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