The Shunt Equation and Content - Based Indices of Oxygenation

Created on Mon, 06/08/2015 - 07:36
Last updated on Sat, 07/01/2017 - 06:32

In brief:

FShunt is the ratio of the A-a and a-v differences of oxygen content.

The normal range for an adult is around 4% to 10%.

Conventionally, it requires a mixed venous sample to be accurate.

When measured correctly, it is the gold standard for assement of hypoxia.

Its accuracy is derived from its allowance for the oxygen content of mixed venous blood which contributes to the oxygen content of arterial blood.

FShunte is the ratio of the A-a and a-v differences of oxygen content with the a-v difference assumed on the basis of normal values. This assumption may render it near-worthless in ICU patients (though still better than tension-based indices).

What is the point of calculating a shunt fraction

Yes, there might be popular, convenient tension-based indices of oxygenation. Sure, they might be a little better than looking at the pO2 all by itself. But oxygen tension and oxygen content are rather different parameters, and the former is rather less interesting than the latter. The best available means of assesing how the pulmonary system contributes to arterial oxygen content is to calculate the intrapulmonary shunt, because it reflects the degree to which the lung deviates from the ideal as an oxygenator of pulmonary blood.

With the availability of a mixed venous sample, it is possible to directly measure the magnitude of the intrapulmonary shunt; and that would be the gold standard. The directly measured variables are plugged into the shunt equation, and an intrapulmonary shunt fraction is calculated. The result is usually reported as FShunt; however a more correct term would probably be Qs/Qt. The PA catheter may even do this automatically, depending on how fancy your equipment.

It is also possible to make certain assumptions about the mixed venous blood, and substitute those assumptions into the shunt equation. This would give us an estimated shunt fraction. The ABG machine can do this calculation on our behalf; the result is usually reported as FShunte where the litte "e" indicates "estimate".

Definition of shunt

The other name for shunt is "venous admixture". However, that implies that there is some known amount of hypoxic venous blood which gets mixed with the arterial circulation. In actual fact, there is no such thing; you never quite know how much shunt blood volume there is, or how hypoxic that blood is. Instead, one calculates a certain shunt fraction.

Thus, "venous admixture" is the calculated estimate of how much hypoxic blood would be required to produce the measured arterial oxygen results, for a given cardiac output.

Various sources of shunt

One might imagine that in a perfect world all the alveolar gas would gladly exchange into the blood, and there would be no difference in oxygen between them. Unfortunately, even with a completely normal alveolar gas exchange, there is a certain difference - inevitably, arterial pO2 is going to be lower.

Why, might one ask?

Numerous factors are in play.

  • Thebesian veins, otherwise known as venae cordis minimae, are tiny valveless veins in the walls of the four cardiac chambers. Their contribution to blood flow is piddling - examination of anaesthetised subjects has suggested that thebesian vein flow contributes 0.12% to 0.43% of the total aortic flow. However, the oxygen content within these veins is probably very low, and the impact on the A-a difference is not trivial.
  • Bronchial veins contribute probably no more than 1% of total cardiac output. This is blood which leaves the aorta, nourishes the bronchial wall, and then rejoins the central circulation by draining into the pulmonary veins. According to Nunn's Respiratory Physiology, in patients with bronchiectasis or COPD this contribution could be considerable - as much as 10% of the cardiac output.
  • Congenital heart disease with right-to-left shunting is a possibility that should be mentioned, as it allows the right heart to eject into the left circulation, bypassing the lungs.
  • Shunt through useless lung: blood passing through a diseased pneumonic lung (or one which has collapsed) will exchange no gas, and contribute to shunt.

The shunt equation

As always, these things are easier to represent as a big confusing diagram.

The Berggren shunt equation diagram

The oxygen content of blood is calculated as (sO2 × ceHb × 1.39) + (PaO2 × 0.03); though usually people will use 1.3 or 1.34 as these are more "realistic" BO2 values, and ctHb if the ceHb is not available (because the normal fractions of dyshaemoglobins are in the 1-2% range, and can be safely ignored). The contribution of dissolved oxygen can also be safely ignored, as it is trivial. This solubility coefficient is variably expressed as 0.03ml/L/mmHg (if you use a haemoglobin concentration measured in g/L) or 0.003ml/100ml/mmHg (if you're using haemoglobin measured in g/dL as in this equation from Cornell).

So, hypothetially, a given volume of arterial blood in the aorta can be said to contain discrete fractions:

fractions of arterial blood oxygen content to demonstrate shunt fraction

Of these quantities, all are known except the Qs, which is the shunt fraction. Well, the pulmonary end-capillary oxygen content is not known, but it is assumed. Obviously nobody is ever going to get into those capillaries and measure it directly. Instead an assumption is made that the ventilated areas of the lung are perfused with "ideal" capillaries, and the gas exchange in them is so perfect that their end-capillary oxygen tension is equal to alveolar oxygen tension, and their saturation is 100%.

Determining Qs is therefore a matter of subtracting (CcO2 + CvO2) from CaO2. However, we don't know what the flow is. We can only say that if all blood were ideally oxygenated the CaO2 should be the same as CcO2, and if all blood were completely shunted the the CaO2 should be the same as CvO2.

The relationship between the different fractions must therefore remain a ratio, rather than a real oxygen difference in ml. Hence shunt is usually represented as Qs/Qt.

The famous relationship below which determines this ratio is the so-called Berggren equation.

normal shunt equation

The equation compares arterial oxygen content to pulmonary end-capillary oxygen content (CcO2).

Thus, we can plug in some values, for a typical hypoxic ICU patient with an arterial saturation of 90%, and a decently anaemic Hb of 100g/L.

shunt fraction diagram with values plugged in

The local ABG machine rearranges the equation, and uses a slightly different nomenclature.

Fshunt equation from the ABg machine

All of the variables used in this equation are measured in the same ABG, with the exception of the O2 content of alveolar air.

Assumptions used in calculating the FShunte

In absence of mixed venous data, the blood gas analyser uses an assumed veno-arterial oxygen content difference. The assumed difference is 2.3mmol/L, according to the reference manual for the local ABG machine.

Fshunt equation with stated assumptions

Let us look at that assumption.

2.3 mmol/L of oxygen seems like a very small difference, but actually it is not.

An easily available online ideal gas law calculator reveals that under standard conditions 2.3mmol of oxygen equates to about 51ml/L. using whatever equation Radiometer happened to use. Now, if the arterial blood is assumed to contain 150g/L of maximally oxygenated haemoglobin, then its oxygen content is actually about 208.8ml/L. The content of venous blood therefore must be about 157.8ml/L. Running this backwards through the DO2 equation, one discovers that an oxygen saturation of around 77% is required, which just so happens to be the high end of average mixed venous oxygen saturation.

From this stems the greatest critique of the estimated FShunte. The ICU patients can vary greatly in their mixed venous oxygen saturation, from the cyanide-poisoned patient with an SvO2 of 90%, to the severe sepsis patient with an SvO2 of 30%. In these two examples, the venoarterial oxygen differences would be 10ml/L and 145.9ml/L, respectively. Obviously, making assumptions about the mixed venous saturation of critically ill patients will lead to errors.

Additionally, a criticism of all shunt calculations is the fact that they use a two-compartment model. If the FShunt is 25%, the equation leads one to believe that in a two-compartment lung, 25% of the blood is travelling through the non-ventilated compartment. In reality, the lung is a mixture of heterogeneous units, each with a different V/Q ratio. The shunt equation is therefore a very gross estimate of oxygenation defects.

In spite of that, many (including Ole Siggaard-Andersen) believe that the FShunte is still superior to oxygen tension-based indices, simply because it deals with oxygen content rather than oxygen tension. Many of the defects of the tension-based indices arise because of the non-linearity of the relationship between oxygen tension and oxygen content.



Fenn, Wallace O., Hermann Rahn, and Arthur B. Otis. "A theoretical study of the composition of the alveolar air at altitude." American Journal of Physiology--Legacy Content 146.5 (1946): 637-653.

Curran-Everett, Douglas. "A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation." Advances in physiology education 30.2 (2006): 58-62.

Rice, Todd W., et al. "Comparison of the SpO2/FIO2 ratio and the PaO2/FIO2 ratio in patients with acute lung injury or ARDS." CHEST Journal 132.2 (2007): 410-417.

Hess, D., and C. Maxwell. "Which is the best index of oxygenation: P (Aa) O2, PaO2/PAO2, or PaO2/FIO2?." Respiratory Care 30.11 (1985): 961-963. - this is not available even as an abstract; Respiratory Care dont seem to care about online back-issues beyond 2003.

Cane, Roy D., et al. "Unreliability of oxygen tension-based indices in reflecting intrapulmonary shunting in critically ill patients." Critical care medicine 16.12 (1988): 1243-1245.

Wandrup, J. H. "Quantifying pulmonary oxygen transfer deficits in critically ill patients." Acta Anaesthesiologica Scandinavica 39.s107 (1995): 37-44.

Araos, Joaquin D., et al. "Use of the oxygen content–based index, Fshunt, as an indicator of pulmonary venous admixture at various inspired oxygen fractions in anesthetized sheep." American journal of veterinary research 73.12 (2012): 2013-2020.

SIGGAARD‐ANDERSEN, Ole, and Ivar H. Gøthgen. "Oxygen and acid‐base parameters of arterial and mixed venous blood, relevant versus redundant."Acta Anaesthesiologica Scandinavica 39.s107 (1995): 21-27.

Aboab, Jerome, et al. "Relation between PaO2/FIO2 ratio and FIO2: a mathematical description." Applied Physiology in Intensive Care Medicine. Springer Berlin Heidelberg, 2006. 41-44.

Sven M. Berggren. "The Oxygen Deficit of Arterial Blood Caused by Non-ventilating Parts of the Lung" 1942; Volume 11 of Acta Physiologica Scandinavica: 4; Supplementum 11. -again, this does not seem to be available anywhere as a full text, which is upsetting because this seminal work is worth preserving.