Corrections of Enghoff's dead space formula for shunt effects still overestimate Bohr's dead space

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Highlights

  • Shunt markedly affects dead space estimations based on Enghoff's original formula.

  • Algorithms correcting for shunt in Enghoff's formula underperform when challenged with true data.

  • These theoretical algorithms cannot replace Bohr's formula for true dead space calculation.

  • Bohr's dead space can non-invasively assess true dead space free from any low V/Q and shunt effects.

Abstract

Dead space ratio is determined using Enghoff's modification (VdB-E/Vt) of Bohr's formula (VdBohr/Vt) in which arterial is used as a surrogate of alveolar PCO2. In presence of intrapulmonary shunt Enghoff's approach overestimates dead space. In 40 lung-lavaged pigs we evaluated the Kuwabara's and Niklason's algorithms to correct for shunt effects and hypothesized that corrected VdB-E/Vt should provide similar values as VdBohr/Vt.

We analyzed 396 volumetric capnograms and arterial and mixed-venous blood samples to calculate VdBohr/Vt and VdB-E/Vt. Thereafter, we corrected the latter for shunt effects using Kuwabara's (K) VdB-E/Vt and Niklason's (N) VdB-E/Vt algorithms. Uncorrected VdB-E/Vt (mean ± SD of 0.70 ± 0.10) overestimated VdBohr/Vt (0.59 ± 0.12) (p < 0.05), over the entire range of shunts. Mean (K) VdB-E/Vt was significantly higher than VdBohr/Vt (0.67 ± 0.08, bias −0.085, limits of agreement −0.232 to 0.085; p < 0.05) whereas (N)VdB-E/Vt showed a better correction for shunt effects (0.64 ± 0.09, bias 0.048, limits of agreement −0.168 to 0.072; p < 0.05).

Neither Kuwabara's nor Niklason's algorithms were able to correct Enghoff's dead space formula for shunt effects.

Introduction

Conceptually, the inefficiency of ventilation in mechanically ventilated patients is assessed by dead space. It is defined as the portion of ventilation that does not participate in gas exchange (Bohr, 1891, Fletcher and Jonson, 1981, Bartels et al., 1954, Fletcher, 1985). Any increase in dead space reduces the clearance of carbon dioxide (CO2) making patients prone to hypercapnea, which has to be compensated for by increasing the amount of total ventilation.

In 1891, Bohr proposed a formula to calculate the ratio of dead space to tidal volume (Vd/Vt) using mixed expired CO2 (Bohr, 1891). He postulated that the degree of CO2 dilution within the lungs determined by the difference between mean alveolar (PaCO2) and mixed expired (PēCO2) partial pressures of CO2 is proportional to the amount of dead space. Due to the practical difficulties in measuring alveolar partial pressure of CO2 (PaCO2), Enghoff modified Bohr's original formula using arterial as a surrogate of alveolar PCO2 (PaCO2) referring to Riley's concept of an ideal lung (Enghoff, 1938, Riley and Cournand, 1949, Riley and Cournand, 1951). However, the use of PaCO2 not only requires invasive arterial blood gas sampling but is also affected by the presence of right-to-left shunt. When high concentrations of CO2 in the venous blood reach the arterial side via intrapulmonary shunt pathways PaCO2 increases above PaCO2. This makes PaCO2 an inappropriate parameter to calculate dead space, especially at elevated levels of shunt (Fletcher and Jonson, 1981, Suter et al., 1975, Wagner, 2008).

For monitoring mechanically ventilated patients traditional Douglas bags have nowadays been replaced by volumetric capnography (VCap), the plot of expired CO2 over the tidal volume (Fig. 1) (Fletcher and Jonson, 1981, Sinha and Soni, 2012). While PēCO2 can easily be estimated from VCap it was believed that accurate estimations of PaCO2 could not be derived from it (Fletcher and Jonson, 1981, Enghoff, 1938). However, we have recently introduced and validated a VCap-based method to estimate PaCO2. It allows for a breath-by-breath non-invasive assessment of Bohr's dead space (Tusman et al., 2011a, Tusman et al., 2011b).

Several authors have described mathematical approaches to correct Enghoff's equation for shunt (Kuwabara and Duncalf, 1969, Mecikalski et al., 1984, Torda and Duncalf, 1974, Niklason et al., 2008). However, these corrections were developed on theoretical grounds only. To our knowledge, the validation of such algorithms using real biological data is still lacking.

We hypothesized that if Enghoff's dead spaces were corrected for shunt they should yield similar values to those obtained by Bohr's original equation. The aim of this work was to test this hypothesis in a cohort of mechanically ventilated animals, in which different degrees of shunts and dead spaces were induced by lung lavages and a wide range of positive-end expiratory pressures (PEEP).

Section snippets

Materials and methods

We analyzed data from a large database including VCap measurements performed in 40 surfactant-depleted pigs (body weight 30.5 ± 6.9 kg). Only a small fraction of these data has been presented in previous publications (Suarez-Sipmann et al., 2007, Tusman et al., 2011a). Measurements were performed at two different centers: the experimental laboratory of the department of clinical physiology at Uppsala University and the experimental laboratory of the Fundación Jiménez Díaz, Madrid, Spain.

Both local

Results

A total of 396 measurements of dead space with their respective corrections for shunt were performed. Animals showed a large intra- and inter individual range of shunt (from 0.05 to 0.82) and VdBohr/Vt (from 0.28 to 0.79).

The quality of Niklason's predictions of the intermediated parameters of gas exchange was compared with those obtained from our real experimental measurements (Table 1, additional file 1).

Uncorrected VdB-E/Vt was weakly correlated with VdBohr/Vt showing an r value of 0.68 (p < 

Discussion

Using real experimental data we found that the theoretical algorithms of Kuwabara and Duncalf (1969) and Niklason et al. (2008) did not completely correct the known effects that shunt has on Enghoff's dead space calculation. When compared to Bohr's dead space, the physiological dead-space unaffected by any shunt-effect, both Kuwabara's and Niklason's algorithms continued to overestimate Vd/Vt. Nonetheless, Niklason's algorithm yielded better approximations of Bohr's dead space and was less

Conclusions

The presented experimental data confirm that shunt markedly affects dead space values derived from Enghoff's but not from Bohr's equation. The results of this study suggest that Enghoff's formula and the proposed algorithms to correct for shunt effects are inadequate to determine reliable estimates of dead space.

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