/ΔO₂ and the presence of tissue hypoxia is controversial.

Indeed, the use of ΔPCO₂/ΔO₂ ratio as a surrogate of RQ supposes that the PCO₂/CCO₂ relationship is quasi-linear, which may be true over the physiological range of PCO₂²⁴. However, this relationship can be influenced by the degree of metabolic acidosis²⁵, hematocrit²⁶, and oxygen saturation (Haldane effect)⁸,²⁷, and it becomes nonlinear if these factors change²⁸. Indeed, severe metabolic acidosis, low hematocrit, and high oxygen saturation can increase PCO₂ for a given CCO₂ since less CO₂ is bound to hemoglobin⁸. Thus, ΔPCO₂ and ΔPCO₂/ΔO₂ ratio might be increased due to several factors unrelated to the blood flow and anaerobic metabolism. We found that metabolic acidosis influenced the PCO₂/CCO₂ relationship significantly. Indeed, when the changes in pHv were ignored, the PCO₂/CCO₂ relationship was almost linear (Fig. 3). However, CCO₂ was not linearly related to PCO₂ when the changes in pH were acknowledged. In fact, PCO₂ and CCO₂ changed in opposite directions as metabolic acid was added to the blood by the hypoxic cells (Fig. 3). That is because metabolic acidosis causes plasma and red blood cell CCO₂ and bicarbonates to decrease²⁹. In our study, the Haldane effect did not influence the PCO₂/CCO₂ relationship as the latter was the same, taking into account or not for the changes in SvO₂ (Supplemental Digital Content 8, Figure S6).
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Hindlimb venous-to-arterial CO₂ content difference calculated with Douglas equation (ΔCCO₂D) over the arterial-to-venous O₂ difference (ΔO₂) ratio (ΔCCO₂D/ΔO₂) as a function of hindlimb oxygen delivery (DO₂) for ischemic hypoxia model (IH) and hypoxic hypoxia model (HH). At DO₂crit, there was no significantly difference between HH model (1.01 ± 0.06) and IH model (0.87 ± 0.05). \*p < 0.006 vs. HH, \*\*p < 0.007 vs. baseline, mixed ANOVA.</figcaption></figure>

groups; (3) metabolic acidosis, but not Haldane effect influenced significantly the PCO₂/CCO₂ relationship explaining the discrepancy between ΔPCO₂ and ΔCCO₂D; (4) the method of CCO₂ calculation had a considerable impact on the results and yielded different conclusions.

Anaerobic metabolism occurrence is usually due to cellular hypoxia¹⁵. Whenever oxygen delivery decreases relative to demand, and the compensatory mechanism is exhausted, extra-mitochondrial anaerobic glycolysis occurs, and lactic acidosis develops¹⁶. We aimed to investigate if ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂ could reflect the development of anaerobic metabolism in two regional models of tissue hypoxia: IH, where the oxygen delivery progressively decreased by decreasing the blood flow, and HH, where the blood flow was maintained unchanged, and the oxygen delivery was reduced by decreasing the arterial oxygen content.

In experimental conditions of tissue hypoxia, the drop in VO₂ leads to decreased total VCO₂ generation, mainly related to the decrease in aerobic CO₂ production. However, under situations of hypoxia, tissue CO₂ increases as hydrogen ions generated by anaerobic sources of energy (hydrolysis of high-energy phosphates) are buffering by bicarbonate existing in the cells (anaerobic CO₂ production)¹⁷. Therefore, VCO₂ being reduced less than VO₂, the RQ (VCO₂/VO₂) should increase. Accordingly, the increase in RQ has been shown to be a useful marker of global tissue hypoxia¹⁸,¹⁹. Indeed, Groeneveld et al.¹⁸ observed, in an experimental model of a graded increase in positive end-expiratory pressure-induced a decrease in cardiac output and oxygen delivery in pigs, that the decline in VCO₂ (by 21 ± 2%) was less than in VO₂ (by 27 ± 2%).

However, airway RQ measurement necessitates a specific monitoring device (indirect calorimetry) that many hospitals might not have. Recently, there has been a growing interest in the ΔPCO₂/ΔO₂ ratio as a surrogate of the RQ to detect the development of global anaerobic metabolism in critically ill patients³⁻⁷. Indeed, several studies found an association between increased ΔPCO₂/ΔO₂ ratio and hyperlactatemia⁵ and decreased lactate clearance⁶,⁷, which were taken as markers of anaerobic metabolism activation. We⁴ and other authors³ have also shown that ΔPCO₂/ΔO₂ ratio had an excellent ability to detect the presence of VO₂/DO₂ dependency phenomenon, better than central venous oxygen saturation and blood lactate levels, in septic shock patients. Recently, Mesquida et al.²⁰ reported an association between ΔPCO₂/ΔO₂ ratio and ICU mortality in septic shock patients. In contrast, in other studies, ΔPCO₂/ΔO₂ was unable to predict hyperlactatemia, poor lactate clearance, or VO₂/DO₂ dependency and was not associated with outcome in septic shock or cardiac surgery patients⁹,²¹⁻²³. Thus, the relationship between ΔPCO₂/ΔO₂ and the presence of tissue hypoxia is controversial.

Indeed, the use of ΔPCO₂/ΔO₂ ratio as a surrogate of RQ supposes that the PCO₂/CCO₂ relationship is quasi-linear, which may be true over the physiological range of PCO₂²⁴. However, this relationship can be influenced by the degree of metabolic acidosis²⁵, hematocrit²⁶, and oxygen saturation (Haldane effect)⁸,²⁷, and it becomes nonlinear if these factors change²⁸. Indeed, severe metabolic acidosis, low hematocrit, and high oxygen saturation can increase PCO₂ for a given CCO₂ since less CO₂ is bound to hemoglobin⁸. Thus, ΔPCO₂ and ΔPCO₂/ΔO₂ ratio might be increased due to several factors unrelated to the blood flow and anaerobic metabolism. We found that metabolic acidosis influenced the PCO₂/CCO₂ relationship significantly. Indeed, when the changes in pHv were ignored, the PCO₂/CCO₂ relationship was almost linear (Fig. 3). However, CCO₂ was not linearly related to PCO₂ when the changes in pH were acknowledged. In fact, PCO₂ and CCO₂ changed in opposite directions as metabolic acid was added to the blood by the hypoxic cells (Fig. 3). That is because metabolic acidosis causes plasma and red blood cell CCO₂ and bicarbonates to decrease²⁹. In our study, the Haldane effect did not influence the PCO₂/CCO₂ relationship as the latter was the same, taking into account or not for the changes in SvO₂ (Supplemental Digital Content 8, Figure S6).
Our findings suggest that, in situations with moderate/severe metabolic acidosis, an elevated ΔPCO₂ might not reflect only low or inadequate blood flow but could also be ascribed to modifications of the CO₂-hemoglobin dissociation curve. Our results are in line with previous studies. Indeed, Sun et al.²⁹ found that, in healthy subjects, during heavy exercise, changes in pH had a significant influence on the PCO₂/CCO₂ relationship with CCO₂ not linearly related to PCO₂ and even varied in opposite directions after the lactic acidosis threshold was reached. However, in that study, changes in SO₂ (Haldane effect) had a minor influence on the PCO₂/CCO₂ relationship. Also, in septic shock patients, Mesquida et al.²⁰ observed that pH was the only best predictor of the discrepancy found between ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂; venous oxygen saturation (Haldane effect) had a minimal effect.

We observed that ΔPCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ significantly increased at DO₂crit and not before (Figs. 4 and 5), suggesting that these variables were able to depict the occurrence of oxygen supply dependency (DO₂crit) in both IH and HH groups. The increases in these variables were mainly due to the decline in ΔO₂ in the HH group and the rise in ΔPCO₂ and ΔCCO₂ in the IH group induced by the decrease in blood flow. In contrast, in an experimental study of hemodilution model of tissue hypoxia, Dubin et al.⁸ found that ΔPCO₂/ΔO₂ significantly increased before the fall in VO₂ and the sharp increase in RQ (measured by indirect calorimetry), and thus, it was a misleading indicator of anaerobic metabolism. The authors explained this finding by the effects of low hemoglobin on the CO₂-hemoglobin dissociation curve⁸. However, it is hard to compare these results together as the two tissue hypoxia models (HH and hemodilution) are different. Indeed, the effects of anemia on the CO₂-hemoglobin dissociation curve could be different from that of the low oxygen saturation (Haldane effect). Also, the magnitude of the decrease in venous oxygen saturation would be much more pronounced in the HH model, where the flow was maintained constant, than in the hemodilution model, where cardiac output increased by 126%⁸. Beyond DO₂crit, we observed a discrepancy between the evolutions of ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂ in both groups (Figs. 4 and 5). That might be explained by the different behavior of ΔPCO₂ and ΔCCO₂D at lower DO₂ values. Indeed, in the IH group, these two variables changed in opposite directions: ΔPCO₂ continued to increase, whereas ΔCCO₂D fell caused by metabolic acidosis (decreases in bicarbonate levels). In the HH model, ΔPCO₂ remained unchanged, whereas ΔCCO₂D decreased at lower DO₂ values (Fig. 1B and Supplemental Digital Content 6, Figure S4). Therefore, below DO₂crit, and at very low DO₂ values, ΔPCO₂/ΔO₂ ratio is confounded by the changes in the CO₂-hemoglobin curve induced by metabolic acidosis, and it does not reliably reflect the oxygen supply dependency phenomenon and the activation of anaerobic metabolism, especially in the IH tissue hypoxia model. However, in clinical practice, in such cases with very low DO₂, the clinical diagnosis of tissue hypoxia would be obvious without the need for such markers.

It is worth to note that the method of calculation of the difference in CCO₂ matters as the McHardy equation¹², and Douglas equation¹³ yielded different findings (Figs. 5 and Supplemental Digital Content 10, Figure S8). However, we think that the Douglas equation is much more used in research papers, and more accurate as it accounts for much more factors such as pH.

There is no reported data, in the literature, on the behavior of ΔCCO₂D/ΔO₂ ratio beyond DO₂crit at very low DO₂ values. This ratio tended to decrease in both tissue hypoxia models, even in the presence of anaerobic CO₂ production. It is possible that in case of advanced tissue hypoxia with massive decreases in VO₂, the anaerobic sources of CO₂ becoming much less important than the dramatically decreased aerobic ones leading to a reduction in VCO₂/VO₂ ratio.

We acknowledge several limitations to our study. First, our study was a secondary analysis that is subject to inherent limitations. Second, computation of CCO₂ is subject to an important potential risk of measurement errors due to the number of variables included in the equation³⁰ that might amplify during the calculation of ΔCCO₂D. Nevertheless, ΔCCO₂D/ΔO₂ ratio was already shown to be associated with mortality in septic shock patients⁹, suggesting that the influence of measurement errors might be limited.

## Conclusions

In both IH and HH regional models of tissue hypoxia, ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂ ratios both widened significantly only at the beginning of oxygen supply dependency. The hypoxic tissue hypoxia model yielded higher increases in ΔPCO₂/ΔO₂ than the IH model. At advanced stages of tissue hypoxia (very low DO₂), ΔPCO₂/ΔO₂ did not only reflect the ongoing anaerobic metabolism, but it was confounded by the effects of metabolic acidosis on the CO₂-hemoglobin dissociation curve, and then it should be interpreted with caution. For clinical practice, in severe metabolic acidosis situations, elevated ΔPCO₂ may not reflect the degree of tissue hypoperfusion. In these cases, calculating the difference in CCO₂ with the Douglas equation is advisable.

Received: 21 March 2021; Accepted: 28 April 2021

Published online: 13 May 2021

## References

1. Vallet, B., Teboul, J. L., Cain, S. & Curtis, S. Venoarterial CO₂ difference during regional ischemic or hypoxic hypoxia. *J. Appl. Physiol.* **89**, 1317–1321 (2000).

2. Gutierrez, G. A mathematical model of tissue-blood carbon dioxide exchange during hypoxia. *Am. J. Respir. Crit. Care Med.* **169**, 525–533 (2004).

3. Monnet, X. *et al*. Lactate and venoarterial carbon dioxide difference/arterial–venous oxygen difference ratio, but not central venous oxygen saturation, predict increase in oxygen consumption in fluid responders. *Crit. Care Med.* **41**, 1412–1420 (2013).

4. Mallat, J. *et al*. Ratios of central venous-to-arterial carbon dioxide content or tension to arteriovenous oxygen content are better markers of global anaerobic metabolism than lactate in septic shock patients. *Ann. Intensive Care* **6**, 10 (2016).

5. Mekontso-Dessap, A. *et al*. Combination of venoarterial PCO₂ difference with arteriovenous O₂ content difference to detect anaerobic metabolism in patients. *Intensive Care Med.* **28**, 272–277 (2002).
Our findings suggest that, in situations with moderate/severe metabolic acidosis, an elevated ΔPCO₂ might not reflect only low or inadequate blood flow but could also be ascribed to modifications of the CO₂-hemoglobin dissociation curve. Our results are in line with previous studies. Indeed, Sun et al.²⁹ found that, in healthy subjects, during heavy exercise, changes in pH had a significant influence on the PCO₂/CCO₂ relationship with CCO₂ not linearly related to PCO₂ and even varied in opposite directions after the lactic acidosis threshold was reached. However, in that study, changes in SO₂ (Haldane effect) had a minor influence on the PCO₂/CCO₂ relationship. Also, in septic shock patients, Mesquida et al.²⁰ observed that pH was the only best predictor of the discrepancy found between ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂; venous oxygen saturation (Haldane effect) had a minimal effect.

We observed that ΔPCO₂/ΔO₂, and ΔCCO₂D/ΔO₂ significantly increased at DO₂crit and not before (Figs. 4 and 5), suggesting that these variables were able to depict the occurrence of oxygen supply dependency (DO₂crit) in both IH and HH groups. The increases in these variables were mainly due to the decline in ΔO₂ in the HH group and the rise in ΔPCO₂ and ΔCCO₂ in the IH group induced by the decrease in blood flow. In contrast, in an experimental study of hemodilution model of tissue hypoxia, Dubin et al.⁸ found that ΔPCO₂/ΔO₂ significantly increased before the fall in VO₂ and the sharp increase in RQ (measured by indirect calorimetry), and thus, it was a misleading indicator of anaerobic metabolism. The authors explained this finding by the effects of low hemoglobin on the CO₂-hemoglobin dissociation curve⁸. However, it is hard to compare these results together as the two tissue hypoxia models (HH and hemodilution) are different. Indeed, the effects of anemia on the CO₂-hemoglobin dissociation curve could be different from that of the low oxygen saturation (Haldane effect). Also, the magnitude of the decrease in venous oxygen saturation would be much more pronounced in the HH model, where the flow was maintained constant, than in the hemodilution model, where cardiac output increased by 126%⁸. Beyond DO₂crit, we observed a discrepancy between the evolutions of ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂ in both groups (Figs. 4 and 5). That might be explained by the different behavior of ΔPCO₂ and ΔCCO₂D at lower DO₂ values. Indeed, in the IH group, these two variables changed in opposite directions: ΔPCO₂ continued to increase, whereas ΔCCO₂D fell caused by metabolic acidosis (decreases in bicarbonate levels). In the HH model, ΔPCO₂ remained unchanged, whereas ΔCCO₂D decreased at lower DO₂ values (Fig. 1B and Supplemental Digital Content 6, Figure S4). Therefore, below DO₂crit, and at very low DO₂ values, ΔPCO₂/ΔO₂ ratio is confounded by the changes in the CO₂-hemoglobin curve induced by metabolic acidosis, and it does not reliably reflect the oxygen supply dependency phenomenon and the activation of anaerobic metabolism, especially in the IH tissue hypoxia model. However, in clinical practice, in such cases with very low DO₂, the clinical diagnosis of tissue hypoxia would be obvious without the need for such markers.

It is worth to note that the method of calculation of the difference in CCO₂ matters as the McHardy equation¹², and Douglas equation¹³ yielded different findings (Figs. 5 and Supplemental Digital Content 10, Figure S8). However, we think that the Douglas equation is much more used in research papers, and more accurate as it accounts for much more factors such as pH.

There is no reported data, in the literature, on the behavior of ΔCCO₂D/ΔO₂ ratio beyond DO₂crit at very low DO₂ values. This ratio tended to decrease in both tissue hypoxia models, even in the presence of anaerobic CO₂ production. It is possible that in case of advanced tissue hypoxia with massive decreases in VO₂, the anaerobic sources of CO₂ becoming much less important than the dramatically decreased aerobic ones leading to a reduction in VCO₂/VO₂ ratio.

We acknowledge several limitations to our study. First, our study was a secondary analysis that is subject to inherent limitations. Second, computation of CCO₂ is subject to an important potential risk of measurement errors due to the number of variables included in the equation³⁰ that might amplify during the calculation of ΔCCO₂D. Nevertheless, ΔCCO₂D/ΔO₂ ratio was already shown to be associated with mortality in septic shock patients⁹, suggesting that the influence of measurement errors might be limited.

## Conclusions

In both IH and HH regional models of tissue hypoxia, ΔPCO₂/ΔO₂ and ΔCCO₂D/ΔO₂ ratios both widened significantly only at the beginning of oxygen supply dependency. The hypoxic tissue hypoxia model yielded higher increases in ΔPCO₂/ΔO₂ than the IH model. At advanced stages of tissue hypoxia (very low DO₂), ΔPCO₂/ΔO₂ did not only reflect the ongoing anaerobic metabolism, but it was confounded by the effects of metabolic acidosis on the CO₂-hemoglobin dissociation curve, and then it should be interpreted with caution. For clinical practice, in severe metabolic acidosis situations, elevated ΔPCO₂ may not reflect the degree of tissue hypoperfusion. In these cases, calculating the difference in CCO₂ with the Douglas equation is advisable.

Received: 21 March 2021; Accepted: 28 April 2021

Published online: 13 May 2021

## References

1. Vallet, B., Teboul, J. L., Cain, S. & Curtis, S. Venoarterial CO₂ difference during regional ischemic or hypoxic hypoxia. *J. Appl. Physiol.* **89**, 1317–1321 (2000).

2. Gutierrez, G. A mathematical model of tissue-blood carbon dioxide exchange during hypoxia. *Am. J. Respir. Crit. Care Med.* **169**, 525–533 (2004).

3. Monnet, X. *et al*. Lactate and venoarterial carbon dioxide difference/arterial–venous oxygen difference ratio, but not central venous oxygen saturation, predict increase in oxygen consumption in fluid responders. *Crit. Care Med.* **41**, 1412–1420 (2013).

4. Mallat, J. *et al*. Ratios of central venous-to-arterial carbon dioxide content or tension to arteriovenous oxygen content are better markers of global anaerobic metabolism than lactate in septic shock patients. *Ann. Intensive Care* **6**, 10 (2016).

5. Mekontso-Dessap, A. *et al*. Combination of venoarterial PCO₂ difference with arteriovenous O₂ content difference to detect anaerobic metabolism in patients. *Intensive Care Med.* **28**, 272–277 (2002).
6. Mesquida, J. et al. Central venous-to-arterial carbon dioxide difference combined with arterial-to-venous oxygen content difference is associated with lactate evolution in the hemodynamic resuscitation process in early septic shock. *Crit. Care* **19**, 126 (2015).

7. He, H. W., Liu, D. W., Long, Y. & Wang, X. T. High central venous-to-arterial CO₂ difference/arterial–central venous O₂ difference ratio is associated with poor lactate clearance in septic patients after resuscitation. *J. Crit. Care* **31**, 76–81 (2016).

8. Dubin, A. et al. Venoarterial PCO₂-to-arteriovenous oxygen content difference ratio is a poor surrogate for anaerobic metabolism in hemodilution: An experimental study. *Ann. Intensive Care* **7**, 65 (2017).

9. Ospina-Tascón, G. A. et al. Combination of arterial lactate levels and venous–arterial CO₂ to arterial–venous O₂ content difference ratio as markers of resuscitation in patients with septic shock. *Intensive Care Med.* **41**, 796–805 (2015).

10. Teboul, J. L. & Scheeren, T. Understanding the Haldane effect. *Intensive Care Med.* **43**, 91–93 (2016).

11. Cain, S. M. & Chapler, C. K. Oxygen extraction by canine hindlimb during hypoxic hypoxia. *J. Appl. Physiol.* **46**, 1023–1028 (1979).

12. Neviere, R. et al. Carbon dioxide rebreathing method of cardiac output measurement during acute respiratory failure in patients with chronic obstructive pulmonary disease. *Crit. Care Med.* **22**, 81–85 (1994).

13. Douglas, A. R., Jones, N. L. & Reed, J. W. Calculation of whole blood CO₂ content. *J. Appl. Physiol.* **65**, 473–477 (1988).

14. Samsel, R. & Schumacker, P. T. Determination of the critical O₂ delivery from experimental data: Sensitivity to error. *J. Appl. Physiol.* **64**, 2074–2082 (1988).

15. Cohen, P. J. The metabolic function of oxygen and biochemical lesions of hypoxia. *Anesthesiology* **37**, 148–177 (1972).

16. Ronco, J. J. et al. Identification of the critical oxygen delivery for anaerobic metabolism in critically ill septic and nonseptic humans. *JAMA* **270**, 1724–1730 (1993).

17. Mallat, J., Lemyze, M., Tronchon, L., Vallet, B. & Thevenin, D. Use of venous-to-arterial carbon dioxide tension difference to guide resuscitation therapy in septic shock. *World J. Crit. Care Med.* **5**, 47–56 (2016).

18. Groeneveld, A. B., Vermeij, C. G. & Thijs, L. G. Arterial and mixed venous blood acid-base balance during hypoperfusion with incremental positive end- expiratory pressure in the pig. *Anesth. Analg.* **73**, 576–582 (1991).

19. Cohen, I. L., Sheikh, F. M., Perkins, R. J., Feustel, P. J. & Foster, E. D. Effect of hemorrhagic shock and reperfusion on the respiratory quotient in swine. *Crit. Care Med.* **23**, 545–552 (1995).

20. Mesquida, J. et al. Respiratory quotient estimations as additional prognostic tools in early septic shock. *J. Clin. Monit. Comput.* **32**, 1065–1072 (2018).

21. Muller, G. et al. Prognostic significance of central venous-to-arterial carbon dioxide difference during the first 24 hours of septic shock in patients with and without impaired cardiac function. *Br. J. Anaesth.* **119**, 239–248 (2017).

22. Abou-Arab, O. et al. The ratios of central venous to arterial carbon dioxide content and tension to arteriovenous oxygen content are not associated with overall anaerobic metabolism in postoperative cardiac surgery patients. *PLoS ONE* **13**, e0205950 (2018).

23. Fischer, M. O. et al. Assessment of macro- and micro-oxygenation parameters during fractional fluid infusion: A pilot study. *J. Crit. Care* **40**, 91–98 (2017).

24. Cavaliere, F. et al. Comparison of two methods to assess blood CO₂ equilibration curve in mechanically ventilated patients. *Respir. Physiol. Neurobiol.* **146**, 77–83 (2005).

25. Jakob, S. M., Groeneveld, A. B. & Teboul, J. L. Venous–arterial CO₂ to arterial–venous O₂ difference ratio as a resuscitation target in shock states?. *Intensive Care Med.* **41**, 91–93 (2015).

26. Chiarla, C. et al. Significance of hemoglobin concentration in determining blood CO₂ binding capacity in critical illness. *Respir. Physiol. Neurobiol.* **172**, 32–36 (2010).

27. Jakob, S. M., Kosonen, P., Ruokonen, E., Parviainen, I. & Takala, J. The Haldane effect—An alternative explanation for increasing gastric mucosal PCO₂ gradients?. *Br. J. Anaesth.* **83**, 740–746 (1999).

28. Mchardy, G. J. The relationship between the differences in pressure and content of carbon dioxide in arterial and venous blood. *Clin. Sci.* **32**, 299–309 (1967).

29. Sun, X. G., Hansen, J. E., Stringer, W. W., Ting, H. & Wasserman, K. Carbon dioxide pressure-concentration relationship in arterial and mixed venous blood during exercise. *J. Appl. Physiol.* **90**, 1798–1810 (2001).

30. Mallat, J. et al. Repeatability of blood gas parameters, PCO₂ gap, and PCO₂ gap to arterial-to-venous oxygen content difference in critically ill adult patients. *Medicine (Baltimore)* **94**, e415 (2015).

**Author contributions**

J.M., and B.V. designed the study. J.M. conducted statistical analyses. J.M. and B.V. participated in manuscript writing and reviewing. All authors read and approved the final manuscript.

**Competing interests**

The authors declare no competing interests.

**Additional information**

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1038/s41598-021-89703-5.

**Correspondence** and requests for materials should be addressed to J.M.

**Reprints and permissions information** is available at www.nature.com/reprints.

**Publisher’s note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

<figure><img src="image_9.png" /></figure>

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

© The Author(s) 2021
6. Mesquida, J. et al. Central venous-to-arterial carbon dioxide difference combined with arterial-to-venous oxygen content difference is associated with lactate evolution in the hemodynamic resuscitation process in early septic shock. *Crit. Care* **19**, 126 (2015).

7. He, H. W., Liu, D. W., Long, Y. & Wang, X. T. High central venous-to-arterial CO₂ difference/arterial–central venous O₂ difference ratio is associated with poor lactate clearance in septic patients after resuscitation. *J. Crit. Care* **31**, 76–81 (2016).

8. Dubin, A. et al. Venoarterial PCO₂-to-arteriovenous oxygen content difference ratio is a poor surrogate for anaerobic metabolism in hemodilution: An experimental study. *Ann. Intensive Care* **7**, 65 (2017).

9. Ospina-Tascón, G. A. et al. Combination of arterial lactate levels and venous–arterial CO₂ to arterial–venous O₂ content difference ratio as markers of resuscitation in patients with septic shock. *Intensive Care Med.* **41**, 796–805 (2015).

10. Teboul, J. L. & Scheeren, T. Understanding the Haldane effect. *Intensive Care Med.* **43**, 91–93 (2016).

11. Cain, S. M. & Chapler, C. K. Oxygen extraction by canine hindlimb during hypoxic hypoxia. *J. Appl. Physiol.* **46**, 1023–1028 (1979).

12. Neviere, R. et al. Carbon dioxide rebreathing method of cardiac output measurement during acute respiratory failure in patients with chronic obstructive pulmonary disease. *Crit. Care Med.* **22**, 81–85 (1994).

13. Douglas, A. R., Jones, N. L. & Reed, J. W. Calculation of whole blood CO₂ content. *J. Appl. Physiol.* **65**, 473–477 (1988).

14. Samsel, R. & Schumacker, P. T. Determination of the critical O₂ delivery from experimental data: Sensitivity to error. *J. Appl. Physiol.* **64**, 2074–2082 (1988).

15. Cohen, P. J. The metabolic function of oxygen and biochemical lesions of hypoxia. *Anesthesiology* **37**, 148–177 (1972).

16. Ronco, J. J. et al. Identification of the critical oxygen delivery for anaerobic metabolism in critically ill septic and nonseptic humans. *JAMA* **270**, 1724–1730 (1993).

17. Mallat, J., Lemyze, M., Tronchon, L., Vallet, B. & Thevenin, D. Use of venous-to-arterial carbon dioxide tension difference to guide resuscitation therapy in septic shock. *World J. Crit. Care Med.* **5**, 47–56 (2016).

18. Groeneveld, A. B., Vermeij, C. G. & Thijs, L. G. Arterial and mixed venous blood acid-base balance during hypoperfusion with incremental positive end- expiratory pressure in the pig. *Anesth. Analg.* **73**, 576–582 (1991).

19. Cohen, I. L., Sheikh, F. M., Perkins, R. J., Feustel, P. J. & Foster, E. D. Effect of hemorrhagic shock and reperfusion on the respiratory quotient in swine. *Crit. Care Med.* **23**, 545–552 (1995).

20. Mesquida, J. et al. Respiratory quotient estimations as additional prognostic tools in early septic shock. *J. Clin. Monit. Comput.* **32**, 1065–1072 (2018).

21. Muller, G. et al. Prognostic significance of central venous-to-arterial carbon dioxide difference during the first 24 hours of septic shock in patients with and without impaired cardiac function. *Br. J. Anaesth.* **119**, 239–248 (2017).

22. Abou-Arab, O. et al. The ratios of central venous to arterial carbon dioxide content and tension to arteriovenous oxygen content are not associated with overall anaerobic metabolism in postoperative cardiac surgery patients. *PLoS ONE* **13**, e0205950 (2018).

23. Fischer, M. O. et al. Assessment of macro- and micro-oxygenation parameters during fractional fluid infusion: A pilot study. *J. Crit. Care* **40**, 91–98 (2017).

24. Cavaliere, F. et al. Comparison of two methods to assess blood CO₂ equilibration curve in mechanically ventilated patients. *Respir. Physiol. Neurobiol.* **146**, 77–83 (2005).

25. Jakob, S. M., Groeneveld, A. B. & Teboul, J. L. Venous–arterial CO₂ to arterial–venous O₂ difference ratio as a resuscitation target in shock states?. *Intensive Care Med.* **41**, 91–93 (2015).

26. Chiarla, C. et al. Significance of hemoglobin concentration in determining blood CO₂ binding capacity in critical illness. *Respir. Physiol. Neurobiol.* **172**, 32–36 (2010).

27. Jakob, S. M., Kosonen, P., Ruokonen, E., Parviainen, I. & Takala, J. The Haldane effect—An alternative explanation for increasing gastric mucosal PCO₂ gradients?. *Br. J. Anaesth.* **83**, 740–746 (1999).

28. Mchardy, G. J. The relationship between the differences in pressure and content of carbon dioxide in arterial and venous blood. *Clin. Sci.* **32**, 299–309 (1967).

29. Sun, X. G., Hansen, J. E., Stringer, W. W., Ting, H. & Wasserman, K. Carbon dioxide pressure-concentration relationship in arterial and mixed venous blood during exercise. *J. Appl. Physiol.* **90**, 1798–1810 (2001).

30. Mallat, J. et al. Repeatability of blood gas parameters, PCO₂ gap, and PCO₂ gap to arterial-to-venous oxygen content difference in critically ill adult patients. *Medicine (Baltimore)* **94**, e415 (2015).

**Author contributions**

J.M., and B.V. designed the study. J.M. conducted statistical analyses. J.M. and B.V. participated in manuscript writing and reviewing. All authors read and approved the final manuscript.

**Competing interests**

The authors declare no competing interests.

**Additional information**

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1038/s41598-021-89703-5.

**Correspondence** and requests for materials should be addressed to J.M.

**Reprints and permissions information** is available at www.nature.com/reprints.

**Publisher's note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

<figure><img src="image_9.png" /></figure>

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

© The Author(s) 2021