Shunt equation

Shunt equation

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

:Qs/Qt = (CcO2 - CaO2) / (CcO2 - CvO2) [Respiratory Physiology: The Essentials, J. West, 2005, 7th ed, Page 169]

Derivation

The total blood emerging from the system will have oxygen flux CaO2.Qt, where CaO2 is oxygen content and Qt is the total cardiac output. This will be made up of blood that bypassed the lungs (Qs) and that which went through the capillaries (Qc).

Clearly Qt = Qc + Qs, so Qc = Qt - Qs.

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

:Qt.CaO2 = Qs.CvO2 + (Qt - Qs).CcO2 Substitute Qc as above, CcO2 is content of capillary oxygen blood.

:Qt.CaO2 = Qs.CvO2 + Qt.CcO2 - Qs.CcO2 Multiply out the brackets.

:Qs.CcO2 - Qs.CvO2 = Qt.Cco2 - Qt.CaO2 Get the Qs terms and the Qt terms on the same side.

:Qs.(CcO2 - CvO2) = Qt.(CcO2 - CaO2) Factor out the Q terms.

:Qs/Qt = (CcO2 - CaO2) / (CcO2 - CvO2) Divide by Qt and by (CcO2 - CvO2).

See also

* Pulmonary shunt
* Ventilation/perfusion ratio
* Pulmonary contusion

References


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