Variation of venous admixture, SF6 shunt, PaO2, and the PaO2/FIO2 ratio with FIO2

J. P. Whiteley1,2, D. J. Gavaghan1,2 and C. E. W. Hahn*,1

1Nuffield Department of Anaesthetics, University of Oxford, Radcliffe Infirmary, Woodstock Road, Oxford OX2 6HE, UK. 2Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK*Corresponding author

Accepted for publication: January 14, 2002


    Abstract
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Background. Measures of impairment of oxygenation can be affected by the inspired oxygen fraction.

Methods. We used a mathematical model of an inhomogenous lung to predict the effect of increasing inspired oxygen concentration (FIO2) on: (1) venous admixture (Q·va/Q·t); (2) arterial oxygen partial pressure (PaO2); (3) the PaO2/FIO2 index of hypoxaemia; and (4) sulphur hexafluoride (SF6) retention (often taken to be true right-to-left shunt). This model predicts whether or not atelectasis will occur.

Results. For lungs with regions of low V·/Q·, increasing the inspired oxygen concentration can cause these regions to collapse. In the absence of atelectasis, the model predicts that Q·va/Q·t will decrease and arterial oxygen partial pressure increase as FIO2 is increased. However, when atelectasis occurs, Q·va/Q·t rises to a constant value, whilst PaO2 falls at first, but then begins to rise again, with increasing FIO2. The SF6 retention increased markedly in some cases at high FIO2.

Conclusions. Venous admixture will estimate true right-to-left shunt at high FIO2, even when oxygen consumption is raised. This model can explain the way that the Pa/FI ratio changes with increasing inspired oxygen concentration.

Br J Anaesth 2002; 88: 771–8

Keywords: heart, right-to-left shunt; veins, venous pressure; oxygen, partial pressure; complications, atelectasis


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Venous admixture, Q·va/Q·t15 and the ratio of arterial oxygen partial pressure to fractional inspired oxygen concentration (the PaO2/FIO2 index)1 57 are commonly used to indicate the degree of impairment of gas exchange.

Venous admixture, often loosely called ‘oxygen shunt’, is calculated from a knowledge of arterial and mixed venous blood oxygen content. This technique provides an estimate of shunt fraction that is derived from the assumption that the lung has a single homogeneous gas-exchanging alveolar compartment. It has long been believed that for sufficiently high levels of inspired oxygen concentration, venous admixture gives an estimate of ‘true shunt’ fraction for inhomogeneous alveolar compartments. This is because for high inspired oxygen concentrations, the end-capillary blood in all compartments will be almost fully saturated. However, for inhomogeneous lungs, it has also been accepted that there is a risk of atelectasis occurring at high inspired oxygen concentrations. Mathematical analysis by Dantzker and colleagues8 in 1975, and by West and Wagner9 in 1977, using a model with one alveolar compartment, and fixing the mixed venous partial pressures of all gases present at constant values, has shown that lung units with low ventilation–perfusion (V·/Q·) ratios may collapse at high inspired oxygen concentrations. More recent work by Whiteley and colleagues,10 using a mathematical model that takes account of alveolar inhomogeneities and does not fix the mixed venous partial pressure of any gas at a constant value, has given qualitatively similar results. Confusingly, there are clinical reports that Q·va/Q·t may decrease, increase, or remain unchanged in response to breathing oxygen. These reports have been summarized by Quan and colleagues,4 and one of our aims is to produce a computer simulation to explain these conflicting clinical observations.

It is also accepted that true right-to-left shunt (that is, blood coming from compartments with zero ventilation) is best measured by the sulphur hexafluoride (SF6) retention technique11 which is a part of the general multiple inert gas elimination technique.12 However, the SF6 method, although believed to be a more accurate measurement of true shunt, is technically difficult to use and is generally confined to specialized centres. It is not used routinely in clinical practice. In addition, SF6 retention can be shown to vary with FIO2 and oxygen consumption with inhomogeneous lungs.10

The PaO2/FIO2 ratio is a widely used clinical index of hypoxaemia, although there is some doubt about the diagnostic value of this index.6 7

We used computer simulations to investigate the effect of the inspired oxygen concentration on the above indices of hypoxaemia. We use the mathematical model described by Whiteley and co-workers,10 which allows us to take account of atelectasis, should it occur.


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Previous work by Olszowka and Farhi,13 West and Wagner,9 and Whiteley and colleagues10 has highlighted the need to consider separately the inspired and expired ventilation–perfusion distribution for abnormal lungs, which we distinguish by the notation V·AI/Q· and V·AE/Q· distributions. We use a mathematical model consisting of: a compartment with a low inspired ventilation–perfusion (V·AI/Q·) ratio (compartment 1); a compartment with a normal V·AI/Q· ratio (compartment 2); and a compartment with a high V·AI/Q· (compartment 3). We may use a discrete compartment to represent each mode of the distribution rather than a collection of compartments distributed around each mode because Whiteley and colleagues14 have shown that both methods give almost identical arterial gas contents. In the simulations considered in this paper, we have either normal V·AI/Q· ratios coupled with low V·AI/Q· ratios, as reported in asthmatics and some patients with chronic obstructive pulmonary disease (COPD); or else normal V·AI/Q· ratios coupled with high V·AI/Q· ratios, as reported in emphysema.16 Thus, for each simulated patient, the model reduces to different ‘two alveolar compartment’ continuous-ventilation computer simulations, as described by Whiteley and colleagues.10 We use this model to calculate the partial pressures of oxygen, carbon dioxide, and nitrogen in each alveolar compartment in the steady state. This model is shown diagramatically in Figure 1. When atelectasis has occurred, all the inspired ventilation is shifted to the remaining alveolar compartment and the blood flow to the collapsed compartment is transferred to the shunt compartment, as has been modelled by other authors.15 Thus, true shunt increases. The only additional equation needed is that used to calculate venous admixture. This formula may be found in any respiratory physiology textbook, for example Nunn.2



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Fig 1 A schematic diagram of the three alveolar compartment model, with each compartment having a different expired alveolar ventilation– perfusion ratio. See the main text for symbols and notation.

 
Data sets and summary of computations
In this work we use five patient simulations. These have been chosen specifically to show how the various gas-exchange indices may change with inspired oxygen concentration, and oxygen consumption. All have three general alveolar compartments (with one of these compartments being redundant in each example) and an initial true right-to-left shunt (Fig. 1).

The data sets used in these simulations are shown in Table 1. The two separate and distinct V·/Q· ratios in first four data sets have been taken from Kapitan and Wagner,16 and describe patients with asthma or COPD.


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Table 1 The values used in the simulations in this paper
 
Data set 1 has alveolar compartment 1, with a low V·AI/Q· of 0.1, and receives 30% of the pulmonary blood flow. Compartment 2 has a normal V·AI/Q· of 1.0, and receives 70% of the pulmonary blood flow. There is a normal body oxygen consumption of 250 ml min–1, and no ventilation or perfusion to the compartment with the high V·AI/Q· ratio, compartment 3. True initial shunt fraction is 0.02.

Data set 2 is identical to data set 1, except for having a raised body oxygen consumption of 400 ml min–1.

Data set 3 is also identical to data set 1, except the initial true right-to-left shunt fraction is increased to 0.2.

Data set 4 is identical to data set 1, except that the V·AI/Q· ratio of compartment 1 is now halved to 0.05.

Data set 5 is taken from the work of Kapitan and Wagner,16 and is described by them as typical of a patient with emphysema. This simulation has alveolar compartment 3 with a high V·AI/Q· ratio of 10.0, which receives 10% of the pulmonary blood flow. Compartment 2 retains the normal V·AI/Q· ratio of 1.0, and receives 90% of the pulmonary blood flow. There is a normal body oxygen consumption of 250 ml min–1. There is no ventilation or perfusion to compartment 1.

Using the values in Table 1, we calculated the oxygen, carbon dioxide, nitrogen, and SF6 partial pressures and contents in both arterial and mixed venous blood, at any given FIO2 and oxygen consumption rate, for a given data set. The data then constitute the ‘patient’ blood gas data, which are used to calculate venous admixture, SF6 shunt, and the PaO2/FIO2 ratio.

This procedure is followed sequentially for the five ‘dummy patient’ data sets shown in Table 1, for FIO2 varying between 0.21 and 1.0. Finally, the calculated values for oxygen venous admixture, SF6 retention, PaO2, and the ratio PaO2/FIO2, are plotted against FIO2 at the given oxygen consumption rate.


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The results for data sets 1–5 are shown in Figures 26. In each of these figures: graph (A) shows the oxygen venous admixture estimate of shunt (solid line) and the SF6 retention (broken line) plotted against FIO2; graph (B) shows PaO2 plotted against FIO2; and graph (C) shows the PaO2/FIO2 ratio plotted against FIO2. The results for data sets 1–3 (a compartment with a low V·/Q· ratio where no atelectasis occurs); data set 4 (a compartment with a low V·/Q· ratio where atelectasis does occur); and data set 5 (a compartment with a high V·/Q· ratio) are described in that order.



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Fig 2 Simulations using data set 1 from Table 1: (A) Venous admixture (solid line) and SF6 retention (broken line); (B) PaO2; and (C) PaO2/FIO2.

 


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Fig 6 Smulations using data set 5 from Table 1: (A) Venous admixture (solid line) and SF6 retention (broken line); (B) PaO2; and (C) PaO2/FIO2.

 
Data sets 1–3
Venous admixture and SF6 retention
In Figures 2A4A we see that venous admixture (solid line) over-estimates true right-to-left shunt at low values of FIO2 and decreases to the correct value of the preset right-to-left shunt (initially 0.02 in Figs 2A and 3A; and initially 0.2 in Fig. 4A) as FIO2 approaches 1.0. Venous admixture in Figure 3A decreases at slower rate than in Figure 2A. The only difference between these two is that the patient simulation in Figure 3A has a higher oxygen consumption of 400 compared with 250 ml min–1 in Figure 2A.



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Fig 4 Simulations using data set 3 from Table 1: (A) Venous admixture (solid line) and SF6 retention (broken line); (B) PaO2; and (C) PaO2/FIO2.

 


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Fig 3 Simulations using data set 2 from Table 1: (A) Venous admixture (solid line) and SF6 retention (broken line); (B) PaO2; and (C) PaO2/FIO2.

 
In Figures 2A4A the SF6 retention is slightly greater than true right-to-left shunt at FIO2. The SF6 retention then begins to increase as FIO2 is increased. This increase is slight in Figures 2A and 4A, but is very significant in Figure 3A, where oxygen consumption is raised to 400 ml min–1. Here, the SF6 retention increases from 0.04 at FIO2=0.21, towards 0.24 at FIO2=1.0.

PaO2 and the PaO2/FIO2 index
In Figures 2B4B we see that PaO2 increases with increasing FIO2, slowly at first and then much more rapidly, as would be expected from classical thought. The PaO2/FIO2 ratio (Figs 2C4C), decreases and then increases with increasing FIO2 in this model.

Data set 4
Venous admixture and SF6 retention
In Figure 5A venous admixture (solid line) and SF6 retention (broken line) behave initially in the same way as in Figures 2A4A as FIO2 is increased. Then, at FIO2=0.87, the alveolar compartment with a low V·AI/Q· ratio of 0.05 (compartment 1) collapses, and atelectasis occurs. The mathematical model now has only one homogeneous alveolar compartment (compartment 2), and so venous admixture measures the true right-to-left shunt that now exists in the simulation. Similarly, the SF6 retention is that which would be seen in a lung model with a large shunt and a single homogeneous alveolar compartment. The venous admixture plot in Figure 5A is discontinuous, with a step increase at FIO2=0.87 but that the SF6 retention plot is continuous with increasing FIO2.



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Fig 5 Simulations using data set 4 from Table 1: (A) Venous admixture (solid line) and SF6 retention (broken line); (B) PaO2; and (C) PaO2/FIO2.

 
PaO2 and the PaO2/FIO2 index
In Figure 5B and C we see that PaO2 and the PaO2/FIO2 ratio behave initially in the same way as Figures 2B4B and Figures 2C4C, as FIO2 is increased, until atelectasis occurs. At this point there is an instantaneous decrease in both the PaO2 and the PaO2/FIO2 ratio. After this, both PaO2 and the PaO2/FIO2 ratio continue to increase once more, as FIO2 is increased.

Data set 5
Venous admixture and SF6 retention
In Figure 6A venous admixture (solid line) over-estimates true right-to-left shunt by a very small amount, but this over-estimation is essentially independent of FIO2. SF6 retention (broken line) is also independent of FIO2.

PaO2 and the PaO2/FIO2 index
In Figures 6B and 6C, both PaO2 and the PaO2/FIO2 index increase with increasing FIO2 and the PaO2/FIO2 ratio does not display the ‘dip’ seen in the other simulations.


    Discussion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Venous admixture
It has been assumed, when FIO2 is 1.0, that venous admixture is an accurate measure of right-to-left shunt. In Figures 24 and 6 this is true as long as the lung remains ‘open’. However, in Figure 5 a high inspired oxygen concentration causes a lung compartment with a low inspired ventilation–perfusion ratio (0.05 in our example) to collapse. For the conditions existing in data set 4 (Fig. 5), at FIO2=0.87, the oxygen, carbon dioxide, and nitrogen expired gas fluxes from the low V·/Q· compartment were insufficient to keep the alveolus ‘open’, and so it collapsed. Thereafter, in this particular case, the venous admixture calculated was the new true right-to-left shunt caused by the collapse.

For all the lung simulations with a low V·/Q· ratio compartment (compartment 1), the calculation of venous admixture decreased significantly when FIO2 was changed from 0.21 (room air) to 1.0 (100% inspired oxygen) provided that collapse did not occur. This decrease was dependent on the oxygen consumption, as illustrated by Figure 3. For the simulation with alveolar compartments with a normal V·/Q· (compartment 2) and a high V·/Q· (compartment 3) (Fig. 6), venous admixture hardly changed at all with FIO2. In this instance, inspired ventilation was always sufficient to ensure that end-capillary blood was always nearly fully saturated, even at the lower FIO2 values.

These findings may be explained simply by the sigmoid shape of the oxyhaemoglobin dissociation curve. Alveolar compartments with low V·/Q· ratios will have, at low FIO2, a blood oxygen content on the steep part of the content–partial pressure dissociation curve. A small increase in FIO2 will cause a relatively large increase in arterial blood oxygen content. This gives the observed large venous admixture at low FIO2, with the venous admixture value decreasing with increasing FIO2. Conversely, for alveolar compartments with high V·/Q· ratios, the blood oxygen content will be on the flat part of the dissociation curve for FIO2 greater than 0.21 (our lowest starting point). Therefore, increasing the FIO2 will have only a small effect on arterial blood oxygen content and, therefore, on the measure of venous admixture.

SF6 shunt
SF6 retention has been believed to be a more reliable technique for estimating true right-to-left shunt.11 However, we found the unexpected result that when an alveolar compartment with a low V·/Q· ratio (compartment 1) is present, as shown in Figures 25, SF6 retention may increase significantly as FIO2 is increased. This is because of the expired ventilation–perfusion ratio decreasing10 because of the fall in expired ventilation as described above. It must be noted here that inert gas retention depends on the expired V·/Q· ratio.10 Thus, as the expired V·/Q· ratio decreases towards zero (that is, it begins to approach true shunt) then the SF6 retention will begin to increase.

The rate of increase in the magnitude of the SF6 retention with respect to FIO2 was greater as oxygen consumption increases (Fig. 3) and for lower inspired V·/Q· ratios (Figs 2 and 3), even when the true initial right-to-left shunt was normal (0.02). In data set 4, the SF6 retention increased until atelectasis occurred (see Fig. 5) and was then constant for all values of FIO2 thereafter.

Arterial oxygen partial pressure
In all the simulations where atelectasis did not occur (Figs 24 and 6), PaO2 increased with increasing FIO2, as expected from classical teaching.2 A slow increase in PaO2 with increasing FIO2 corresponds to the arterial blood oxygen content lying on the steep part of the oxygen dissociation curve. In this region, increases in arterial blood content led to only small increases in arterial PO2. Greater increases in PaO2, with increasing FIO2, correspond to the arterial blood oxygen content lying on the flat part of the oxygen dissociation curve, where the opposite argument applies. In Figure 5 we see that PaO2 increases until collapse occurs at an FIO2 of 0.87. At this point, the collapse of the poorly ventilated alveolar compartment (compartment 1) causes a large decrease in PaO2, because of the increase in true shunt. After this, PaO2 continues to increase almost linearly.

The PaO2/FIO2 index
The variation of the PaO2/FIO2 ratio with increasing FIO2 is complex. Taken on one level, the ratio is simply the mathematical result of dividing each abscissa point by the corresponding ordinate point in Figures 2B6B. However, the ratio may also be explained physiologically by the shape of the oxyhaemoglobin dissociation curve, without recourse to mathematics.

For simulations with a normal initial shunt fraction of 0.02, and with an alveolar compartment having a low V·/Q· ratio (compartment 1), Figures 2C5C show that the PaO2/FIO2 ratio initially decreased with FIO2 and then increased. At low values of FIO2, arterial blood oxygen content will lie on the steep part of the dissociation curve. The result of this is that an increase in FIO2 will increase arterial blood oxygen content considerably, with only a small increase in PaO2. Thus, PaO2/FIO2 ratio will decrease as FIO2 is increased. However, when FIO2 is increased sufficiently enough for the PaO2 to lie on the flat part of the dissociation curve, then any further increase in FIO2 will lead to a relatively large increase in PaO2. Thus, once the shoulder of the dissociation curve is reached, the PaO2/FIO2 ratio will increase as FIO2 is increased.

In Figures 2C4C (data sets 1–3), atelectasis had not occurred and all the PaO2/FIO2 ratio curves were continuous functions of FIO2. In Figure 5 (data set 4), the same argument applies until collapse produces a sudden drop in PaO2. This causes a discontinuity in the PaO2/FIO2 ratio, shown by a sudden decrease in the ratio followed by a linear increase in PaO2/FIO2 with FIO2.

In Figure 6 there was one alveolar compartment with a normal ventilation–perfusion ratio (compartment 2) and one with a high ventilation–perfusion ratio (compartment 3). Arterial blood oxygen content is always on the ‘flat’ part of the dissociation curve, even for room air (FIO2=0.21). Thus, in this situation, the PaO2/FIO2 ratio increases as FIO2 is increased, but then ‘flattens off’ at high FIO2 values.

Clinical application
In previous clinical studies ‘oxygen shunt’ can remain constant, increase, or even decrease as FIO2 is increased.4 Our simulation shows that oxygen Q·va/Q·t will either decrease with increasing FIO2 (Figs 25), or remain constant (Fig. 6), depending upon the V·/Q· units making up the lung. We were not able to simulate Q·va/Q·t increasing with increasing FIO2, except at the point when collapse occurred. However, our results confirm that, as FIO2 approaches 1.0, venous admixture is a good approximation to true right-to-left shunt, even when atelectasis has occurred at high FIO2.

When a patient with an unknown very low V·/Q· compartment (as in data set 4), and a low true shunt when breathing room air, is given pure oxygen to breathe, atelectasis could occur. This will, in turn, induce a true shunt of much greater magnitude than had existed before the pure oxygen was administered. We are uncertain how this can be avoided, as the physician will have no a priori knowledge of either the patient’s inspired or expired V·/Q· distributions and, therefore, the lung’s predisposition to collapse at high FIO2.

The PaO2/FIO2 ratio has also been shown to be complex when mapped against FIO2, when low V·/Q· lung regions, true shunt and oxygen consumption are all taken into account. Figure 2 shows that the decrease in the ratio is almost ‘flat’ with increasing FIO2 (up to almost 70% inspired oxygen) because of the increased oxygen consumption in this example. Thus, the magnitude of the ratio, and its relationship to FIO2 in clinical practice, make the ratio difficult to interpret in a simple and logical fashion. Too many variables affect its magnitude. The rough ‘rule of thumb’ that a ratio of less than 150 mm Hg indicates a ‘high’ venous admixture, or true shunt, is not borne out by the results shown in Figures 3 and 4, taken from data sets 2 and 3, respectively. Both figures show almost identical PaO2/FIO2 ratios between 21 and 60% inspired oxygen, and yet data set 3 has a true shunt of only 2%. The low PaO2/FIO2 ratio is caused by the low V·/Q· compartment plus the raised oxygen consumption.

To conclude, we have shown that oxygen venous admixture will estimate true right-to-left shunt at high inspired oxygen concentrations, even when oxygen consumption is raised. If an alveolar compartment with a low V·/Q· ratio is present, then collapse may occur. The PaO2/FIO2 ratio, and its variation with changes in FIO2, depends on many clinical variables, and may not be a robust index for determining the state of arterial hypoxaemia.


    Acknowledgements
 
The authors are pleased to acknowledge grant GR/M60705 from the Engineering and Physical Sciences Research Council of Great Britain to support J.P.W., and the Medical Research Council of Great Britain for a Career Development Fellowship for D.J.G., which has allowed them to undertake this research.


    References
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
1 Cane RD, Shapiro BA, Templin R, Walther K. Unreliability of oxygen tension–based indices in reflecting intrapulmonary shunting in critically ill patients. Crit Care Med 1988; 16: 1243–5[ISI][Medline]

2 Nunn JF. Applied Respiratory Physiology, 4th Edn. Oxford, UK: Butterworth–Heinemann, 1993

3 Oliven A, Abinader E, Bursztein S. Influence of varying inspired oxygen tensions on the pulmonary venous admixture (shunt) of mechanically ventilated patients. Crit Care Med 1980; 8: 99–101[ISI][Medline]

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7 Gowda MS, Klocke RA. Variability of indices of hypoxaemia in adult respiratory distress syndrome. Crit Care Med 1997; 25: 41–5[ISI][Medline]

8 Dantzker DR, Wagner PD, West JB. Instability of lung units with low V·A/Q· ratios during O2 breathing. J Appl Physiol 1975; 38: 886–95[ISI]

9 West JB, Wagner PD. Pulmonary gas exchange. In: West JB, ed. Bioengineering Aspects of the Lung. New York: Dekker, 1977; 361–457

10 Whiteley JP, Gavaghan DJ, Hahn CEW. The effect of inspired oxygen concentration on the ventilation–perfusion distribution in inhomogeneous lungs. J Theor Biol 2000; 204: 575–85[ISI][Medline]

11 Pesenti A, Latini R, Riboni A, Gattinoni L. Simple estimate of true right to left shunt Q·s/Q·t at maintenance FIO2 by sulphur hexafluoride retention. Intensive Care Med 1982; 8: 283–6[ISI][Medline]

12 Wagner PD, Saltzman HA, West JB. Measurement of continuous distributions of ventilation–perfusion ratios: theory. J Appl Physiol 1974; 36: 588–99[Free Full Text]

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