Department of Anaesthetics, University of Sydney, Royal Prince Alfred Hospital, Sydney, NSW 2050, Australia
* Corresponding author: Department of Anaesthetics, Royal Prince Alfred Hospital, Building 89 Level 4, Missenden Rd, Camperdown, NSW 2050, Australia. E-mail: bbaker{at}usyd.edu.au
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Abstract |
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Methods. Pulmonary shunt, /
distribution and VDalv were varied in a tidally breathing cardiorespiratory model. Respiratory data generated by the model were analysed to calculate dead-spaces by the Fowler, Bohr, BohrEnghoff and Koulouris methods.
was calculated by the method of Koulouris.
Results. When VDalv is increased, VDphys can be recovered by the Bohr and BohrEnghoff equations, but not by the Koulouris method. Shunt increases the calculated BohrEnghoff dead-space, but does not affect Fowler, Bohr or Koulouris dead-spaces, or VDphys estimated by the shunt-corrected equation if pulmonary artery catheterization is available. BohrEnghoff but not Koulouris or Fowler dead-space increases with increasing severity of /
maldistribution. When alveolar
is increased by any mechanism,
calculated by Koulouris' method does not agree well with average alveolar PCO2.
Conclusions. Our studies show that increased pulmonary shunt causes an apparent increase in VDphys, and that abnormal /
distributions affect the calculated VDphys and VDalv, but not Fowler dead-space. Dead-space and
calculated by the Koulouris method do not represent true Bohr dead-space and
respectively, but the shunt-corrected equation performs well.
Keywords: computers ; lung, shunting ; ventilation, deadspace ; ventilation, ventilationperfusion
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Symbols used in the paper |
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Introduction |
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Bohr7 dead-space (VDBohr) is a function of ideal alveolar partial pressure of carbon dioxide (). Because
is difficult to estimate, Enghoff8 substituted arterial partial pressure of carbon dioxide (
) for
, giving rise to the BohrEnghoff dead-space (Appendix A), usually referred to as physiological dead-space (VDphys). Alveolar dead-space9 is commonly defined as the difference between VDphys and the anatomical dead-space (VDFowler), which is estimated by a method proposed by Fowler10 (Appendix A). Disadvantages of the BohrEnghoff method are that it is invasive and cannot be used breath-by-breath when
is changing rapidly. Recently, Koulouris and colleagues11 reported a new non-invasive method to calculate Bohr dead-space and
based on an analysis of the expired carbon dioxide volume vs expired tidal volume curve from a single expiration (Appendix A). This technique is apparently simple and non-invasive, but has not been validated independently.
Shunt reduces the overall efficiency of gas exchange and results in arterial blood gas tensions closer to those of mixed venous blood, thus increasing the measured apparent physiological dead-space by increasing .12 A method for correcting dead-space measurements for the effects of shunt has been reported by Kuwabara and Duncalf13 (Appendix A) but its validity has not been demonstrated.
Inhomogeneity of ventilation/perfusion (/
) ratio increases the measured alveolar dead-space by two mechanisms. Firstly, the venous admixture is increased from lung regions with low
/
ratio; secondly, lung units with high
/
ratio contribute to physiological dead-space.
Although series dead-space can be altered easily in studies in vivo, it is difficult to control changes in alveolar dead-space and the /
distribution. Thus the effects of changes in
/
distribution on measures of respiratory dead-space have not been studied systematically.
The aims of this study were to assess the method of Koulouris and colleagues11 for calculating Bohr dead-space and alveolar PCO2, to demonstrate the validity of the correction proposed by Kuwabara and Duncalf13 for calculating physiological dead-space in the presence of pulmonary shunt, and to evaluate the effects of varying alveolar dead-space, pulmonary shunt and abnormal /
distributions on
and dead-space calculated by five different methods.7 8 10 11 13
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Methods |
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Part 3. Effect of /
ratio heterogeneity on respiratory dead-space measurements
The ratio of alveolar dead-space to alveolar tidal volume and the pulmonary shunt were set to 1% and 2% respectively. The minute alveolar ventilation of 5.30 litre min1 and the pulmonary perfusion of 5.40 litre min1 were unevenly distributed to the three ventilated and perfused alveolar compartments to create /
values of 0.1, 1.0 and 10 to simulate patients with chronic obstructive pulmonary disease.20 The percentage perfusion to the middle
/
compartment (
/
=1) was set in turn to 98, 78, 58, 38 and 18% of pulmonary blood flow to simulate increasing severity of
/
mismatch, and the ventilation and perfusion of all three ventilated and perfused compartments were calculated by the method described in Appendix C. The model was run for 7200 s simulation time at each setting to reach steady-state PCO2 and PO2 in mixed venous blood and alveolar and body compartments, and the respiratory parameters were measured and analysed. Log standard deviations of the perfusion distributions were calculated for each condition.
Data analysis
fluctuated during respiration and was therefore averaged over a complete respiratory cycle.
is the volume-weighted average of the PCO2 in the three perfused and ventilated alveolar compartments averaged over one respiratory cycle in Parts 1 and 2 of this study.
is the volume-weighted average of the PCO2 in all the alveolar compartments, including the alveolar dead-space compartment, averaged over one respiratory cycle. VDFowler was calculated by the equal area method (Appendix A).10 21 22 VDBohr (Parts 1 and 2 of this study) and VDBE (Parts 1, 2 and 3 of this study) were calculated according to Equations 1 and 2 (Appendix A) respectively. BohrEnghoff dead-space corrected for the effects of shunt (VDCorr) was calculated using Equation 3 (Appendix A). The calculation of Bohr dead-space by the method of Koulouris and colleagues11 (VDK) is described in Appendix A. An estimate of the Bohr dead-space was also calculated by substituting end-tidal carbon dioxide partial pressure (
) for
(Equation 4, Appendix A). We refer to this dead-space as VDET. The physiological dead-space of the model (VDphys) was calculated as follows:
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Results |
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The BohrEnghoff dead-space increases with increasing pulmonary shunt (Fig. 3B). VDCorr and VDBohr are greater than VDFowler but smaller than VDK and are approximately independent of shunt.
Part 3. Effect of /
ratio heterogeneity on respiratory dead-space measurements
The perfusion and ventilation of each compartment, the respiratory variables and the arterial partial pressures of carbon dioxide and oxygen are shown in Table 3. In the /
ratio heterogeneity study it was not appropriate to calculate Bohr dead-space due to the variation of PCO2 among the ventilated and perfused alveoli.
and the PCO2 in each individual alveolar compartment increase with increasing heterogeneity of the
/
ratio (Fig. 4A). The PCO2 of each alveolar compartment is inversely related to the
/
ratio of the compartment. The VDBE/VT ratio increases from 30.5% at optimal
/
distribution to 64.9% when 78% of the pulmonary perfusion is distributed to the compartments with
/
of 0.1 and 10 (Fig. 4B).
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Discussion |
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Pulmonary embolism results in lung units that are poorly perfused but maintain approximately normal ventilation.23 Although pulmonary embolism is a complex pathological entity with mixed presentation of shunt and dead-space, the increased pulmonary dead-space in Part 1 of this study approximately simulates the main features of gas exchange in patients with pulmonary embolism. The BohrEnghoff dead-space accurately follows the increase in the model alveolar dead-space, while the Fowler dead-space is unaffected (Fig. 2B). Hence, calculated alveolar dead-space, one of the diagnostic markers of pulmonary embolism,23 increases. Dead-space calculated by the Koulouris method does not correlate well with alveolar dead-space or Bohr dead-space, suggesting that the Koulouris method cannot contribute to the diagnosis of pulmonary embolism.
Pulmonary shunt increases VDBE but does not affect VDFowler or VDBohr. The equation of Kuwabara and Duncalf13 (Equation 3, Appendix A) calculates model dead-space correctly in the presence of substantial shunt. Use of this correction equation requires pulmonary artery catheterization due to the need for measurement of shunt, mixed venous PCO2 and .
The invalidity of the Koulouris method can be demonstrated theoretically. The Bohr dead-space equation (Equation 1, Appendix A) assumes that expired gas emanates from two compartments: a perfused alveolar compartment and an unperfused dead-space. The Bohr equation makes no assumptions regarding the sequence in which gas from the two compartments is expired. In contrast, the Koulouris method (Fig. A1B in Appendix A) assumes that an expiration comprises two sequential volumes: a dead-space (VDK=ia) containing a volume of carbon dioxide [VCO2(d)=ay] is expired first at a mean carbon dioxide concentration of Fd=ya/ia, and the remaining carbon dioxide (ce') is assumed to be expired in a subsequent volume ae of alveolar gas at end-tidal carbon dioxide concentration FE'CO2=ce'/ae=ya/da. In Figure A1B in Appendix A the lines ia and id represent VDK and VDET respectively. Hence the line da, which represents the difference between VDK and VDET, can be expressed as VCO2(d)/FE'CO2. VDK and VDET are therefore related by:
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In this study the simulated subject was assumed to be anaesthetized and paralysed and was allowed to rise as high as 8.1 and 9.2 kPa when alveolar dead-space and
/
ratio heterogeneity respectively were increased. In a study of COPD patients with severe
/
heterogeneity, Conti and colleagues28 reported
values as high as 11.6 kPa in mechanically ventilated patients. Breen and colleagues29 studied the effects of large pulmonary embolism on carbon dioxide kinetics and physiological dead-space. They found that after 70 min of occlusion of a large pulmonary artery, the
increased from 5.5 to 7.3 kPa and
decreased by 13% of baseline value while physiological dead-space increased from 31 to 52%. Our simulation results are consistent with the in vivo observations of Conti and colleagues28 and Breen and colleagues.29
We used a mathematical model for this study to facilitate the controlled variation of alveolar dead-space, anatomical dead-space, pulmonary shunt and /
ratio distribution, which are difficult to change prospectively in in vivo studies. A computer model study also avoids the confounding effects associated with biological variations and measurement errors. The main limitations of our computer model include the lumped approximation of the respiratory tree and alveoli, the approximations used to estimate diffusion and convection in the airways and the assumption of equal respiratory time constants and consequent simultaneous emptying of alveolar compartments. The model does not automatically redistribute ventilation or perfusion when these parameters are perturbed and does not simulate hypoxic pulmonary vasoconstriction. These approximations and limitations may affect the shape of the expirogram and hence the calculated dead-space and PCO2 values. We expect, however, that the limitations of the model affect only the magnitude of the results, not their form or direction.
In conclusion, our simulation results suggest that while the physiological dead-space is estimated well by the BohrEnghoff equation when alveolar dead-space and /
ratio distribution vary, respiratory dead-space and alveolar carbon dioxide partial pressure calculated by the Koulouris method do not represent the true Bohr dead-space or alveolar carbon dioxide partial pressure. Increasing pulmonary shunt can cause an apparent increase in VDphys, and abnormal
/
distributions affect calculated VDphys and VDalv, but not Fowler dead-space. The equation suggested by Kuwabara and Duncalf13 for the calculation of dead-space in the presence of shunt performs well, but requires invasive measurements.
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Appendix A. Dead-space calculation methods and symbols |
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Bohr dead-space
Bohr dead-space (VDBohr) is the dead-space calculated by the original Bohr equation:7 21
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BohrEnghoff dead-space
Because of the controversy concerning the definition and estimation of ,21 Enghoff8 suggested substituting
for
in the Bohr equation. The dead-space so calculated is termed the BohrEnghoff dead-space (VDBE):
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Shunt correction method
In the presence of right-to-left shunt, venous blood mixes with pulmonary capillary blood and raises , thus increasing the difference between
and
. Hence the BohrEnghoff dead-space calculated by Equation 2 is increased. Kuwabara and Duncalf13 applied simple mass balance principles and derived an equation to estimate a corrected physiological dead-space (VDcorr) in the presence of right-to-left shunt.
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VDET
Dead-space calculated by using in place of
in the Bohr equation (Equation 1) is termed VDET in this paper:
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Koulouris dead-space
Figure A1B shows expired carbon dioxide volume vs expired volume. Line cb is drawn such that areas p and q are equal. Point d is chosen such that the slope of line cd is end-tidal concentration. The volume de is the volume the expired carbon dioxide would occupy at end-tidal carbon dioxide concentration (total volume of carbon dioxide divided by end-tidal carbon dioxide concentration), hence id represents VDET as calculated by Equation 3 above. Line dx is perpendicular and intersects cb at x. Line xy is parallel to the x-axis and intersects cd at y. Line ya is perpendicular and intersects the x-axis at a. According to Koulouris and colleagues,11 lines ee' and e'c represent the quantities of carbon dioxide expired in the dead-space and alveolar gas respectively. The line ae represents alveolar tidal volume, line ia represents Bohr dead-space and the slope of line ac is the alveolar concentration of carbon dioxide.
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Appendix B. Validation of the cardiorespiratory model |
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Figure A2A shows the realistic airway, arterial, alveolar and mixed venous PCO2 changes with time in the tidally breathing model. The model simulated a 70-kg male subject who was mechanically ventilated with a tidal volume of 9 ml kg1 at a respiratory rate of 10 bpm. Other parameters are the same as shown in Table 1. Both arterial and alveolar PCO2 fluctuate during the respiratory cycle but arterial PCO2 lags alveolar PCO2. Also demonstrated is that alveolar PCO2 peaks shortly after the end of expiration. The average mixed venous and arterial PCO2 are in agreement with the literature.30 31
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Figure A2C shows the model's prediction of and
and comparison with a published study.32 In that study, 12 patients were ventilated with tidal volumes of 10, 7.5, 5 and 2.5 ml kg1 and respiratory rates of 10, 13, 21 and 40 bpm respectively. Each setting was maintained for 10 min and
and
were measured and recorded.32 The model was set to simulate a 75-kg male subject ventilated with the same tidal volumes and respiratory rates as the patients. Other parameters are the same as in Table 1. The anatomical dead-space was adjusted as a function of tidal volume.33 At each setting, the model was run for 10 min and the
and
were recorded.32 The average absolute error of the model predictions was 0.94% of the mean and 9.1% of the SD for measured
, and 4.4% of the mean and 28.4% of the SD for measured
. This result is comparable with a model study by Hardman and Aitkenhead.34
Our results show that the model simulates realistically the gas exchange of a human lung both dynamically and in steady state.
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Appendix C. Calculation of ventilation and perfusion to the three perfused and ventilated compartments in the model |
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The total ventilation , total perfusion
, shunt blood flow (
s) and alveolar dead-space ventilation (
Dalv) were known, therefore:
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There were six unknown parameters in five equations (Equations 5 9). We assigned values to
2 and calculated the remaining five unknown parameters (
1,
2,
3,
1 and
3) by solving Equations 5
9 simultaneously. We used software written in Matlab (Mathworks, Natick, MA, USA) to solve the equations and hence determine the fractions of ventilation and perfusion directed to each alveolar compartment.
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Acknowledgments |
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References |
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