Shunt Equation Formula — FRCA Primary MCQ

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HardPhysiology - RespiratoryShunt Equation FormulaFRCA Primary

In the three-compartment model of pulmonary gas exchange, total pulmonary blood flow (Qt) consists of shunted flow (Qs), which retains mixed venous oxygen content (CvO2), and non-shunted flow, which reaches pulmonary end-capillary oxygen content (Cc'O2). These streams mix to produce arterial oxygen content (CaO2). Assuming conservation of oxygen content, which expression gives the shunt fraction Qs/Qt?

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Correct answer: B — (Cc'O2 - CaO2) / (Cc'O2 - CvO2)

Explanation lettering: E = shown as A · C = shown as B · B = shown as C · A = shown as E

The correct answer is C. Oxygen-content balance gives QtCaO2 = (Qt − Qs)Cc'O2 + QsCvO2. Rearrangement yields Qs/Qt = (Cc'O2 − CaO2)/(Cc'O2 − CvO2). The numerator is the oxygen-content deficit of arterial blood relative to ideal pulmonary end-capillary blood. The denominator is the maximum possible oxygen-content increase between mixed venous and ideal end-capillary blood. Option B represents the arterial–venous extraction expressed relative to that maximum and is complementary to the shunt fraction in this idealised model. Option A uses arterial rather than end-capillary content in the denominator. Options D and E invert or combine the relevant differences incorrectly. A true shunt is relatively resistant, rather than necessarily completely unresponsive, to increased inspired oxygen.

Reference: Roe PG, Jones JG. Analysis of factors which affect the relationship between inspired oxygen partial pressure and arterial oxygen saturation. British Journal of Anaesthesia. 1993;71(4):488-494. https://pubmed.ncbi.nlm.nih.gov/38449055/