Shunt equation

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

Q s / Q t = (C c O 2 - C a O 2) / (C c O 2 - C v O 2)

^[1]

[edit] Derivation

The total blood emerging from the system will have oxygen flux $C a O 2. Q t$ , where CaO2 is oxygen content and Qt is the total cardiac output. This will be made up of blood that bypassed the lungs ( $Q s$ ) and that which went through the capillaries ( $Q c$ ).

Clearly $Q t = Q c + Q s$ , so $Q c = Q t - Q s$ .

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

Q t . C a O 2 = Q s . C v O 2 + (Q t - Q s). C c O 2

Substitute Qc as above, CcO2 is content of capillary oxygen blood.

Q t . C a O 2 = Q s . C v O 2 + Q t . C c O 2 - Q s . C c O 2

Multiply out the brackets.

Q s . C c O 2 - Q s . C v O 2 = Q t . C c o 2 - Q t . C a O 2

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

Q s .(C c O 2 - C v O 2) = Q t .(C c O 2 - C a O 2)

Factor out the Q terms.

Q s / Q t = (C c O 2 - C a O 2) / (C c O 2 - C v O 2)

Divide by Qt and by (CcO2 - CvO2).

[edit] See Also

Pulmonary shunt

[edit] References

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

v • d • e Respiratory system, physiology: respiratory physiology

Volumes	lung volumes - vital capacity - functional residual capacity - respiratory minute volume - closing capacity - dead space - spirometry - body plethysmography - peak flow meter - thoracic independent volume - bronchial challenge test

Airways	ventilation (V) (positive pressure) - breath (inhalation, exhalation) -respiratory rate - respirometer - pulmonary surfactant - compliance - hysteresivity - airway resistance

Blood	pulmonary circulation - perfusion (Q) - hypoxic pulmonary vasoconstriction - pulmonary shunt

Interactions	ventilation/perfusion ratio (V/Q) and scan - zones of the lung - gas exchange - pulmonary gas pressures - alveolar gas equation - hemoglobin - oxygen-haemoglobin dissociation curve (2,3-DPG, Bohr effect, Haldane effect) - carbonic anhydrase (chloride shift) - oxyhemoglobin - respiratory quotient - arterial blood gas - diffusion capacity - Dlco

Control of respiration	pons (pneumotaxic center, apneustic center) - medulla (dorsal respiratory group, ventral respiratory group) - chemoreceptors (central, peripheral) - pulmonary stretch receptors (Hering-Breuer reflex)

Insufficiency	high altitude - oxygen toxicity - hypoxia