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Critical Care, Trauma, and Resuscitation: Research Reports

Ventilation-Perfusion Ratio in Perflubron During Partial Liquid Ventilation

Scholz, Alexander-Wigbert K. MD*; Eberle, Balthasar MD*,†; Heussel, Claus P. MD; David, Matthias MD*; Schmittner, Marc D. MD§; Quintel, Michael MD; Schreiber, Laura M. PhD; Weiler, Norbert MD#

Author Information
doi: 10.1213/ANE.0b013e3181d3e1d5

Partial liquid ventilation (PLV), i.e., mechanical gas ventilation while the lungs are filled with perfluorocarbons up to the functional residual capacity, has been suggested as a treatment to improve gas exchange in patients with acute respiratory distress syndrome. This view changed, however, when a multicenter study revealed no benefit of PLV compared with conventional ventilation.1 Although the optimal setting of PLV was unknown, the patients in that study underwent volume-controlled ventilation with high tidal volumes (9 mL/kg) and airway pressures, which could have been more detrimental for the PLV group. In addition, patients in the PLV group were disconnected from the ventilator every 3 hours to evaluate the perfluorocarbon level, which probably caused unstable lung regions to collapse. In addition, as described in the protocol, weaning of PLV patients was delayed. The PLV patients also received more sedation and muscle paralysis. At that time, the PLV treatment protocol seems to have still been immature, whereas conventional ventilation was already fully developed.

One approach to improving PLV efficacy is to focus on the mechanisms of action by which PLV contributes to oxygenation. Methods such as microspheres,2 positron emission tomography (PET),3,4 and single photon emission computed tomography5 showed a redistribution of pulmonary blood flow from the dependent lung regions to the nondependent, less-injured lung regions. In accordance with these findings, the multiple inert gas elimination technique (MIGET) revealed that pulmonary shunt was reduced during PLV in acute lung injury.6,7 The majority of the shunt units were converted to units of low ventilation-perfusion ratios (VA/Q). Furthermore, a study based on 13NN-PET demonstrated that ventilation was also redistributed from the dependent to the nondependent lung regions.4

These studies, however, used tracer gases whose specific solubility in perfluorocarbons differed from that of oxygen. Because gas transport within the perfluorocarbons depends on this specific solubility, the results of these studies cannot be considered as allowing a characterization of oxygen transport. Thus, the aim of this study was to analyze the direct effects of perfluorocarbons on oxygen transport during PLV.

Magnetic resonance imaging (MRI) techniques allow tracing of perfluorocarbons, because these contain the 19F isotope. With this method (19F-MRI), the alveolar oxygen partial pressure (PAO2) in perfluorocarbons can be measured by the paramagnetic effect on the relaxation time (T1) of the MR signal.810 Methodology allowing quantification of the local VA/Q by PAO2 during gas ventilation has been described.11 In this study, these techniques were combined and adapted to quantify VA/Q in alveolar perfluorocarbons. The method was tested in numerical simulations and applied in an animal model during PLV to analyze VA/Q distributions at different inspiratory oxygen fractions (FIO2) and perfluorocarbon doses.


Theory of VA/Q Estimation by PAO2

Olszowka and Wagner12 have analyzed the effect of VA/Q on PAO2. Based on the mass balances of oxygen, carbon dioxide, and nitrogen, and under the precondition that all gas partial pressures in the alveoli add up to the barometric pressure, a system of 4 equations with 4 unknowns, which could be solved numerically, was obtained. Rizi et al.11 have adapted this method to determine VA/Q from PAO2 obtained by oxygen-sensitive 3He-MRI of the lung.

When the alveolar space is filled by liquid with its own vapor pressure, the requirement that alveolar partial pressures of respiratory gases add up to the barometric pressure is, however, not fulfilled. A possible approach in such an instance is to quantify VA/Q from PAO2 by a single mass balance of oxygen, which is the Fick principle (Fig. 1). As in the theory of Olszowka and Wagner, the following assumptions need to be made: that the analyzed lung region behaves as a single compartment; that the diffusion gradient between alveolar space and capillary blood is negligible; and that measurements are performed during steady-state conditions. In addition, it is assumed that the oxygen-hemoglobin dissociation curve is independent of carbon dioxide partial pressure. It follows that oxygen uptake into the alveolar unit, which is alveolar ventilation (VA) multiplied by the difference between FIO2 and alveolar oxygen fraction (FAO2), equals oxygen delivery into pulmonary capillary blood, which is perfusion (Q) times the difference between end-capillary (CC′O2) and mixed venous blood oxygen content (CV[Combining Macron]O2):

Figure 1
Figure 1:
Model of the functional lung unit during perfluorocarbon (PFC) partial liquid ventilation. Calculation of the ventilation-perfusion ratio (VA/Q) is based on the Fick principle. According to mass flow balance during steady-state, oxygen delivery by alveolar ventilation (VA) (top) balances oxygen uptake by perfusion (Q) (bottom). Net oxygen delivery equals alveolar ventilation multiplied by the difference between the inspiratory oxygen fraction (FIO2) and the alveolar oxygen fraction (FAO2). Net oxygen uptake into the blood corresponds to pulmonary capillary perfusion (Q) times the difference between end-capillary oxygen (CC′O2) and mixed venous (CV[Combining Macron]O2) content. As a first approximation, diffusional equilibrium between oxygen partial pressures in perfluorocarbon (PPFCO2) and in end-capillary blood (PC′O2) is assumed.

Transposition produces a term for VA/Q calculation:

  1. CV[Combining Macron]O2 is measured by blood gas analysis and hemoximetry of pulmonary arterial blood. The oxygen content, conventionally calculated for standard temperature pressure dry conditions, is converted to that of body temperature (TB) using the factor (273°C + TB)/273°C.
  2. PC′O2 is assumed to equal PAO2, which can be assessed by 19F-MRI.10 CC′O2 is estimated by considering the oxygen dissociation curve and the measured hemoglobin (Hb) concentration.
  3. FIO2 is measured by a gas analyzer under ambient temperature pressure dry conditions. FIO2 under body temperature pressure saturated conditions is calculated by considering water (PH2O) and perflubron (PPFB) vapor and barometric pressure (PB): FIO2(BTPS)=FIO2(ATPD) · (PB−PH2O−PPFB)/PB.
  4. FAO2 under body temperature pressure saturated conditions is determined from MRI-derived PAO2 divided by PB: FAO2 = PAO2/PB.

Simulation of VA/Q Estimations

The methods based on the Fick principle and described by Rizi et al. were compared by simulations of VA/Q determinations. The method of Rizi et al.11 has been described in detail; only the final equation was modified (see Appendix; Online Supplement [Supplemental Digital Content 1,]). Normal human physiology and the following parameters were assumed: Hb 15 g/dL, PV[Combining Macron]O2 40 mm Hg, PV[Combining Macron]CO2 45 mm Hg, FIO2 0.21 or 0.8. PAO2 was defined to be the independent variable ranging between PV[Combining Macron]O2 and the inspiratory oxygen partial pressure. When the analysis was performed according to the Fick principle, the Bohr effect was neglected. Instead, Severinghaus standard dissociation curve was applied to compute O2 contents from PAO2 values. In the case of the Fick principle, the impact of a 5% error in PAO2 on the resultant VA/Q value was quantified to identify a reliable PAO2 range. Appropriate programming software (Mathcad 2001 SE; MathSoft, Cambridge, MA) was used.

Experimental Application

The method was applied to a data subset from a previous study13 in which 19F-MRI was used to measure PAO2 during PLV and additional physiological data were recorded.

Animal Model

The animal procedures were approved by the state animal welfare committee. Anesthesia and relaxation were induced in 7 healthy domestic pigs with a mean body weight of 18 ± 1 kg by IV administration of 1 mg · kg−1 midazolam, 10 mg · kg−1 ketamine, and 0.2 mg · kg−1 pancuronium. Anesthesia was maintained using a continuous infusion of 1.5 mg · kg−1 · h−1 midazolam and 15 mg · kg−1 · h−1 ketamine. Animals were tracheally intubated and pressure-control ventilated (Servo Ventilator 900C®; Siemens-Elema, Solna, Sweden) at a respiratory rate of 20 breaths/min, inspiratory pressure 20 cm H2O, positive end-expiratory pressure (PEEP) 5 cm H2O, inspiration-expiration time ratio 1:2, and FIO2 1.0. A 20-gauge catheter was inserted into the femoral artery. A double-lumen monitor catheter (Swan-Ganz® monitor catheter; Baxter, Irvine, CA) was advanced into a pulmonary artery under pressure guidance through a 6F venous sheath (Inter-Flex® polyurethane sheath; Baxter) positioned in a femoral vein.

PLV and Study Protocol

The pigs received an endotracheal instillation of 10 mL · kg−1 body weight perflubron (low dose) (perfluorooctyl bromide, Liquivent®; Alliance Pharmaceutical Corp., San Diego, CA). FIO2 was set to 1.0 and inspiratory pressures were adjusted to maintain PaCO2 in the range 30 to 50 mm Hg. Measurements were taken after a stabilization period of at least 20 minutes and were repeated with FIO2 of 0.8, 0.6, and 0.4. In a second step, perflubron was administered to result in a cumulative dose of 20 mL · kg−1 (high dose), and all measurements were repeated.

Data Acquisition

Physiological Measurements

Systemic and pulmonary blood pressures were determined by invasive monitoring (Sirecust 404 1A; Siemens, Erlangen, Germany). FIO2 was measured by a sidestream analyzer under ambient temperature pressure dry conditions (Capnomac® Ultima, Datex-Ohmeda, Helsinki, Finland). Ventilatory variables were recorded from the respirator. The monitoring equipment was placed outside the scanner room to avoid imaging artifacts and ferromagnetic interactions. Pressure lines and all tubing were extended to a length of 6 m. Arterial and mixed venous blood samples were obtained and immediately analyzed for oxygen partial pressure (PaO2 and PV[Combining Macron]O2), carbon dioxide partial pressure (PaCO2 and PV[Combining Macron]CO2), and pH using standard blood gas electrodes (ABL 500®; Radiometer, Copenhagen, Denmark). Arterial and mixed venous oxygen saturation (SaO2 and Sv[Combining Macron]o2) and Hb were obtained by species-specific hemoximetry (OSM 3®; Radiometer).


The methodology of Laukemper-Ostendorf et al. was applied to image PAO2 in liquid perflubron.10,13 Investigations were performed with the animals in a supine position using a 19fluorine birdcage coil (Rapid Biomedical, Wurzburg, Germany) inside a 1.5-T magnet (Vision®; Siemens, Germany) during expiratory breath hold. A snapshot fast low-angle shot sequence was used to quantify PAO2 in perflubron (slice thickness 40 mm, matrix 20 × 64 [internally interpolated to matrix 128 × 128], rectangular field of view 175 × 280 mm, repetition time 2.7 milliseconds, echo time 1.2 milliseconds, flip angle 6°, acquisition time 6 seconds). After a single, nonselective inversion pulse, a series of 64 T1-weighted images were obtained. Three transversal planes through the lung (lung apex, mid, and base) were selected (Fig. 2).

Figure 2
Figure 2:
Example of 19F magnetic resonance imaging. Means of the series of 64 images for quantification of oxygen partial pressure (PO2) are depicted. The images were obtained in 3 transversal planes (apex, mid, and base) at 2 different perflubron doses (10 mL · kg−1 at low dose, 20 mL · kg−1 at high dose). The arrows indicate an implanted perflubron probe to calibrate PO2.

Data Processing


In the high-dose perflubron group, the lung of the 64 snapshot images was segmented into 4 horizontal layers of equal height and defined as regions of interest (ROI). In the low-dose group, only 2 layers of larger size were defined to improve the signal-to-noise ratio and to obtain reliable data. The 64 snapshot data of each ROI were noise corrected and fitted to a nonlinear curve (PV-WAVE; Visual Numerics, Houston, TX) to estimate T1. Considering the calibration data of Laukemper-Ostendorf, T1 corresponded to an absolute oxygen partial pressure (PO2).10

VA/Q Estimation

Local VA/Q values were calculated according to Eq. (2). To consider species-specific physiology, an oxygen dissociation curve was calculated by using a localized second-order polynomial fit14 of the porcine blood gas sample pool (n = 257). Saturation (SO2) was described as a nonlinear function (f) of PO2 (SO2 = f[PO2]). Subsequently, the content (CO2) was calculated according to:

Here, the porcine oxygen-carrying capacity of Hb (βO2) was set to 1.36 mLO2 · gHb−1 and the solubility coefficient of oxygen in blood (αO2) to 0.0304 mLO2 · L−1 · mm Hg−1.15,16 The same equations were used to estimate global VA/Q by substituting PaO2 for PAO2.

Statistical Analysis

Statistical analysis of VA/Q data was performed on a logarithmic scale. Explorative analysis of differences was performed using 2-tailed Student t tests for dependent samples. VA/Q at different FIO2, VA/Q at different horizontal layers, and median VA/Q and ventral-to-dorsal VA/Q ratio between the dose groups were compared. For the latter, the first and second as well as third and fourth layer data of the high-dose perflubron group were combined to create 1 ventral and 1 dorsal layer as in the low-dose group. Statistical software (SPSS 15.0.1; SPSS, Chicago, IL) was used.


In the simulation of VA/Q estimates (Fig. 3), both methods resulted in a similar interdependence between PAO2 and VA/Q. However, during air ventilation, VA/Q values obtained using the Fick principle were 23% larger than values calculated according to Rizi et al., and during ventilation with an FIO2 of 0.8, the estimates according to Fick were 42% larger. Because VA/Q is commonly scaled logarithmically, a systematic error of this linear magnitude seems to be of minor importance.

Figure 3
Figure 3:
Comparison of 2 methods to calculate VA/Q from alveolar oxygen partial pressure (PAO2). For these models, the following physiological values for humans were assumed: hemoglobin 15 g/dL, PV[Combining Macron]O2 40 mm Hg, PV[Combining Macron]CO2 45 mm Hg. Inspiratory oxygen fraction (FIO2) 0.21 (A) and FIO2 0.8 (B). When using the method based on the Fick principle, Severinghaus standard dissociation curve was applied to compute the O2 contents.

VA/Q estimation by PAO2 was regarded as sensitive when a 5% deviation of PAO2 resulted in a VA/Q error of <10% on the log scale. During air ventilation, this safe PAO2 ranged between 40 and 120 mm Hg and corresponded to a VA/Q between 0.2 and 2.5. During ventilation with an FIO2 of 0.8, the safe PAO2 was between 40 and 455 mm Hg and corresponded to a VA/Q range between 0.04 and 0.7. During oxygen ventilation, the safe PAO2 was between 40 and 570 mm Hg and corresponded to a VA/Q range between 0.02 and 0.5. Outside these ranges, small errors in the PAO2 measurement resulted in substantial errors in VA/Q.

In the animal experiments, ventilatory and hemodynamic measurements in both perflubron dose groups were reproducible with minor intergroup differences (Table 1). Blood gases during PLV (Table 2) corresponded to those found in other PLV investigations.17

Table 1
Table 1:
Cardiorespiratory Data for Each of the Partial Liquid-Ventilated Dose Groups
Table 2
Table 2:
Blood Gas Partial Pressures for Each of the Partial Liquid-Ventilated Dose Groups

The 95% confidence interval (CI) of 19F-MRI–measured VA/Q at low perflubron dose PLV ranged from 0.08 to 0.29 and did not significantly differ from that of the high-dose group (CI 0.09–0.22). This VA/Q is low compared with the VA/Q expected during gas ventilation, but in fact corresponds to the VA/Q estimated by arterial blood gases (low dose: CI 0.08–0.21; high dose: CI 0.09–0.18).

Marginally lower VA/Q values were found at higher FIO2 in the high perflubron dose group (Fig. 4) (CI at FIO2 0.4: 0.11–0.24; CI at FIO2 1.0: 0.08–0.19; P = 0.03), but not in the low-dose group (CI at FIO2 0.4: 0.09–0.22; CI at FIO2 1.0: 0.06–0.23; P = 0.60).

Figure 4
Figure 4:
Influence of the inspiratory oxygen fraction on the ventilation-perfusion ratio (VA/Q) in perflubron. The box plots show first quartile, median, third quartile, maximum, and minimum. Outliers (circles) were defined to be 1.5 interquartile ranges lower than the first quartile, or 1.5 interquartile ranges higher than the third quartile. A, Low-dose perflubron partial liquid ventilation (PLV). B, High-dose perflubron PLV. The trend toward a lower VA/Q at high FIO2 is at best only marginal.

When the lung in the high-dose group was subdivided into 4 ROI, a strong gravitational VA/Q gradient (quantified by the nondependent VA/Q divided by the dependent VA/Q) was found: CI 1.5–4.9, P = 0.006 (Fig. 5). When the lung was subdivided into 2 ROI to compare dosing groups, this gradient was higher in the high-dose group (CI 1.5–3.4) than in the low-dose group (CI 0.9–2.5) (P = 0.045).

Figure 5
Figure 5:
Distribution of the ventilation-perfusion ratio (VA/Q) in perflubron between nondependent and dependent lung regions. Regions of interest (ROI) 1 relates to the ventral, nondependent lung area and ROI 4 to the dorsal, most dependent lung area. A, Results of the low-dose perflubron group in which ROI 1 and ROI 2, as well as ROI 3 and ROI 4, had to be combined to achieve a better signal-to-noise ratio. B, Results of the high-dose perflubron group. A strong VA/Q gradient from dependent (ROI 4) to nondependent (ROI 1) lung regions was found. P values were derived from 2-tailed paired t testing.


A method was developed to estimate regional VA/Q in the lung by combining MRI-detected PAO2 and the Fick principle. Numerical simulations provided results approximating those of a PAO2-based approach that has been described by Rizi et al. The method performed adequately in the VA/Q range between 0.02 and 2.5. The main finding in the experimental application is a generally low VA/Q in the perflubron, which supports the notion of restrained oxygen transport in the close vicinity of perflubron. In addition, the VA/Q distribution was found to be dependent on the gravitational plane and perflubron dosage.

Comparison to the Approach of Rizi et al.

Compared with the approach of Rizi et al., the Fick-based technique for calculation of VA/Q contains certain physiological simplifications. In the Fick-based technique, neither the oxygen dilution caused by gas transfer (e.g., CO2) into the alveolar space nor the reduction of gas volume as a result of gas uptake into the blood (e.g., O2) with consecutive inflow of fresh gas is considered. However, a liquid-filled alveolar space would maintain its volume, which averts these mechanisms. Moreover, interactions between pH and PCO2 and the oxygen-Hb dissociation curve are ignored by the Fick-based approach. Nevertheless, a comparison of model simulations of both methods resulted in an acceptable overestimation of VA/Q by the Fick principle compared with the approach by Rizi et al. when scaled logarithmically (as is the convention in VA/Q plots). To conclude, the approach by Rizi et al. considers all interdependences of alveolar gas exchange, whereas the Fick principle is simple and therefore easier to apply. The Fick principle seems to be especially suitable when species-specific details of respiratory gas exchange are not exactly known (animal models), when dissolved gas is transferred between liquids, as in the liquid phase of PLV, or when the solution of Rizi et al. does not work (use of pure oxygen).

Methodological Considerations

Diffusion Limitations

The Fick principle relies on the assumption that PAO2 equals PC′O2, as is usually the case in an air-breathing, healthy lung. If the PAO2 were to exceed the PC′O2, the calculated VA/Q would be overestimated. Model estimations of PLV by Mates vanLöbensels et al.18 and Suresh et al.19 suggest that the PO2 difference between central alveolar gas and capillary blood gas remains small during PLV, at approximately 10 mm Hg at end-expiration. The PO2 of perflubron, if regarded to range between PAO2 and PC′O2, should differ even less.

Steady-State Conditions

Breath-holding affects PAO2, with a bias toward a decreased calculated VA/Q. To make an error estimate, we assumed an oxygen consumption20 of 6 mLO2 · kg−1 · min−1 and the functional residual capacity of the lung21 of 25 mL · kg−1 to be filled with perflubron. Considering the oxygen solubility in perflubron22 of 50 vol%/760 mm Hg, a mean PO2 decrease of 6 mm Hg/s in the liquid phase was calculated. Thus, during the 6-second measurement, a mean PO2 decrease of approximately 18 mm Hg is expected. According to the simulation, this results in a median VA/Q decrease of 60% when using air and a 7% decrease at an FIO2 of 1.

Limitation of the PO2 Probe

In contrast to other methods, any PO2 indicator-based approach can assess lung regions only if the PAO2 tracer substance (which in this case is perflubron) is present in these regions. Hence, the method cannot be applied before perflubron administration unless another technique for quantification of PO2, e.g., 3He-MRI,11,23,24 is used. Because PAO2 depends on the 19F-MR signal, the estimated VA/Q is perflubron weighted. During PLV, the alveolar space may be subdivided into the perflubron phase and the gas phase, which are likely to have identical PO2 if arranged close together. This is presumably the case in the nondependent lung regions, in which the amount of perflubron is relatively small. In the dependent lung regions, however, the perflubron may fill and occlude the whole alveolus or even the acinus. Because of the lack of contact surface, the oxygen exchange in this perflubron-filled region is likely to be restricted, whereas another region nearby may be well ventilated with gas.

Spatial Resolution

The MRI technique we used was developed to prove the principle. Therefore, large-scale ROI, which are an average of many smaller units, were drawn to achieve a reliable signal. The low resolution obtained may have been problematic for interpreting heterogeneity information. However, the resolution was sufficient to demonstrate the unequal distribution of VA/Q between dependent and nondependent lung regions. Options remain to improve the spatial resolution and better maintain steady-state conditions. For instance, the measurement was performed during a single 6-second period. Sampling over a longer time period in connection with triggering would advance image quality and consequently enable a higher resolution.

Experimental Application

Our data suggest that the overall efficiency of oxygen transport in the perflubron phase is rather limited. This finding is supported by the reduced PaO2/FIO2 ratios, which have been reported by others in healthy animals during PLV.6,17 Furthermore, Uchida et al.25 measured equivalently reduced PO2 values in perflubron that were sampled via catheters. Contrary results were found, however, by Harris et al.4 using 13NN-PET. Their VA/Q data (mean 1.0) were much higher than those found using 19F-MRI (CI 0.09–0.22 at the high perflubron dose). Besides the differences between experimental settings, the discrepancy in VA/Q may be explained by the fact that 13NN-PET estimates VA/Q in both the gas and liquid phase, whereas 19F-MRI predominantly determines VA/Q within the perflubron phase. Furthermore, 13NN-PET was perfusion weighted, whereas the 19F-MRI was perflubron weighted. Finally, the dissolubility of nitrogen in perflubron differs from that of oxygen,26 and therefore different results might be expected.

Using the MIGET in an acute respiratory distress syndrome model, Lim et al.7 found that PLV reduces intrapulmonary shunt. However, the shunt units were mostly converted to units showing low VA/Q. The (perfusion-weighted) VA/Q means were slightly higher (0.4) than those obtained by 19F-MRI. As before, the discrepancies may be explained by the differences in both the experimental setting and the VA/Q quantification. The dissolubility of the MIGET tracer gases in perfluorocarbons is significantly higher compared with that of oxygen.6 Therefore, from our observations, it can be maintained that VA/Q in the liquid perflubron phase is rather poor.

In accordance with the PET study by Harris et al.,4 we found a significant increase in VA/Q from dependent to nondependent lung regions. In addition, using MIGET during PLV, Lim et al.7 found an increased ventilation-perfusion heterogeneity. The heterogeneity increased with the perfluorocarbon dose, as in this study.

The relationship between oxygenation and PLV is particularly attributed to the characteristics of perfluorocarbons. Liquid perflubron is about 1400 times as dense as oxygen, and thus preferentially distributed to the dependent lung. The hydrostatic pressure of the fluid acts as a selective PEEP, which is able to reopen collapsed alveoli in the dependent lung regions. In addition, perflubron might compensate for the missing surfactant because of its low surface tension. These properties may stabilize the dependent lung regions and may reduce the intrapulmonary shunt.

However, the high viscosity and density of the fluid reduce the convective gas transport. The surface area between gas and liquid within the airways and the alveoli is probably too small. Besides that, one may expect overdistension of the dependent lung regions in large-animal models, when high perfluorocarbon doses result in a highly selective PEEP. Tarczy-Hornoch et al.27 presented corresponding findings based on numerical computations, in which PLV caused the gas ventilation to redistribute toward the nondependent lung regions. The effect was dose dependent. To conclude, a low V[Combining Dot Above]A/Q[Combining Dot Above] and a gravitational V[Combining Dot Above]A/Q[Combining Dot Above] gradient within the perfluorocarbons are likely.


A-WKS helped in study design, conduct of the study, data collection, data analysis, and manuscript preparation; BE helped in data analysis and manuscript preparation; CPH helped in study design, conduct of the study, data collection, data analysis, and manuscript preparation; MD helped in data collection and manuscript preparation; MS helped in conduct of the study, data collection, and manuscript preparation; MQ, LMS, and NW helped in study design and manuscript preparation.


The authors thank Debra Bickes-Kelleher (Institute of Anatomy and Cell Biology, Johannes Gutenberg-University, Mainz, Germany) for proofreading.


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The derivation of the equation described by Olszowka and Wagner12 and applied by Rizi et al.11 has been described in detail in their publications. In this study, the final equation was used with the following modification:

where CV[Combining Macron]CO2= mixed venous carbon dioxide (CO2) content; CC′CO2 = end-capillary CO2 content; PACO2 = alveolar CO2 partial pressure; PV[Combining Macron]N2 = mixed venous nitrogen (N2) partial pressure; FIN2 = inspiratory N2 fraction; λN2 = blood gas partitioning coefficient for N2; and k = converting factor considering gas expansion caused by temperature and replacement of gas fraction by partial pressure.

Because CC′CO2 as well as CC′O2 are nonlinear functions of PACO2, the equation is an implicit function of PACO2, which can be solved by numerical analysis. Subsequently, the PACO2 value is used to estimate first the expiratory VA/Q by using the mass balance equation of CO2 and second the inspiratory VA/Q by using the mass balance equation for O2.

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