Abstract

Background. Studies of the accuracy of partial rebreathing measurements of pulmonary blood flow (PBF) in patients with abnormal lungs have not fully explained the sources of error.

Methods. We used computer models of emphysema and pulmonary embolism incorporating both ventilation-perfusion (V˙/Q˙) and ventilation-volume (V˙/V) heterogeneity to investigate systematic errors in partial rebreathing PBF measurements. We studied (i) errors produced under usual conditions, (ii) effects of recirculation, (iii) effects of alveolar–proximal airway and alveolar-capillary Pco2 and V˙CO2 differences, (iv) effects of alveolar V˙/Q˙ inhomogeneity and (v) effects of rebreathing time.

Results. In the pulmonary embolism model the systematic error is only acceptable (<10%) when the simulated PBF is low (2–3 litre min−1). In the emphysema model PBF is underestimated by more than 20% at all cardiac outputs studied. Four sources of systematic errors were found. (i) Alveolar–proximal airway Pco2 gradients and flux differences between the proximal airway and alveolar compartments contribute most to the systematic error. (ii) V˙/Q˙ inhomogeneity causes Pco2 gradients between the alveolar compartments and pulmonary capillary blood, and between pulmonary capillary compartments. (iii) Rebreathing times are inadequate in the presence of V˙/V mismatch. (iv) The apparent effect of venous blood recirculation is small in emphysema but significant in pulmonary embolism.

Conclusions. We conclude that PBF cannot be measured accurately by partial rebreathing in lungs with emphysema or embolism. Systematic errors are caused mainly by errors in end-tidal Pco2 values.

Partial rebreathing is a non-invasive technique for measuring pulmonary blood flow (PBF), which is based on a differential form of the Fick equation.1 Numerous studies have investigated the accuracy of this method.2–7 but few studies have assessed the accuracy of this method in subjects with abnormal lungs.8–10 Odenstedt and colleagues9 evaluated a non-invasive cardiac output instrument that uses partial rebreathing (NICO, Novametrix Medical Systems Inc., CT, USA) in critically ill patients and found it to provide an accurate estimate of cardiac output (CO). This monitor uses a number of corrections to the classical partial rebreathing method,11 some of which have not been published.11,12 Gama de Abreu and colleagues10 studied the performance of the partial rebreathing technique and found that it deteriorates when dead-space is increased or the lungs are injured.

The partial rebreathing method is based on the mass balance of CO2 between the circulation and the ventilation before and after a short period of partial rebreathing during which PACO2 and the CO2 excretion rate change but PBF and mixed venous CO2 content remain constant. Under these conditions PBF is given by:  

(1)
PBF=ΔV˙CO2ΔCCO2,
where ΔV˙CO2 and ΔCCO2 are the changes in the pulmonary capillary CO2 excretion rate and pulmonary end-capillary CO2 content respectively during rebreathing. In the non-invasive partial rebreathing method ΔV˙CO2 and ΔPCO2 (changes in Pco2 during rebreathing) are estimated from proximal airway CO2 excretion rate and end-tidal Pco2 measurements. The systematic errors in the non-invasive partial rebreathing method were analysed by Yem and colleagues6 using a computer model of a normal homogeneous lung. Diseases affecting gas exchange are likely to degrade the method, but the extent and nature of these effects have not been studied and are not well understood.

There are multiple potential causes of error in partial rebreathing measurements. It is well known that in diseased lungs the end-tidal Pco2 often does not represent arterial Pco2 well.13 Ventilation-perfusion mismatch is known to create regions of different alveolar partial pressures in lungs and hence results in increased differences between end-tidal and arterial CO2 partial pressure.13 Ventilation-volume mismatch alters the partial pressure equilibration time constants after a perturbation in ventilation and is therefore likely to cause errors in partial rebreathing measurements.

We studied the effects of rebreathing time, re-circulation, alveolar-proximal airway Pco2 differences and alveolar-pulmonary capillary Pco2 differences on systematic errors in partial rebreathing estimates of cardiac output using mathematical models of emphysema and embolism.

Materials and methods

The models

We have developed a mathematical model of the cardio-respiratory system that can simulate normal subjects and subjects with emphysema and embolism. The model incorporates both ventilation-perfusion (V˙/Q˙) and ventilation-volume (V˙/V) heterogeneity. The model was developed using a rational approach designed to yield mutually consistent sets of parameters14 and was evaluated against published measured data.14 The model predicts dynamic and steady state behaviour of gases covering a wide solubility range.

The model simulates tidal breathing through a branched respiratory tree and incorporates the effects on CO2 dynamics of lung tissue mass, vascular transport delays, multiple body compartments and realistic blood-gas dissociation curves, and is implemented using Matlab and Simulink (Mathworks, Natick, MA, USA).

A block diagram of the model is shown in Yem and colleagues.14 The emphysema model has a pure shunt of <1% in addition to three perfused and ventilated alveolar compartments and its airway structure is shown in Figure 1. The embolism model has a pure shunt of 20% and two alveolar compartments, and its airway structure is similar to Figure 1 with one less terminal branch. The volume, perfusion and effective ventilation of each alveolar compartment in the models are shown in Figure 2.

Fig 1

Respiratory tree of the emphysema model. The respiratory tree contains three perfused alveolar compartments and shunt. The grey areas indicate alveolar compartments that have similar V˙/Q˙ ratios. WG, Weibel generations.

Fig 1

Respiratory tree of the emphysema model. The respiratory tree contains three perfused alveolar compartments and shunt. The grey areas indicate alveolar compartments that have similar V˙/Q˙ ratios. WG, Weibel generations.

Fig 2

(a) The emphysema model alveolar compartment parameters. (b) The pulmonary embolism model alveolar compartment parameters.

Fig 2

(a) The emphysema model alveolar compartment parameters. (b) The pulmonary embolism model alveolar compartment parameters.

For the purposes of this study an additional airway dead-space, which can be switched in or out to simulate the rebreathing process, was incorporated into the model.6 The original model was verified by comparing dynamic and static predictions of arterial Pco2 with PCO2 measured in clinical studies.6,15 In addition, the modified model used in this study was verified by analysis of the mass balance of O2, N2 and CO2 during a 10 min partial rebreathing run and by comparing capillary blood flow in each alveolar compartment calculated using equation (1) with the true capillary flow at a PBF of 5 litre min−1 with no recirculation.

Study 1: standard conditions

The model was run for 15 000 s with parameters shown in Table 1 and with the rebreathing dead-space by-passed to create a set of initial conditions for cardiac outputs 1.5 and 2–15 litre min−1 in steps of 1 litre min−1. The initial gas in the additional dead-space was air. At each cardiac output a series of datasets were generated by running the model from an appropriate initial condition and switching the additional dead-space for 50 s at intervals of 180 s. Ten rebreathing cycles were simulated. The PBF values were calculated from PETCO2 and airway V˙CO2 averaged over single breaths obtained immediately before the start and at the end of the last rebreathing cycle. Complete CO2 dissociation equations16 were used to calculate CO2 content to avoid errors because of variations in the slope of the CO2 dissociation curve.

Table 1

Model parameters

Parameters Units Emphysema17,18 Embolism18,19 
Subject data directly obtained from articles 
    Age/sex Years/sex 61/M 71/F 
    Weight/height kg cm−1 70/175 –/– 
     V˙total litre min−1 – 13.2 
     Q˙s 0.3 20 
    MIGET V˙DS 53 42 
    fr bpm 22 29 
     FIO2 21 50 
     PACO2 kPa 6.8 3.2 
     PaO2 kPa 7.06 13.1 
Calculated based on subject data 
    VD/VT (Bohr–Enghoff) 72 61 
     Q˙A/V litre min−1 6.0 2.9 
     Q˙total litre min−1 6.0 3.7 
     V˙total litre min−1 15.8 – 
    VT litre 0.72 0.46 
    FRC20 litre 4.05 3.18 
    VA litre 3.68 2.97 
     V˙O2 consumption μmol s−1 186.6 114.9 
     V˙CO2 production μmol s−1 186.6 106.3 
Model default values 
    VInstDS litre 0.05 0.05 
    VrebreathDS litre 0.15 0.15 
    I:E21 ratio 1:4 1:2.33 
    Hb g 100 ml−1wholeblood 15 15 
    BE mEq litre−1 
Parameters Units Emphysema17,18 Embolism18,19 
Subject data directly obtained from articles 
    Age/sex Years/sex 61/M 71/F 
    Weight/height kg cm−1 70/175 –/– 
     V˙total litre min−1 – 13.2 
     Q˙s 0.3 20 
    MIGET V˙DS 53 42 
    fr bpm 22 29 
     FIO2 21 50 
     PACO2 kPa 6.8 3.2 
     PaO2 kPa 7.06 13.1 
Calculated based on subject data 
    VD/VT (Bohr–Enghoff) 72 61 
     Q˙A/V litre min−1 6.0 2.9 
     Q˙total litre min−1 6.0 3.7 
     V˙total litre min−1 15.8 – 
    VT litre 0.72 0.46 
    FRC20 litre 4.05 3.18 
    VA litre 3.68 2.97 
     V˙O2 consumption μmol s−1 186.6 114.9 
     V˙CO2 production μmol s−1 186.6 106.3 
Model default values 
    VInstDS litre 0.05 0.05 
    VrebreathDS litre 0.15 0.15 
    I:E21 ratio 1:4 1:2.33 
    Hb g 100 ml−1wholeblood 15 15 
    BE mEq litre−1 

Study 2: the effects of recirculation

The partial rebreathing method assumes that mixed venous blood concentrations of CO2 remain constant immediately before and during the rebreathing phase of each measurement cycle. To examine the effects of changes in mixed venous Pco2 caused by recirculation, the model was modified by removing all the body compartments. The mixed venous Pco2 and PO2 inputs to the pulmonary capillaries were then kept constant at values appropriate to the cardiac output thus effectively removing the effects of recirculation of the inspired CO2. The simulations described above in Study 1 were repeated.

Study 3: the effects of alveolar–proximal airway and alveolar-capillary Pco2 and V˙CO2 differences

The partial rebreathing method is based on the mass balance of CO2 at the pulmonary capillary-alveolar interface but uses measurements in the proximal airway. In both the emphysema and the pulmonary embolism models, there is significant ventilation, perfusion and volume in alveolar compartments with high V˙/V ratios. To examine the effects of the alveolar-proximal airway differences, PBF to each alveolar compartment was calculated using PACO2 and pulmonary capillary V˙CO2 for each alveolar compartment averaged over a single breath. Total PBF was calculated by the summation of PBF values in each individual alveolar compartment and compared with PBF calculated using proximal airway measurements. The effects of alveolar-capillary gradients were examined by comparing individual compartment PBFs calculated using alveolar measurements with model capillary blood flow parameters. The simulations described in Study 1 were repeated with recirculation included and excluded.

Study 4: the effects of V˙/Q˙ spread

The V˙/Q˙ ratio in a compartment determines the steady-state PCO2 in that compartment; therefore, it is likely the V˙/Q˙ ratio affects the change in alveolar and capillary PCO2 during rebreathing (ΔPco2). To examine the effect of V˙/Q˙ inhomogeneity, the Pco2 in the alveoli and pulmonary capillaries and the pulmonary capillary V˙CO2 were analysed and compared with corresponding values in the mixed arterial and the proximal airway over a rebreathing cycle. The analysis was done for 50 s rebreathing time with and without recirculation, and 550 s rebreathing time with no recirculation.

Study 5: the effects of rebreathing time

The time constant for alveolar CO2 turnover depends strongly on PBF and the ventilation-volume ratio of the alveolar compartments. Therefore the time required to achieve a quasi-equilibrium in PACO2, Petco2 and airway V˙CO2 after a perturbation is increased when PBF is low and when the ventilation–volume ratio is low. PBF values were calculated using an extended rebreathing time of 550 s to make sure that quasi-equilibrium was achieved. No recirculation was included in these simulations. The simulations described above in Study 1 were repeated.

Results

The modified model maintained mass balances of O2, N2 and CO2 to within 5×10−8 mol during a 10 min partial rebreathing run. The difference between compartment pulmonary capillary flows calculated using equation (1) and the model capillary flow parameters at a PBF of 5 litre min−1 were all <0.5%.

Study 1: standard conditions

Typical proximal airway Pco2 and breath-by-breath proximal airway and pulmonary capillary V˙CO2, generated using cardiac output values most closely approximating the conditions of the patients on whom the models are based,14 6 litre min−1 in the emphysema model and 4 litre min−1 in pulmonary embolism model, are shown in Figure 3. Before rebreathing both Pco2 and V˙CO2 reflect the quasi-equilibrium achieved after the previous rebreathing cycle. The V˙CO2 at the pulmonary capillaries and at the proximal airway are not the same at the end of rebreathing and the difference is greater in emphysema. Changed Pco2 and changed V˙CO2 were recorded at end-expiration on the last completed breath before 50 s.

Fig 3

(a) Arterial, mixed venous and proximal airway Pco2 responses to a partial rebreathing cycle. (B) Pulmonary capillary and proximal airway CO2 flux responses. Rebreathing starts at 0 s and finishes at 50 s.

Fig 3

(a) Arterial, mixed venous and proximal airway Pco2 responses to a partial rebreathing cycle. (B) Pulmonary capillary and proximal airway CO2 flux responses. Rebreathing starts at 0 s and finishes at 50 s.

The differences between the simulated true PBF and the PBF calculated from rebreathing measurements are shown in Figure 4a for the emphysema model and Figure 4b for the pulmonary embolism model (Proximal airway curve), and also in Table 2. The errors vary systematically with the true PBF in both models. The measurements are most accurate when the simulated PBF is low, but PBF is underestimated across most of the cardiac outputs studied.

Table 2

Percentage error of the estimated PBF using normal, emphysema and pulmonary embolism models

CO (litre min−1Normal6 (%) Emphysema (%) Embolism (%) 
31 −33 
−4 −64 −30 
10 −29 −77 −49 
CO (litre min−1Normal6 (%) Emphysema (%) Embolism (%) 
31 −33 
−4 −64 −30 
10 −29 −77 −49 
Fig 4

(a) The systematic error in the simulated partial rebreathing measurements of PBF in the emphysema model, as a function of simulated true PBF. (b) The systematic error in the simulated partial rebreathing measurements of PBF in the pulmonary embolism model, as a function of simulated true PBF. recir, recirculation.

Fig 4

(a) The systematic error in the simulated partial rebreathing measurements of PBF in the emphysema model, as a function of simulated true PBF. (b) The systematic error in the simulated partial rebreathing measurements of PBF in the pulmonary embolism model, as a function of simulated true PBF. recir, recirculation.

Study 2: the effects of recirculation

The effects of removing recirculation are shown in curve ‘Proximal airway+no recir’ of Figure 4a and b. Removal of recirculation reduces systematic error in the measurements. The reduction in error is up to 25% in the pulmonary embolism model, but only up to 4% in the emphysema model.

Study 3: the effects of alveolar–proximal airway and alveolar-capillary Pco2 and V˙CO2 differences

Systematic errors in PBF obtained using PACO2 as an estimate of arterial Pco2 and true pulmonary capillary V˙CO2 (without recirculation) in the differential Fick equation are reduced to approximately −11 and −39% at COs of 5 and 15 litre min−1, respectively, in emphysema (Fig. 4A) and −6 and −13% at COs of 5 and 15 litre min−1 (corresponding to PBFs of 4.0 and 12.1 litre min−1) respectively in embolism (Fig. 4B).

Table 3 summarizes the measurements made in each of the ventilated alveolar compartments, and each of the perfused pulmonary capillary compartments, generated using CO values of (i) 6 litre min−1 in the emphysema model and (ii) 4 litre min−1 in the pulmonary embolism model. The rebreathing period was 50 s. In emphysema, the change in PACO2 during rebreathing (ΔPACO2) was at most 0.029 kPa more than the change in PcCO2 (ΔPcCO2). The ΔPCO2 is low in the mid-V˙/Q˙ compartment, thus a small absolute difference between the alveolar and pulmonary capillary ΔPCO2 causes a large difference in pulmonary capillary flow (17.5%). In embolism, the differences between ΔPACO2 and ΔPcCO2 are both <0.008 kPa.

Table 3

Changes in V˙CO2, PCO2, CCO2V˙CO2, ΔPCO2, ΔCCO2) caused by rebreathing and Q˙A/v calculated using time-averaged alveolar and pulmonary capillary measurements. Rebreathing time was 50 s and no recirculation wasincluded in these simulations. The percentage differences between the alveolar and pulmonary capillary estimated Q˙A/v are calculated for each compartments. The emphysema model was simulated at CO of 6 litre min −1, and before rebreathing, time-averaged PaCO2=7.44 kPa and PETCO2=3.45 kPa. The embolism model was simulated at CO of 4 litre min−1, and before rebreathing, time-averaged PACO2=3.12 kPa and PETCO2 = 2.58 kPa. *Indicates where a total does not exist

 V˙CO2 (μmol s−1ΔV˙CO2 (μmol s−1PACO2 (kPa) A-c grad (kPa) ΔPACO2 (kPa) PcCO2 (kPa) ΔPcCO2 (kPa) ΔCCO2 (μmol litre−1Q˙A/V (litre min−1Q˙A/V diff (%) 
Emphysema (6 litre min−1
    Mid (V˙A/Q˙) 82.69 12.14 7.86 0.24 0.103 8.10 0.085 160.0 4.52 17.5 
    Hi (V˙A/Q˙) 67.69 10.30 3.24 0.24 0.680 3.49 0.651 1488 0.415 4.3 
    Hi (V˙A/Q˙) slow 29.69 2.17 2.74 0.02 0.374 2.76 0.372 752 0.173 0.5 
    Total 180.1 24.61 * * * * * * 5.14 14.4 
Embolism (4 litre min−1
    Mid (V˙A/Q˙) 45.40 14.40 3.19 0.04 0.209 3.23 0.201 464 1.86 3.8 
    Hi (V˙A/Q˙) 63.32 19.60 2.40 0.04 0.373 2.44 0.368 988 1.19 1.3 
    Total 108.7 34 * * * * * * 3.05 3.9 
 V˙CO2 (μmol s−1ΔV˙CO2 (μmol s−1PACO2 (kPa) A-c grad (kPa) ΔPACO2 (kPa) PcCO2 (kPa) ΔPcCO2 (kPa) ΔCCO2 (μmol litre−1Q˙A/V (litre min−1Q˙A/V diff (%) 
Emphysema (6 litre min−1
    Mid (V˙A/Q˙) 82.69 12.14 7.86 0.24 0.103 8.10 0.085 160.0 4.52 17.5 
    Hi (V˙A/Q˙) 67.69 10.30 3.24 0.24 0.680 3.49 0.651 1488 0.415 4.3 
    Hi (V˙A/Q˙) slow 29.69 2.17 2.74 0.02 0.374 2.76 0.372 752 0.173 0.5 
    Total 180.1 24.61 * * * * * * 5.14 14.4 
Embolism (4 litre min−1
    Mid (V˙A/Q˙) 45.40 14.40 3.19 0.04 0.209 3.23 0.201 464 1.86 3.8 
    Hi (V˙A/Q˙) 63.32 19.60 2.40 0.04 0.373 2.44 0.368 988 1.19 1.3 
    Total 108.7 34 * * * * * * 3.05 3.9 

In emphysema, most of the CO2 exchange occurs in the mid-V˙/Q˙ and high-V˙/Q˙ compartments (83 and 68 μmol s−1 respectively before rebreathing). The mid-V˙/Q˙ compartment has the largest error (17.5%) in pulmonary capillary flow calculated from alveolar values (Q˙A/v), followed by the high-V˙/Q˙ compartment (4.3%). In embolism, the mid-V˙/Q˙ compartment accounts for 42% of CO2 exchange (45 μmol s−1 before the rebreathing cycle), and has the larger error (3.8%) in pulmonary capillary flow calculated from alveolar values.

Study 4: the effects of alveolar V˙/Q˙ spread

PCO2 in the ventilated alveolar compartments, generated using PBFs of (i) 6 litre min−1 in the emphysema model and (ii) 4 litre min−1 in the pulmonary embolism model, are shown in Figure 5. Before rebreathing, PCO2 levels reflect the quasi-equilibrium achieved after the previous rebreathing cycle. There are large differences in PCO2 between compartments. In emphysema, the proximal airway end-tidal PCO2 is ≈3.5 kPa while the arterial and mixed venous PCO2 are >7 kPa (Fig. 3). PCO2 in the mid-, high- and high-slow V˙/Q˙ alveolar compartments is ≈7.9, ≈3.2 and ≈2.7 kPa, respectively (Fig. 5). In pulmonary embolism, the proximal airway PCO2 is ≈2.5 kPa while the arterial and venous PCO2 are >3 kPa (Fig. 3), and PCO2 in the mid- and high-V˙/Q˙ alveolar compartments is 3.2 and 2.4 kPa, respectively (Fig. 5).

Fig 5

Alveolar PCO2 during a partial rebreathing manoeuvre, for (A) emphysema model and (B) pulmonary embolism model. Note: Although the vertical axes cover different PCO2 values, the scale factors are the same within each disease. Rebreathing starts at 0 s and finishes at 50 s. VQ=V˙/Q˙ and ‘hi’=high.

Fig 5

Alveolar PCO2 during a partial rebreathing manoeuvre, for (A) emphysema model and (B) pulmonary embolism model. Note: Although the vertical axes cover different PCO2 values, the scale factors are the same within each disease. Rebreathing starts at 0 s and finishes at 50 s. VQ=V˙/Q˙ and ‘hi’=high.

There are large differences in ΔPCO2 between compartments (Table 3). In both models, ΔPCO2 is smallest in the mid-V˙/Q˙ alveolar compartment. In the emphysema model, ΔPCO2 in the high-V˙/Q˙ compartment is greater than the high-slow V˙/Q˙ compartment. ΔPCO2 in the high-V˙/Q˙ slow compartment does not reach quasi-equilibrium in the 50 s rebreathing period (Fig. 5A).

Study 5: the effects of rebreathing time

At a rebreathing time of 550 s without recirculation, the changes in proximal airway PCO2 across all the cardiac outputs studied were >95% complete when rebreathing ended. In both emphysema, and embolism without recirculation, long rebreathing time paradoxically increased the errors in PBF (Fig. 4A and B) when recirculation was omitted. PCO2 and the V˙CO2 at the proximal airway are shown in Figure 6 for emphysema, with a rebreathing time of 550 s without recirculation. Both PCO2 and V˙CO2 reach quasi-equilibrium at 550 s. At 50 s into the rebreathing, the ΔPCO2 of 0.557 kPa underestimates the equilibrium value by 20%, while ΔV˙CO2 of −33.6 μmol s−1 overestimates the equilibrium CO2 exchange by 12%. The resulting overestimation of PBF partially compensates for underestimation of PBF resulting from other mechanisms.

Fig 6

Analysis of long rebreathing time with no recirculation. Plots of end-expired PCO2 and CO2 flux in the proximal airway. The PCO2 and CO2 flux are normalized by subtracting the steady-state value before the start of the rebreathing. The vertical dashed line indicates where a 50 s rebreathing period would end, showing that at this time the equilibrium is not achieved.

Fig 6

Analysis of long rebreathing time with no recirculation. Plots of end-expired PCO2 and CO2 flux in the proximal airway. The PCO2 and CO2 flux are normalized by subtracting the steady-state value before the start of the rebreathing. The vertical dashed line indicates where a 50 s rebreathing period would end, showing that at this time the equilibrium is not achieved.

Discussion

The present study found that PBF determined by the non-invasive partial rebreathing technique is underestimated by more than 20% in the emphysema model at all PBFs, and in the pulmonary embolism model when PBF is above ∼3 litre min−1. In embolism, PBF is overestimated when PBF is below ∼2 litre min−1. The ability of the partial rebreathing technique to estimate PBF is greatly reduced in the presence of the ventilation, volume and perfusion inhomogeneity associated with emphysema and embolism.

This study identified four sources of systematic error in the partial rebreathing technique in the presence of ventilation, volume and perfusion inhomogeneity.

  1. Ventilation–volume and ventilation–perfusion inhomogeneities cause PCO2 gradients and V˙CO2 differences between the proximal airway and the alveolar compartments.

  2. Ventilation–perfusion inhomogeneity causes PCO2 and flux differences between pulmonary capillary compartments and uneven PCO2 gradients between the alveolar compartments and arterial blood.

  3. Rebreathing times are inadequate especially when long alveolar gas turnover time constants exist.

  4. In addition, the study found that the direct effect of recirculation of mixed venous blood is small in the emphysema model, but significant in the pulmonary embolism model.

Gama de Abreu and colleagues10 evaluated the partial rebreathing method in sheep with induced lung injuries. In their Phase II study they inflated a balloon in a branch of the pulmonary artery and therefore their study is similar to our embolism simulation. When a substantial fraction of the lung had a high V˙/Q˙ ratio both our study and theirs found overestimation of PBF at PBFs of 1–2 litre min−1 and both studies found that PBF was underestimated by ∼6 litre min−1 when true PBF was 10 litre min−1. In their Phase III study they increased alveolar dead-space and introduced lung damage, and their sheep model study may be considered to have produced similar V˙/Q˙ and V˙/V lesions to our emphysema simulation. Both studies found ∼4.5 litre min−1 underestimation at PBF of 6 litre min−1.

The limitations of the partial rebreathing method are not predictable from the differential indirect CO2 Fick principle. However, they are not unexpected as the technique measures the composition of expired gases, which can differ greatly from that of alveolar gases in inhomogeneous lungs. A commercially available device (NICO, Novametrix-Respironics, Wallingford, CT, USA) applies proprietary algorithms to correct measurements made from the proximal airways6,11,12 in an endeavour to compensate for such problems.

V˙/Q˙ inhomogeneity

In the emphysema model the mid-V˙/Q˙ compartment receives ≈90% of the total PBF and pulmonary capillary flow calculated by the differential Fick equation (equation 1) is greater than nine times higher than the flow in the high-V˙/Q˙ compartments (Table 3). The large PBF is associated with a small change in CO2 content (ΔCCO2) during rebreathing while the change in CO2 transfer (ΔV˙CO2) in this compartment is similar in magnitude to the ΔV˙CO2 in the high-V˙/Q˙ compartment. Thus a small absolute error in the estimation of mid-V˙/Q˙ compartment ΔCCO2 results in a large percentage error in PBF.

In the emphysema model, most of the V˙CO2 takes place in the mid-V˙/Q˙ compartment (Table 3). However, the volume of the mid-V˙/Q˙ compartment is ≈10% of the total alveolar volume, thus this compartment has the lowest alveolar-capillary diffusion coefficient and hence the largest PCO2 gradient. Therefore the mid-V˙/Q˙ compartment shows the greatest differences between alveolar and pulmonary capillary ΔPCO2.

In the embolism model, the differences in the V˙/Q˙ ratio of the two compartments is much smaller, thus the percentage error in PBF in both compartments is much smaller. The error in PBF is larger in the mid-V˙/Q˙ compartment, because the mid-V˙/Q˙ compartment has larger perfusion and a smaller ΔCCO2 during rebreathing.

When the V˙/Q˙ distribution is inhomogeneous the differential Fick principle can produce accurate estimates if PBF is calculated for each compartment individually and summed. However, the non-invasive partial rebreathing technique estimates PBF from proximal airway measurements, assuming the lung is one compartment, thus V˙/Q˙ mismatch results in additional errors. PACO2 may be predicted from end-tidal PCO2 with precision that is similar to the precision with which PACO2 can be measured directly.13 However, in the presence of abnormal lung function, the prediction equations13 do not predict arterial CO2 partial pressures well because of the complex relationships amongst end-tidal, mean alveolar and arterial CO2 partial pressures.13

Rebreathing times

In lungs, which contain units with long gas turnover time constants, increased rebreathing time would be expected to improve estimates of PBF, particularly when recirculation is absent. Increasing the rebreathing time in the study, however, paradoxically increases the error in estimated PBF in the emphysema model and in the embolism model when recirculation is omitted (Fig. 4A and B). In emphysema after 50 s rebreathing with no recirculation, ΔPCO2 and ΔV˙CO2 are not at equilibrium (Fig. 6). Therefore ΔCCO2 is underestimated and ΔV˙CO2 is overestimated, causing PBF to be overestimated (equation 1). This overestimation partially compensates for the underestimation associated with V˙/Q˙ and V˙/V. Odenstedt and colleagues9 suggested that over- and underestimations may balance each other by coincidence.

Recirculation

The effect of CO2 recirculation on the PBF estimate made from proximal airway measurements is different in the two disease models. In the pulmonary embolism model,14 the effect of CO2 recirculation increases with increasing CO. CO2 recirculation contributes ≈25% to systematic errors at PBF=11.3 litre min−1 and ≈0% to systematic errors at PBF <3 litre min−1. The effect of CO2 recirculation on the PBF estimate made from proximal airway measurements is smaller in the emphysema model, because of the dominant effects of ventilation inhomogeneity and V˙/Q˙ mismatch. Figure 7 shows that when PBF estimates are made from alveolar measurements, the effect of CO2 recirculation is much greater. Removing CO2 recirculation in emphysema reduces the error in alveolar PBF estimates by 40% at PBF=15 litre min−1. Therefore, based on the alveolar measurements, systematic error because of CO2 recirculation is clearly observable and significant. However, in these diseases the proximal airway measurements are poor approximations of alveolar values, and as a result systematic error because of CO2 recirculation is obscured by other systematic errors. Similarly, Figure 7 shows that when comparing the PBF estimates made from alveolar measurements in the pulmonary embolism model, removing CO2 recirculation improves PBF estimates up to 75%.

Fig 7

Error in PBF estimates made from the simulated (theoretical) alveolar measurements, using the emphysema and pulmonary embolism lung models with and without CO2 recirculation.

Fig 7

Error in PBF estimates made from the simulated (theoretical) alveolar measurements, using the emphysema and pulmonary embolism lung models with and without CO2 recirculation.

In the presence of significant ventilation and perfusion inhomogeneities, removing CO2 recirculation improves estimates only slightly. Therefore, using a shorter rebreathing time, which reduces the effect of CO2 recirculation in a perfectly homogeneous lung, will not improve PBF estimates in an inhomogeneous lung.

Conclusions

In addition to sources of error found in a perfectly homogeneous lung, the ventilation, volume and perfusion mismatches in emphysema and pulmonary embolism create other sources of systematic errors in the partial rebreathing technique for measuring PBF. Almost all systematic errors found in the present study are because of incorrect PCO2 measurements. The majority of the systematic errors are caused by ventilation–volume inhomogeneity, while ventilation–perfusion inhomogeneity causes additional errors. The rebreathing time creates additional systematic errors because of the inability of the system to reach quasi-equilibrium. At rebreathing times that are long enough for quasi-equilibrium for the normal compartment but still inadequate for the abnormal compartments, systematic errors because of ventilation, volume and perfusion mismatches are reduced. The effect of CO2 recirculation is much less in an inhomogeneous lung than in a normal lung. Manoeuvres such as shorter rebreathing time at high cardiac outputs will not reduce systematic errors significantly in an inhomogeneous lung.

This work was funded by Australian Research Council ‘Strategic Partnership with Industry—Research and Training’ grant (ARC-SPIRT), Dräger Australia Pty Ltd, The Joseph Fellowship, The Jobson Foundation, The University of Sydney and the Australian National Health & Medical Research Council (NHMRC).

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Author notes

Conference presentations: Sources of error in non-invasive pulmonary blood flow measurements by partial rebreathing in lungs with emphysema or pulmonary embolism. XIII World Congress Of Anaesthesiologists, April 2004, Paris, France.

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