Shunt equation

In Medicine shunt may also refer to Cardiac shunts, Cerebral shunts, Lumbar-peritoneal shunts, or Peritoneovenous shunts, for additional shunts in medicine see Shunt (medical).

The Shunt equation quantifies the extent that 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 does not meet the other in the lung as it should for gas exchange to take place. They 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 extents. Some 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 $Q_s/Q_t$ , to the content of oxygen in venous, arterial, and pulmonary capillary blood.

Q_s/Q_t = (Cc_{O_2} - Ca_{O_2}) / (Cc_{O_2} - Cv_{O_2})

^[1]

Derivation

The blood entering the pulmonary system will have oxygen flux $Q_t \cdot Cv_{O_2}$ , where $Cv_{O_2}$ is oxygen content of the venous blood and $Q_t$ is the total cardiac output.

Similarly, the blood emerging from the pulmonary system will have oxygen flux $Q_t \cdot Ca_{O_2}$ , where $Ca_{O_2}$ is oxygen content of the arterial blood.

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

We can solve for $Q_c$ :
$Q_c = Q_t - Q_s$ .

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

$Q_t \cdot Ca_{O_2} = Q_s \cdot Cv_{O_2} + (Q_t - Q_s) \cdot Cc_{O_2}$
Substitute Qc as above, CcO2 is content of capillary oxygen blood.

$Q_t \cdot Ca_{O_2} = Qs \cdot Cv_{O_2} + Q_t \cdot Cc_{O_2} - Qs \cdot Cc_{O_2}$
Multiply out the brackets.
$Q_s \cdot Cc_{O_2} - Qs \cdot Cv_{O_2} = Q_t \cdot Cc_{O_2} - Qt \cdot Ca_{O_2}$
Get the Qs terms and the Qt terms on the same side.
$Q_s \cdot (Cc_{O_2} - Cv_{O_2}) = Q_t \cdot (Cc_{O_2} - Ca_{O_2})$
Factor out the Q terms.

$\dfrac {Q_s} {Q_t} = \dfrac {Cc_{O_2} - Ca_{O_2}} {Cc_{O_2} - Cv_{O_2}}$
Divide by Qt and by (CcO2 - CvO2).

References

↑ Respiratory Physiology: The Essentials, J. West, 2005, 7th ed, Page 169

Respiratory physiology

Respiration	positive pressure ventilation breath (inhalation exhalation) respiratory rate respirometer pulmonary surfactant compliance elastic recoil hysteresivity airway resistance bronchial hyperresponsiveness bronchoconstriction/Bronchodilatation

Control	pons pneumotaxic center apneustic center medulla dorsal respiratory group ventral respiratory group chemoreceptors central peripheral pulmonary stretch receptors Hering–Breuer reflex

Lung volumes	VC FRC Vt dead space CC PEF calculations respiratory minute volume FEV1/FVC ratio methods of lung testing spirometry body plethysmography peak flow meter nitrogen washout

Circulation	pulmonary circulation hypoxic pulmonary vasoconstriction pulmonary shunt

Interactions	Perfusion (V) ventilation (V) ventilation/perfusion scan zones of the lung gas exchange pulmonary gas pressures alveolar gas equation alveolar–arterial gradient hemoglobin oxygen–haemoglobin dissociation curve (Oxygen saturation 2,3-BPG Bohr effect Haldane effect) carbonic anhydrase (chloride shift) oxyhemoglobin respiratory quotient arterial blood gas diffusion capacity (DLCO)

Insufficiency	high altitude oxygen toxicity hypoxia

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Shunt equation

Derivation

See also

References