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Research ArticleOriginal Research

Validity of Empirical Estimates of the Ratio of Dead Space to Tidal Volume in ARDS

Jose Dianti, Arthur S Slutsky and Ewan C Goligher
Respiratory Care April 2021, 66 (4) 559-565; DOI: https://doi.org/10.4187/respcare.08246
Jose Dianti
Interdepartmental Division of Critical Care Medicine, University of Toronto, Toronto, Canada.
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Arthur S Slutsky
Department of Medicine, Division of Respirology, University Health Network, Toronto, Canada.
Keenan Centre for Biomedical Research, Li Ka Shing Knowledge Institute, St. Michael’s Hospital, Toronto, Canada.
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Ewan C Goligher
Interdepartmental Division of Critical Care Medicine, University of Toronto, Toronto, Canada.
Department of Medicine, Division of Respirology, University Health Network, Toronto, Canada.
Toronto General Hospital Research Institute, Toronto, Canada.
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  • For correspondence: [email protected]
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Abstract

BACKGROUND: The ratio of dead space to tidal volume (VD/VT) is a clinically relevant parameter in ARDS; it has been shown to predict mortality, and it determines the extent to which extracorporeal CO2 removal reduces tidal volume (VT) and driving pressure (ΔP). VD/VT can be estimated with volumetric capnography, but empirical formulas using demographic and physiological information have been proposed to estimate VD/VT without the need of additional equipment. It is unknown whether estimated and measured VD/VT produce similar estimates of the predicted effect of extracorporeal CO2 removal on ΔP.

METHODS: We performed a secondary analysis of data from a previous clinical trial including subjects with ARDS in whom VD/VT and CO2 production (Embedded Image) were measured with volumetric capnography. The estimated ratio of dead space to tidal volume (VD,est/VT) was calculated using standard empiric formulas. Agreement between measured and estimated values was evaluated with Bland-Altman analysis. Agreement between the predicted change in ΔP with extracorporeal CO2 removal as computed using the measured ratio of alveolar dead space to tidal volume (VDalv/VT) or estimated VDalv/VT (VDalv,est/VT) was also evaluated.

RESULTS: VD,est/VT was higher than measured VD/VT, and agreement between them was low (bias 0.05, limits of agreement –0.21 to 0.31). Differences between measured and estimated Embedded Image accounted for 57% of the error in VD,est/VT. The predicted reduction in ΔP with extracorporeal CO2 removal computed using VDalv,est/VT was in reasonable agreement with the expected reduction using VDalv/VT (bias –0.7 cm H2O, limits of agreement –1.87 to 0.47 cm H2O). In multivariable regression, measured VD/VT was associated with mortality (odds ratio 1.9, 95% CI 1.2–3.1, P = .01), but VD,est/VT was not (odds ratio 1.2, 95% CI 0.8–1.8, P = .3).

CONCLUSIONS: VD/VT and VD,est/VT showed low levels of agreement and cannot be used interchangeably in clinical practice. Nevertheless, the predicted decrease in ΔP due to extracorporeal CO2 removal was similar when computed from either estimated or measured VDalv/VT.

  • dead space
  • ARDS
  • mechanical ventilation
  • volumetric capnography
  • extracorporeal life support
  • driving pressure

Introduction

An increase in the ratio of dead space to tidal volume (VD/VT) is a hallmark of ARDS.1 Alveolar flooding by protein rich fluids causes shunt and hypoxemia,2 while an increase in dead space develops secondary to microthrombi, maldistributed hypoxic pulmonary vasoconstriction, and the collapse of small pulmonary vessels due to alveolar overdistention with positive-pressure ventilation.3,4 VD/VT has consistently been shown to predict mortality in ARDS with greater discrimination than the severity of hypoxemia.5-7 VD/VT is also important in determining the extent to which a given rate of extracorporeal CO2 removal reduces VT and driving pressure (ΔP).8 VD/VT values may therefore play a central role in the selection of subjects for trials of ultra-protective ventilation facilitated by extracorporeal CO2 removal.

VD/VT can be measured with volumetric capnography or with a dedicated metabolic monitor at the bedside.9 However, these techniques require dedicated equipment and some expertise to ensure accurate measurements.10 Empirical formulas using demographic and physiological information have been proposed to estimate VD/VT without the need of any additional equipment. Siddiki et al11 reported that an empirically estimated VD/VT (VD,est/VT) using a modified Harris-Benedict equation (adjusting for hypermetabolic factors) correlated with mortality in a secondary analysis of 2 large prospective studies of subjects with ARDS. A larger study, however, reported that using the unadjusted Harris-Benedict equation best predicted the association between VD,est/VT and mortality.12 A smaller study (N = 13 subjects)13 noted that the agreement between empirically estimated and measured values for VD/VT was poor; in that study, the estimated approach systematically underestimated measured VD/VT.

We set out to (1) quantify the agreement between measured and estimated VD/VT, (2) compare their relationships to clinical outcomes, and (3) assess whether the error in empirical estimates of VD/VT significantly modifies the predicted change in ΔP with extracorporeal CO2 removal.

Quick Look

Current Knowledge

The ratio of dead space to tidal volume (VD/VT) is a better prognostic factor than the severity of hypoxemia in ARDS. It is also important in determining the extent to which a given rate of extracorporeal CO2 removal reduces driving pressure. However, dedicated equipment and expertise are required for its measurement, making it infrequently available. Empiric formulas have been proposed to estimate VD/VT without the need of specific equipment, but there is conflicting evidence regarding the accuracy of these formulas in critically ill subjects.

What This Paper Contributes to Our Knowledge

In a secondary analysis of a randomized clinical trial, measured and estimated VD/VT showed low levels of agreement, suggesting that their values should not be used interchangeably. However, the predicted decrease in driving pressure from initiating extracorporeal CO2 removal was similar using either approach, suggesting that the estimated VD/VT can be used to assess the potential benefit of extracorporeal CO2 removal. This could have implications in the design of future trials of extracorporeal life support, allowing for better subject selection.

Methods

Study Population

We conducted a secondary analysis of data from the Aerosolized β2-Agonist for Treatment of Acute Lung Injury (ALTA) trial.14 Briefly, this multi-center, randomized clinical trial evaluated the use of aerosolized albuterol versus placebo for the treatment of ARDS. This dataset was selected for analysis because it includes VD/VT measurements with volumetric capnography (NM3, Philips Respironics, Philadelphia, Pennsylvania) in a well-defined cohort of subjects with ARDS. Subjects in whom VD/VT and CO2 production (Embedded Image) were measured on day 1 after randomization were included in this analysis. This study was approved by the local research ethics board at St. Michael’s Hospital, Toronto, Canada (REB# 17–022).

Physiological Measurements

In the ALTA trial, VD/VT was measured with volumetric capnography using Enghoff’s modification of Bohr’s formula, where alveolar CO2 partial pressure (Embedded Image) is replaced with Embedded Image15: Embedded Imagewhere Embedded Image represents the mixed exhaled pressure of CO2. Anatomical VD/VT was also measured, and VDalv/VT was calculated by subtraction of anatomical VD/VT from VD/VT (see the supplementary materials at http://www.rcjournal.com).16

Empirical Estimation of VD/VT

First, estimated Embedded Image (Embedded Image) was calculated according to the Harris-Benedict equation17 (see the supplementary materials at http://www.rcjournal.com). We then estimated VD/VT (VD,est/VT) by rearranging the alveolar air equation for Embedded Image using Embedded Image as: Embedded Image where Embedded Image represents minute volume and 0.86 is a standard constant necessary for converting fractional concentrations to pressures and correcting to standard conditions. The estimate of alveolar subcomponent (VDalv,est/VT) was determined using VD,est/VT and the predicted anatomical VD/VT (see the supplementary materials at http://www.rcjournal.com).

Predicting the Effect of Extracorporeal CO2 Removal on ΔP

ΔP was computed as the difference between plateau pressure and PEEP. Respiratory system compliance (CRS) was computed as the quotient of VT and ΔP. The predicted change in ΔP achieved by applying extracorporeal CO2 removal at a clearance rate of 80 mL/min (Embedded Image) was computed from CRS and VDalv/VT following a previously described model derived from the theoretical equation used to define alveolar ventilation (see the supplementary materials at http://www.rcjournal.com).18 This model was recently validated in a large cohort of subjects with ARDS receiving extracorporeal CO2 removal to achieve ultra-protective mechanical ventilation.8

Statistical Analysis

Continuous variables are described as mean ± SD or median (interquartile range) according to their distribution, and categorical variables are described as counts and percentages. The t test and the Wilcoxon rank-sum test were used to analyze normally and non-normally distributed continuous variables, respectively. Analysis of variance was used to compare means across multiple groups. Categorical variables were compared using the chi-square test.

Relationships among physiological variables (Embedded Image, VD/VT, VDalv/VT, and CRS) were compared with linear regression. Agreement between measured and estimated VD/VT variables and between the predicted changes in ΔP with the application of extracorporeal CO2 removal computed using either measured or predicted VDalv/VT was evaluated with Bland-Altman analysis. Linear regression was used to analyze the error between measured and estimated VD/VT, comparing the difference between VD/VT and VD,est/VT and the difference between Embedded Image and Embedded Image.

The association between physiological variables and the risk of death was evaluated with multivariable logistic regression. Mortality was defined as 60-d hospital mortality according to the information available in the dataset. Variables previously known to be associated with an increased risk of death (eg, VD/VT, Embedded Image, CRS, SOFA score, and age) were included in the logistic regression model. For the multivariable analysis, VD/VT and CRS were considered the primary predictor variables. All analyses and figures were performed using RStudio 1.2.5019 (RStudio, Boston, Massachusetts).

Results

VD/VT measurements were obtained in the first 24 h after randomization in 107 (38%) of the 282 subjects. Baseline subject characteristics and demographics are described in Table 1. Overall mortality was 19%.

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Table 1.

Baseline Characteristics of the Study Cohort*

Measures of agreement between estimated and measured values for VD/VT are shown in Table 2 and Figure 1. Measured VD/VT and VD,est/VT were moderately correlated (R2 = 0.21, P < .001). VD,est/VT slightly overestimated measured VD/VT on average (bias 0.05, limits of agreement –0.21 to 0.31), likely because Embedded Image tended to underestimate measured Embedded Image (bias –29.7 mL/min, limits of agreement –132 to 73 mL/min). Error in Embedded Image accounted for 57% of the error in VD,est/VT (Fig. 2). Correcting VD,est/VT by correcting Embedded Image using the mean bias in the estimation of Embedded Image (30 mL/min) reduced the bias between VD,est/VT and measured VD/VT (bias –0.007, limits of agreement –0.26 to 0.25).

Fig. 1.
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Fig. 1.

Correlation and agreement between measured and estimated ratio of dead space to tidal volume (VD/VT) and Embedded Image. Shaded area represents confidence 95% confidence intervals. Center line represents the mean difference between both variables. Dashed lines represent 95% limits of agreement.

Fig. 2.
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Fig. 2.

Correlation between differences in measured and estimated values for physiologic dead space and CO2 production. Error in the estimation of Embedded Image (Embedded Image) accounted for 57% of the error in the estimation of VD/VT (VD,est/VT). Shaded area represents confidence 95% confidence intervals. Center line represents the mean difference between both variables. Dashed lines represent 95% limits of agreement.

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Table 2.

Measured and Estimated Values of Dead Space and CO2 Elimination

The expected reduction in ΔP with extracorporeal CO2 removal at 80 mL/min based on VDalv/VT was in reasonable agreement with the value obtained using VDalv,est/VT (bias –0.3 cm H2O, limits of agreement –1.4 to 0.8 cm H2O) (Fig. 3). The mean ± SD predicted reductions in ΔP in the ALTA trial subjects if they were to put on extracorporeal CO2 removal at a flow that removed 80 mL/min of CO2 were –3.3 ± 1.5 cm H2O and –3.5 ± 1.3 cm H2O using the measured and estimated approaches, respectively.

Fig. 3.
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Fig. 3.

Correlation and agreement analysis between the predicted change in driving pressure (ΔP) with extracorporeal carbon dioxide removal with alveolar dead space (VDalv/VT) and estimated alveolar dead space (VDalv,est/VT). The estimated approach slightly overestimated the response in ΔP. Shaded area represents confidence 95% confidence intervals. Center line represents the mean difference between both variables. Dashed lines represent 95% limits of agreement.

Neither measured VD/VT nor VD,est/VT were correlated with Embedded Image (R2 = 0.05 and 0.02, respectively) or CRS (R2 = 0.07 and 0.01, respectively). Embedded Image also showed no correlation with CRS (R2 = 0.01). Correlation between ΔP and both VD/VT and VD,est/VT was also low (R2 = 0.05 and 0.03, respectively).

In univariable analysis, measured VD/VT, but not Embedded Image or CRS, was associated with mortality (Table 3). The association between measured VD/VT and mortality persisted in multivariable analysis after adjusting for Embedded Image, CRS, SOFA score, and age (odds ratio 1.9, 95% CI 1.2–3.1, P = .01). VD,est/VT was not significantly associated with mortality in univariable analysis (odds ratio 1.3, 95% CI 0.8–1.9, P = .20) or in multivariable analysis (odds ratio 1.2, 95% CI 0.8–1.8, P = .33).

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Table 3.

Association of Physiologic Variables With 60-d Mortality

Discussion

In this secondary analysis of a previous randomized trial of subjects with ARDS, we observed low agreement between measured and estimated VD/VT variables. Nevertheless, we observed a satisfactory level of agreement in the predicted decrease in ΔP from extracorporeal CO2 removal between both approaches, suggesting that empiric VD/VT estimates can be used to evaluate the predicted response to extracorporeal CO2 removal.

Embedded Image and VD/VT are infrequently measured with volumetric capnography in routine clinical practice because its measurement requires dedicated equipment and technical expertise to address potential subtleties of the method.10 Considering the important prognostic information conferred by measurement of VD/VT, the ability to estimate Embedded Image and VD/VT based on readily available information such as age, height, weight, and sex is appealing from a clinical standpoint. In this analysis, however, estimated VD/VT overestimated measured values with relatively low agreement, indicating that these values should not be used interchangeably in everyday clinical practice. This is in keeping with the findings of Beitler et al.12 Calculated values rely on the Harris-Benedict equation of resting energy expenditure, which, in the setting of critically ill subjects with elevated shunt, tends to underestimate Embedded Image.19 In this analysis, more than half of the observed error between measured and estimated VD/VT was related to differences in measured and estimated Embedded Image.

Despite the significant differences observed between measured and estimated VD/VT, we found a reasonable agreement in the predicted decrease in ΔP using VDalv/VT and VDalv,est/VT. This could be explained by the fact that the formula used to predict the decrease in ΔP from extracorporeal CO2 removal is more influenced by easily measured variables such as CRS, breathing frequency, and Embedded Image than by VD/VT. Two previous studies reported that the change in ΔP and VT which could be achieved using extracorporeal CO2 removal was associated with the baseline VDalv/VT and CRS, and that the change in ΔP could be predicted by integrating these parameters into an equation derived from the alveolar ventilation equation.8,18 In subjects with a high probability of benefiting, extracorporeal CO2 removal would permit a reduction in CO2 to further reduce VT and ΔP and achieve an ultra-protective ventilation strategy in a population at higher risk of developing ventilator-induced lung injury.20,21 Our findings suggest that integrating estimated VD/VT values with CRS in a formula to predict the expected change in ΔP would yield similar results to the use of measured VD/VT values. Because the predicted change in ΔP has been shown to predict the response to extracorporeal CO2 removal, our findings suggest that estimated VD/VT is adequate for this purpose.8

Measured VD/VT was associated with increased odds of mortality after adjusting for confounding variables (Table 3), similar to previous studies. The relationship between measured VD/VT and mortality was more significant than the relationship between Embedded Image and mortality, reinforcing the relative prognostic importance of VD/VT, as shown previously.5,6,22,23 Estimated VD/VT, on the other hand, was not associated with increased risk of death, a finding that contrasts with previous observations analyzing larger cohorts.11,12

Interestingly, we found no correlation between VD/VT and Embedded Image or CRS. The relationship between these variables is complex. In all of the previously cited studies, as well as in our study, VD/VT was measured using the Enghoff modification of Bohr’s original formula, using Embedded Image instead of Embedded Image. This approach is usually acceptable in subjects with “normal” lungs24; however, in subjects with increased shunt, such as subjects with ARDS, it has been suggested that Embedded Image could be increased due to the shunt, therefore overestimating the true VD/VT.19,25 However, correcting the Enghoff VD/VT using 2 different mathematical approaches to account for shunt effect failed to improve the agreement between the Enghoff modification and Bohr’s original formula.15 Thus, the lack of correlation between Embedded Image and VD/VT observed in our study suggests that the shunt is not the primary mechanism of altered VD/VT in this population. The absence of correlation between VD/VT and CRS is perhaps less surprising. As a marker of gas exchange, VD/VT can be affected by changes in either alveolar ventilation or perfusion. Gogniat et al26 reported that ΔP was only correlated to VD/VT when CRS decreased after an increase in PEEP, suggesting that a reduction in ventilation secondary to overdistention plays an important role in the relationship between VD/VT and lung mechanics. As such, an improvement in VD/VT measured using the Enghoff approach in response to increased PEEP might represent either an improvement in lung mechanics or a reduction in shunt. Aside from this specific scenario of attempted lung recruitment, VD/VT and CRS are generally not correlated, as also shown in subjects with ARDS secondary to COVID-19.27

Our study has limitations. First, more than half of the subjects from the original dataset had to be removed for analysis because they had no VD/VT measurements on the first day. This could mean our analysis is underpowered to observe an association between Embedded Image and mortality and between estimated VD/VT and mortality (a finding reported in 2 previous studies11,12). Moreover, the low overall mortality observed in this study may have further reduced statistical power. Second, we are using a theoretical model to predict the response to extracorporeal CO2 removal, although this model was recently validated in a trial evaluating the feasibility of lung ultra-protective ventilation in subjects with ARDS,8 thus enhancing the reliability of our findings.

Conclusions

We found that measured and estimated VD/VT values showed low levels of agreement and should not be used interchangeably in clinical practice. Nevertheless, the predicted decrease in ΔP from extracorporeal CO2 removal was similar when using either estimated or measured VDalv/VT. Empirical estimates of VD/VT can be used to predict the effect of extracorporeal CO2 removal on driving pressure.

Footnotes

  • Correspondence: Ewan C Goligher MD PhD, Toronto General Hospital, 585 University Ave, 11-PMB Room 192, Toronto, Ontario M5G 2N2. E-mail: ewan.goligher{at}utoronto.ca
  • See the Related Editorial on Page 703

  • The authors have disclosed no conflicts of interest.

  • Supplementary material related to this paper is available at http://www.rcjournal.com.

  • Copyright © 2021 by Daedalus Enterprises

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Respiratory Care: 66 (4)
Respiratory Care
Vol. 66, Issue 4
1 Apr 2021
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Validity of Empirical Estimates of the Ratio of Dead Space to Tidal Volume in ARDS
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Validity of Empirical Estimates of the Ratio of Dead Space to Tidal Volume in ARDS
Jose Dianti, Arthur S Slutsky, Ewan C Goligher
Respiratory Care Apr 2021, 66 (4) 559-565; DOI: 10.4187/respcare.08246

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Validity of Empirical Estimates of the Ratio of Dead Space to Tidal Volume in ARDS
Jose Dianti, Arthur S Slutsky, Ewan C Goligher
Respiratory Care Apr 2021, 66 (4) 559-565; DOI: 10.4187/respcare.08246
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Keywords

  • dead space
  • ARDS
  • mechanical ventilation
  • volumetric capnography
  • extracorporeal life support
  • Driving pressure

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