Shunt equation

The Shunt equation quantifies the extent to which venous blood bypasses oxygenation in the capillaries of the lung.

“Shunt” and “dead space“ are terms used to describe conditions where either blood flow or ventilation do not interact with each other in the lung, as they should for efficient gas exchange to take place. These terms can also be used to describe areas or effects where blood flow and ventilation are not properly matched, though both may be present to varying degrees. Some references refer to “shunt-effect” or “dead space-effect” to designate the ventilation/perfusion mismatch states that are less extreme than absolute shunt or dead space.

The following equation relates the percentage of blood flow that is not exposed to inhaled gas, called the shunt fraction , to the content of oxygen in venous, arterial, and pulmonary capillary blood.

[1][2]
Where:
Qs = Pulmonary Physiologic Shunt (mL/min)
Qt = Cardiac Output (mL/min)
CCO2 = End-pulmonary-capillary Oxygen Content
CaO2 = Arterial oxygen content
CVO2 = Mixed Venous Oxygen Content

Derivation

The blood entering the pulmonary system will have oxygen flux , where is oxygen content of the venous blood and is the total cardiac output.

Similarly, the blood emerging from the pulmonary system will have oxygen flux , where is oxygen content of the arterial blood.

This will be made up of blood that bypassed the lungs () and that which went through the pulmonary capillaries (). We can express this as
.

We can solve for :
.

If we add the oxygen content of Qs to Qc we get the oxygen content of Qt:


Substitute Qc as above, CcO2 is the oxygen content of pulmonary (alveolar) capillary blood.


Multiply out the brackets.

Get the Qs terms and the Qt terms on the same side.

Factor out the Q terms.


Divide by Qt and by (CcO2 - CvO2).

See also

References

  1. West, John B. (2008). "Figure 5.3 Measurement of shunt flow". Respiratory Physiology: The Essentials (8th ed.). Lippincott Williams & Wilkins. p. 60. ISBN 978-0-7817-7206-8.
  2. Leigh, J.M.; Tikrell, M.F.; Strickland, D.A. P. (1969-04-01). "Simplified Versions of the Shunt and Oxygen Consumption Equations". Anesthesiology. 30 (4): 468–470. doi:10.1097/00000542-196904000-00020. PMID 5773959.
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