1University Department of Anaesthesia and MRC Trauma Unit, Manchester, UK. 2North Western Medical Physics, Manchester, UK. 3Intensive Care Unit, South Manchester University Hospitals, Manchester, UK*Corresponding author: MRC Trauma Group, Stopford Building, University of Manchester, Manchester M13 9PT, UK
Presented in part to the Anaesthetic Research Society, Aberdeen and Edinburgh Meetings (Br J Anaesth 1999; 82: 170P and Br J Anaesth 2000; 84: 273P).
This article is accompanied by Editorial I.
Accepted for publication: September 21, 2000
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Abstract |
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Br J Anaesth 2001; 86: 47785
Keywords: complications, acute respiratory distress syndrome; complications, hypoxaemia; lung, damage; oxygen, measurement; model, lung; oxygen, consumption; ventilation; lung, blood flow; ventilation, ventilationperfusion
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Introduction |
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The difference in oxygen content between arterial and mixed venous blood (C(a)O2) is an important variable in the assessment of pulmonary oxygen transfer. Although considerable within- and between-patient variability is common in critical illness,6 indices such as PaO2/FIO2 remain popular for clinical and research purposes. Furthermore, the inclusion of PaO2/FIO2 in the American European Consensus Conference recommendations on acute respiratory distress syndrome (ARDS)7 has led to the widespread impression that the PaO2/FIO2 ratio is the preferred method of assessing pulmonary oxygen transfer in clinical studies.8 For example, in a recent multicentre trial on inhaled nitric oxide, the efficiency of pulmonary oxygen transfer was assessed over several days using PaO2/FIO2, no data or comment being provided on variations in mixed venous oxygen content that may have influenced the findings.9 This approach compromises the critical evaluation of the effects of a given intervention on pulmonary oxygen transfer.
Direct assessment of the effect of C(a)O2 involves manipulation of the delicate physiological balance that is frequently seen in critically ill patients, and raises difficult ethical issues. Mathematical models have therefore been considered appropriate tools to address similar problems.1 5 Such models require formal validation if conclusions are to receive wider acceptance.
This study was therefore undertaken, with the following objectives: (i) to describe and validate a mathematical model of an ARDS lung; and (ii) to use the above model in a theoretical study evaluating the effect of C(a)O2 and FIO2 on four commonly used indices of pulmonary oxygen transfer.
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Materials and methods |
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Stage 1: lung model of ARDS
To derive a lung model of ARDS, a multicompartment model of a normal lung10 11 was modified by incorporating data on shunt, dead space and /
scatter obtained by Dantzker et al. in patients with ARDS12 (Appendix 1). Validity of the model was verified using new data collected from 10 consecutive patients treated for ARDS in our intensive care unit. After institutional approval had been obtained, between four and seven sets of arterial and mixed venous blood gas measurements and cardiac output estimations were obtained from each patient. The following measurements were recorded: PaO2, PaCO2, arterial haemoglobin saturation (SaO2), mixed venous oxygen tension (P
O2), mixed venous carbon dioxide tension (P
CO2), mixed venous haemoglobin saturation (SvO2), haemoglobin concentration (Hb), venous admixture (
s/
t), cardiac output and fractional inspired oxygen (FIO2). The position of the pulmonary artery catheter was confirmed radiologically and all blood gas/cardiac output measurements were made by trained nursing staff. The blood gas machine and co-oximeter (BGE and IL282 respectively; Instrumentation Laboratory, Milan, Italy) were calibrated according to the manufacturers guidelines. Cardiac output,
s/
t, Hb, P
O2, SvO2, P
CO2 and FIO2 for each set of readings were used as input variables to obtain a predicted PaO2 through an iterative process.
PaO2 predicted by the model and the true (measured) PaO2 were compared by analysis of covariance (ANCOVA) to determine the within-subject correlation coefficient (r). Agreement was assessed using the intraclass correlation coefficient (ri)13 and BlandAltman analysis.14
Stage 2: evaluation of indices of pulmonary oxygen transfer
After validation, the lung model was used to derive four commonly used indices of pulmonary oxygen transfer (s/
t, Cc'O2CaO2, P(Aa)O2 and PaO2/FIO2) as FIO2 was varied between 0.21 and 1.0. We assumed constant minute ventilation, temperature (37°C), acidbase balance (base excess=0) and respiratory exchange ratio (RER=0.85) and a normal oxygen dissociation curve (P50=3.6 kPa). The oxygen content of arterial blood (CaO2) was determined by weighting of compartmental perfusion and ventilation. Mixed venous oxygen content (C
O2) was derived from CaO2 and peripheral oxygen extraction. End-capillary oxygen content was derived in the customary fashion using the alveolar gas equation.3 The process was repeated for three fixed C(a
)O2 values: 22.0, 35.6 and 49.2 ml litre1. This range represents the mean ± two within-subject standard deviations for C(a
)O2 in critically ill patients.6 Patient data used for validation of the model were not used in deriving any of the indices.
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Results |
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Discussion |
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The model does not account for effects of FIO2 on pulmonary vascular autoregulation, which is an important physiological compensatory mechanism18 and may account for the underestimation of PaO2 by the model. The effects of metabolic acidosis/alkalosis, temperature and 2,3-diphosphoglycerate (2,3-DPG) on the oxyhaemoglobin dissociation curve and the effects of abnormal forms of haemoglobin on pulmonary oxygen transfer have also not been modelled. The above factors may account for the relatively wide limits of agreement seen in the study. In spite of these limitations, the model is sufficiently accurate (r= 0.93, ri=0.91, bias=+1 kPa, SD=1.5 kPa) to justify its use. The difficulties in measuring high PaO2 using standard oxygen electrodes is well known. However, the range of PaO2 values in our patients (3.327 kPa) was well within the stipulated measuring range for the blood gas machine (0106 kPa). Therefore, measurement errors are unlikely to have contributed to any of the observed discrepancies. In deriving the indices of pulmonary oxygen transfer, a fixed shunt (true shunt) was assumed despite changes in FIO2. It is well recognized that in patients with a large contribution from areas with /
mismatch, changes in FIO2 lead to changes in
s/
t. Our model describes these changes well (Fig. 2). The absorption atelectasis that may occur in the presence of high FIO2, on the other hand, may lead to increased shunting. However in order to quantify the effects of extrapulmonary factors such as FIO2 and C(a
)O2 on the indices, it was necessary to hold the intrapulmonary factors (shunt,
/
scatter and dead space) constant. Absorption atelectasis was therefore not included in the present model.
Oxygen tension based indices
Indices based on PaO2 may be popular because they are simple. In patients with normal lungs, stable cardiovascular status and constant peripheral oxygen extraction, good correlation has been demonstrated between s/
t and PaO2/FIO2 or P(Aa)O2.1 19 20 In a theoretical study, Rasanen et al. demonstrated the relationship between
s/
t and these three indices to be non-linear and greatly influenced by FIO2 and C(a
)O2.1 The range of C(a
)O2 used by Rasanen et al. (2080 ml litre1) was, however, arbitrary and therefore the study failed to convince many clinicians of the disadvantages of indices such as PaO2/FIO2. We have therefore revisited the subject to determine whether the range of variation that is known to occur within individual patients6 is small enough to justify the continued use of indices such as PaO2/FIO2.
The disadvantage of using P(Aa)O2 to quantify pulmonary oxygen transfer is evident from Fig. 5. On the other hand, PaO2/FIO2 is a simple index and has gained widespread acceptance for clinical and research purposes.7 8 21 A review of the literature shows conflicting data on the accuracy with which PaO2/FIO2 reflects s/
t. Some studies have shown good correlation in groups of critically ill patients, and the evidence presented forms the basis for its current popular use.2 5 19 23 Other studies, however, show poor correlation.2426 Because of the inclusion of multiple readings obtained from individual patients with a variety of illnesses, the correlation coefficients cited in studies comparing PaO2/FIO2 and
s/
t2 19 23 24 may be erroneously high and not reflect the true relationship between the two indices.27 Nevertheless, there is no doubt that PaO2/FIO2 is a useful clinical parameter as long as the underlying assumptions are appreciated and regularly evaluated. In the present study most of the observed FIO2-related variations were at low FIO2, and in the 0.50.8 range variability was less than 5 kPa. The relationship between PaO2/FIO2 and FIO2 is more complex when C(a
)O2 is low (22 ml litre1), a condition likely in septic patients with a hyperdynamic circulation. Under these circumstances, PaO2/FIO2 increases when FIO2>0.7. The problem may be compounded by changes in C(a
)O2 at the same time. For example, when FIO2=0.7 the ratio varied between 18 and 10 kPa with changes in C(a
)O2, and when FIO2=0.9 the ratio varied between 22 and 8 kPa. These changes are large enough to result in misclassification on the gas exchange scale suggested by the American European Consensus Conference.7 Despite this, a recent review quoting Gowda et al. states that the PaO2/FIO2 ratio is the preferred method of assessing gas exchange in clinical trials.8 The group of patients represented by Gowda et al. in their theoretical models, in reality, represents patients likely to require many interventions that lead to changes in C(a
)O2. This limits the usefulness of PaO2/FIO2 in this patient group. What is not disputed is that PaO2/FIO2 is not an objective marker of pulmonary oxygen transfer in patients with haemodynamic and metabolic instability. It therefore follows that PaO2/FIO2 in ARDS should be interpreted with caution, particularly when pulmonary oxygen transfer is assessed over several days.
Indices based on oxygen content
s/
t derived at the clinically chosen FIO2 is a widely used method and has been used as the gold standard measure of pulmonary oxygen transfer.2 19 23 By comparing calculated
s/
t at FIO2 of 0.5 and 1.0, Gowda et al. demonstrated that the variability in
s/
t (related to FIO2) was directly proportional to the fraction of cardiac output perfusing alveolar units with
/
ratios of less than 0.1.5 Therefore, the relative contribution to
s/
t from shunt and areas of low but finite
/
is an important determinant of the variability in
s/
t with FIO2. In the present study, although approximately 10% of cardiac output perfused alveolar units with
/
<0.1, the magnitude of changes in
s/
t due to variation in C(a
)O2 or FIO2 was small (<2%) and clinically unimportant. Rossaint et al.17 demonstrated a similar distribution of ventilation and perfusion in a study of 12 ARDS patients (shunt, 35%; flow to areas of lung with
/
<0.1, 10%; dead space, 34%). In a more recent study, Santos et al. confirmed that the primary mechanism for impaired pulmonary oxygen transfer in patients with acute lung injury was right-to-left shunt and blood flow to alveolar units with
/
<0.1 less than 10%.28 In the absence of mixed venous blood samples, Kerr in 197529 and Drummond and Zhong in 198330 used Cc'O2CaO2 to quantify pulmonary oxygen transfer in clinical studies conducted in stable patients over relatively short periods. The present study confirms that variation in C(a
)O2 limits its clinical application.
The ventilation/perfusion distribution shown in our model has important implications in the management of patients with ARDS. Simply increasing FIO2 beyond 0.5 may not achieve worthwhile improvements in arterial oxygen content, because the contribution from /
mismatch to
s/
t is almost completely eliminated at an FIO2 of approximately 0.5.3 If right-to-left shunting is the dominant cause of abnormal pulmonary oxygen transfer, then further increases in FIO2 do not compensate for this defect.3 Measures that are intended to achieve a reduction in shunt, such as higher positive end-expiratory pressure and prone position, are more appropriate and should be considered early in patients with ARDS if adequate arterial oxygen content is not achieved with FIO2 above 0.5.
In conclusion, in ARDS there may be marked cardiorespiratory and metabolic abnormalities resulting from the underlying disease and/or interventions. In such patients, there is no reliable substitute for s/
t to quantify defects in pulmonary oxygen transfer. There is also a need to clarify the criteria used in research in which interventions that may influence pulmonary oxygen transfer are assessed over relatively long periods. We believe that the inclusion of PaO2/FIO2 in the American European Consensus Conference recommendations without qualification may lead to its inappropriate use.
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Acknowledgement |
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Appendix 1: ARDS lung model |
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where CCO2 and Cc'CO2 refer to the carbon dioxide concentration of mixed venous blood and end-capillary blood respectively, in units of ml dl1, and PACO2 is the alveolar partial pressure of carbon dioxide in mm Hg. In solving the above equation it is necessary to take into account the Haldane and Bohr effect, whereby the relationship between partial pressure and the end-capillary concentrations of carbon dioxide and oxygen in the blood draining from each compartment alters with changes in
A/
C. Because the equations defining the oxygen and carbon dioxide dissociation curves are non-linear and interdependent, an iterative procedure incorporating a root-finding algorithm based on bracketing and bisection33 was used in deriving the solution. The method was used to find a common solution for compartmental ventilation, compartmental blood flow and the end-capillary concentration of oxygen and carbon dioxide in the blood draining from each of the compartments. This iterative process was stopped when the oxygen saturation on the oxygen and carbon dioxide dissociation curves agreed within 0.001%.
The oxygen dissociation curve was described by the Hill function:34
(where SO2 is the haemoglobin oxygen saturation (%) and PO2 is the partial pressure of oxygen in the blood). Reference values of n=2.7 and P50=3.576 kPa (26.8 mm Hg) were used, based on the work of Siggard-Anderson.35 36
The alveolar oxygen tension PAO2 in each of the compartments for the respiratory exchange ratio (R) associated with each A/
C and PACO2 was calculated from the alveolar gas equation:32
PAO2 = 713 x FIO2 PACO2[FIO2 + (1 FIO2)/R](3)
In deriving the oxygen saturation of end-capillary blood, the transformation described by Kelman37 was used to calculate a value of P50 (P'50) for the oxygen dissociation curve to account for different values of saturation and partial pressure of carbon dioxide in the blood (PcO2) from the equation:
where pH is calculated from the equation:
pH=7.59+0.0031xHb(1SO2)0.2741x1n(PCO/20)(5)
The shape of the curve was assumed to be invariant under this translation and the effects of pH caused by metabolic changes, temperature and 2,3-DPG were omitted from the equation. Similar Kelman transformations for the CO2 dissociation curves were carried out for each alveolar compartment.31 Because oxygen saturation is not known, it was calculated, for each alveolar compartment, by an iterative process designed to terminate when the values of oxygen content, carbon dioxide content, PCO2, PO2 and oxygen saturation satisfy both the oxygen and carbon dioxide dissociation curves.
Distribution of lung compartments in the model
For each lung compartment, alveolar ventilation may be described by the logarithmic normal distribution function31 multiplied by a scaling constant:
(where f(x)=A, x=ln(
A/
C), µ is the log mean value and
is the log standard deviation of the ventilation/perfusion distribution with scaling constant k).
Based on the data provided by Dantzker et al.,12 the following values were used to describe the ARDS lung: =0.43, µ=2.921 and k=2.13. Alveolar ventilation of 9.28 litres (dead space 3.75 litres) and cardiac output of 6.65 litres (shunt 2.71 litres) were derived from Dantzker et al.12 Following Lee et al.,15 the lung compartments were spaced evenly on a logarithmic scale of 0.1 log10 units from 2 to +2, which covers the range of
A/
C from 0.01 to 100 in 41 compartments. Shunt and dead space were included as two separate compartments, resulting in a total of 43 compartments in the entire model. Because for each compartment the ventilation
A is known and
A/
C is known, the corresponding
C may be derived from equation 6. Thus, the weighted sum of the end-capillary oxygen concentration for each lung compartment with the associated
A/
C, R, PACO2, PAO2 and Cc'O2 from all the compartments accounts for the gas exchange from the entire lung model.
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Appendix 2. Data used to validate ARDS lung model |
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References |
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